Polymer Reviews, Volume 50, Issues 1-4 (2010)

R Journal of Macromolecular Science , Part C: Polymer Reviews, 50:1–13, 2010 Copyright © Taylor & Francis Group, LLC I...

Author: Elliot P. Douglas (Editor-in-Chief)

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R Journal of Macromolecular Science , Part C: Polymer Reviews, 50:1–13, 2010 Copyright © Taylor & Francis Group, LLC ISSN: 1558-3724 print / 1558-3716 online DOI: 10.1080/15583721003624859

Perspective Scattering from Polymers YVONNE A. AKPALU Department of Chemical & Materials Engineering, University of Cincinnati, Cincinnati, Ohio Knowledge and understanding from scattering provides a scientific basis of control of polymer properties. This understanding has fueled technological advances in synthetic polymers that have revolutionized our daily lives. This issue of Polymer Reviews focuses on recent advances in scattering instrumentation, data analysis and modeling, and its application to the structure-property characterization of polymers. We highlight research directions where the structure-property characterization by scattering measurements can enable polymer products and technologies that significantly reduce reliance on fossil feedstock and environmental pollution. Keywords X-ray scattering, neutron scattering, renewable resources, polyhydroxyalkanoates

1. Introduction In this special issue of Polymer Reviews, we present four articles that review recent advances in structure-property characterization of polymers by X-ray and neutron scattering. Scattering techniques have been employed since the beginning of polymer science to provide information on the structure and properties of polymers.1 As early as the 1920s C.W. Bunn used X-rays to determine the crystal structure of polyethylene via the Bragg law. nλ = 2D sin(θ/2),

(1)

where D is the distance between crystallographic planes, λ, is the wavelength of the radiation used, θ , is the angle of scatter and n is the (integer) order of reflection. The scattering angle θ , is determined by the spatial period of the Fourier component that is responsible for the scattering; thus, for each scattering angle there is a corresponding Bragg spacing, D, which is given by Eq. (1). The scattering intensity I(Q), measured as a function of the momentum transfer vector, Q, is related to θ via Q=

4π sin(θ/2), λ

(2)

Received January 11, 2010; accepted January 13, 2010. Address correspondence to Dr. Yvonne Akpalu, Chemical & Materials Engineering, 400 Rhodes Hall, Cincinnati, OH 45221-0012, United States. E-mail: [email protected]

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Combining equations (1) and (2) gives D 2π/Q

(3)

which indicates the distance scale probed by a measurement at a given value of Q. The Fourier or inverse relationship between the structure of a material in real space (r) and the scattering in Q-space, means that Eq. (3) can be applied to first order for all types of scattering. Experiments in the range 0.6 < Q < 15Å−1 , commonly referred to as wideangle scattering (WAS), contain most of the information for determining the unit cell dimensions of crystals.2–10 WAS probes a distance scale ∼ 0.4 < D < 10Å. The technique of small-angle scattering (SAS) is used to study the structure of the size on the order of 10Å or larger.11–16 Information such as the typical size, shape, and arrangement of the structure is contained in the intensity of the scattering X-rays, neutrons, and light at small angles. In general, data from the SAS measurements can provide information on the average size and distribution of the scattering unit or heterogeneity as long as the wavelength of the incident radiation is comparable to the size of the scattering unit or heterogeneity.17 Analysis of the scattering profiles can provide information on the nature of the interfaces, size, shape, and distribution of domains. Furthermore, contrast variation using isotopic substitutions allows one to distinguish between the shape and the spatial correlation of the different polymeric domains, ion-rich or ion-poor, crystalline or amorphous. Most polymer systems exhibit a large-scale structure that necessitates the use of multiple scattering techniques. To illustrate this complexity, we use a semicrystalline polymer as an example. In semicrystalline polymers, the macroscopic behavior is strongly dependent on the underlying microstructure consisting of molecules arranged in the unit cell (∼Å), lamellar crystals (∼10 nm), and the aggregation of these lamellae into fibrils (∼100 nm) and larger structures such as spherulites (∼µm) (Fig. 1). Quantitative relationships between microstructure and properties in these materials requires a knowledge of microstructural features on the scale of lamellar (∼10 nm), fibrils/lamellar stacks (∼100 nm) to spherulites (∼µm). The morphological characterization of crystalline polymers involves determining the unit cell dimensions and the average size of the crystal (lamella) from wide-angle scattering and interlamaller morphology from small-angle scattering.14, 18–21 Determining interfibrillar and interspherulitic parameters requires the use of ultra-small angle X-ray scattering (USAXS)22 and small-angle light scattering (SALS).23–25 Thus determining quantitative structure-property relationships from scattering studies of polymers with large-scale structures or hierarchical microstructures necessitates the use of multiple techniques to span all length scales of structure that influence the properties of the polymer. Many polymers self-organize into hierarchical structures with spatial heterogeneities in the range 10–100 nm. These polymers include block copolymers, ionomers, and liquid crystalline polymers. Scattering experiments give information on the time-averaged structure and conformation of polymer molecules and form the bulk of the large body of work undertaken to characterize the polymer structure, and understand the interrelationships among polymer properties, structure, and morphology. The review articles included in this special issue of Polymer Reviews provide a comprehensive treatment of the principles of small-angle X-ray and neutron scattering techniques as well as recent advances in instrumentation and data analysis and their application to structure-property characterization of polymers. The first contribution by Hammouda focuses on recent advances and applications of neutron scattering for polymer solutions, copolymers, polymer blends, branch or grafted polymers, polymer gels, polymer networks,

Scattering from Polymers

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Figure 1. Schematic representation of the morphology of semicrystalline polymers and characteristic structural variables. Volume fraction of structures characteristic of each morphological level are the volume fraction of superstructures/spherulites (xs ), volume fraction of lamellar stacks (xL ), and fraction of crystals within lamellar stacks (xCL ). Interlamellar morphological variables are the average distance between crystals (L), the average crystal thickness (lc ), and the average amorphous thickness (la ). Interfibrillar morphological variables are the average size of the lamellar stack (ξ L ) and the interfibrillar amorphous regions (LD ). The crystalline fraction within spherulites (xcs = xL xCL ) is an averaged nanoscale quantity. The assumption here is that all crystals are within lamellar stacks and spherulites.

polymer micelles, polymeric nanomaterials, and polymer membranes. The prospects for the measurement capabilities that will allow probing of polymer structures from the near atomic scale to well into the optical (20 micrometers) size scale are described. Zhang and Ilavksy focus on the application of ultra-small angle scattering for probing polymers with structural heterogeneities in the size range of 1–1000 nm. The review focuses on USAXS structure-property characterization of polymer nanocomposites, polymer gels and solutions, polymer blends, polymer micelles, and microemulsions. New advances in instrumentation that support the wider use of USAXS for polymer research, including new capabilities for measuring the “complete” small-angle scattering curve for polymers are described. The next two contributions focus on recent progress in structure-property characterization of polymers with fiber symmetry. Stribeck provides a critical review of the experimental methods and data analysis required for monitoring fabrication processes, mechanical properties, and the resulting fluctuations in polymeric materials with fiber symmetry. Burger, Hsiao, and Chu provide a theoretical treatment of structural information to be determined in scattering from natural and synthetic polymer fiber systems. This review emphasizes the calculation of complete X-ray scattering patterns required for building structure-property relationships in natural and synthetic fiber polymers or polymers with self-assembled meso-structures exhibiting density and orientation fluctuations that can be described by fiber symmetry.

2. X-rays and Neutrons The physics of X-ray and neutron scattering from polymers are covered in several standard texts.17,26,27 Here, we borrow heavily from these texts to present aspects that are important

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for understanding the importance of X-ray and neutron scattering for characterizing polymers. For most applications in polymer science, the scattering of X-rays and neutrons is elastic, where the energies of the incident and scattered radiation have the same energy or wavelength. X-rays and neutrons are scattered by atomic centers at discrete angles represented as sinusoidal (Fourier) components of the electron density and nuclear scattering potential of the specimen, respectively. X-rays and neutrons have wavelengths comparable to interatomic distances in materials. The manner in which these types of electromagnetic radiation are scattered by a material depends on the mechanism of scattering from individual atoms and on their relative positions in space. X-rays are electromagnetic radiation with wavelength, λ = 10−2−102Å. X-rays used for the study of the structure of materials have typical wavelengths of 0.5–2.5 Å and are most typically generated by conventional anode generators that offer the advantage of inhouse capabilities found in individual laboratories worldwide, as well as the bright light of synchrotron sources that are available only at national facilities.14 Studies on polymers are performed mostly with Kα characteristic radiation from a copper target tube having a wavelength of 1.5418 Å, but occasional work is also done with Kα line of wavelength 0.7107 Å from a molybdenum target tube. X-rays of similar wavelength can also be selected by means of a monochromator from a broad spectrum emitted by a synchrotron radiation source.14 X-rays, like light, exhibit particle-wave duality. Certain properties of X-rays are better understood when a beam of X-rays is regarded as a stream of photons rather than a wave with wavelength λ and frequency ν. The energy of an X-ray photon is characterized by its energy E and momentum p, which are related to λ and ν by E = hν

(4)

h p= λ

(5)

c v

(6)

and λ=

where c is the speed of light (= 2.998 × 108 m/s), and h is Planck’s constant (= 6.626 × 10−34 J s). The flux of photons produced by X-ray synchrotrons is several orders of magnitude higher than the flux on a neutron beamline. The increased flux can be very beneficial when collimating the beam to a spot size of a few millimeters in diameter and for increasing the experimental throughput based on reduced exposure time needed.16, 28 A neutron is an uncharged elementary particle with a mass m = 1.675 × 10−24 g and spin 12 . It kinetic energy E and momemtum p are E=

1 2 mv 2

(7)

and p = mv

(8)

where ν is its velocity. Neutrons also exhibit wave-like behavior, with the wavelength given by the de Broglie relation λ=

h h = p mv

(9)


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Table 1 Typical values of ν, E, and λ of neutrons from Cold, Thermal and Hot Sources17 Polymer

Cold

Thermal

Hot

T (K) v (m/s) E (meV) λ (Å)

25 642 2.16 6.16

330 2333 28.4 1.696

2000 5743 172 0.689

Table 1 shows the most probable velocity v in the Maxwell-Boltmann Distribution, given by Eq. (11). The corresponding kinetic energy E = mv 2 /2 = kT , and wavelength λ, are listed for the three typical moderator temperatures 25, 330, and 2000 K. Cold source neutrons emerge from a small volume (∼20 liters) of liquid deuterium maintained around 25 K while thermal neutrons are those moderated usually with heavy water D2 0 around 330 K. It is worthwhile to note that the wavelengths of cold, thermal, and hot neutrons are on the order of 1 Å, similar to X-rays. As a result, neutron scattering is also a useful tool for investigating the structure of materials. The way neutrons are produced determines the energy and wavelength. The source of neutrons for most scattering experiments is a nuclear reactor, although spallation sources have gained importance in recent years. Neutrons produced by a nuclear fission reaction in a reactor or by bombardment of high-energy protons onto a heavy metal in a spallation source are of very high velocities. For neutron scattering studies these high velocity neutrons are moderated, i.e. they are allowed to slow down by repeated collisions with atoms in a moderating material. Moderation produces neutrons with a Maxwell-Boltzmann velocity distribution, given by m 32 1 2 (10) v 2 exp − 2 mv kT f (v) = 4π 2π kT where f (v)dv is the fraction of gas molecules with velocities between v and v + dv and k is Boltzmann’s constant (1.381 × 10−23 J/K). The maximum function of f (v) or most probable velocity v occurs at v=

2kT m

12 (11)

In many ways the scattering behavior of neutrons is similar to those exhibited by X-rays, so that experimental and theoretical tools developed for X-rays can be applied to neutron scattering and vice versa. There are, however, some important differences between X-rays and neutrons, and these differences often make the two methods complementary to each other, providing the required information for characterizing polymer structure and its relation to properties. 2.1 Energy The difference in energy between X-rays and neutrons determine what kind of structure is probed. Whereas the energy of an X-ray photon is on the order of 10 keV, the kinetic energy of a thermal neutron is of the order of 10 meV. The average energy associated

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with the motion of atoms, arising from vibrational, rotational, and translational motions of molecules, is of the order of kT. At ambient temperatures, kT is about 20 meV. Thus, when X-rays are scattered by matter, even when there is an exchange of energies between the motions of atoms and the X-ray photon, the energy of the photon is scarcely affected. On the other hand, when neutrons are scattering inelastically, their energies can be modified to an appreciable extent that can be measured experimentally. This difference can be understood also from a slightly different viewpoint as follows. The time (τ = ν1 ) associated with one wave period is of the order of 10−19 s for X-rays and 10−13 s for thermal neutrons. Since a typical time period for atomic motions is 10−13 s, an X-ray, unlike a neutron, does not see a change in the atomic position. Measuring the inelastic scattering of neutrons is a very useful method for investigating the motions of atoms in materials,30,31 which is beyond the focus of this special issue. 2.2 Mechanism for Interaction of Radiation with Matter The differences in the mechanism by which incident neutrons and X-rays interact with a material leads to several important differences in how the experimental data is obtained and corrected. X-rays are scattered by the electron density of an atom or molecule, and the scattering cross-section of an atom increases in direct proportion to the square of the number of electrons or atomic number, Z; in the case of hydrocarbon polymers the X-rays “see” the electron clouds contributed by carbon’s six electrons better than the single electron attributable to hydrogen. X-rays probe atomic dimensions within an order of magnitude of the X-ray wavelengths, so that the radiation scattered by the electron cloud on opposite sides of the atom results in a different path length that gives rise to a shift in phase and decreasing the scattering power with increasing scattering angle. Neutrons interact directly with the nuclei within a molecule, and the strength of the scattering interaction varies irregularly with the atomic number, so that even isotopes of the same element do not have the same neutron scattering cross-section or scattering length.17 For example, the most significant isotopic variation occurs for hydrogen, which has a coherent scattering length of −3.74 fm, while for deuterium the scattering length is 6.67 fm. Neutrons are therefore sensitive to hydrogen and the differences between its isotopes, which permits observation and measurement of the hydrogen structural correlations in polymers, that are not easily obtainable by X-rays. Scattering experiments probe the differential scattering cross-section defined as the ratio of the scattering cross-section dσ scattered into the solid angle d about the scattering angle θ . This can be analyzed in terms of the first Born approximation32 N dσ = bi bj e(iQ·rij ) d i,j

(12)

where the sum is over the N nuclei (in the case of neutrons) or electrons (in the case of X-rays) in the sample, b is the scattering length for neutrons of a given element, while b is replaced by a Q-dependent form factor in the case of X-rays; the {rij } are the positions of nuclei, electrons, and heterogeneities larger than atomic dimensions; Q = 4π sin(θ/2)/λ is the momentum transfer for the elastic scattering process where λ is the wavelength; and the brackets correspond to a thermal average in Eq. (12). The specific form of Eq. (12) depends on (i) the scattering length of the heterogeneity, (ii) the relative size of the heterogeneity compared to the probe radiation wavelength, and (ii) the spatial arrangement of the heterogeneities.17 When the scatterers are numerous (e.g., electrons on every atom


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for X-rays) and are more or less continuously dispersed in space in the sample, we replace the summation in Eq. (12) with an integral. In applying Eq. (12) and its simplified forms, it is required that various corrections to the measured scattering intensity, I (Q), has been made, accounting for effects such as incoherent scattering, beam polarization, multiple scattering, inelastic effects, container absorption, etc. Details on how to perform these corrections correctly for X-ray and neutron scattering experiments are given in standard texts.16,17,26 The articles included in this special issue of Polymer Reviews provide examples of simplified forms of Eq. 12 for different types of scattering from polymers. In a typical scattering experiment, the scattered radiation signal is captured by a detector, or detector element, of dimensions dx × dy positioned at some distance, L, and the scattering angle from the sample. This detector records the flux of radiation scattered . Single-point detectors have been used to collect into a solid angle element, d = dxdy Lz X-ray structural information from polymers, but area detectors offer several important advantages over single-point detectors, including the reduction of the background signal and greater statistics, a larger range of Q-space data collected at the same time, and the collection of several perspectives of the same data that provides an important benchmark for validation of the subsequent data processing and modeling. The use of charge-coupled device (CCD) area detectors for X-ray diffraction began around 1995 and has become increasingly popular.14 The detection of neutrons is typically accomplished through an array of individual detectors (although one- and two-dimensional linear and area detectors are sometimes used) composed of a gas of 3He, for example, or scintillator materials based on 6Li that detect the neutron as a charge produced from a nuclear reaction.17 The primary issue in devising a neutron detector is to create high sensitivity to neutrons while remaining insensitive to background events (such as γ -rays) and to minimize the loss of signal due to the “dead-time” of the detector. Gas detectors have the advantage of good discrimination against γ -rays, while scintillator detectors have better sensitivity relative to gas detectors, with a dead time on the order of hundreds of nanoseconds.17 Scattering yields measurements in reciprocal (Fourier Transform) space and depends therefore on data interpretation using models33 and not on real space imaging like microscopy. Electron microscopic imaging is in principle more powerful than small-angle scattering (SAS) for elucidating nanoscale structure and morphology. The main reason is that the phase information is lost in scattering, so one cannot uniquely determine structure. Although the loss of phase information can be viewed as a severe limitation, the loss can be beneficial34 for understanding the spatial dependence of fluctuations in polymers arising from heterogeneities in backbone structure of polymers and mesoscale morphologies. The articles included in this special issue of Polymer Reviews provide several examples of the unique scientific benefits of scattering from polymers.

3. Renewable Polymers with Controlled Properties Within the last few decades, synthetic polymers have revolutionized our daily lives.35 Globally, we use in excess of 260 million tons of plastic per year, accounting for about 8 percent of world oil production. The dwindling of fossil resources, coupled with increasing public preference for environmentally friendly plastics, has increased academic and industrial interest in biodegradable polymers prepared from renewable sources. Biopolymers differ from petroleum-based in that their feedstock is from renewable biomass rather than being oilbased. These polymers may be natural polymers (e.g., cellulose), synthetic polymers made from biomass monomers (e.g., polyactic acid), or synthetic polymers made from synthetic

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monomers derived from biomass (e.g., polyethylene derived from bioethanol).36 Although materials with functionality comparable to conventional plastics can now be produced on an industrial scale; they are more expensive than conventional polymers and account for less than 1% of plastics production.36 Below, we highlight key structure-property characterization challenges of recently developed cost-competitive renewable polymers. These renewable polymers have the potential to replace petroleum-based polymers on scales that can lead to significant reductions in reliance on fossil feedstock and environmental pollution. Recently, polyhydroxyalkanoates (PHAs), which are biodegradable and compostable thermoplastics polyesters synthesized by bacteria, were introduced to the market as competitors for polyethylene and polypropylene.37–39 These materials are particularly interesting as one looks forward to the next 10–50 years since they can replace polymers based on fossil feedstock without loss of performance. Further, adding small amounts of nanofillers (100 nm) readily assessable by the combined use of small-angle and ultra-small angle scattering techniques.

Acknowledgements This research is supported by the Department of Energy Basic Energy Science under contract DE-SC0002253. The author is indebted to Prof. Elliot Douglas and the editorial staff at Polymer Reviews. Without their guidance and patience this Special Issue of Polymer Reviews would not have been possible.

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57. 58. 59. 60.

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biologically-based poly-beta-hydroxybutyric acid using life cycle analysis,” J. Biotechnol. 2007, 130, 57–66. Yu, J.; Chen, L. “The greenhouse gas emissions and fossil energy requirement of bioplastics from cradle to gate of a biomass refinery,” Environmental Science & Technology 2008, 42, 6961–6966. Noda, I. “Biodegradable copolymers and plastic articles comprising biodegradable copolymers.” 1996, US: 5,498,692 Yoshie, N.; Menju, H.; Sato, H.; Inoue, Y. “Complex composition distribution of poly(3hydroxybutyrate-co-3-hydroxyvalerate),” Macromolecules 1995, 28, 6516–6521. Satkowski, M. M.; Melik, D. H.; Autran, J.-P.; Green, P. R.; Noda, I.; Schechtman, L. A. “Physical and processing properties of polyhydroxyalkanoate copolymers.” In Biopolymers; Doi, Y. and Steinbuchel, A., Eds.; Wiley-VCH: Weinheim, 2001; Vol. 3b; pp 231–263. Noda, I.; Satkowski, M. M.; Dowrey, A. E.; Marcott, C. “Polymer alloys of Nodax copolymers and poly(lactic acid),” Macromol. Biosci. 2004, 4, 269–275. Poliakoff, M.; Noda, I. “Plastic bags, sugar cane and advanced vibrational spectroscopy: taking green chemistry to the Third World,” Green Chemistry 2004, 6, G37–G38. Noda, I.; Bond, E. B.; Green, P. R.; Melik, D. H.; Narasimhan, K.; Schechtman, L. A.; Satkowski, M. M. “Preparation, properties, and utilization of biobased biodegradable Nodax(tm) copolymers.” In Polymer Biocatalysis and Biomaterials; Cheng, H. N. and Gross, R. A., Eds.; American Chemical Society: Washington, DC, 2005; pp 280–291. Federle, T. W.; Barlaz, M. A.; Pettigrew, C. A.; Kerr, K. M.; Kemper, J. J.; Nuck, B. A.; Schechtman, L. A. “Anaerobic biodegradation of aliphatic polyesters: Poly(3-hydroxybutyrateco-3-hydroxyoctanoate) and poly(epsilon-caprolactone),” Biomacromolecules 2002, 3, 813–822. Peacock, A. J. Handbook of Polyethylene: Structures, Properties and Applications; Marcel Dekker: New York, 2000. Lenz, R. W.; Marchessault, R. H. “Bacterial polyesters: Biosynthesis, biodegradable plastics and biotechnology,” Biomacromolecules 2005, 6, 1–8. Qiu, Y. Z.; Ouyang, S. P.; Shen, Z. Y.; Wu, Q.; Chen, G. Q. “Metabolic engineering for the production of copolyesters consisting of 3-hydroxybutyrate and 3-hydroxyhexanoate by Aeromonas hydrophila,” Macromol. Biosci. 2004, 4, 255–261. Nakamura, K.; Goto, Y.; Yoshie, N.; Inoue, Y. “Biosynthesis of Poly(3-Hydroxyalkanoate) from Amino-Acids,” International Journal of Biological Macromolecules 1992, 14, 321–325. Madison, L. L.; Huisman, G. W. “Metabolic engineering of poly(3-hydroxyalkanoates): From DNA to plastic,” Microbiol. Mol. Biol. Rev. 1999, 63, 21. Gagnon, K. D.; Lenz, R. W.; Farris, R. J.; Fuller, R. C. “Chemical Modification of Bacterial Elastomers .1. Peroxide Cross-Linking,” Polymer 1994, 35, 4358–4367. Gagnon, K. D.; Lenz, R. W.; Farris, R. J.; Fuller, R. C. “Chemical Modification of Bacterial Elastomers .2. Sulfur Vulcanization,” Polymer 1994, 35, 4368–4375.


Reviews SANS from Polymers—Review of the Recent Literature BOUALEM HAMMOUDA National Institute for Standards and Technology, Center for Neutron Research, Gaithersburg, MD This paper reviews the recently published literature on Small-Angle Neutron Scattering (SANS) from polymers. Papers published over the past three years and resulting from the use of the NIST Center for Neutron Research (NCNR) are included. Those with which this author is most familiar are summarized in a brief format. The intent of this review paper is to demonstrate the usefulness of the SANS technique and its impact on polymer research. SANS is a structural characterization method and a good probe for miscibility thermodynamics in polymer mixtures. SANS topics covered include polymer solutions, copolymers, polymer blends, branched or grafted polymers, polymer gels, polymer networks, polymer micelles, polymeric nanomaterials, and polymer membranes. Keywords small range neutron scattering, polymer structures, nanoscale, polymer solutions, copolymers, blends, gels, networks, branched polymers

1. The SANS Technique Small-angle neutron scattering (SANS) is an effective characterization method to investigate nanoscale structures. It is based at neutron scattering facilities and has experienced steady growth over the past thirty years. It probes structures with sizes from the near atomic to the near micrometer scale and has had impact in many research areas including polymers, complex fluids, biology, and materials science. The partial deuteration method (which consists of replacing hydrogen by deuterium atoms) gives the SANS technique unique advantage. Like other scattering methods, SANS yields measurements in the reciprocal (Fourier transform) space and depends therefore on data interpretation using models and not on direct space imaging like microscopy. The SANS instrument uses the following basic steps: 1. monochromation, 2. collimation, 3. scattering and 4. detection (Fig. 1). Monochromation consists of producing a monochromatic neutron beam from the Maxwellian neutron source spectrum and is performed using a velocity selector. Collimation is performed using a source aperture and a sample aperture in order to define an Received June 18, 2009; accepted October 27, 2009. Address correspondence to Dr Boualem Hammouda, Center for Neutron Research, 100 Bureau Drive, Gaithersburg 20899-6102, United States. E-mail: [email protected]

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Figure 1. Schematics of a SANS instrument. This Figure is not to scale; the total horizontal size is 30 m whereas the neutron detector height is 64 cm.

incident neutron beam with very small divergence. Scattering from samples of various forms (liquids, solids, gels, etc.) and in various environments (heating, pressure, shear, applied magnetic field, etc.) is measured in special cells. Detection of the scattered neutrons is performed using a 2D area sensitive detector. The pre-sample and the post-sample flight paths can be adjusted between 1 m and 15 m distance. The overall size of a SANS instrument is typically 30 m. The sample thickness is between 1 mm and 2 mm making the SANS technique a bulk probe. The NIST Center for Neutron Research (NCNR) facility operates two 30 m SANS instruments at the core of a thriving user program. Research on SANS from polymers constitutes the most active component.

2. SANS Data Analysis and Modeling Various aspects of the SANS technique including data analysis methods can be found in a recent book available online.1 SANS data analysis consists of one of three methods. 1. Rapid interpretation using standard (linear) plots such as the Guinier plot (to obtain a radius of gyration) or the Porod plot (to obtain a Porod exponent). Porod exponents vary between 1 (for 1D object such as a rod) and 4 (object with smooth surface). For example, the Porod exponent of a polymer coil in a good solvent is 5/3 while that for a polymer coil in poor solvent is 3. A Porod exponent of 2 characterizes either a polymer coil in theta solvent or a 2D structure (such as a lamella). This first data analysis method is used routinely. Extensive description of linear plots can be found in Chapter 22 of the SANS Toolbox.1 2. Nonlinear least-squares fitting to appropriate models. A large number of models are available for the analysis of SANS data from polymer systems. These are either for macromolecular scattering such as the Random Phase Approximation (RPA) or for particulate scattering such as the analytical solutions of the Ornstein-Zernike (OZ) equation. Polymer solutions and homogeneously mixed blends are well described by the RPA model while the various microphases in block copolymers (spherical, cylindrical, lamellar, etc.) are best described by solutions to the OZ equation. One such solution, the Percus-Yevick equation, offers a simple analytical form for hard-sphere interaction potential between spherical particles. The Mean Spherical Approximation is another analytical solution of the OZ equation for charged particulate systems. The zero average contrast method consists of using deuterated and non-deuterated polymer mixtures as well as deuterated and nondeuterated solvent

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B. Hammouda mixtures in order to isolate the single-chain form factor even from concentrated polymer solutions. This method has been applied to polymer blend mixtures as well. Smearing of the models to account for instrumental resolution is performed prior to the fitting step. This second data analysis method is the most used. The RPA, the zero average contrast method, and the OZ models are described in detail in Chapters 31 and 32 of the SANS Toolbox respectively.1 3. Particle shape reconstruction and inverse Fourier transform methods are sophisticated approaches that perform in-depth analysis of SANS data using canned software packages. This data analysis method is rarely used owing to its high level of specificity.

The SANS signal is characterized by a constant (Q-independent) part due to incoherent scattering from (mostly) hydrogen in the sample as well as by a Q-dependent coherent scattering part which contains information about structure, morphology and phase transitions in the sample. Here Q is the scattering variable given in terms of the neutron wavelength λ and scattering angle θ as Q = (4π/λ) sin(θ/2). The coherent scattering cross section (units of cm−1) can be expressed as: d(Q) = φρ 2 VP P(Q)SI (Q). d

(1)

Here φ is the volume fraction and VP is the volume of the scattering “objects,” ρ 2 is the neutron contrast factor, P(Q) is the single object form factor, and SI (Q) is the inter-object structure factor. The scattering objects can be either polymer coils for macromolecular scattering or compact “particles” in the case of particulate scattering. The SANS Toolbox1 contains the form factors for various shape objects (Chapter 27) as well as for polymer chains with excluded volume (Chapter 28). The SANS technique is sensitive to composition fluctuations and is therefore a good probe for phase transition studies in polymer mixtures. The thermodynamics of miscibility are well described by the RPA model which predicts (for instance) the spinodal phase transition condition. Polymer mixtures (solutions or blends) either phase separate upon heating and are characterized by a lower critical solution temperature (LCST) or upon cooling and are characterized by an upper critical solution temperature (UCST). The mean field RPA approach uses the Flory-Huggins interaction parameters which can be measured by SANS.

3. SANS from Polymers A large number of SANS research from polymers has been covered at the tutorial level in the SANS Toolbox1 which contains a great deal of topics borrowed from this author’s research efforts. Chapter 37 describes the use of an empirical model to extract the correlation length (average distance between entanglements) in a semidilute polymer solution, applies the zero average contrast method to extract single-chain properties such as the radius of gyration and uses a simple extrapolation method to obtain an estimate of the spinodal (phase separation) temperature for an LCST system. Chapter 38 uses the Flory-Huggins Gibbs free energy to map out the phase diagram for a model polyolefin blend. Flory-Huggins interaction parameters were estimated and found to depend inversely on (absolute) temperature. The binodal and spinodal temperatures and the nucleation-and-growth region in-between were plotted. Chapter 39 describes SANS from copolymers. Here also, the RPA method is used to predict the order-to-disorder line for a diblock copolymer. SANS from copolymer spectra

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are characterized by a peak due to the correlation hole effect in the homogeneous phase or due to inter-domain spacing in the ordered phases. Ordered phases correspond to spherical, cylindrical, and lamellar morphologies (mostly). Chapter 40 summarizes SANS results from a ternary blend mixture in which two of the homopolymers are hydrogenated (i.e., non-deuterated). The Flory-Huggins interaction parameters were extracted for all three polymer pairs including the hydrogenated pair. Chapter 43 makes use of a sophisticated model to interpret SANS data from a crystalline polymer in solution. Thicknesses of the amorphous and lamellar regions as well as the number of lamellae per stack were obtained. A material balance approach was used along with nonlinear least squares fits to this model. Chapter 44 describes micelle formation in a triblock (Pluronic) copolymer solution. The unimers-to-spherical micelles conditions (temperature and concentration) were estimated. Cylindrical and lamellar micelles were also obtained upon further heating. The use of judicious sample environments has contributed greatly to the SANS from polymers research effort. Chapter 52 and 53 illustrate some of this effort using in-situ pressure and shear respectively. Use of the compressible RPA model along with an equationof-state yielded an estimation of the amount of free volume present in polymer blends. The use of the Clausius-Clapeyron equation helped predict the effect of pressure on the spinodal line. In some systems, pressure favored mixing while in other cases, it favored demixing. In-situ shear produces appealing 2D spectra with lots of spots and anisotropic features. Pluronic spherical micelles formed body-centered cubic structures that changed into facecentered cubic structures under Couette shear. Twinned structures were also observed. This review paper references some 76 papers on SANS from polymers resulting from use of the NCNR over the past three years. They are cataloged into broad categories that include polymer solutions,2–9 copolymers,10–19 polymer blends,20–23 branched or grafted polymers,24–32 polymer gels,33–40 polymer networks,41–48 polymer micelles,49–63 polymeric nanomaterials,64–70 and polymer membranes.71–77 Of these papers, about half are briefly summarized in order to represent the breadth of ongoing research. Those summarized are the ones with which this author is the most familiar with.

4. Polymer Solutions Chain conformations and demixing phase behaviors are common topics investigated using SANS from polymer solutions. Such topics include characteristic chain dimensions for various stiff or flexible polymers, polymer-solvent interactions, and phase transitions. Investigations of solution crystallization have been included in this section. Poly(cyclohexdiene) (PCHD) polymers contain six-member rings on the main chain. This characteristic gives them much desired mechanical properties and good thermal stability when compared to other vinyl polymers. For instance, PCHD polymers have the highest glass-rubber transition temperature (Tg around 231◦ C) of all hydrocarbon polymers. Solution properties of PCHD polymers in tetrahydrofuran and in chloroform solutions were investigated using conventional methods that included light scattering and SANS.2 These two techniques measured the radius of gyration (Rg ) and the second virial coefficient (A2 ) as a function of polymer concentration, temperature, and solvent quality. The Zimm plot method was used; it consists of an extrapolation to low scattering variables (Q) and low polymer fractions. A simple wormlike chain model reproduced the measured radii of gyration. It was found that the PCHD chain conformations were stiffer in chloroform than in tetrahydrofuran solutions.

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Figure 2. SANS spectrum from 4% poly(ethylene oxide) mass fraction in d-water (left) showing the high-Q coherent signal (solvation intensity) and the constant incoherent background. The solvation intensity is plotted for 4% PEO in d-water/d-alcohol solvent mixtures (right). Non-ideal mixing is observed in all cases. The error bars correspond to one standard deviation.

The model water-soluble polymer poly(ethylene oxide) [–CH2 CH2 O–]n was used to investigate solvation properties in binary solvent mixtures consisting of water and other solvents (methanol, ethanol, ethylene glycol). The SANS technique was used to obtain a wide Q range.3 Deuterated solvents were used in order to enhance the neutron contrast. At low-Q, large length-scale features are characteristic of clustering (PEO in d-water) or crystallization (PEO in alcohols). The high-Q region probes polymer-solvent interactions (the solvation layer) as well as their mixing behavior (Fig. 2). The measurement temperature was kept above the crystal melting temperature when crystallization was present. A simple empirical model was used to fit SANS data and obtain solvation intensity, a correlation length, and a Porod exponent. The correlation length is an estimate of the average entanglement distance in the semidilute PEO solutions. Moreover, the random phase approximation model was used to back out Flory-Huggins interaction parameters for the ternary mixture PEO/d-water/d-methanol. It was found, for instance, that the solvation intensity for PEO in binary solvent mixtures was always lower than the ideal mixing prediction; non-ideal mixing seems to be the norm for PEO in mixed solvents. Mixed solvents seem to be better solvating agents for PEO than the individual solvents. The SANS technique was also used to investigate the solvation behavior of PEO in d-water in the dilute and semidilute regimes.4 The correlation length (obtained from the empirical model) was seen to decrease in dilute solutions but to increase in semidilute solutions. This behavior change yields an accurate method for measuring the overlap concentration used to delimit dilute from semilute solutions. The decrease in coil size in the dilute region is the precursor to the single-coil collapse transition that occurs in extremely dilute solutions of polymers with extremely high molecular weights. The temperature dependence of the correlation length shows that its inverse follows a linear behavior when plotted versus 1/T (where T is the absolute sample temperature). It remains to be seen whether this “universal” behavior observed for PEO would hold for other polymers in solution. Poly(ethylene oxide) assumes a coil conformation when dissolved in water, but it assumes a helical conformation when dissolved in isobutyric acid along with trace amounts

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Figure 3. Pair distribution function for a poly(ethylene oxide) solution in d-water (left) and in disobutyric acid (right). This distribution was obtained through the Fourier transform of the SANS data. The distribution on the right is characteristic of a mixture of helix and coil phases.

of water. The helix-to-coil transition can be reversibly effected by adding/removing trace amounts of water. SANS and polarimetry measurements were used to investigate the helical and coil structures in various solvent and temperature conditions.5 A number of data analysis methods and software packages were used to analyze the SANS data. These included standard plots (such as the Porod plot), fits to cylindrical structure models (to represent the helical structure), and inverse Fourier transform of the data to obtain a pair distribution function p(r). Porod exponents close to 1 were observed for rod-like (helical) structures at low-Q and close to 5/3 for swollen polymer coils. Note that the helical structures are characterized by high-Q Porod exponents close to 4 (smooth rod surfaces). The pair distribution functions showed pure coil phases for PEO/d-water and helical phases in PEO/d-isobutyric acid (Fig. 3). Mixtures of coil and helical phases were observed for high molecular weight PEO/d-isobutyric acid. The helical structure in solution was reminiscent of the crystalline structure of pure PEO (whereby 7 monomeric units form 2 helical turns). Similar investigations were performed on another (similar) water-soluble polymer, poly(ethylene imine), referred to as PEI [–CH2 CH2 NH–]n both in d-water and in d-isobutyric acid and similar conclusions were obtained. The helical structures were better developed with PEI than with PEO. The partitioning of PEO in water/isobutyric acid solvent mixtures was further investigated using SANS. Low molecular weight polymers (with Mw < 10 kg/mol) were seen to prefer dissolving in the isobutyric acid rich (top) phase and higher molecular weight ones end up mostly in the water (bottom) phase. Investigations of the phase boundaries for the PEO/water/ isobutyric acid ternary mixture were conducted.6 It was found that the addition of PEO tends to favor demixing in water/isobutyric acid solvent mixtures. Similar conclusions were obtained using star branched PEO instead of linear PEO. The early stages of crystallization of (low-molecular weight) polyethylene in d-xylene solutions were investigated by SANS.8 Crystallization was obtained upon cooling from the melt state (at 120◦ C) down to temperatures varying from 110◦ C to 85◦ C. Very early stages of crystal growth were investigated. The SANS technique was found to be sensitive to crystal volume fractions as small as 10−5. This sensitivity is much better than for SAXS where

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low-Q background interferes with the useful signal. SAXS is the main diagnostic tool for investigations of polymer crystallization. Two competing modes of early-stage crystallization were presented with either spinodal decomposition or nucleation-and-growth as the driving force. The high sensitivity SANS measurements reported here favor the nucleation-andgrowth (crystal seeding-and-growth would be a better name) mechanism. Investigations of the late-stage crystal growth with well-formed lamellae were also discussed. Poly(ethylene oxide) forms a crystalline structure when dissolved in ethanol. SANS investigations were conducted on dilute and semidilute solutions of PEO/d-ethanol for temperatures above and below the crystallization temperature.9 Above the crystal melting temperature, fully-swollen polymer coils were observed while below the crystallization temperature, a sponge-like lamellar morphology was reported. DSC, WAXS, and confocal microscopy confirmed the SANS findings. The PEO/d-ethanol phase diagram showing both the crystallization and the extrapolated spinodal line has been mapped out. The extrapolated upper critical solution temperature (UCST) was found to be well below the crystallization temperature and therefore unreachable. The addition of a small amount of d-water to the PEO/d-ethanol mixture was found to destroy the crystalline morphology and yield regular polymer solution behavior. The phase diagram was seen to change to a lower critical solution temperature (LCST) when the water amount is increased.

5. Copolymers There are three categories of SANS investigations from copolymers; these used pure copolymers, copolymers in solution, and copolymers added to blends. These categories are represented here. The conformation of polymer chains in regular symmetric multiblock copolymers was investigated using SANS measurements from previously sheared samples.10 Symmetric copolymers tend to form lamellar structures which, when sheared, tend to align according to the “parallel” or A alignment (lamellae oriented in the shear/shear gradient plane) or the “perpendicular” C alignment (lamellae orientated in the shear/vorticity plane). The B alignment (lamellae oriented in the shear gradient/vorticity plane) is never observed under shear; it is observed only after shear cessation. The undecablock (containing 10 blocks) of poly(cyclohexylethylene) and poly(ethylene propylene) was used for these investigations. Mixtures of undecablocks and deuterated undecablocks (in equal fractions) were prepared in order to separate out scattering from the multiblock structure (characterized by an interblock Bragg peak) and scattering from partially deuterated polymer chain conformations (characterized by the radius of gyration for the entire copolymer). The Guinier plot at low scattering variable Q was used to measure this radius of gyration. These investigations showed that polymer chains tend to align in the B alignment plane when lamellae are aligned along the C alignment plane. Shear cessation relaxes the stretched copolymers into a 3D random walk spread out over many lamellar microdomains. The SANS technique was used to investigate vesicle formation when a poly(ethylene oxide)-poly(butylene oxide) diblock copolymer (EO6 BO11 ) is dissolved in water.12 The hydrophobic nature of the BO block drives the vesicle formation. At low diblock fraction and temperature, a wormlike micelle phase is observed. This is characterized by a 1/Q Porod behavior at low-Q (cylindrical structures). As the diblock fraction or temperature is increased, unilamellar, then multilamellar vesicles form. These are characterized by a 1/Q2 Porod behavior at low-Q (2D structures) and a Bragg peak at high-Q. At even higher diblock fraction or temperature, the vesicles form a lamellar phase. Indirect Fourier transform of the SANS data produced pair correlation functions which yielded estimates of vesicle sizes.

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Figure 4. Variation of the d-spacing (left) and of its ratio to the swelling asymmetry factor d/ξ for the PS-PDMS diblock copolymer in CO2 .

A morphology phase diagram (temperature versus diblock copolymer fraction in d-water) was mapped out. Pressurized CO2 plays the role of a selective solvent in a polystyrene-poly(dimethyl siloxane) diblock copolymer.16 This PS-PDMS copolymer is characterized by lamellar morphology with well-defined interdomain d-spacing. This d-spacing is inversely proportional to the scattering peak position. The SANS technique is useful for the characterization of this d-spacing as well as estimation of the various Flory-Huggins interaction parameters between each of the blocks (PS or PDMS) and the solvent (CO2 ) and between the two blocks (PS-PDMS). The swelling conditions are described by swollen block volume fractions fPS/CO2 and fPDMS/CO2 . These are determined from an equation-of-state for the swelling of the pure components (PS and PDMS) in CO2 along with the Flory-Huggins equation for polymer/solvent mixtures. Their ratio defines a swelling asymmetry factor ξ = fPS/CO2 /fPDMS/CO2 . SANS data were taken from the PS-PDMS diblock copolymer under CO2 pressure for three temperatures (40◦ C, 100◦ C, and 140◦ C). It was noted that whereas the interlamellar d-spacing (noted d) varies with the copolymer volume fraction φ diblock differently for each temperature, the ration d/ξ follows the same power law for all temperatures (Fig. 4). The microphase behavior for a series of poly(styrene sulfonate)-poly(methyl butylene) diblock copolymers was investigated using the SAXS and SANS techniques.17 High resolution of the SAXS technique allows the indexing of numerous Bragg reflections and therefore the possibility of resolving a wide range of ordered diblock copolymer microstructures. The observed copolymer morphologies include lamellae, gyroid, hexagonally perforated lamellae, and hexagonally packed cylinders. These morphologies were obtained by varying the copolymer molecular weight and sulfonation level as well as temperature. This range of morphologies was obtained with nearly symmetric diblock copolymers. TEM images confirmed some of the observed morphologies. SANS data were taken to estimate the Flory-Huggins interaction parameter which was used to predict the order-disorder transition conditions.

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Figure 5. Phase diagram for the PEP/PBO/PEP-PBO ternary mixture for increasing copolymer fraction (left); i.e., along the isopleth line which is depicted within the triangle phase diagram (right).

The ternary phase diagram for a polymer mixture consisting of two homopolymers, poly(ethylene propylene) and poly(butylene oxide), and their diblock copolymer PEP-PBO has been investigated using a host of characterization methods that include SANS, smallangle x-ray scattering (SAXS), rheology, and optical microscopy.18 Deuterated PEP was used in order to enhance the SANS contrast. A ternary phase diagram similar to the one for a nonionic surfactant/water/oil micellar system was mapped out close to the isopleth line (line for equal homopolymer fractions but with increasing copolymer fraction). The upper critical binodal line for the PEP/PBO binary blend was also mapped out. Along the isopleth line, the phase separation boundaries between the mixed phase, the macrophase separated region, and the microphase separated region were delimited. Within the microphase separation region, the order-to-order phase transition lines for the lamellar and hexagonal microphases were obtained (note that no cubic phase was observed). SAXS was effective at differentiating the ordered phases. The macrophase separation region contains two-phase droplets (rich in PEP or PBO with PEP-PBO forming the boundary between them) and three-phase droplets (rich in PEP, in PBO, or in PEP-PBO). The SANS technique was useful for the characterization of a narrow bicontinuous microemulsion channel obtained for high copolymer fraction (80%) and high temperature (around 120◦ C). The Teubner-Strey model was used to fit the SANS data (Fig. 5). A-C diblock copolymers were mixed to weakly-segregated A/B homopolymer blends. Components A, B, and C used were polybutadiene (89% 1,2 addition), polyisobutylene and polybutadiene (63% 1,2 addition) respectively.19 The C block was characterized by attractive interactions with the B block but repulsive interactions with the A block. This SANS study showed that organized domains form with the addition of as little as 1% A-C diblock to a 50%/50% A/B blend. SANS data were taken from a series of samples for which the copolymer fraction as well as its molecular weight were varied. The random phase approximation (RPA) model was used to analyze SANS data in the homogeneous (mixed) phase region. The Teubner-Strey (TS) model and a self-consistent-field theory

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(SCFT) were used in the ordered microphase region. The RPA approach yielded FloryHuggins interaction parameters and mean-field phase boundary predictions. The TS model and the SCFT approach yielded predictions of characteristic microdomain d-spacings as observed by SANS. The combination of measurements and models produced reasonable agreement for most of the probed range except for the case with very small copolymer fractions where there is room for improvement.

6. Polymer Blends Polymer blends constitute another active area of SANS research. The SANS technique is sensitive to density and composition fluctuations and is therefore a good thermodynamic probe for investigation of phase transitions in blends. The same polymer blend A/B/A-C discussed before19 was used to investigate the effects of pressure on phase transitions.20 Block C is characterized by repulsive interactions with block A and attractive interactions with block B. At ambient pressure, the blend forms a lamellar microphase at low temperature, a bicontinuous microemulsion phase at intermediate temperature, and is macrophase separated at high temperature. The same blend, however, exhibits a mixed (homogeneous) phase when pressurized. This behavior was traced to intricate dependences of the Flory-Huggins interaction parameters on temperature and pressure; χ AC (positive) decreased with temperature but did not change with pressure, χ BC (negative) increased with temperature but decreased (became more negative) with pressure, and χ AB (positive) increased with temperature but decreased with pressure. The random phase approximation (RPA) and the self-consistent-field theory (SCFT) were used to analyze SANS data with in-situ pressure. The Teubner-Strey model was also used to fit data in the microemulsion phase region. A pressure-temperature phase diagram was mapped out showing boundaries between the microphase separation, the macrophase separation, and the homogeneous mixed-phase regions (Fig. 6). The observation that pressure induces the formation of a homogeneous phase (favoring mixing) in the A/B/A-C polymer blend is contrary to the observed effect of pressure in nonionic surfactant/water/oil ternary mixtures where pressure tends to favor demixing. The SANS technique can map out both the binodal line and the spinodal line. The binodal line is reached when the intercept of the Zimm plot I−1(0) becomes negative (here I(0) is the scattering intensity in the forward Q = 0 direction). The spinodal line is obtained by extrapolating the I−1(0) versus T−1 linear behavior to the limit I−1(0) = 0 (here T is the absolute sample temperature). This helps delimit the nucleation-and-growth region located between the binodal and spinodal lines. Growth kinetics were studied by SANS from a deuterated poly(methylbutylene)/poly(ethylbutylene) off-critical polyolefin blend sample following pressure jumps from the homogeneous (mixed) phase region into the nucleation-and-growth region.21 Pressure jumps are more rapid than temperature jumps and therefore more effective. Prior to jump experiments, the pressure-temperature phase diagram (showing both the binodal and spinodal lines) was mapped out for the same dPMB/PEB blend. Nucleation-and-growth kinetics measurements were performed for a number of pressure jumps and for many quench depths. Both single jumps and double jumps were performed. In the case of double jumps, the first jump was deep into the nucleation-and-growth region (to form the nucleation seeds) and the second jump was shallow (to follow the growth kinetics). Critical nucleus sizes and the times required to conclude the early stage of nucleation were measured. These were obtained from the time-dependent SANS intensity characterizing the growth kinetics.

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Figure 6. SANS data from A/B/A-C polyolefin blend mixture of two homopolymers A/B and a diblock copolymer A-C under pressure (0.3 kbar) and for a sample temperature of 50 ◦ C (left) and pressure-temperature phase diagram (right). The Teubner-Strey model yields good model fit to the SANS data in the bicontinuous (microphase separated) phase region. The error bars correspond to one standard deviation.

SANS studies were performed to assess the possibility of swelling for high molecular weight “tracer” polymers (poly(ethylene oxide) and poly(methyl methacrylate) in low molecular weight polymer matrix.23 The same polymers (PEO and PMMA) were used for the matrix component. Three matrices were considered—pure PEO, pure PMMA, and 50%/50% (mass fractions) PEO/PMMA blend. Deuterated polymers were used for the tracer polymers and hydrogenated polymers were used for the matrix polymers. Low tracer polymer fractions were used. Measurement temperatures were chosen to be above the crystal meting temperature of PEO and above the glass-rubber transition temperature of PMMA. The SANS intensity was fit to a Debye function (form factor for unperturbed coils) in order to extract a radius of gyration in each case. The tracer polymers were found to follow unperturbed coil configurations in all cases; no chain swelling was observed.

7. Branched or Grafted Polymers Many investigations on SANS from branched or grafted polymers have been reported. These include single generation branching (stars and combs) as well as multi-generation branching (dendrimers and arborescent graft polymers). Polymer chain architecture plays a role in the mixing behavior of polymer blends. A systematic investigation has been undertaken24 using a series of branched polystyrene macromolecules (Fig. 7) with either varying number of branch points (and fixed number of chain ends) or varying number of chain ends (and fixed number of branch points). All polystyrene macromolecules were carefully synthesized and characterized. They all correspond to the same molecular weight. Blends were prepared using 50%/50% mixtures of linear deuterated polystyrene and branched (hydrogenated) polystyrenes. SANS data were taken from the two groups of blend samples at various temperatures. Random phase approximation (RPA) equations for blend mixtures of linear and specifically branched

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Figure 7. Polymer chain architectures with increasing number of branch points (left) or with increasing number of chain ends (right).

polymers were used to obtain an effective Flory-Huggins interaction parameter χ eff in each case. Partial form factors corresponding to the various regular branching architectures were used as inputs to the RPA fitting approach. The results showed that χ eff increases with increasing number of branch points (group I) and with increasing number of chain ends (group II). Branching seems to favor demixing in polymer blends. A Gaussian field theory was successful in predicting the overall χ eff trend for group II but not for group I. Arborescent graft polymers containing hyperbranched structures with a polystyrene comb-like backbone and poly(2-vinyl pyridine) chains grafted onto the “teeth” of the comb were investigated in either deuterated water or deuterated methanol dilute solutions.26 SANS and dynamic light scattering (DLS) were used to characterize the “fast” mode representing the local polyelectrolyte structure and the “slow” mode representing longrange clustering. SANS data showed a polyelectrolyte peak only when the pH was changed by adding hydrochloric acid. This peak is due to the so-called correlation-hole effect and is characteristic of an average distance between charged domains. The peak position scales like polymer fraction to the third power owing to the spherical (3D) symmetry of arborescent polyelectrolytes. Note that for linear polyelectrolytes, the peak position scales like the square root of the polymer fraction (2D symmetry). When enough acid is added to completely neutralize the charges on the P2VP blocks, the polyelectrolyte peak disappears again. Arborescent polymers with longer P2VP grafted blocks resulted in the formation of a gel for fractions greater than 1% mass fraction. The mean spherical approximation model for charged spheres was used to analyze the SANS data when long-range Coulomb interactions are present. Arborescent polymer sizes and degree of chain swelling were investigated using arborescent polystyrenes with two different size polystyrene side chains (with either 5K or 30K molecular weight) in dilute d-toluene solutions. Generations from G0 to G3 were measured using the SANS technique.27 A radius of gyration was obtained from the Guinier

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Figure 8. Representation of an arborescent copolymer corresponding to two generations (plus backbone) of h-polystyrene onto which one generation of d-polystyrene was grafted. The h-polystyrene forms the “core” structure whereas the outer d-polystyrene forms the “shell” structure. When the solvent is hydrogenated, only the shell is visible (left) while when the solvent is deuterated, only the core is visible (right).

and the Kratky data analyses methods and compared to the Zimm-Stockmayer model for branched polymer systems with different architectures. This model gives reasonable agreement for the case with short (5 K) side branches but not for the case with long (30 K) side branches. The measured radius of gyration scales with molecular weight for the various generations like Rg ∼ Mw 0.26 for short side branches and Rg ∼ Mw 0.32 for long side branches. Arborescent polymers with long side branches act like compact particles with tight packing. The influence of polymer-solvent interactions on Rg was expressed in terms of the expansion factor due to excluded volume. Swelling effects were clearly observed for short side chains but not for long side chains. Inverse Fourier transforms of the SANS data yielded pair distance distribution functions p(r) which contain information about internal arborescent particle inhomogeneities within the core and within the shell regions. Furthermore, arborescent polymers were synthesized using hydrogenated polystyrene for the core and deuterated polystyrene for the side branches. This helped realize solvent contrast match conditions for either the hydrogenated core or the deuterated shell (Fig. 8) using solvents with more convenient scattering length densities (THF and cyclohexane and their deuterated versions). The higher generation arborescent polymers showed a better-defined core-shell structure than the lower generation ones. Comblike copolymers with polynorbornene (PNB) backbone and oligo ethylene glycol (OEG) side chains were measured in dilute d-water solutions.30 The diblock copolymer consists of a (hydrophobic) block with short OEG3 chains and the other (hydrophilic) block with long OEG6.6 chains. SANS measurements were performed over a temperature range between 25◦ C and 68◦ C. At 25◦ C, the copolymers were found to associate into micelles with the hydrophobic block forming an inner spherical core and the hydrophilic block forming cylindrical structures within the outer shell. As the temperature is increased, even long OE G6.6 chains become hydrophobic and phase separation occurs at the cloud point temperature of 60◦ C. Above this temperature, a transition to another phase characterized by sharp Bragg d-spacing of 349 Å is observed. A hybrid model for micelles with spherical core and cylindrical “spokes” radiating out to form the shell was used to analyze the SANS data for low temperatures. A scattering density profile for the micellar shell was obtained

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along with an aggregation number. The aggregation number was found to increase and the micellar size was found to decrease with increasing temperature. This is due to the increasing hydrophobicity of OEG chains upon heating. The hydrophilic block of the previously described diblock copolymer was used to investigate solvent effects in d-toluene and d-water dilute solutions.31 This corresponds to 50 monomers of norbornene backbone (NB) and oligo ethylene glycol side chains (OEG6.6 ). Four polymer fractions in the dilute solution range and four temperatures between 25◦ C and 74◦ C were measured by SANS. Chain dimensions (radius of gyration) and polymer-solvent interactions (second virial coefficient) were obtained from the familiar Zimm plot for dilute polymer solutions. Polymer chains were seen to follow random-coil conformations at low temperature and low polymer fraction when dissolved in d-toluene. Polymers were found to contract with increasing polymer fraction. Deuterated water is a selective solvent for the OEG blocks which tend to take a cylindrical shape forming the teeth of the comblike polymer. The theta temperature was estimated to be 45◦ C. At 74◦ C, hydrophobic interactions take over and most of the polymer precipitates out of solution (in d-water).

8. Polymer Gels Polymer gels form when crosslinking is introduced. The various microstructures formed are in the nanometer length scale making the SANS technique a useful characterization method. Gels were formed through (electron beam) radiation crosslinking of two diblock copolymers; poly(α-methylstyrene)-polyisoprene (PaMS-PI) and poly(vinylferrocenium triflate)-polyisoprene (PVFT-PI). Radiation crosslinks the PI blocks, induces chain scission in the PaMS blocks, and has no effect on the PVFT blocks. Swelling of the formed gels in partially deuterated solvents allowed the characterization of the crosslink density as function of the radiation dose by SANS, as well as by standard gel characterization methods.35 This allowed characterization of the copolymer microdomain morphology in the presence of crosslinks. It was found, for instance, that uncrosslinked PaMS blocks play an important role in the swelling behavior of PaMS-PI gels. Chain scission in PaMS seems to release stresses that may appear during gel formation. It was also found that chains in the PVFT blocks undergo stretching as the gel crosslinking becomes tighter. Information about solvent partitioning in the two swollen gels was obtained. Solvent-filled open channels were observed in the PaMS-PI gels whereas large length-scale clustering was observed in PVFT-PI gels. Poly(vinyl alcohol) hydrogels were formed by introducing physical crosslinks consisting of small ice crystals. These were created through freeze/thaw cycles. Samples that were stretched after the first cycle remained oriented. The PVA hydrogels are intended for potential use in biomedical applications. Their morphology and stress response were investigated using SANS and mechanical testing.36 Other characterization methods were also used (SAXS, TEM, C-13 NMR, etc.). The Debye-Bueche model was used to obtain a correlation length characterizing the average distance between crosslinks. The Teubner-Strey model was also used to obtain a correlation length along with a quasi-periodic d-pacing characterizing the hydrogel network at the local level. The dominant low-Q feature of the SANS signal was fitted to a power law behavior to represent long-range correlations. SANS results showed that the PVA hydrogel comprises a polymer-rich local phase formed

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Figure 9. Representation of the flower-like spherical micelle (left) and lamellar micelle (right) formed of triblock copolymers where the central block is hydrophilic and the outer blocks are hydrophobic.

of nanopores 150 to 300 Å in size surrounded by a larger overall structure containing micron size morphology. This structure is held together through the small crystal crosslinks. PLA-PEO-PLA triblock copolymers are formed of hydrophyllic poly(ethylene oxide) blocks and hydrophobic poly(lactide) blocks. Since the hydrophilic block is the middle block, a flowerlike structure is obtained in water solution (Fig. 9). SANS measurements were made from PLA-PEO-PLA solutions in order to understand the morphology as function of PLA block length and stereospecifity.38 It was found that spherical micelles form when amorphous D/L-lactic acid blocks are used whereas lamellar micelles form when crystalline L-lactic acid blocks are used. Moreover, an increase in the triblock fraction (in d-water solutions) leads to gel formation. SANS data were analyzed using single micelle form factors and inter-micelle structure factors. In the case of spherical micelles, the familiar Percus-Yevick solution of the Ornsterin-Zernike equation was used while in the case of lamellar micelles, a lamellar stack model introduced to interpret data from lamellar stacks in crystalline polymers in solution was used. Micellar sizes and inter-distances were obtained. The association characteristics of the micelles were found to be controlled by the length and crystallinity of the PLA blocks. Double-network hydrogels formed of a charged crosslinked polymer network (PAMPS) and neutral linear polyacrylamide (PAA) polymers were investigated using the SANS and Ultra-SANS techniques.40 The USANS technique can probe size scales up to 20 µm. Deuterated PAA and d-water were used in order to enhance the neutron contrast. Investigation of PAMPS solutions in d-water and of PAMPS/d-PAA solutions in mixtures of d-water and h-water were conducted in order to measure the various Flory-Huggins interaction parameters for the various components. It was found that χ PAMPS/PAA χ PAMS/water < χ PAA/water . Measurements from PAMPS/d-PAA/d-water were also taken from the fully formed double-network hydrogels. A random phase approximation model that incorporates charge interactions (through a Debye-Huckel factor) and a crosslinked network (though a characteristic mesh size) was used to fit the SANS data. This model reproduces the high-Q SANS data well and yields some understanding of double-network hydrogel structures at the molecular level.

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Figure 10. Inhomogeneous structure of PAA (left) and PAMPS (right) polymerized in water as inferred from SANS data.

9. Polymer Networks The boundary between gels and networks is fuzzy. These appellations could be used interchangeably. Gels usually form beyond a sol-gel transition which is reversible while networks are usually not reversible; they involve covalent crosslinking. The PAMPS/PAA double-network hydrogel described earlier40 was used to understand the molecular origin of some unusual mechanical properties (Fig. 10). In-situ SANS investigations were undertaken using samples deformed in a compression device.41 Molecular conformations of the deuterated PAA chains were monitored. Possible molecular origin of the correlation between enhancement in solution viscosity and fracture toughness of crosslinked gels was discussed. It was argued that molecular association between the PAMPS and PAA components of the double-network could be at the origin of the unusual mechanical performance. The attractive interactions between these two polymers could explain the increased toughness of these polymeric materials. Polymer blends consisting of stiff liquid crystalline polyurethane and flexible polystyrene-poly(vinyl phenol) copolymers form hydrogen bonded networks characterized by a wide miscibility window.45 The polystyrene blocks were deuterated to enhance the neutron contrast. SANS measurements from the pure copolymer and with increasing amount of polyurethane allowed the monitoring of crystalline polyurethane chain conformations within an amorphous flexible polymer matrix. FTIR studies showed clear evidence of hydrogen-bonding between the two network components. Increasing the polyurethane fraction succeeded in breaking down the network of hydrogen bonds and led to the formation of new large-scale structures. The semiflexible polyurethane chains assume anisotropic conformations as observed by the SANS high-Q data and fits to the Kratky-Porod wormlike chain model. Interpenetrating polymer networks (IPNs) are formed through the in-situ synthesis of a network within the matrix of another. The state of miscibility of the mixed components during synthesis dictates the resulting network morphology. SANS and dynamic mechanical thermal analysis (DMTA) were performed on a series of methacrylate/epoxy interpenetrating polymer networks in order to assess the extent of molecular miscibility.46 SANS is sensitive to composition fluctuations and DMTA can measure the glass-rubber transition temperatures (Tg s) for polymeric materials precisely. A single Tg is a signature of a homogeneously mixed phase while two Tg s point to a demixed two-phase system. The

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Debye-Bueche model was used to interpret SANS data from the interpenetrating polymer networks and yielded a phase separation size scale of order 180 Å. DMTA of the rubbery region of some of the IPNs revealed bicontinuous structures and the extent of phase separation. A number of amphiphilic co-networks of methacrylic acid (MAA) and 2-butyl-1-octyl methacrylate (BOMA) were synthesized and characterized using a host of methods.48 Some were model co-networks containing A-B-A copolymer chains between cross-links of precise length and composition. Here the A block contains multiple MAA monomers and the B block contains multiple BOMA monomers. The linear co-network precursors used in the group transfer polymerization were characterized by GPC and NMR for their molecular weight and composition. The degree of swelling of these amphiphilic polymer co-networks was investigated in water and in THF over a broad ionization range of the MAA monomers. It was found that the degree of swelling in water increased with the degree of ionization and the size of the MAA blocks. The degree of swelling in THF also increased with the length of the copolymers between cross-link points. The SANS technique and atomic force microscopy were used to characterize the co-network morphology.

10. Polymer Micelles Water-soluble polymers can form nonionic micelles owing to their hydrophobic/ hydrophilic characteristics. Here also, the SANS technique has been an effective tool for the characterization of structure and miscibility. Wormlike micelles are formed using trimethylammonium cations and 4-vinylbenzoate counterions in aqueous solution. The resulting polymer-surfactant aggregates were polymerized to obtain rodlike ionic micelles.49 The micelle radius was controlled by varying the hydrocarbon length on the trimethylammonium and its length was controlled by varying the initiator decomposition half-life. This was done by varying temperature or using different initiators. The micelle radius was varied between 17 Å and 24 Å and its length was varied between 800 Å and 5000 Å as characterized by SANS measurements. This approach yielded stable polymerized rodlike micelles with controllable sizes that are independent of surfactant concentration (provided that it is higher than the critical micelle concentration). Long polymerized micelles were obtained using low initiator content and low temperature. Free radical polymerization of the mixture of cetyltrimethylammonium (CTVB) and sodium 4-styrenesulfonate (NaSS) in aqueous solution produced stable rodlike particles (Fig. 11) with controlled surface charge density.51 Rodlike particle dimensions were

Figure 11. Chemical representation of CTVB and NaSS (left) and schematic representation of the polymerized rodlike micelle (right).

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characterized by SANS; the diameter was found to be constant (equal to 40 Å) and the length varied between 240 Å and 850 Å depending on NaSS concentration. When the NaSS concentration was increased, the rodlike particle length increased then decreased. The longest particles were obtained at the charge neutralization condition. Zeta potential measurements were also performed to characterize NaSS charge effects. Polymer micelles were formed using an A-C diblock copolymer (acting as surfactant) mixed with A and B homopolymers. The C block was characterized by repulsive interactions with the A block but attractive interactions with the B block.56 This project was also included in earlier sections (SANS from copolymers and blends). The SANS technique was effective at mapping out a microphase separation region, a macrophase separation (twophase) region, and a homogeneously mixed (one-phase) region in-between. The random phase approximation (RPA), the self-consistent-field theory (SCFT) and Teubner-Strey (TS) model were used to analyze the SANS data. Reasonable agreements were found. Small molecule surfactants cause the melting of polymeric micelles formed of amphiphilic diblock copolymers. The poly(butylacrylate)-poly(acrylic acid) (PBA-PAA) diblock forms micelles in aqueous solution. Neutral or ionic surfactants (such as C12E6 for example) break the polymer micelles as documented by light scattering (SLS and DLS), SAXS, SANS, cryo-TEM, and capillary electrophoresis;58 they reduce the interfacial tension and gradually produce two populations—one rich in large polymer micelles and one rich in small surfactant micelles. Before adding small surfactants, fits of a core-shell model to SANS data yielded an estimate of the core radius for the polymeric micelles around 80 Å (polydispersity of 0.2). After adding 1.5% mass fraction of C12E6 small molecule surfactant, the mean micelle radius decreased to 34 Å (polydispersity of 0.14). This size (34 Å) is very close to the size of pure-surfactant micelles. Simple interfacial tension arguments with and without surfactant permits the interpretation of the observed trends. A model hydrophobically modified polymer was used to crosslink wormlike micelles59 in water. Water-soluble poly(ethylene oxide) containing hydrocarbon tails (C14 to C22 ) at their ends was used to form bridges across wormlike micelles (1% mass fraction CTAT in water). SANS and rheology were used to characterize crosslinked network. The hydrophobic end groups stick to the wormlike micelles while PEO chains remain dissolved. Three types of PEO chains were used— 1. PEO chains with a sticker at one end, 2. PEO chains with a sticker at each end, and 3. 3-arm PEO stars with a sticker at each end. The wormlike micelles are likely breaking locally and reforming to shield the hydrophobic stickers from contact with water. The PEO chains form bridges between the wormlike micelles (Fig. 12). Pluronic triblock copolymers (PEO-PPO-PEO) form micellar structures at ambient temperatures. Spherical micelles formed when Pluronic F127 solutions in d-water (20% mass fraction) were sheared in a Couette shear cell. In-situ SANS investigations were performed using the radial and tangential neutron beam configurations.60 The spherical micelles were seen to form layered macrolattice structures characterized by single-crystal type scattering (with bright diffraction spots). Transition from face-centered cubic structure at low shear rates to random layer stacking at high shear rates was observed. This was the cause of the observed shear thinning behavior. A model comprising intra-layer sphere arrangement as well as inter-layer structure was used to interpret the SANS data under shear. This model incorporated oriented stacks of micellar layers and allowed for disorder

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Figure 12. Two possible clustering configurations. There is evidence that the configuration on the left is more likely than the one on the right.

effects; it reproduced the observed cubic structures and a transition to random layer stacking leading to a hexagonal phase. The SANS technique was used to investigate the structure of polystyrene-poly(acrylic acid, sodium salt) copolymers in water solution under Couette and plate-plate shear.63 This investigation reported a wide range of copolymer fractions in water solution using PSPAA of Mn = 4,700–11,300 g/mol. Since the polystyrene block is hydrophobic, wormlike micelles form. These were found to form hexagonally close-packed cylinders under shear with the cylinder axis parallel to the shear gradient direction; i.e., perpendicular to the shear flow direction. SAXS and electron microcopy confirmed the oriented cylinders structure. Evidence for bridging between cylinders was reported. This may be due to the long PAA block length and some clustering driving force which depends on the cylindrical micelle fraction.

11. Polymeric Nanomaterials This is a category gathering SANS investigations from various materials including those described here. SANS from mixtures of deuterated and non-deuterated isotopic blends is a good monitor of chain orientation in (for instance) injection-molded samples. A series of isotopic polystyrene blends has been injection molded, while varying a number of experimental conditions, including injection molding speed, mold thickness, and mold temperature.64 Elliptical averaging of the anisotropic 2D data yielded an eccentricity factor which is a measure of the degree of chain orientation. This eccentricity factor was found to decrease with injection speed, mold thickness, and injection molding temperature. It was also found to decrease with the length scale probed showing that nano-stresses acting upon polymer chains relax at the local chain segment level. SANS and x-ray reflectometry have been used to characterize the porosity of a poly(phenylene) low-k dielectric thin film material.65 This material contains porogen which degrades upon baking at elevated temperatures thereby forming the pores. Three baking temperatures were used (150◦ C, 400◦ C, and 430◦ C). Since the thickness of each film was around 1 micron, many wafers were stacked in order to enhance the SANS signal. The

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Figure 13. Porosity representation of the low-k dielectric material containing porogen after baking at 400◦ C without (left) and with solvent contrast match (right). The partially deuterated solvent vapor matches the scattering length density of the matrix and fills the pores making them invisible.

samples were placed in a custom-built flow-through cell in order to control the vapor pressure. Mixtures of deuterated and non-deuterated methanol or toluene solvent vapors were used to adjust the neutron contrast by filling the pores (Fig. 13). The pore size distribution and pore fraction were determined for each baking strategy. The fraction of porogen that remains in the low-k films was estimated and found to decrease with baking temperature. Body armors are made out of high strength material containing poly(p-phenylene-2,6benzobisoxazole) fibers. An extensive study of such material aged at elevated temperatures for extended periods of time (around half a year) was conducted using a battery of characterization methods including mechanical testing (tensile strength measurements), SANS, FTIR, atomic force microscopy, and confocal microscopy.66 A 30% decrease in yarn tensile strength upon aging in humid environment was correlated with the hydrolysis of specific chemical groups as observed by FTIR. When aging was performed in an inert (argon) environment, this decrease went down to 4%. This demonstrates that moisture is a key factor in fiber degradation. SANS studies were conducted on composites formed of isotopic polystyrene blends mixed with silica nanoparticles under contrast match condition.69 It was found that polymer chain conformations follow unperturbed Gaussian chain statistics regardless of polymer molecular weight and nanoparticle loading. The polymer reference interaction site model (RISM) was used to model polymer/nanoparticle interactions.

12. Polymer Membranes The hydrogen fuel cell technology has become an active SANS area of research. Fuel cells use hydrogen to produce electricity. Hydrogen fuel is channeled to the anode on one side while oxygen is channeled to the cathode on the other side. At the anode, a catalyst causes hydrogen to ionize into protons and electrons. The polymer membrane allows only the protons to pass through to the cathode. The electrons, on the other hand, travel along an external circuit thereby generating an electrical current (Fig. 14). SANS has been used to characterize the structure of some polymer membranes.

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Figure 14. Schematics of a hydrogen fuel cell (left) and bicontinuous morphology of a polymer membrane (right).

Poly(perfluorosulfonic acid) also referred to as Nafion is a fuel cell membrane material. SANS investigations have been conducted on Nafion membranes in an in-situ vapor sorption cell used to control the relative humidity.71 Different membrane processing conditions (melt extrusion or solvent casting), thermal pretreatment histories, and submicron membrane thicknesses were studied. The SANS data showed features characterizing semicrystalline copolymers and porous media with ion channels in the nanometer size range. A strong correlation was found between the interionic domain distance and the relative humidity. Diffusion coefficients of water vapor were estimated based on the observed structural evolution. Diblock copolymer films composed of a fluorocarbon block and a sulfonated polystyrene block were investigated by SANS and TEM.73 These are the potential proton exchange membranes for low-temperature fuel cells. Two hierarchical structure levels were observed—one due to the block copolymer microstructure and one due to the charged domains structure. The copolymer microstructure shows clearly fluorous domains and sulfonated polystyrene (darker) domains by TEM. Longer and partially sulfonated polystyrene blocks yield well-ordered microdomains, whereas shorter and fully sulfonated polystyrene blocks yield more disordered structures. Polystyrene sulfonate-b-poly(methyl butytlene) block copolymers have also been investigated as potential membrane material for hydrogen fuel cells.75 The microdomain morphology was controlled by varying the molecular weight of the polystyrene sulfonate (PSS) block and therefore the size of the hydrophilic proton channels. A drastic trend reversal was observed for channel sizes around 50 Å. The proton conductivity was found to decrease with increasing temperature for channel sizes higher than 50 Å (i.e., when high molecular weight PSS blocks are used) and to increase with increasing temperature for channel sizes smaller than 50 Å (i.e., when low molecular weight PSS blocks are used).

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These findings were supported from evidence based on TEM and SANS studies. Some of these studies were conducted under systematic moisture control. The correlation between the moisture content and proton conductivity in these membranes was clearly demonstrated. The phase behavior of one of the above-described block copolymer PSS-PMB used as ion-containing membrane has been investigated as function of relative humidity (RH). The copolymer ion content (sulfonation level) represented by the ion-exchange capacity (IEC) parameter was varied as well as the membrane temperature.76 SAXS, TEM, SANS, DSC and water content measurements were used to probe the rich phase behavior. Indexing of the various SAXS Bragg peaks helps in structure determination. The disordered phase was observed for low IEC and low RH values, the gyroid phase was observed for high IEC and low RH values, whereas the lamellar phase was observed for high RH values.

13. Summary and Future Prospect Use of the SANS technique has been ever-growing in the area of polymer research. Improvements of SANS instrument capabilities, sophistication of data analysis methods, and the advent of judicious sample environments have brought about renewed interest over the past thirty years. One of the leading SANS research centers, the NCNR, operates two 30 m SANS instruments in the user mode. This attracts over 200 SANS users per year resulting in over 80 publications in refereed journals. Polymer research constitute about one-third of this effort. Increased demand for additional SANS beamtime is the driving force behind a major upgrade of the NCNR facility. This upgrade includes the construction of a higher resolution SANS instrument. The new 40 m VSANS instrument (V is for “very”) will lower the measurement range (Qmin ) by an order of magnitude without too much loss in neutron flux on sample. The new (lower) Qmin will be around 0.0002 Å−1 which will be achieved by using multiple-hole converging collimation. The measurement window of the VSANS instrument will overlap nicely with the Bonse-Hart USANS instrument. The new capability VSANS/USANS combination will cover 5 orders of magnitude in scattering variable. This will allow the probing of polymer structures from the near atomic (nanometer) scale to well into the optical (20 micrometers) size scale and will open up exciting new prospects for polymer research. Other neutron scattering facilities in the US, in Europe, as well as elsewhere are also thriving. The SANS technique is the major driving force fueling the success of these facilities.

Disclaimer/Acknowledegments Certain commercial equipment, instruments, or materials are identified in this paper to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipments identified are necessarily the best available for the purpose. This work is based upon activities supported in part by the National Science Foundation under Agreement No. DMR-0454672.

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by ultra-small-angle neutron scattering and optical microscopy,” Macromolecules, 2008, 41, 471–477. Zeroni, I.; Lodge, T. P. “Chain dimensions in poly(ethylene oxide)/poly(methyl methacrylate) blends,” Macromolecules, 2008, 41, 1050–1052. Lee, J. S.; Foster, M. D.; Wu, D. T. “Effects of branch points and chain ends on the thermodynamic interaction parameter in binary blends of regularly branched and linear polymers,” Macromolecules, 2006, 39, 5113–5121. Rathgeber, S.; Monkenbusch, M.; Hedrick, J. L.; Trollsas, M.; Gast, A. P. “Starlike dendrimers in solutions: Structural properties and internal dynamics,” The Journal of Chemical Physics, 2006, 125, 204908-1 to 204908-11. Yun, S. I.; Briber, R. M.; Kee, R. A.; Gauthier, M. “Dilute-solution structure of charged arborescent graft polymer,” Polymer, 2006, 47, 2750–2759. Yun, S. I.; Lai, K. C.; Briber, R. M.; Teertstra, S. J.; Gauthier, M.; Bauer, B. J. “Conformation of arborescent polymers in solution by small-angle neutron scattering: Segment density and core-shell morphology,” Macromolecules, 2008, 41, 175–183. Chen, W. R.; Porcar, L.; Liu, Y.; Butler, P. D.; Magid, L. J. “Small angle neutron scattering studies of the counterion effects on the molecular conformation and structure of charged G4 PAMAM dendrimers in aqueous solutions,” Macromolecules, 2007, 40, 5887–5898. Cheng, G.; Melnichenko, Y. B.; Wignall, G. D.; Hua, F.; Hong, K.; Mays, J. W. “Conformation of oligo(ethylene glycol) grafted polystyrene in dilute aqueous solutions,” Polymer, 2007, 48, 4108–4113. Cheng, G.; Hua, F.; Melnichenko, Y. B.; Hong, K.; Mays, J. W.; Hammouda, B.; Wignall, G. D. “Association and structure of thermosensitive comblike block copolymers in aqueous solutions,” Macromolecules, 2008, 41, 4824–4827. Cheng, G.; Hua, F.; Melnichenko, Y. B.; Hong, K.; Mays, J. W.; Hammouda, B.; Wignall, G. D. “Conformation of oligo(ethylene glycol) grafted poly(norbornene) in solutions: A small angle neutron scattering study” European Polymer Journal, 2008, 44, 2859–2864. Mortensen, K.; Gasser, U.; Gursel, S. A.; Scherer, G. G. “Structural characterization of radiationgrafted block copolymer films using SANS technique,” Journal of Polymer Science: Part B: Polymer Physics, 2008, 46, 1660–1668. Loizou, E.; Butler, P.; Porcar, L.; Schmidt, G. “Dynamic responses in nanocomposite hydrogels,” Macromolecules, 2006, 39, 1614–1619. Matos, M. A.; White, L. R.; Tilton, R. D. “Electroosmotically enhanced mass transfer through polyacrylamide gels,” Journal of Colloid and Interface Science, 2006, 300, 429–436. Durkee, D. A.; Gomez, E. D.; Ellsworth, M. W.; Bell, A. T.; Balsara, N. P. “Microstructure and solvent distribution in cross-linked diblock copolymer gels,” Macromolecules, 2007, 40, 5103–5110. Millon, L. E.; Nieh, M. P.; Hutter, J. L.; Wan, W. “SANS characterization of an anisotropic poly(vinyl alcohol) hydrogel with vascular applications,” Macromolecules, 2007, 40, 3655–3662. Jiang, J.; Malal, R.; Li, C.; Lin, M. Y.; Colby, R. H.; Gersappe, D.; Rafailovich, M. H.; Sokolov, J. C.; Cohn, D. “Rheology of thermoreversible hydrogels from multiblock associating copolymers,” Macromolecules, 2008, 41, 3646–3652. Agrawal, S. K.; Sanabria-DeLong, N.; Tew, G. N.; Bhatia, S. R. “Structural characterization of PLA-PEO-PLA solutions and hydrogels: Crystalline vs amorphous PLA domains,” Macromolecules, 2008, 41, 1774–1784. Tirumala, V. R.; Tominaga, T.; Lee, S.; Butler, P. D.; Lin, E. K.; Gong, J. P.; Wu, W. L. “Molecular model for toughening in double-network hydrogels,” J. Phys. Chem. B, 2008, 112, 8024–8031. Tominaga, T.; Tirumala, V. R.; Lee, S.; Lin, E. K.; Gong, J. P.; Wu, W. L. “Thermodynamic interactions in double-network hydrogels,” J. Phys. Chem. B, 2008, 112, 3903–3909. Tominaga, T.; Tirumala, V. R.; Lin, E. K.; Gong, J. P.; Furukawa, H.; Osada, Y.; Wu, W. L. “The molecular origin of enhanced toughness in doublenetwork hydrogels: A neutron scattering study,” Polymer, 2007, 48, 7449–7454.

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42. Sun, Y. S.; Jeng, U. S.; Huang, Y. S.; Liang, K. S.; Lin, T. L.; Tsao, C. S. “Complementary SAXS and SANS for structural characteristics of a polyurethethane elastomer of low hard-segment content,” Physica B, 2006, 385–386, 650–652. 43. Li, Y. C.; Chen, K. B.; Chen, H. L.; Hsu, C. S.; Tsao, C. S.; Chen, J. H.; Chen, S. A. “Fractal aggregates of conjugated polymer in solution state,” Langmuir, 2006, 22, 11009–11015. 44. Burford, R. P.; Markotsis, M. G.; Knott, R. B. “Real-time SANS study of interpenetrating polymer network (IPN) formation,” Physica B, 2006, 385–386, 766–769. 45. Mehta, R.; Dadmun, M. D. “Small angle neutron scattering studies on miscible blends of poly(styrene-ran-vinyl phenol) with liquid crystalline polyurethane,” Macromolecules, 2006, 39, 8799–8807. 46. Dean, K. M.; Cook, W. D.; Lin, M. Y. “Small angle neutron scattering and dynamic mechanical thermal analysis of dimethacrylate/epoxy IPNs,” European Polymer Journal, 2006, 42, 2872–2887. 47. Kali, G.; Georgiou, T. K.; Ivan, B.; Patrickios, C. S.; Loizou, E.; Thomann, Y.; Tiller, J. C. “Synthesis and characterization of anionic amphiphilic model co-networks based on methacrylic acid and methyl methacrylate: Effects of composition and architecture,” Macromolecules, 2007, 40, 2192–2200. 48. Kali, G.; Georgiou, T. K.; Iván, B.; Patrickios, C. S.; Loizou, E.; Thomann, Y.; Tiller, J. C. “Synthesis and characterization of anionic amphiphilic model co-networks of 2-Butyl-1-octylmethacrylate and methacrylic acid: Effects of polymer composition and architecture,” Langmuir, 2007, 23, 10746–10755. 49. Gerber, M. J.; Walker, L. M. “Controlling dimensions of polymerized micelles: Micelle template versus reaction conditions,” Langmuir, 2006, 22, 941–948. 50. Kuntz, D. M.; Walker, L. M. “Solution behavior of rod-like polyelectrolyte-surfactant aggregates polymerized from wormlike micelles,” J. Phys. Chem. B, 2007, 111, 6417–6424. 51. Kim, T. H.; Choi, S. M.; Kline, S. R. “Polymerized rodlike nanoparticles with controlled surface charge density,” Langmuir, 2006, 22, 2844–2850. 52. Kim, T. H.; Doe, C.; Kline, S. R.; Choi, S. M. “Water redispersible isolated single-walled carbon nanotubes fabricated by in-situ polymerization of micelles,” Adv. Mater. 2007, 19, 929– 933. 53. Pozzo, D. C.; Walker, L. M. “Shear orientation of nanoparticle arrays templated in a thermoreversible block copolymer micellar crystal,” Macromolecules, 2007, 40, 5801–5811. 54. Pozzo, D. C.; Walker, L. M. “Small-angle neutron scattering of silica nanoparticles templated in PEO–PPO–PEO cubic crystals” Colloids and Surfaces A: Physicochem. Eng. Aspects, 2007, 294, 117–129. 55. Pozzo, D. C.; Walker, L. M. “Macroscopic alignment of nanoparticle arrays in soft crystals of cubic and cylindrical polymer micelles,” Eur. Phys. J. E, 2008, 26, 183–189. 56. Ruegg, M .L.; Reynolds, B. J.; Lin, M. Y.; Lohse, D. J.; Balsara, N. P. “Microphase and macrophase separation in multicomponent A/B/A-C polymer blends with attractive and repulsive interactions,” Macromolecules, 2006, 39, 1125–1134. 57. Gomez, E. D.; Ruegg, M. L.; Minor, A. M.; Kisielowski, C.; Downing, K. H.; Glaeser, R. M.; Balsara, N. P. “Interfacial concentration profiles of rubbery polyolefin lamellae determined by quantitative electron microscopy,” Macromolecules, 2008, 41, 156–162. 58. Jacquin, M.; Muller, P.; Cottet, H.; Crooks, R.; Thé odoly, O. “Controlling the melting of kinetically frozen poly(butylacrylate-b-acrylic acid) micelles via addition of surfactant,” Langmuir, 2007, 23, 9939–9948. 59. Lodge, T. P.; Taribagil, R.; Yoshida, T.; Hillmyer, M. A. “SANS evidence for the cross-linking of wormlike micelles by a model hydrophobically modified polymer,” Macromolecules, 2007, 40, 4728–4731. 60. Jiang, J.; Burger, C.; Li, C.; Li, J.; Lin, M. Y.; Colby, R. H.; Rafailovich, M. H.; Sokolov, J. C. “Shear-induced layered structure of polymeric micelles by SANS,” Macromolecules, 2007, 40, 4016–4022.

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61. Jiang, J.; Li, C.; Lombardi, J.; Colby, R. H.; Rigas, B.; Rafailovich, M. H.; Sokolov, J. C. “The effect of physiologically relevant additives on the rheological properties of concentrated Pluronic copolymer gels,” Polymer, 2008, 49, 3561–3567. 62. O’Driscoll, B. M. D.; Hawley, A. M.; Edler, K. J. “Incorporation of sparingly soluble species in mesostructured surfactant–polymer films,” Journal of Colloid and Interface Science, 2008, 317, 585–592. 63. Grandjean, J.; Mourchid, A. “Restricted swelling and its orientation effect on copolymer micellar solutions of hexagonal-packed cylinders under steady shear flow,” Langmuir, 2008, 24, 2318–2325. 64. Healy, J.; Edward, G. H.; Knott, R. B. “Residual orientation in injection micro-molded samples,” Physica B, 2006, 385–386, 620–622. 65. Silverstein, M. S.; Bauer, B. J.; Hedden, R. C.; Lee, H. J.; Landes, B. G. “SANS and XRR porosimetry of a polyphenylene low-k dielectric,” Macromolecules, 2006, 39, 2998–3006. 66. Chin, J.; Forster, A.; Clerici, C.; Sung, L.; Oudina, M.; Rice, K. “Temperature and humidity aging of poly(p-phenylene-2,6- benzobisoxazole) fibers: Chemical and physical characterization,” Polymer Degradation and Stability, 2007, 92, 1234–1246. 67. Stefanescu, E. A.; Dundigalla, A.; Ferreiro, V.; Loizou, E.; Porcar, L.; Negulescu, I.; Garno, J.; Schmidt, G. “Supramolecular structures in nanocomposite multilayered films,” Phys. Chem. Chem. Phys., 2006, 8, 1739–1746. 68. Li, J.; Jiang, J.; Li, C.; Lin, M. Y.; Schwarz, S. A.; Rafailovich, M. H.; Sokolov, J. “Effect of temperature on shear-induced anisotropic structure in polymer clay hydrogels,” Macromol. Rapid Commun. 2006, 27, 1787–1791. 69. Sen, S.; Xie, Y.; Kumar, S. K.; Yang, H.; Bansal, A.; Ho, D. L.; Hall, L.; Hooper, J. B.; Schweizer, K. S. “Chain conformations and bound-layer correlations in polymer nanocomposites,” Phys. Rev. Lett., 2007, 98, 128302-1 to 128302-4. 70. Chatterjee, T.; Krishnamoorti, R. “Dynamic consequences of the fractal network of nanotubepoly(ethylene oxide) nanocomposites,” Physical Review E, 2007, 75, 050403-1 to 050403-4. 71. Kim, M. H.; Glinka, C. J.; Grot, S. A.; Grot, W. G. “SANS study of the effects of water vapor sorption on the nanoscale structure of perfluorinated sulfonic acid (Nafion) membranes,” Macromolecules, 2006, 39, 4775–4787. 72. Gao, J.; Yang, Y.; Lee, D.; Holdcroft, S.; Frisken, B. J. “Self assembly of latex particles into proton-conductive membranes,” Macromolecules, 2006, 39, 8060–8066. 73. Rubatat, L.; Shi, Z.; Diat, O.; Holdcroft, S.; Frisken, B. J. “Structural study of proton-conducting fluorous block copolymer membranes,” Macromolecules, 2006, 39, 720–730. 74. Shin, K.; Obukhov, S.; Chen, J. T.; Huh, J.; Hwang, Y.; Mok, S.; Dobriyal, P.; Thiyagarajan, P.; Russell, T. P. “Enhanced mobility of confined polymers,” Nature Materials, 2007, 6, 961–965. 75. Park, M. J.; Downing, K. H.; Jackson, A.; Gomez, E. D.; Minor, A. M.; Cookson, D.; Weber, A. Z.; Balsara, N. P. “Increased water retention in polymer electrolyte membranes at elevated temperatures assisted by capillary condensation,” Nano Letters, 2007, 7, 3547–3552. 76. Park, M. J.; Nedoma, A. J.; Geissler, P. L.; Balsara, N. P.; Jackson, A.; Cookson, D. “Humidityinduced phase transitions in ion-containing block copolymer membranes,” Macromolecules, 2008, 41, 2271–2277. 77. Nieh, M. P.; Guiver, M. D.; Kim, D. S.; Ding, J.; Norsten, T. “Morphology of comb-shaped proton exchange membrane copolymers based on a neutron scattering study,” Macromolecules, 2008, 41, 6176–6182.


X-ray Scattering for the Monitoring of Processes in Polymer Materials with Fiber Symmetry NORBERT STRIBECK Department of Chemistry, University of Hamburg, Hamburg, Germany Synchrotron facilities with improved equipment will grant the execution of very advanced scattering experiments to every interested polymer scientist. The patterns recorded are two-dimensional, high-resolution, and low-noise images. They permit to monitor structure evolution during the processing of polymer materials with repeat rates of several Hertz. In a different class of novel experiments the structure gradient inside of graded polymer materials will be determined with a spatial resolution of less than 1 µm. Scattering patterns must be complete. In order both to record complete patterns, and to evaluate them within tolerable time it appears reasonable to study parts with fiber symmetry. In the present paper a review of corresponding methodical work and the results of test experiments is presented that has recently been compiled in the group of the author. Keywords

polymers, fibers, WAXD, SAXS, tomography

1. Introduction Presently we are experiencing that intense, reliable X-ray sources and fast detectors become generally available. At DESY in Hamburg PETRA III will provide one of the most brilliant X-ray sources worldwide. There less than a second will be sufficient to expose a lownoise two-dimensional (2D) scattering pattern of a polymer sample. Moreover, in detector development a similar breakthrough has been achieved. Cycle times of less than a second can easily be realized with the novel PILATUS1, 2 detectors. It may be objected that for a long time low-noise scattering curves can be recorded with repeat frequencies of several Hertz. Nevertheless, the value of those older data is limited. Either the material is exhibiting isotropic scattering—in this case a comprehensive analysis requires assumptions on the structure (e.g. the assumption of an ideal lamellar stack). Or the material is anisotropic—then a measured curve does not describe the complete scattering pattern or the old 2D pattern is noisy. On the other hand, by application of the new technology it will become possible for many polymer scientists to monitor the structure evolution in oriented polymer materials in real time. The results of such experiments offer the potential to strengthen the understanding of structure evolution mechanisms in polymers. Moreover, the new instruments provide very narrow X-ray beams with diameters of less than 1 µm (“microbeams”) that permit to study the variation of structure inside the material with respective spatial resolution. A complete sweep of a polymer fiber by a microbeam Received September 21, 2009; accepted November 5, 2009. Address correspondence to Norbert Stribeck, Department of Chemistry, University of Hamburg, D-20146 Hamburg, Germany. E-mail: [email protected]

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will take ca. 30 s. Thus, spatial resolution and time resolution may be combined to study the response of different annular zones in a polymer fiber to, e.g. mechanical or thermal load. Parts with fiber symmetry, like fibers, rods, or tubes, are not only of practical interest because they are ubiquitous in everyday life. Moreover, they appear particularly suited for investigation by means of scattering methods. As the part is rotated about its axis, the 2D scattering pattern does not change. Thus, there is no need to take patterns at different rotation angles, as it would be necessary for materials with less symmetry. The recorded 2D scattering pattern of a fiber is oriented and contains all the accessible information on the structure of the sample. Nevertheless, it will not be sufficient to simply engage the novel instruments—the anticipated data must be adequately evaluated in due time, as well. In this connection two big problems are arising. On the one hand, the data flood is increasing to such an extent that automated evaluation methods must be developed. On the other hand, the data structure has changed, in principal. Instead of scattering curves scattering images must be evaluated. In fact, reasonable scattering curves can be extracted from scattering images as well,3 if loss of information is accepted. Nevertheless, it appears more reasonable to develop evaluation methods adapted to the processing of images as a whole. This goal can be achieved by combining digital image processing and scattering theory.4 In this review several methods are presented that have recently been developed in our group in order to quantitatively evaluate extensive sets of 2D scattering patterns from polymer materials with fiber symmetry. Two previously published reviews deal with other aspects of the scattering experiments from polymer materials, namely a presentation of scattering theory5 from the point of view of the materials scientists and a presentation of instrumental development.6

2. Practice of Experiment and Data Analysis It is not seldom that users who have carried out experiments at a synchrotron source return with incomplete data. In the worst case only images (the TIFF files from the detector) have been collected and relevant environmental data are missing. Such data are the primary beam intensities before and after the sample, exposure time, exposure mode, time stamp, etc. More frequently the user has forgotten to record a machine background or parameters of the setup are incomplete. Such errors could be reduced if the operator of the synchrotron source would offer a data pre-evaluation service. The required data and the steps of data preevaluation are described in a text book4 of the author. With respect to the description given in the book the procedure of machine-background elimination has recently been changed so that it becomes consistent with tomographic experiments, as well. Now the intensity in the scattering pattern is divided by the linear absorption factor of the sample and from this image the measured machine background is subtracted. This method compensates intensity loss by absorption inside the sample. For the professional analysis of anisotropic 2D scattering patterns of polymer materials there are no user-friendly standard computer programs, because materials scientists do not carry out standard experiments (like, e.g. protein crystallographers). Therefore some program modules must be adapted to the experiment in order to reflect the actual setup or the actual mode of operation. After adaption and proper combination of modules the data can be evaluated automatically. The other option is cumbersome frame-by-frame manual evaluation that is prone to inconsistency or incompleteness.

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The sequence of evaluation steps is a function of several parameters like the setup, the individual scattering power of the studied material, and the features of the anisotropic scattering pattern. New program modules must be constructed if the experimental procedure is fundamentally changed. Complex correction modules may be required if experimental shortcomings are detected during data evaluation. A typical shortcoming is insufficient synchronization among the different recorders of the experiment. Thus, the acquisition of programming skills is recommended. Moreover, it is helpful to choose a computing language that is optimized for the processing of multidimensional data. Suitable commercial platforms are, e.g. PV-WAVE, IDL or MatLab. If free programming tools shall be used, ImageJ offers a good starting point for arduous programmers. Actual references are readily found by search engines on the worldwide web. Our group uses PV-WAVE.7 The sources of the modules are free and available.8

3. WAXD Fiber Mapping 3.1 Motivation and Method Design In wide-angle X-ray diffraction (WAXD) experiments the diffraction patterns must be mapped into reciprocal space before they can be analyzed quantitatively. For this purpose interactive computer programs9, 10 are utilized that rest upon unnecessary11 approximations. Such a design is no disadvantage in crystallography, because sophisticated interactive refinement methods are required anyway for the exact determination of crystal structure parameters in manageable series. In contrast, in materials science frequently time-resolved experiments are carried out, and voluminous series of diffraction patterns must be processed. The materials scientist already knows the unit cell parameters. Thus, minor inaccuracy of the mapping can be tolerated, if in the experiment variation of peak intensity or shape shall be monitored. Here it is important to carry out the mapping fast and automatically. Because the fiber tilt may change during the experiment, the algorithm must be able to track and to compensate such variation. By revisiting the theoretical treatment of the fiber mapping it has been demonstrated11 that there is no principal reason to refine an approximate center of the fiber pattern iteratively. Moreover, instead of an approximation12, 13 of the tilt angle β of the fiber an exact equation11 can be employed. In the methodical paper14 an algorithm is presented by which the mapping can be performed automatically. Its design rests on the application of the mentioned findings. Intricate parametrization is simplified, and slow trigonometric functions are avoided to a large extent. The method is unsuitable for diffuse scattering patterns. If inaccuracies of 2 pixels can be tolerated, a pattern is automatically mapped into reciprocal space in real time.

3.2 Actions Required by The User For each series of diffraction patterns from a time-resolved experiment, some mapping parameters must once be determined interactively. Our procedure wf premap assumes that the studied material exhibits a sharp reflection that is located neither on the equator nor on the meridian. In the example we investigate polypropylene and select the (131) reflection of the crystallographic α2 -modification as the internal standard. With the crystallographic c-axis parallel to the meridian, the reflection is characterized by the parameters15 dhk = d131 = 0.406 nm and by c/ = 0.6504 nm that defines the position of the reflection ring


43

Figure 1. (a) Interactive mode of wf premap: Draw the reflection circle through the centers of the reflection spots of an internal standard reflection (here: polypropylene (131) reflection), and widen the circle into a belt that contains the maxima of the reflection spots. Finally input 4 circles (one indicated at bottom right). (b) The procedure wf map has mapped the fiber diffraction pattern into reciprocal space.

on the Polanyi sphere.11, 16, 17 The wavelength of X-radiation (here: λ = 0.15 nm) must be known, too. In this case the first pre-mapping run of the series is started by wave> ab = wf premap(ss,a,0.15,0.406,0.6504)

The procedure requires a diffraction pattern as input (a). It generates output both in a “saveset” (ss), and in a background-corrected diffraction pattern (ab). If the provided save-set has never been used before, the procedure enters interactive mode and the user is presented the pattern as shown in Fig. 1. Obviously, in Fig. 1a the meridian is not vertical and the fiber is tilted. By means of the pointing device the user draws the reflection circle through the maxima of the reflection spots of the (131)-reflection. Thereafter he transforms the circle into a belt that is wide enough to contain the maxima of the spots (Fig. 1a). Now the procedure cuts out this belt and presents it to the user, who finally specifies 4 disjoint clips (regions of interest on the reflection circle). This is done by punching out circular regions from the belt (the bottom right one is shown in Fig. 1a. The clips are the intersections of the belt (white double-band) and the smaller circles. The program determines the positions of the maxima in the clips. From these 4 maxima-positions the best reflection circle is determined by regression. The error of determination is computed. In general, it is below 1 pixel. After that the orientation of the meridian is computed both from the upper and from the lower pair of spots. The difference is, in general, approximately 0.1o . Based on this information the diffraction pattern is centered and aligned. Finally, the program computes the tilt angle β of the fiber from the orientation angles11 δ and δ of the spots using the exact equation11 4 − λ2 sr2 tan β = (cos δ − cos δ). 2λsr Here sr = 1/d131 is the radius of the Polanyi sphere of the reference (131)-reflection. Finally, the save-set ss is filled with several data: the tilt angle β; the true radius pr

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of the reference-reflection circle on the detector; the crystallographic data of the reference reflection; the wavelength λ; and the geometrical data of the 4 clips. This information is sufficient for an automatic processing of the complete series of diffraction patterns recorded in a time-resolved X-ray diffraction experiment of materials with fiber symmetry. 3.3 Automated Mapping If the procedure wf premap is called with a filled save-set, the interactive part is skipped, and the geometry of the 4 clips is taken from the save-set. For each clip the position of the spot maximum is computed. From these positions the fiber tilt angle β is computed, and the image is centered and aligned. Finally, the mapping into reciprocal space is accomplished by the routine wf map. The function call wave> rec=wf map(ss,ab)

maps the diffraction pattern ab into reciprocal space using the save-set ss. The result is called rec. A more detailed description is in the original paper.14 Figure 1b shows a typical result obtained by automatic direct mapping. In the example the computed tilt angle is β = 5.85◦ . Because the result pattern is in reciprocal space, it should exhibit symmetry in 4 quadrants. Thus, the quality of the mapping can be assessed by comparison to a 4-quadrant average of the pattern. 3.4 Application In a study18 that applies the method, uniaxially oriented polypropylene (PP) is molten and crystallized isothermally from the oriented, quiescent melt. The results show that nucleation and growth of differently oriented sets of crystallites (c-set and a ∗ -set) are decoupled. After shallow quench crystallization is preceded by (spinodal) decomposition. Peak integrals (crystallinity) and minimum crystallite size are tracked. In the commercial starting material a ∗ -set crystallites melt at 158◦ C. The c-set melts at 170◦ C furnace temperature. After recrystallization both sets melt at 170◦ C. Isothermal crystallization is divided in two distinct phases. During nucleation the crystallinity stays low. The second phase is dominated by crystallinity growth. At 150◦ C the c-set is seeded first. At 145◦ C and 140◦ C a ∗ -oriented crystallites are the first. The first-seeded set starts to grow first, as well. c-set crystallinity is always growing faster than a ∗ -set crystallinity. The evolution of the corresponding SAXS19 cross-diagram in the growth phase can both be explained by lamellae growing at right angles, and by block merging. Figure 2 shows β (t, T ) of one of the experiments. The tracking curve appears smooth and demonstrates the reliability of the tilt-angle determination. Tilt-angle variation is an issue, because the oriented PP film is heated until it becomes a viscous melt. Therefore the material shrinks and bends in the synchrotron X-ray beam. After the mapping the intensity distribution is known almost everywhere in reciprocal space except for a wedge region near the meridian (cf. Fig. 1b). Thus, reflection intensities can readily be integrated in reciprocal space. In reciprocal space the relation between scattering and structure is clear from scattering theory,4, 18 and structural data can be computed,18 e.g., from total intensities (crystallinity) and integral breadths (crystallite sizes). Figure 3 shows the evolution of the weight crystallinities of the two sets of crystallites at 3 different crystallization temperatures. As shown by Ruland,20 such reflection integrals that


45 200

20

10

T(t)

T [°C]

β(t) [°]

150 0 100 -10 50 -20 -20

-10

0

10

20

30

40

t [min] Figure 2. Tilt-angle tracking curve β (t, T ) from the automatic fiber-mapping procedure in an experiment in which β is changing considerably (hard-elastic polypropylene; melt-annealing at 171◦ C 18 c with permission of the ACS). and recrystallization at 150◦ C) (Reproduced

are complete in reciprocal space are proportional to the weight crystallinity of the perfect crystallites that produce the reflections. Latency periods between the quench and the start of the crystallization, as well as crystallization velocities of the two kind of crystallites can be extracted from these data. Finally, conclusions concerning the crystallization mechanisms can be drawn.18

Figure 3. Evolution of relative weight crystallinities S, and S ∗ of c-oriented crystallites (dashed regression lines) and a ∗ -oriented crystals (solid regression lines), resp. during isothermal, oriented crystallization of hard-elastic PP from a quiescent melt as a function of crystallization temperature. Double-head arrows pointing at the t-axis indicate the first sighting of the a ∗ -set (full arrow head), and of the c-set (open arrow head), respectively.

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4. X-Ray Scattering Fiber Tomography 4.1 Motivation The structure inside a polymer part is not necessarily homogeneous. With fibers, extrudates, and latex particles21 frequently a core-shell structure is reported. Moreover, engineers deliberately generate structure gradients in polymer parts for special functionality.22, 23 If such a part is irradiated by an X-ray beam, the recorded pattern is an integral superposition of all the SAXS patterns emerging from the sequence of volume elements (voxels) along the beam path. From the mathematical point of view such a superposition is a projection, and a single projection is of little use for the study of graded materials. A first step towards a study of structure gradients has been the development of the X-ray microbeam technique.24–26 Here only the diameter of the beam is limiting the lateral spatial resolution. Nevertheless, the longitudinal spatial resolution is simply the thickness of the sample. Microbeam scanning experiments, in particular of fibers, have been performed for many years and the raw data have been discussed, although the corresponding shortcoming has been known (Paris et al.:27 “The long-term goal is to proceed from microbeam scanning experiments to a real imaging technique”). The solution of the problem is tomographic reconstruction. Problems arise from the fact that scattering patterns are multidimensional but not simply a number (like the absorption in classical tomography). Thus, approximate tomographic reconstruction of scattering data with a manageable amount of artifacts is difficult. An exception is the case of part with uniaxial symmetry. In this case a reconstruction of the scattering patterns is possible that would have emerged from individual voxels in a plane perpendicular to the “fiber” axis.28 Nevertheless, this method is only of academic value. The exposure time for the recording of scattering data of one cross-section of the part is in the order of days. The computing time for the tomographic reconstruction of the scattering patterns is at least a week.28

4.2 Introduction of the Method A more practical tomographic method can be applied, if the part to be studied both exhibits macroscopic fiber symmetry, and the structure only varies as a function of the distance from its central axis. By means of this method fibers, pipes, and extruded strands can be investigated. Thus, we call it “X-ray scattering fiber computer tomography” (XSF-CT). A complete set of projected scattering patterns is collected in a single microbeam scan across the fiber, because the set of projections does not change as the sample is rotated about its axis. Such an experiment is completed in about 30 min. Moreover, compared to the general tomography the mathematics of image reconstruction is simplified considerably and the computational effort decreases by 5 orders of magnitude. A set of 40 measured scattering patterns is reconstructed in typically less than 10 min. From medicine and other fields of science the considerable potential of information increase after tomographic imaging is well-known. In a general tomographic X-ray experiment,29 a voluminous sample is scanned by a thin X-ray beam. As a function both of the position x of the scanning beam on the sample, and of the sample rotation angle φ, projections (notation: { }) of the absorption {A} (x, φ) or even of complete scattering patterns {I } (s, x, φ) are measured, in order to analyze the structure variation in the plane of the sample that is scanned by the X-ray beam.28, 30, 31 Here s is the scattering vector with |s| = s = (2/λ) sin θ , the X-ray wavelength λ and the scattering angle 2θ . In the examples mentioned, a tomographic image reconstruction29, 32, 33 returns


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Figure 4. (a) cross-section irradiated by an X-ray beam at an offset x from its center. The Fiber structure ρ ρf shows fiber symmetry. From all structures along the beam path a superposition is probed. y is the variable of the integration. (b) One-dimensional tomographic reconstruction turns the measured series of projected scattering patterns that carry the accumulated the structure information passed by the beam (vertical bars) into the image patterns from voxels (quadratic boxes) residing on the fiber radius.

either the spatial variation of the absorption in the plane, or of the scattering emanating from the resolved voxels in the plane. The smearing caused from projection is eliminated by application of the Fourier transform theory, and a clear image of the inner structure is obtained. If the studied material shows cylindrical symmetry, the results of the measurement are no function of φ any more, and the complete image information is in a single microbeam scan. The fundamental geometry is sketched in Fig. 4a. The information in the measured signal {A} (x) or {I } (s, x), respectively, does not represent the sought information A (x) or I (s, x) originating from the small square (voxel) around the position x. Instead, to a first approximation it is represented by the projection integral ˆ ∞ {I } (s, x) = 2 I (s, x 2 + y 2 ) dy (1) ˆ

x ∞

=2 x

I (s, ρf ) ρf dρf . ρf2 − x 2

(2)

In the equation only the accumulated attenuation of the primary beam by X-ray absorption is not accounted for. This is no problem for very thin polymer parts with low absorption. For thicker samples the absorption correction from Section 2 is sufficient to account for it. The sought information in image space (I (ρf )) along the radius ρf of the fiber has to be reconstructed from the information in projection space ({I } (x)). Equation (1) is the definition of the Abel transform.33 In X-ray scattering Eq. (1) is established textbook knowledge.4, 34–39 There it describes the slit smearing. Even the inverse Abel transform ˆ 1 ∞ d{I }(s, ρf ) dy I (s, x) = − (3) π 0 dρf ρf ˆ 1 ∞ d{I }(s, ρf ) dρf , (4) =− π x dρf ρf2 − x 2

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Figure 5. Sketch of local fiber symmetry inside the cross-section of the fiber. Each voxel has its own fiber axis. Inside the voxel there is only axial grain.

which first has been derived by Niels Abel40 is found in scattering textbooks since Guinier41 and DuMond.42 Similar to the filtered backprojection algorithm of the general tomography, low-noise reconstruction algorithms43–45 for the tomography of materials with cylindrical symmetry are readily available in the field of “one-dimensional tomography.” The principle of one-dimensional tomographic reconstruction is sketched in Fig. 4b. It must be mentioned that here we implicitly assume that the scattering from every irradiated voxel in the fiber shows fiber symmetry itself (local fiber symmetry). Otherwise characteristic reconstruction aberrations are expected.28, 46 The meaning of local fiber symmetry is sketched in Fig. 5. Deviations from local fiber symmetry (i.e. tangential or radial grain, resp.46 ) cause restricted or shifted visibility of scattering features along the fiber radius. These aberrations can be detected and result in additional information on the structure inside the fiber.46 4.3 Application In an application-oriented feasibility study46 precursors of polymer microfibrillarreinforced composites (MFC) containing poly(ether)-block-amide (PEBA) and poly (ethylene terephthalate) (PET) with varying cold-draw ratio are studied. The studied strands are relatively thick, because presently the achievable “microbeam” at HASYLAB in Hamburg is relatively wide. The results from a direct analysis of the smeared measured patterns are compared to results obtained after tomographic reconstruction. Ideas for advanced practical applications of the XSF-CT method are discussed. Data are presented from a cold-drawn (draw ratio λd ≈ 3) co-extrudate of 70 wt.-% PEBA and 30 wt.-% PET (abbreviated: MFC73). In the scanning-microbeam experiment


49

Figure 6. Cold-drawn (λd ≈ 3) MFC73 in a scanning microbeam experiment. Measured scattering intensity {I }(s12 , s3 , ρf ) (top row) and reconstructed scattering I (s12 , s3 , ρf ) (bottom row) for short distances ρf from the fiber axis. The patterns display the range −0.1 nm−1 ≤ s12 , s3 ≤ 0.1 nm−1 in uniform logarithmic scale (s = (2/λ) sin θ).

the strand shows an isotropic long period and an equatorial streak at almost every beam position (Fig. 6, top row). Only the tomographically reconstructed patterns (bottom row) exhibit that the long-period ring-reflection is not present in the core of the fiber. As the feature becomes visible, it first shows up at the equator. With increasing distance from the fiber axis, reflection arcs are growing towards the meridian. Above ρf = 300 µm the arcs join into a closed circle. Because such behavior has been observed with neat PEBA as well, this orientation phenomenon is not indicating some interaction between the PEBA and the PET microfibrils. The reconstructed central voxel (ρf = 0) is dominated by one of the reconstruction aberration effects (from voxels with tangential grain).46 Examination of the equatorial streak exhibits only in the reconstruction that it grows broader towards the center of the fiber. The streak is allocated to needle-shaped domains, and is only observed with strands from co-extruded blends. If these needles are thin PET microfibrils, the tomography shows that in the center of the fiber these microfibrils are shorter than in an intermediate region. The structure gradient in the outer region of the strand is discussed in the original paper.46

5. SAXS Monitoring of Mechanical Tests 5.1 Motivation and Method Development Advanced polymer materials are urgently sought after e.g. in the automotive industry in order to accomplish the goals of climate protection by reduction of weight. Such newly engineered materials have to prove their serviceability in mechanical tests. Classical tensile tests are performed to determine the modulus and ultimate properties. Load cycling experiments are carried out to determine the fatigue behavior. In order to reveal the mechanisms of, e.g., failure or fatigue, it is desirable to monitor mechanical tests by SAXS. In this way the response of the nanostructure to mechanical load is revealed. Since about 2005 the advance of instrumentation at synchrotron beamlines facilitates considerable reduction of the exposure required for the recording of low-noise SAXS patterns. Such quality is

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required for a quantitative analysis by, e.g., the CDF method.47, 48 Concerning the monitoring of tensile tests by SAXS this advance has meant that change-over from the stretch-hold technique49 to the more practical continuous straining has become possible,50 although the achievable strain rate is frequently still by a factor of 100 lower than that relevant in industry and service. With the advent of very high-brilliance synchrotron sources even this limitation is presently being abolished. In order to gain full control on tensile and load-cycling tests a tensile tester has been R built for operation at synchrotron beamlines.50 The control program written in LabVIEW is continuously adapted to more complex experiments. Presently it can handle different kinds of continuous load-cycling programs that now are strictly synchronized with both the SAXS detector and a video grabber module (recording sequences of pictures of the sample with fiducial marks). The latest methodical development51 is an automatic evaluation method of the video frames, by which the true macroscopic elongation of the sample can be determined with an accuracy of 3 decimals. Such high accuracy is required for thermoplastic materials that fail at low elongations (ca. 0.1). The method extracts the grating of the fiducial marks on the sample from the actual video image, computes the 1D correlation function,52, 53 and evaluates its “long period.”

5.2 Results In a study50 of hard-elastic polypropylene (PP), scattering patterns recorded during continuous straining differ considerably from those recorded in the step-hold technique. Even though during exposure the elongation is no longer constant when applying the dynamic technique, the images collected in stretch-hold technique appear much more blurred (Fig. 7). This result indicates relaxation of nanostructure while the extensometer stands still. Quantitative analysis shows that during relaxation the extension of crystalline lamellae

Figure 7. Oriented PP films in tensile tests. Comparison between SAXS patterns I (s12 , s3 ) recorded during continuous straining (top row, ε˙ ≈ 10−3 s−1 ) and patterns from an experiment in stretch-hold technique (bottom row). Straining direction and meridian is vertical (s3 ). Equator (s12 ) is horizontal 50 c with permission of Wiley Interscience). (Reproduced


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Figure 8. Oriented PP. Load cycling monitored by SAXS. Circular dots show where SAXS patterns have been recorded. Numerical labels indicate their sequence. The highlighted part of the curve near label 11 indicates the part traversed during the recording of pattern 11. The drawing direction with 48 c with permission of respect to the patterns, s3 , is indicated by a double-head arrow (Reproduced Wiley-VCH).

is increasing. Lamellae thicknesses are becoming non-uniform. The range of order is shortening. Cross-hatched lamellae are formed. In another study48 slow continuous mechanical tests of oriented PP are monitored by SAXS and quantitatively evaluated by the CDF method.47 A continuous-strain test exhibits fracture and release of weak lamellae (2 – 10% strain). Beyond that conversion of lamellae into needles is observed. As all layers are consumed, the material breaks. Fatigue is studied in a load-reversal experiment (between 10% and 35% strain, Fig. 8). In each cycle crystallization, layer break, and relaxation melting are observed. Figure 9 presents the result. The top chart shows the true elongation, ε (t), imposed to the material and measured at the point of X-ray irradiation. The four load-reversal cycles are easily identified. The chart in the middle reports the extracted nanostructure parameters, L (t), ecac (t), and S (t). The bottom diagram presents the macroscopic resistance, σ (t), which the material is opposing to strain. The figure shows that crystallization, rupture of lamellae, and melting of fragments are continuously reshaping the domains of the PP material in the cycles of the fatigue test. The long-period cycle exhibits a phase shift with respect to the imposed strain cycling. Moreover, there is an indication of amplitude attenuation. Fatigue is demonstrated in the curve σ (t) by decreasing stress peaks. An in-depth discussion of the zones indicated in Fig. 9 is in the original paper.48 In particular, the combination of SAXS and fatigue test shows the transition from stress-induced crystallization to crystallite rupture σ (t) ≈ 20 MPa. In a recent study51 of microfibrillar reinforced blends based on polyethylene we have switched from hard-elastic materials to materials that fail at the low elongations typical for plastic polymers. Because of the much lower elongation at break (εb ≈ 0.1), now the macroscopic elongation εm and nanoscopic elongation εn must be determined with high precision. Respective methods are presented. The results show that the hardest materials exhibit a very inhomogeneous nanodomain structure. During straining their domains appear to be wedged together and inhibit transverse contraction on the nanometer scale.

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Figure 9. Dynamic load-reversal mechanical test of hard-elastic PP film. As a function of the elapsed time t the macroscopic parameters elongation, ε (top graph), and tensile stress, σ (bottom graph) are displayed together with topological nanostructure parameters (middle). In the middle diagram the solid line shows the long period, L. The broken line displays the lateral extension, ecac , of a sandwich made from two crystalline lamellae. The line with circular dots exhibits the variation of the strength, S, of the CDF. Vertical bars indicate zones of strain-induced crystallization (dark bars) c Reproduced48 with permission of and relaxation-induced melting (light gray bars), respectively ( Wiley-VCH).

Further components are polyamides (PA6, PA12) (20–30%) and as compatibilizer R 8102 (YP) (0–10%). Some HDPE/PA6 blends are additionally loaded with nanoYparex R R clays (Nanomer or Cloisite ). Blending of HDPE with PA12 causes no synergistic effect. In the absence of nanoclay, PA6 and HDPE form a heterogeneous nanostructure with high Young’s modulus. After addition of YP a more homogeneous scaffold structure is observed in which some of the PA6 microfibrils and HDPE crystallites appear to be rigidly connected, but the modulus has decreased. Both kinds of nanoclay induce a transition from a structure without transverse correlation among the microfibrils into a macrolattice with 3D correlations among HDPE domains from neighboring microfibrils. For extensions between 0.7% and 3.5% the scattering entities with 3D correlation exhibit transverse elongation instead of transverse contraction. The process is interpreted as overcoming a correlation barrier executed by the crystallites in an evasion-upon-approaching mechanism. During continued straining the 3D correlation is reduced or removed. The true macroscopic elongation εm is determined from video frames taken of the sample that carries fiducial marks (see Fig. 10a). Once for an experiment the user has to provide some input. It is based on the first image (Fig. 10a) of the series. The center of the X-ray beam on the sample is marked by a cross in the image. Close to this center the user defines a rectangular region of interest (ROI), ρm (x, y). In Fig. 10a this region is bordered by a dashed line. x and y are pixel coordinates in the direction of strain and perpendicular to it, respectively. The same ROI is applied to all video frames of the experiment. The ROI is structured by the fiducial marks running perpendicular to the straining direction. As is known from scattering theory,4 from such a structure function ρm (x, y) the 2D correlation


53

Figure 10. Elongation from recorded video frames. Inset a: In the first video frame a region of interest (ROI) with fiducial marks is defined. Inset b: From the ROI the 2D correlation function γ2 (x, y) is computed. Main drawing: The center of the long-period peak in γ1 (x) = γ2 (x, 0) is fitted c Reproduced51 by a parabola (dashed line) to compute the distance between the fiducial marks ( with permission of Wiley Interscience).

function γ2 (x, y) =

ρm 2 (x, y) ρm 2 (0, 0)

can be computed, with ρm (x, y) = ρm (x, y) − ρ¯ m representing the fluctuation of ρm (x, y) about its average ρ¯ m , and the autocorrelation being defined by the integral ¨ ∞ f 2 (x, y) = f (u, v) f (u + x, v + y) dudv. −∞

In Fig. 10b the colored caps demonstrate, where γ2 (x, y) is positive. The macroscopic elongation εm in straining direction is the section γ1 (x) = γ2 (x, y) 1 (x) of γ2 in straining direction. Figure 10 presents this curve and its analysis. Its first positive peak is the longperiod peak that is related to the actual average distance of the fiducial marks, . A parabola (dashed line) is fitted to the long-period maximum, and the position of its vertex is determined (arrow). Thus, can be determined with an accuracy of 0.01 pixels. Let 0 the initial distance between the marks, then the macroscopic elongation is εm = /0 − 1. Concerning the scattering patterns, similar analysis is possible. Nevertheless, the peaks observed in the scattering pattern or in the CDFs47 computed from the pattern are no longer one-dimensional but two-dimensional – positioned in the plane (s12 , s3 ) or (r12 , r3 ), respectively. Again, the user defines a ROI in which the analysis procedure searches for the peak maximum, extracts the peak cap, and fits now a bivariate54 polynomial of 2nd order to it. From the coefficients of the polynomial several parameters are readily determined. Most important are the peak position and the widths of the peak in meridional and equatorial

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Figure 11. MFC precursor blends from HDPE, two different polyamides (PA12, PA6) and a compatibilizer (YP) in tensile tests. Evolution of macroscopic stress and strain (σ , ε) as well as of nanostructure parameters. εnano is the nanoscopic elongation computed from the HDPE long period. DL is the relative change of the width of the long period distribution. DM is the relative change of the extension of the microfibrils in transverse direction.

directions, respectively. Thus, the evolution of these parameters during the experiment can be tracked automatically. Figure 11 presents the results of a quantitative nanostructure analysis for the blends which do not contain nanoclays. Elongations are illustrated by dashed lines. Bold lines show the macroscopic elongation, ε. Thin lines report the nanoscopic elongation εnano of the HDPE matrix. Circular marks indicate regions in which ε ≈ εnano . All materials reinforced by PA12 exhibit this similarity of macroscopic and nanoscopic deformation. Dashed-dotted lines show DL , the relative variation of the breadth of the long-period


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distribution. The increase of all curves demonstrates increasing inhomogeneity of the long periods with increasing elongation. Dotted lines show DM , the relative variation of the microfibrillar diameter during the straining process. In all materials the elongational deformation causes the microfibrils to thin. Variation of the material composition does not cause considerable changes. This is different with the samples reinforced by PA6 (Fig. 11d-f). Here an increase of the PA6 content to 30% causes strong thinning of the microfibrils. In the PA6 blends the strong transverse decrease is going along with only moderate nanoscopic elongation εnano of the HDPE. An explanation for this finding could be microfibrillation by fracture of crystalline domains of the polyethylene. Moreover, the diagrams in Fig. 11d-f demonstrate a considerable difference (vertical arrows) between the two dashed curves. In Fig. 11e-f (εnano < ε) the nanoscopic elongation of the HDPE phase is considerably lower than the macroscopic elongation. Similarity is only observed during the initial deformation in Fig. 11f (circular mark). In the 80/20 HDPE/PA6 blend (Fig. 11d) the nanoscopic elongation of the HDPE microfibrils is considerably longer than the macroscopic elongation (εnano > ε). Although this finding appears to be unreasonable, an indication for a possible mechanism is in the strong increase of DL (Fig. 11d). This is discussed in the original paper.51

6. Conclusions Considering the present instrumental development at synchrotron radiation facilities the development of advanced data evaluation methods appears to be both promising and necessary in order to master the future data flood. The three presented methods demonstrate the potential of such work. In order to discharge the user, a part of the data evaluation may be carried out at the synchrotron facility. Such added service would require not only considerable computing power, but also additional manpower. In addition to the beamline scientist an evaluation specialist would become necessary. It would be his job to detect if raw data must be smoothed. He would have to eliminate the machine background, would generate detector masks, would center and align each scattering pattern, and would fill blind areas from consideration of symmetry. As an added service, the community of the evaluation specialists could select some standard experiments for which complete user-friendly programming environments could be built. Nevertheless, for the predominant fraction of individually designed setups it will remain necessary for the polymer scientist himself to familiarize with adapted programming techniques. This will be of particular importance, if methods shall be developed that grow with the growth of instrumental capacity. Ultimately, it is expected that an increase of the quality of results returned from scattering experiments will be closely correlated to the manpower dedicated to the programming of data evaluation modules.

Acknowledgment The author thanks the Hamburg Synchrotron Radiation Laboratory (HASYLAB) for beam time granted in the frame of project II-20080015. Development of the reported methods has been supported by the 7th framework program of the European Union (Project NANOTOUGH FP7-NMP-2007LARGE-2.1.1).

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R Journal of Macromolecular Science , Part C: Polymer Reviews, 50:59–90, 2010 ISSN: 1558-3724 print / 1558-3716 online DOI: 10.1080/15583720903503486

Ultra-Small-Angle X-ray Scattering of Polymers FAN ZHANG1,2 AND JAN ILAVSKY3 1

Materials Science and Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, MD, USA 2 Department of Physics, Northern Illinois University, Dekalb, IL, USA 3 X-ray Science Division, Advanced Photon Source, Argonne National Laboratory, Argonne, IL, USA Ultra-small-angle X-ray scattering (USAXS) is capable of probing structural inhomogeneities in the size range of 1 to 1000 nm. Recent developments of X-ray sources and optics make USAXS increasingly relevant to polymer research. In this review, we examine the current technical state of USAXS instrumentation, and briefly introduce the method of data reduction and analysis. We emphasize USAXS’s application in areas such as polymer nanocomposites, polymer gels and solutions, polymer blends, polymer micelles and microemulsions, and colloidal sciences. Finally, we predict more USAXS studies on polymeric systems, especially those with large-scale structures or hierarchical microstructures. Keywords ultra-small-angle X-ray scattering, small angle X-ray scattering, polymers, colloids

Introduction Small-angle X-ray scattering (SAXS)1 is a nondestructive scattering technique that records elastic scattering of X-rays at scattering angles close to the direction of the incident beam. SAXS data contain information about important microstructural parameters such as the size, shape, volume, and total surface area of the scatterers, as well as characteristic distances if the scatterers are ordered or partially ordered. In a typical pinhole setup, SAXS is capable of delivering structural information between 1 and 100 nm. Much larger objects can be viewed directly with optical microscopes. The intermediate size range, however, is difficult for both microscope and SAXS, especially when the specimen is either highly absorbent or optically opaque. Ultra-small-angle X-ray scattering (USAXS) has been developed to extend the scattering q range (where its modulus q = (4π /λ)sinθ , λ is the wavelength of the X-ray, Received September 3, 2009; accepted November 22, 2009. The submitted manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne”). Argonne, a U.S. Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357. The U.S. Government retains for itself, and others acting on its behalf, a paid-up nonexclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, by or on behalf of the Government. Address correspondence to Jan Ilavsky, X-ray Science Division, Advanced Photon Source, Argonne National Laboratory, Argonne, IL, 60439, USA. E-mail: [email protected]

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F. Zhang and J. Ilavsky

and 2θ is the scattering angle) of SAXS to 10−4 Å−1 and bridge the gap between SAXS and the optical microscope.2,3 USAXS features very high angular collimation in one or both collimating directions, which enables a small minimum scattering momentum that can be distinguished from the direct beam. This collimation is usually performed with single-crystal optics, first proposed by Compton nearly a century ago.4 The first experimental realization of crystal collimation was achieved in the early 1920s.5 This technique, however, suffered significant parasitic scattering from the surface scattering from the imperfect crystals and could hardly compete with slit- and curved-crystal collimation introduced by Guinier.1 In 1965, Bonse and Hart in their seminal work demonstrated that the parasitic scattering tails can be greatly suppressed with multiple reflections on channel-cut crystals.6 This result, together with the increasing availability of near-perfect Ge or Si crystals, makes double-crystal multiple-reflection collimation preferable when high angular collimation is desired. The Bonse-Hart configuration enables small-angle scattering which is commonly “behind the beamstop” in pinhole SAXS to be probed, and forms the basis of modern USAXS instruments. Many USAXS instruments have been constructed over the years using various X-ray sources, for example lab sources,7–11 second-generation synchrotron sources,8,12–14 and third-generation synchrotron sources.15–17 By making use of very long camera length (sample-to-detector distance), pinhole SAXS can also reach the low-end scattering angle offered by the Bonse-Hart configuration, albeit the total scattering range is comparatively limited.18,19 In a recent development, Cerbino et al.20 showed that analysis of near-field coherent speckles could provide scattering information in a range even lower than that afforded by Bonse-Hart cameras, though with limitations. In addition to a broad q range, USAXS also offers several distinct advantages such as high angular resolution (limited mainly by the width of the crystal rocking curve), wide dynamic range of intensity (∼8 to 9 orders of magnitude in instruments operated in thirdgeneration synchrotrons15,17), accurate energy tuning (E/E as small as 0.00015 which enables anomalous-USAXS15), and primary calibration of the X-ray scattering cross section.14 The advancement of X-ray sources, especially the availability of high-flux undulator beamlines in third-generation synchrotrons, further facilitates the quest for low photon counting statistics for samples with low scattering contrast, which makes USAXS a useful technique for obtaining bulk and ensemble-averaged structural information at the micron range and below for soft matter such as polymers, colloids, and biomaterials. Furthermore, USAXS is often unique for the study of concentrated, opaque systems or systems that are prone to structural damage during the preparation for microscopy measurements, which are common among soft materials. USAXS has been utilized in the study of polymers and other soft materials since the operation of the first USAXS instrument.21 However, when compared with pinhole SAXS, USAXS is often regarded as underutilized.22 This is largely due to the deficiencies of previous versions of USAXS instruments, where low X-ray flux and high parasitic scattering hinders the successful applications of USAXS in such systems. Recent technical improvements have resolved these obstacles and made USAXS an increasingly appealing technique for studies of soft matter in general and polymers in particular. This review will cover USAXS studies of polymers and colloids, especially those employing synchrotron radiation, to demonstrate its versatility and effectiveness. We will start with recent advancements in USAXS instrumentation and data processing, which make USAXS more relevant to soft matter research. We will emphasize USAXS applications

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in areas such as polymer nanocomposites, polymer gels and solutions, polymer blends, polymer micelles and microemulsions, and colloidal sciences. We hope that this review will act as a bridge to the existing instrumental capabilities and exciting sciences for which USAXS may be found suitable.

2. USAXS Instrumentation All Bonse-Hart USAXS instruments have schematic layouts similar to the one shown in Fig. 1. The main difference is the radiation source that is employed. Conventional X-ray sources, while easier to access, have disadvantages such as high beam divergence, low X-ray flux, and very limited availability of X-ray wavelength, which makes it difficult for USAXS to study specimens with low scattering contrast. Synchrotron sources, on the other hand, do not suffer these restrictions. It is especially true in the case of third-generation synchrotrons, where the X-ray energy from an undulator source is continuously tunable in a wide range (3.2 to 80 keV and above for Undulator A of the Advanced Photon Source23), X-ray flux at the sample position about 1013 photons s−1mm−1,15,16 and beam divergence about 10 microradian.24 These features contribute greatly to the sprouting of USAXS studies of polymeric systems in the past decade. After passing through beam defining slits and X-ray mirrors, the X-ray beam is collimated with multiple reflections in the collimating crystals. The angular divergence of the incident beam is fixed by the monochromator, and the angular width is decided by the full width at half maximum (FWHM) of the collimating crystal reflection curve, which is given by the dynamical diffraction theory. For a single reflection, the tails of the rocking curve roughly follow a (θ -θ B )−2 law, where θ is the diffraction angle away from the surface, and θ B is the Bragg angle for the collimating crystal. Multiple reflections between the crystal pairs, although having no effect on the FWHM of the reflection curve, greatly reduce the tail reflection following (θ -θ B )−2n, where n is the number of reflections. In this manner, a large number of reflections act to deliver an optimized signal-to-noise ratio in the scattering data. The original Bonse-Hart design employed triple and fivefold reflections on channelcut crystals,21,25 which has been adopted in many USAXS instruments.7,11,16 An alternative is to employ an even number of reflections in both the collimating and analyzing crystal pairs.8,14,15 This geometry does not change the propagation direction of the X-ray beam, and therefore makes alignment easier when energy tuning is required. We note that in recently built USAXS instruments pseudo-channelcut crystals consisting of two pieces of separate crystals are preferred. This design enables better polishing of the crystal surfaces, and therefore significantly reduces parasitic scattering from loose

Figure 1. Schematic of a Bonse-Hart USAXS instrument in the one-dimensional collimation mode.

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or disoriented crystallites. Brief polishing and etching procedures can be found in Ilavsky et al.15 and Sztucki and Narayanan.17 The scattered beam, after being analyzed by the analyzing crystals, is recorded by the detector. USAXS employs a point detection system, such as an avalanche photodiode detector (APD),13,16 PIN photodiode,15,26 and scintillation counting detector.7,8 To ensure the reliability and reproducibility of USAXS data, the detector is required to be linear over the entire dynamic range of USAXS. For example, a low-cost, low-noise, high quantum efficiency PIN photodiode detector is shown to be linear over 10 decades of X-ray intensity.26 Several operational modes of USAXS are available. When the sample is isotropic and the X-ray flux is the bottleneck, one-dimensionally collimated (slit-smeared) USAXS is normally preferred. For an anisotropic sample, however, true scattering data cannot be recovered from slit-smearing data. An additional dimension of collimation and analyzing would be required along the direction orthogonal to the directions of both beam propagation and first collimation. This two-dimensionally collimated USAXS offers effective pinhole collimation, and is capable of recording scattered intensity as a function of both momentum transfer q and azimuthal angle χ .27 Collimation along vertical and horizontal directions, however, greatly reduces the photon flux on the detector. This geometry, therefore, is practical only with high flux sources, such as an undulator source in a third-generation synchrotron. Within the framework of one- and two-dimensionally collimated USAXS, anomalous USAXS and selected-area USAXS measurements can be made by taking advantage of the high energy resolution and high stability of both sample and high-resolution beam defining slits. Examples of these configurations can be found in Ilavsky et al.15 We mention that USAXS imaging, a size-sensitive imaging technique, can be operated in a setup very similar to that of one-dimensional collimated USAXS, except that the camera length is very small and imaging data are collected with a two-dimensional charge-coupled device (CCD) camera instead of a point detector.28 USAXS imaging has been used to investigate a wide range of systems, from polymer composites29 to plastically deformed metals.30 The imaging contrast mechanism of USAXS imaging has been explained based on wave propagation and dynamical diffraction theory. Zhang et al.31 found that refraction in the form of Porod scattering and, to a much less extent, reflection, fully account for USAXS imaging contrast. In the end of this section, we take advantage of a comparison of SAXS and USAXS scattering profiles of the same sample to illustrate the capability of USAXS, as shown in Fig. 2. The sample is a polydispersed silica suspension in water. The USAXS profile was collected at the USAXS beamline (32ID-B) at the Advanced Photon Source (APS), Argonne National Laboratory. The SAXS profile was collected with a desktop SAXS instrument. The SAXS intensity was absolutely calibrated to match the USAXS intensity. Figure 2 clearly shows that USAXS offers a broader q range and dynamic range of the intensity. In addition, the USAXS intensity is automatically calibrated (details in Section 3). The very low-q end of the USAXS scattering profile demonstrates the angular resolution of USAXS, which can be as high as 1 × 10−4 Å−1.

3. Data Reduction and Analysis Data reduction process for USAXS consists of several standard procedures such as absolute intensity calibration, desmearing (for one-dimensional collimated USAXS), and (if necessary) correction for multiple scattering.


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Figure 2. Comparison of USAXS and intensity-calibrated SAXS profiles of silica in water suspension.

For small-angle X-ray scattering, the scattering intensity I(q) is written as14 I (q) = 0 AtT ε

d d

(1)

where 0 is the incident X-ray flux in photons s−1 area−1, A is the illuminated sample area, t is the sample thickness, T is the sample transmission, ε is the converting efficiency of the detector, is the detector solid angle, and d (q)/d is the differential scattering cross section per unit volume per unit solid angle. It can be shown that absolute calibration of the scattering cross section only depends on the known quantities t, T, , and I0 .14 Therefore, a Bonse-Hart USAXS camera provides inherent absolute scattering intensity, which is essential for many important aspects of quantitative small-angle scattering analysis, such as obtaining the number density, volume fraction, and the specific surface area of the scatterers. Taking advantage of these properties, Zhang et al. established glassy carbon as an absolute intensity calibration standard, which is readily available for SAXS laboratories so as to incorporate absolute intensity analysis.32 For one-dimensional collimated USAXS, correction for slit smearing is required to recover the correct scattering cross section. The schematic of finite slit scattering is shown in Fig. 3. The vertical slit width 2w0 is decided by the FWHM of the crystal rocking curve. The horizontal slit length 2l0 is only restricted by the detector. The vertical slit-width 2w0 is comparable to the angular resolution of the instrument and is much smaller than 2l0 . Thus its correction is negligible. Consequently, the slit-smeared USAXS intensity is described

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Figure 3. Schematic of finite slit scattering in one-dimensional collimated USAXS. 2θ is the scattering angle, 2l0 is the slit length, 2w0 is the slit width. Pl and Pw are the slit-length and slit-width weighing functions, respectively.

by ˜ 1 d (q) = d l0

0

l0

d 2 q + l 2 dl, d

(2)

˜ where d (q)/d is the measured, slit-smeared scattering intensity; d (q)/d is the unsmeared scattering cross section; and l is the reciprocal vector of integration in the slit direction. d (q)/d can be accurately calculated following an iterative algorithm developed by Lake.33 Because USAXS data are obtained in directions very close to that of the incident beam, multiple scattering can sometimes be significant. Multiple scattering is indicated by the apparent broadening of the rocking curve when the sample is in the beam. This effect can be corrected following a procedure described in Ilavsky et al.15 We note that multiple scattering is mostly negligible for samples with low scattering contrasts, such as polymer melts, and solutions. The reduced data are analyzed within the framework of small-angle scattering theory, which is outside the scope of this paper and will not be discussed in detail here. Interested readers are encouraged to refer to standard small-angle scattering references1,34,35 or related articles in this issue. We do note, however, that Irena, a tool suite that is developed for the support of the USAXS instrument at the Advanced Photon Source, brings together a variety of advanced small-angle scattering data modeling and evaluation tools and is in free circulation.36

4. Radiation Damage USAXS measurements making use of the Bonse-Hart configuration scan the reciprocal space point-by-point. Accordingly, samples are exposed to the X-ray beam much longer


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(∼10 min) than normally required with a pinhole camera. X-ray radiation damage to the sample therefore becomes a concern, especially for soft materials. It is well known that polymers degrade when exposed to intense X-ray radiation.37–41 Many chemical processes take place concurrently, each progressing at a different rate. For example, intense X-rays create photoelectric electrons, which are shown to be linearly dependent on the X-ray dose.42 For this effect, commonly known as primary radiation damage, an upper limit of the radiation damage was observed. In polymeric and biological materials, photoelectric electrons are capable of further damaging the specimen through the creation of free radicals, which lead to hydroperoxidation and consequent chain scission43 thus altering the polymeric microstructure. This process is normally referred to as secondary radiation damage. Despite the understanding of the chemical pathways, various aspects of X-ray radiation damage still have not been elucidated. Its prevention remains largely empirical. Practical mitigating approaches include monitoring a sample’s discoloration, repeating USAXS measurements to monitor the reproducibility of scattering profile as a function of time, and employing a flow-cell for polymer or colloidal suspensions.44 Extra attention needs to be paid to the prevention of radiation damage so as to ensure the quality of data.

5. Applications In this section, we present an overview of various USAXS applications in the studies of polymer gel and solution, colloidal dispersion, microemulsion, etc. The broad q range, high dynamic range, and very high angular resolution make USAXS a unique technique in these examples, which we will address. Here, we will not go into the details of individual analysis. Instead, we will devote the next section to the fundamentals and general principles of USAXS analysis.

5.1 Polymer Gels and Solutions Polymer gels form when polymers arrange into three-dimensional networks by virtue of covalent or noncovalent bonding in a second medium. Depending on the binding mechanism, polymer gels can be classified into chemical gels and physical gels. Polymer gels often exhibit hierarchical structure, with the largest dimensions on the length scale of or greater than 100 nm, which makes USAXS an appealing technique. Much effort has been conducted in the USAXS study of various polymer gels,45–66 such as hydrogels,45–49 organogels,51–54 xerogels,56, 57 and aerogels.57, 60–66 Hydrogels are composed of water-insoluble polymer chains and are highly absorbent of water. Hydrogels have a complicated structure on both the nano- and micro- scale. Due to their significant water content, hydrogels possess a degree of flexibility that resembles natural tissue. Agrawal et al.45 studied the nano- and micro-scale structures of biocompatible poly(L -lactic-acid)–poly(ethylene oxide)–poly(L -lactic acid) (PLLA-PEO-PLLA) gels. The USAXS spectra at low q were fit to a power law. The exponent monotonically increased with increasing length of crystalline PLLA blocks, which suggested that the internal structure of the hydrogel became denser during this process. Ando and Konishi46 studied the structure of transparent (VI-P) and translucent (VI-L) cellulose hydrogels prepared by coagulation and regeneration of viscose in acid solutions with and without acetone. By assuming a twophase model, the authors determined the volume fraction and average size of a high-density phase that only consists of cellulose in both types of gels.

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When ambient conditions such as temperature, solvent quality, and electric field change, hydrogels are often subject to a first-order volume phase transition (VPT). Tirumala et al.48 studied temperature-induced VPT in neutral poly(N-isopropylacrylamide) (PIPAAm), poly(N,N-diethylacrylamide) (PDEAAm), and poly(N-isopropylmethacrylamide) (PIPMAm) hydrogels and their weakly charged counterparts prepared by copolymerizing with sodium methacrylate. USAXS results showed an abrupt VPT in both PIPAAm and PIPMAm gels, but a continuous one in PDEAAM gels. Furthermore, the VPTs were suppressed in poly(N-alkylacrylamide)s but not in PIPMAm with the addition of sodium methacrylate. The authors attributed these observed difference in VPTs to the hydrogen-bonding constraints on thermal fluctuations instead of relative hydrophobicity, as one would normally expect. Grigoriew et al.51–54 conducted a series of USAXS studies on organogels, a group of thermoreversible, viscoelastic materials formed from low-molecular-weight organic gelators. The authors found that the gel structure of monosaccharide is highly dependent on the gelator concentration.51,53 When the concentration increases, the sizes of the gelator aggregates decrease and their shapes change from disk-like to rod-like. Additionally, the sizes of the primary aggregates were found to depend strongly on the polarity of the gelators.54 Xerogel and aerogel form when the solvent is removed. Xerogels undergo unhindered shrinkage during drying, while aerogels are obtained under hypercritical conditions, which lead to no shrinkage. Both are highly porous materials and possess extremely high surface areas. USAXS is often utilized to understand the nature of the porosity in these materials. For example, a study of organosilioxane-aerosil aerogel provided evidence of two fractal structures, one built up by the organosilioxane, the other by the added silica soot.64 Schaefer et al.57 observed porosity in the nanometer range with a distinct feature of fractal in arylenebridged polysilsesquioxane xerogels and aerogels. The pore morphology shows a systematic dependence on the bridging group, but is only weakly dependent on the catalyst type, concentration, and the drying protocol. Pahl et al.66 showed that the average pore size and mass fractal dimension of resorcinol-formaldehyde (RF) aerogels change systematically as a function of resorcinol-to-catalyst ratio. Brandt and Fricke63 studied subcritically dried RF aerogels with very high catalyst concentrations. A wide range of pore size, from 30, the blends also exhibit disordered bicontinuous and double-gyroid-like structures. The same research group also explored a ternary blend of a poly(styrene-b-isoprene) dilock copolymer, polystyrene, and polyisoprene solution-casted from cumene as a candidate of photonic crystals.72,73 The dried sample showed a well-defined peak in the reflectivity curve in the visible wavelength range (350–600 nm), which indicates a large structure formed in the blend. USAXS measurements for samples containing 20% and 40% homopolymers confirmed that the morphology of the blend was a highly ordered lamellar. The alternating layers of styrene and isoprene were found to possess a periodic dielectric structure, with their thicknesses 0.52 L and 0.48 L, respectively, where L is the lamellar thickness. Based on this structure, the band diagram was calculated, and pass- and stop-band were consequently obtained. To strengthen microphase separation and increase the inter-domain spacing of block copolymer melts, Tirumala et al.74 studied the effect of adding an additive poly(acrylic acid) homopolymer with a molar mass 1–13 times that of the poly(oxyethylene-oxypropyleneoxyethylene) copolymer on the Flory-Huggins segment-segment interaction parameter χ . While the neat copolymer was disordered, the addition of poly(acrylic acid) resulted in a well-ordered lamellar structure with an interdomain distance of 10 ± 1 nm. Powerlaw decay was consistently observed in the low-q region of slit-smeared USAXS profiles with exponent between 2 and 2.5, which is below the Porod exponent 3. This result showed that the droplet macrophase separation of homopolymers is not present in the blend regardless of its molar mass. Instead, the homopolymer was expected to uniformly distribute through the polyoxyethylene domains of the lamellae-forming blends. Kobayashi et al.75 combined light scattering (LS), USAXS, and SAXS and studied the self-assembly and morphology of l,3:2,4-bis-O-(p-methylbenzylidene)-D-sorbitol/ndibutylphthalate in the parameter space of temperature T and solute concentration PDTS in detail. In particular, USAXS was found useful for establishing the characteristic distances in the self-assembled states and the power-law slope in the gel states. Again, a mass fractal dimension was observed, which excluded the presence of a sharp interface. Combined with the previous example, this result suggests that USAXS is a powerful technique for investigating the degree of phase separation in the polymer blends.

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5.3 Polymer Micelles and Microemulsions Surfactant molecules dispersed in selective solvents can self-assemble into various micellar morphologies such as sphere, ellipsoid, cylinder, and bilayer. Similarly, microemulsions form when two immiscible liquids are mixed together with at least one component being surface active. Polymer micelles and microemulsions often have sizes that make USAXS a suitable technique. In this section, we show a few recent USAXS applications for these systems. One example is the determination of the structure of casein micelles by Pignon et al.76 Casein micelles (calcium-protein complexes), milk fat globules, and milk sugar (lactose) are the three main biological components of milk. Despite being the subject of extensive investigation, the exact structural details of casein micelles have remained elusive.77 Using USAXS and unified analysis, as is shown in Fig. 4, the authors found two characteristic length scales for the equilibrium structure of casein, with radius of gyrations Rg about 100 and 5.6 nm pertaining to the globular micelles and their non-globular internal structure, respectively. The low-q region of the USAXS curve followed a q−4 power-law decay, which suggests the existence of a smooth interface of the large, globular micelles. The high-q region showed a decay following q−2, which was described by the Debye formula for entangled flexible polymer chains. This physical picture was in agreement with a recently proposed casein micelle model, which negated the existence of the submicellar structure within the micelle.78 In a subsequent work, Marchin et al.79 considered the environmental factors on the casein micelle structures. The casein micelles were fractionated into six fractions using a sequence of six consecutive centrifugation steps. In the low-q region, different Rgs were obtained, as expected. The globular structure of the micelles was confirmed in all cases. In the high-q region, the USAXS curves showed identical fractal-like features, which demonstrated that micelles of different fractions, albeit with different sizes, possessed the same internal structure. Furthermore, the authors studied the effects of temperature, pH, and calcium chelation on the structure of casein micelles. Thermo-treatments were found to have little influence on the structure as the USAXS curves overlapped. Reducing pH did not change the low-q region of the scattering curve, which suggested that the globular structure was independent of the acidity, at least in the range of pH probed. The change in the high-q

Figure 4. Static SAXS and USAXS measurements of casein micelle suspensions at 25◦ C and pH = 6.6. The continuous lines in the figure are obtained with unified fit.


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region confirmed that the internal structure of casein micelles was related to the presence of micellar calcium phosphate, which was disassociated at a lower pH value of 5.2. When the casein micelles were depleted of calcium by chelation, the USAXS curves completely changed over the entire q range and suggested the destruction of globular structure of the micelles. Di Cola et al.80 studied the morphologies of micelles formed by linear and cyclic poly(styrene-b-isoprene) (PS166 -b-PI278 ) copolymers in different solvents as a function of temperature. The micelles have one characteristic length scale of the order 100 nm, which makes USAXS suitable. For linear copolymers, the morphology of micelles formed in good solvents for PS blocks does not vary with temperature. A detailed analysis of USAXS spectra of linear copolymer in good solvents for PI blocks for temperatures above 60◦ C showed that the micelles undergo a cylinder-vesicle transition. For a cyclic copolymer, its morphology was found to be independent of both temperature and concentration. Zemb and coworkers utilized USAXS to study the structures of microemulsions.81,82 For example, Testard et al.81 examined the effect of apolar solute lindane on the microstructure of water-didodecyldimethylammoniumbromide (DDAB)-dodecane ternary microemulsion. The absolute intensity in the high-q region of USAXS curves showed a q−4 power-law dependency, demonstrating the presence of a sharp oil/water interface. The specific area measured at the Porod limit yielded the area per surfactant, which was shown to be irrelevant to the solute concentration. In addition, with increasing solute concentration, the characteristic size of the microemulsion cell was found to decrease. These structural results, together with conductivity measurements, were consistent with a disordered, open connected cylinders model. 5.4 Polymer Nanocomposites Modification of polymers with an inorganic or organic material as fillers or additives to produce polymer composites is one of the most successful examples of polymer engineering in the chemical industry. Polymer nanocomposites, in which the secondary, or in uncommon cases, ternary materials have dimensions of less than 100 nm, or structures with comparable repeating distances, offer exciting opportunities not possible with conventional polymer composite materials.83,84 Compared with macroscopic or microscopic composite fillers, the nanoscale fillers offer advantages such as ultra-high surface area per unit mass, ultra-low filler mass concentration to achieve filler percolation, and small interparticle distances in the polymer matrices. As a result, polymer nanocomposites are lighter than the conventional polymer composites and exhibit large increases in tensile modulus, strength, toughness, and heat resistance. Due to their outstanding properties, polymer nanocomposites have found many applications such as conducting polymers,85 optical materials,86 and fire retardants.87 The physical mechanism behind these applications, however, remains controversial and elusive, largely due to the complex, and often hierarchical structures of polymer nanocomposites. In polymer nanocomposites, the nanoscale fillers present an enormous amount of interfacial areas, which leads to direct interaction between polymers and the filler components. This effect introduces heterogeneity within the polymer matrix on the nanoscale and deforms the polymer from its bulk confirmation. The primary filler particles, with a length scale of tens of nanometers, form aggregates, which in turn could form agglomerates. Understanding this structural variation is crucial in terms of understanding various material behaviors of polymer nanocomposites. USAXS, because of its favorable q range, is an ideal tool for this investigation. Due to the hierarchical nature of the structure, unified analysis developed

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by Beaucage88 is often the method of choice, which results in interpretation based on an analogy of surface or mass fractals.89,90 Narayanan et al.91 studied the structure of silica-polyvinyl acetate nanocomposites with matrices of two different molecular weights. They found that particle aggregation is independent of the molecular weight of the matrix for a fixed filler concentration and surface treatment. They also reported that various surface treatments reduce the bonding strength to the polymer matrix, as well as reduce the particle aggregation. This result was in agreement with a nonlinear viscoelastic study of the same nanocomposites above glass transition temperatures by Sternstein et al.92 Ehrburger-Dolle et al.93 studied the anisotropic structure of carbon black (CB)-filled, high-density polyethylene (HDPE) polymers. No anisotropy was observed when the CB concentration was below its percolation threshold. For concentrations above the threshold, CB aggregates with a fractal dimension less than 2 were found, and their role in the mechanical properties of CB filled nanocomposites was consistent with the model for reinforcement of rubber by fractal aggregates proposed by Witten et al.94 In a separate study of CB and polymethylmethacrylate (PMMA) nanocomposites, Levine et al.95 found that mechanically prepared samples exhibit very high electric conductivity at an extremely low CB loading percentage. USAXS measurements were used to explain this phenomenon as the formation of a three-dimensional CB-assembled nanowire network, with the mean diameter and length of the nanowire about 24 nm and up to 100 µm, respectively, which was further confirmed by USAXS imaging. Thill et al.96,97 studied spray-dried nanocomposites of silica and bromostyrene-styrene copolymer prepared by a one-step droplet drying process. The fine structure of the grains and the localization of the polymers were described. Instead of having empty pores in the dried composites, copolymers were found to fill half of the porous volume. Bellare et al.98–100 performed a series of studies on PMMA and barium sulfate nanocomposites as bone cement materials. To strengthen and provide a higher resistance to cracking, 100-nm barium sulfate particles were used instead of conventional 1–3 µm barium sulfate or zirconium oxide radiopacifiers. By comparing the analyzed total specific area with the theoretical value, they found that the nanoparticles were well dispersed in the PMMA matrix and the number of voids was limited. The stronger bonding resulting from this structure was confirmed by the increases in tensile strain-to-failure, tensile work-of-fracture, and fatigue life obtained through mechanical measurements. Chemin et al.101 studied the structure and mechanical properties of mesostructured functional hybrid coatings based on anisotropic nanoparticles dispersed in poly(hydroxylethyl methacrylate) (PHEMA). They reported that at low volume fraction, the anisotropic goethite nanorods and isotropic nanospheres form a homogeneous dispersion within the polymer matrix, which led to a strong reinforcement effect of PHEMA. Ikeda et al.102 reported an isotropic dispersion of silica nanoparticles in an in situ study of the morphological variation of silica/isoprene rubber nanocomposites. The scattering patterns change according to the stretching ratio in a manner similar to that of liquid crystalline elastomers under stress103 which indicated that the nanoparticles displaced affinely with the elastomer network. These results were further utilized as data input for reverse Monte Carlo simulation104,105 which showed that the structural change of the nanoparticles during elongation was minimal. Recenly, Kumar et al.106 observed anisotropic assembly of isotropic nanoparticles in a polymer nanocomposites system. Polystyrene chains were grafted onto the surface of spherical silica nanoparticles, the average diameter of which was about 14 nm. These


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Figure 5. USAXS profiles of silica grafted with different molecules mass (Mg ) of polystyrene brush. The continous lines are obtained with unified fit.

isotropic particles were implanted into isotropic polystyrene matrices of different molecular masses. USAXS, shown in Fig. 5, and TEM measurements found that after prolonged annealing, the isotropic grafted nanoparticles were capable of assembling into spherical aggregates, connected sheets, and strings, or stay well dispersed (unstructured) depending on the relative grafting density and grafted chain length. This extraordinary behavior was explained by the balance between the short-range interparticle attraction and the entropy loss of the distorted grafted polymers, and opens a new paradigm for the control of nanoparticle dispersion in a polymer matrix. Most notably, Schaefer and his coworkers68,107–126 have performed an extensive survey of various polymer nanocomposites using USAXS. The nanoscale fillers range from single-walled carbon nanotube68,124 (SWCNT) and multi-walled carbon nanotube118,123 (MWCNT) to precipitated silica.107,111,114,125,126 For these fillers, a typical small-angle scattering profile is shown in Fig. 6, where light scattering and USAXS data for Dimosil precipitated silica120 are combined to illustrate the levels of structures present in the sample. It is evident from the data that the primary particles (in this case, silica) form aggregates, which are further clustered into two types of agglomerates. Similar results were found in SWCNT124 and MWCNT118 dispersions as well, which directly showed that the nanoparticles, instead of being well dispersed, form aggregates and agglomerates. Considering that the presumption of nanoparticle reinforcement in nanocomposites is that the smaller nanoparticles offer more surface area and hence stronger bonding, these results pose a serious question for the overall effectiveness of polymer nanocomposites. For example, for the nanocomposite of MWCNT and melt-processed thermoplastic polyamide 6 (PA6), Zhao et al.117 found that the CNTs are quite flexible, regardless of the degree of chemical modification. Due to the flexibility of CNT, the yield strength of CNTs/PA6 nanocomposites is almost unchanged, and the tensile strength is only slightly increased. In a recent work, Schaefer et al.122 further showed that despite the formation of aggregates and agglomerates and the unremarkable performance in nanocomposites with hard matrices, carbon nanofibers are still capable of reinforcing soft materials (in this case, a

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Figure 6. Combined light and USAXS scattering data for Dimosil precipated silica in the wet and dried states.

carbon nanofiber/thermoplastic polyurethane nanocomposite), although through a different mechanism. The fractal clusters formed by the nanofiber agglomerates are capable of storing elastic energy, which in turn explains the improvement in the mechanical strength. For a detailed and in-depth review of Schaefer’s work on nanocomposites, interested readers can refer to Schaefer et al.120 5.5 Colloidal Suspensions and Gels Colloidal suspensions and gels often have intrinsic sizes or characteristic distances befitting the q range of USAXS. The high-q resolution serves to obtain an accurate scattering structure factor, and the inherent absolute intensity calibration enables determination of number density of scattering particles. All these features are important to the understanding of basic statistical mechanical interactions and microstructures of such systems. Because of these reasons, USAXS has enjoyed great success in various colloidal systems, such as monocomponent dispersions,127–136 binary or ternary mixtures,137–139 colloidal gels,125,140–146 and colloidal crystals.147–151 In addition to the aforementioned advantages, USAXS allows precise measurement of the scattered intensity as q approaches 0. The normalized scattering intensity at q = 0 is related to the osmotic compressibility of the suspension. Furthermore, as previously mentioned, the structure factor of a colloidal suspension is often conveniently obtained in USAXS measurements. Therefore, USAXS profiles can be used to determine interparticle potentials or test models that govern the stability of colloidal suspension. For example, Tara et al.152 reported amorphous clustering of highly charged poly(chlorostyrene-styrene sulfonate) colloids in dilute deionized suspensions of various concentrations. In all cases, the structure factors showed a first peak and a split second peak, which indicated the formation of glasslike order despite the dilute nature of the dispersion. This research was


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among the first experimental evidence of long-range attraction in colloidal suspensions of low volume fraction. When the colloidal particles interact via an attractive, short-range potential, which is significantly greater than the thermal energy, a gas-liquid-type jamming transition can happen at a very low colloidal packing fraction. Pontoni et al.153 studied the static microstructure of charged silica colloidal particles in a binary mixture of 2,6 lutidine and heavy water near the fully reversible colloidal aggregation temperature TA . They found that at a low volume fraction (8% volume), the colloidal particles undergo repulsive to short-range attractive transition by a temperature dependent absorption process. Furthermore, the first maximum of the structure factor S(q) well above TA is below the Hansen-Verlet criterion 2.85, which suggests that the aggregated state has the dense, liquid-like packing feature of gas-liquid transition of colloids, instead of that of a freezing transition. In a similar, but more detailed study, Sztucki et al.154 investigated the static structure of a short-range interacting colloidal system over a large range of colloidal concentrations, including the vicinity of a reentrant glass-liquid-glass transition. The structure factor was modeled with an attractive square-well potential. The results, including the depth and range of the interparticle attraction and the structure of the aggregates, were found to be consistent with the predictions of a mode-coupling theory.155 The fine angular resolution and wide q range of USAXS make it an excellent technique for binary colloidal suspensions. Lutterbach et al.137 studied the static structure of the charge-stabilized polystyrene (PS) and perfluorinated (PFA) particles with diameters of 79 and 162 nm with a total volume fraction of 9%. PS and PFA have greatly different scattering length densities in water. Due to this property, the authors were able to extract the PFA-PFA partial structure factor and found the intensity of the first peak of this partial structure factor decreases with decreasing number fraction of PFA, which suggested the weakening of liquid-like order. The results were found to be in good agreement with predictions made by DLVO theory. USAXS is also applied in a binary suspension with large size ratio. Zhang et al.139 investigated the arrangement of highly charged zirconia nanoparticles (mean radius 2.57 nm) near the surface of negligibly charged silica microspheres (mean radius 280.11 nm), as shown in Fig. 7. The nanoparticles were shown to form a loose layer near the surface of the microspheres, with average nanoparticle-to-microsphere surface separation distance of 2 nm, which is nearly equivalent to the Debye length. The nanoparticle concentration in this layer is significantly higher than that in the bulk solution, and the average nanoparticle separation distance within the layer is about 9 times that of the nanoparticle radius. This result experimentally illustrated the static structure of a colloidal nanoparticle halo156 which has remained elusive since its discovery mainly because of the size discrepancy between the nanoparticles and microspheres. When the colloidal particles are anisotropic in shape, 2-D collimated USAXS is preferred over slit-smeared USAXS because of the complicated desmearing involved. Mock et al.157 used 2-D collimated USAXS to study the static microstructures of anisotropic polystyrene particles of various degree of anisotropy. The particle form factors of the anisotropic particles are represented by two interpenetrating spheres, with one sphere possessing a constant diameter and the other possessing a varying diameter. By changing the volume concentration, the colloids undergo a disorder-order transition. An example of anisotropic homonuclear colloids and corresponding USAXS profiles is shown in Fig. 8. Interestingly, the authors found that when the volume concentration is below 45%, the anisotropic colloids form a rotary or plastic crystal phase, where the centers of mass of the particles are ordered, but not the particle director. When the concentration is higher, the colloids form a body-center tetragonal structure, where both the center of mass and

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Figure 7. USAXS measurements of monodisperse silica, zirconia, and the mixture of silica and zirconia. The continuous lines are least-squares fitting with user-defined mode in the framework of Irena SAS analysis package. Note the greatly different size (q) range of silica and zirconia.


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Figure 8. USAXS of anisotropic homonuclear colloids. The colloids, shown in Fig. 8(a), can be approximated with overlapping particles models obtained with Debye model for single particle scattering. Figure 8(b) shows its USAXS at 5% vol and its fit with Debye model.

the director are ordered. In a separate experiment, Levitz et al.158 studied the suspension of charged, disk-like synthetic clay Laponite/particles at very low ionic strength (in the order of 10−5M). By changing the concentration of the clay particles, a liquid-soft solid transition driven by electrostatic repulsive interaction was observed. The soft solid features a correlation peak at low-q. A detailed inspection of the peak showed that the clay particles form clusters, instead of being uniformly dispersed. In a rather unusual, gaseous colloidal suspension, Beaucage et al.159,160 studied the in situ nanoparticle nucleation and growth in flame aerosols at different positions inside the flame. The nanoparticles were found to form aggregates and agglomerates, the size and morphology of which were in turn mapped with the height above the burner and lateral distance from the axial center of the flame. The height above the burner was further converted to a kinetic time with the known gas flow rate. The dynamics of nanoparticle growth in flames was thus acquired. When attractive interaction exists between colloids, it is well known that the colloidal particles can aggregate to form colloidal gels which often have the characteristics of a fractal.161 For a mixture of hard-sphere colloids and nonadsorbing polymers, depletion attraction arises from the entropy-driven exclusion of the polymers from the region between closely neighbored colloids, where the range and strength of this effective attraction can be delicately tuned. Zukoski et al.141–146,162,163 performed a series of detailed and in-depth investigation of such concentrated depletion gels. In one example, Shah et al.141 studied the influence of polymer concentration and radius of gyration of the polymer on the microstructure of model hard-sphere nanocolloids, where the volume fraction of colloids was fixed at 0.40. For the given system where the radius of gyration was significantly smaller than the mean radius of the colloids, a direct homogeneous fluid to nonequilibrium gel transition was observed with increasing polymer concentration. The authors deducted the scattering structure factor S(q) by comparing the concentrated USAXS profile with corresponding dilute profile of the same particles and modeled S(q) with the polymer reference site interaction model (PRISM).164,165 The elastic modulus of the gel, yielded by

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Figure 9. USAXS measurements of highly monodisperse silica beads. The insert shows a magnified curve near q = 3.2 × 10 −4 Å−1, where the oscillations are still clearly visible due to the very high angular resolution that USAXS provides.

this model, was found to depend on the polymer-colloid size ratio and the reduced polymer concentration in a power-law fashion. This study was extended further by Ramakrishnan et al.142 where the volume fraction dependence of the collective structure and the elastic modulus of colloidal gels of the same type was investigated. The elastic modulus extracted from PRISM was shown to have a power-law dependence on the volume fraction of the colloids, with an effective exponent decreasing with increasing depletion attraction strength. Despite the fact that the discussion in this section is confined to colloidal suspensions and gels, it is necessary to point out that USAXS is a valuable and often unique tool when investigating large particles with narrow size distribution in their ordered states due to the small angular resolution of USAXS. One example as shown in Fig. 9 is given in Ilavsky et al.,15 where USAXS profiles of monodisperse silica beads in their dilute and ordered states were compared. At q as large as 3 × 10−2 Å−1, the oscillations from the scattering form factor were still clearly visible. This feature facilitates the accurate and reliable extraction of the structure factor, and predictably, will also be useful to identify sharp diffraction peaks, if present. 5.6 Other Materials In addition to the examples shown in the previous sections, USAXS has been successfully utilized in other areas of polymeric and colloidal research, such as non-affine deformation of soft colloidal films,166 self-assembly of cellulose that is artificially synthesized via enzymatic polymerization,167 structure of dendrimers with univalent and bivalent counterions in ionic dilute solutions,168 forced assembly of two immiscible polymers produced by layer-multiplying extrusion,169 water-swollen perfluorinated ionomer membranes,170


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structure of hydroxypropyl cellulose as flavor-barrier membrane,171 morphology of dry lignins and size and shape of dissolved lignin particles,172 nanostructure evolution of polyethylene,173–175 the failure mechanism of glass-beads filled polystyrene,176,177 the domain-interface sharpening process during crystallization,178 and the degree of homogeneity of homogeneous dispersions.179 These examples, together with the aforementioned examples, explicitly demonstrate the wide-range applicability of USAXS. Recent technical improvements to the available instruments have made USAXS an increasingly attractive tool to study large scale and hierarchical structures in complex fluids. As a result, more effort has been made to employ the unique capability of USAXS to understand physical, chemical, or engineering properties of these materials. There is no doubt that USAXS, as a proven structure-characterization technique, will continue to tackle complex, yet important and interesting scientific problems in soft condensed matter.

6. State of Analysis for USAXS Data USAXS instruments, when compared with pinhole SAXS instruments, provide a wider range of scattering vector as well as a larger dynamic range of scattering intensity. The information content of USAXS data, therefore, is more complete. In principle, the results obtained from proper analyses of USAXS data ought to be more accurate and more representative of the microstructures studied. However, it sometimes seems that the exact opposite is true. Developing a model which would describe the microstructure over up to four decades in size, such as that in the case of USAXS study of binary colloidal mixture with great size disparity139 is not a simple feat; and many studies significantly fail in this regard. In this review we have reported the wide range of USAXS applications in polymers, while realizing that the quality of data analysis varies. So far, we have avoided pointing out specific flaws in data analysis to keep the review easier to follow. In this section we will identify the major challenges facing USAXS data analysis, and will offer some general suggestions regarding good practices in this area. We will also provide a few examples where analysis may have fallen short. While ab initio small angle scattering (SAS) analysis can still be seen in literature, it has become more popular to construct SAS analysis based on existing SAXS analysis packages. The availability of these packages not only makes the analysis more convenient, but also establishes a degree of confidence to the analysis, considering that the software packages, which are tested and employed by many users, are less error-prone. Some packages were developed on the basis of the Igor Pro commercial scientific software (Wavemetrics, 2008), for example, NIST analysis tools,180 Motofit,181 and Irena.36 Self-standing SAS packages developed with more common programming languages (Fortran, C, Java, Pascal, etc.) also exist, such as Scatter,182 SASFit,183 Fish,184 and ATSAS, a suite of software developed by Svergun et al.185–189 The exact functionalities of these packages vary, and there are usually specific areas where they excel. For example, ATSAS186 is the undisputed standard for bio-SAXS analysis. The wide availability of these packages may lead the users to enjoy the seemingly large freedom regarding curve fitting, and sometimes base their analysis on convenience, rather than facts. It is worth being aware that proper usage of any SAS analysis package or any SAS analysis method in general, stresses on the reliance of the users to be knowledgeable about the specific problem and capable of choosing an appropriate tool/method. This is more evident for USAXS analysis because most SAS analysis packages except Irena are not primarily developed to be used with USAXS data.

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As stated above, the main challenge to USAXS data analysis lies in the fact that USAXS probes a wide range of scattering vector. Therefore it is necessary to design either one model to describe the microstructure over such a wide range of sizes—potentially from Angstrom to micron, or to find a valid approach to split the data into different segments, analyze each segment with an appropriate method, and then combine the results in a meaningful way to describe the microstructure. For example, Unified fit is developed for the latter case88,90 in which the microstructure is modeled as a sequence of hierarchical structural levels. These levels could be independent or could also possess complex relationships among themselves. One needs to have a fundamentally sound understanding of the sample to assign the true meaning of each structural level in terms of the underlying microstructure. Having clearly stated and defendable basis for the chosen analysis method is of essential importance for fitting of any small-angle scattering data. It is especially this case for USAXS data analysis, as its q range is extensive and various portions of data may need to be analyzed with different assumptions. It is also crucial to realize that different methods (packages) may have different foundations. For instance, ATSAS assumes that the scatterers are mono-sized and mono-shaped; volume size-distribution analysis assumes that the scatterers have the same shape but varying sizes, and fractal analysis assumes self-similarity of the microstructure over an extended length scale. A good example of proper USAXS analysis with several methods combined can be found in the investigation of the structure of nanocomposites by Schaefer and Justice,120 where scattering from primary particles was analyzed by Guinier analysis or size-distribution analysis, and the structure of large-scale aggregates and agglomerates were obtained with fractal analysis. We do note, however, that in some cases multiple analysis methods are used without befitting justification.51,54 One example is shown in Fig. 10, which is an attempt to fit USAXS data from apolar and polar gels by fractals analysis.54 The data do not aid this analysis by presenting clearly separated regions with different power-law dependence. In the same articles, pair distribution function and Guinier analysis are also employed, again without discussion about their applicability. Here we strengthen the misuse of fractal analysis when there is no clearly defined fractal region and/or the power law slope obtained strongly depends on the selection of the fitting interval. Another common issue in USAXS analysis is the inability to distinguish between highly asymmetric particles (long rods, high aspect-ratio disks, etc.) and fractals. It is commonly recognized that for these particles the region bound by two “Guinier type regions” features a power-law slope of -1 (randomly oriented rod) or -2 (disk or sheet-like object). But it is much less realized that it is also possible to have particles with these shapes to cause the scaling to have a nearly arbitrary power law component. This possibility is manifested in recent USAXS studies of aerogels.190,191 These materials are constructed by solid materials in various shapes (sheet-like or rod-like) and not fractals. Their USAXS profiles, however, exhibit varying power-law slopes. These results suggest that simple fractal analysis of USAXS data such as in the case of silica aerogels192 may require further discussion to eliminate other possible microstructures. USAXS analysis is often not unique. Without constraints, data fitting can be meaningless. It is therefore important to keep in mind that the more one knows, the more one can learn from USAXS, or SAS in general. We are glad that most USAXS applications so far show deep appreciation of these principles. We also recognize that improvement could also be made, and awareness of these principles should be steadily promoted especially as USAXS instrumentation has greatly matured and USAXS, as a technique, is ready to make greater contribution to polymer research.


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Figure 10. USAXS data of (a) apolar gels and (b) polar gels with fractal analysis.

7. Summary and Outlook Small-angle X-ray scattering is a very useful technique to study the size, shape, and structural inhomogeneities of polymers. USAXS, by taking advantage of a wide q range, acts to bridge pinhole SAXS and light scattering, and provides access to large-scale structures and hierarchical structures. Recent developments in high-flux sources and crystals with low parasitic surface scattering enhance the capability of USAXS to probe samples with low scattering contrast. Many applications of USAXS have been found in areas such as

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polymer gels and solutions, polymer nanocomposites, polymer blends, polymer micelles and microemulsions, and colloidal sciences. We acknowledge that despite the success that USAXS enjoys, it remains largely a static scattering approach due to point-scanning detection in the reciprocal space. Efforts are currently under way to perform on-fly USAXS scans, which will reduce the scan time by an order of magnitude (from ∼10 min to ∼1 min). This will have two major implications—1) for polymers and biomaterials, radiation damage will become less of a concern; 2) probes of slow kinetics will be possible. Undoubtedly this improvement will open a window into future scientific discoveries. There is also a plan at APS to incorporate a short pinhole camera that covers the q range from 0.05–1 Å−1 with the existing Bonse-Hart setup to facilitate automatic measurement of a “complete” small-angle X-ray scattering profile. This combination not only greatly improves the q resolution of USAXS at high qs, but also allows probing from the molecular structure to the self-assembled microstructure, and will be especially useful to characterize structures with multiple length scales. USAXS, as a technique, has reached a stage where technical developments have made it ready to greatly contribute to research into polymers and other soft materials. USAXS has, and will continue to enjoy success in areas such as nanocomposites and colloidal sciences. It is also foreseeable that USAXS will be adopted as an ideal technique to study biomaterials with hierarchical structures and to answer the related open questions.

Acknowledgment Research at the Advanced Photon Source, Argonne National Laboratory is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-06CH11357.

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Preferred Orientation in Polymer Fiber Scattering CHRISTIAN BURGER, BENJAMIN S. HSIAO, AND BENJAMIN CHU Chemistry Department, Stony Brook University, Stony Brook, NY Fiber symmetry is one of the most important sample geometries encountered in both wide-angle x-ray scattering (WAXS) and small-angle x-ray scattering (SAXS) of polymers, applicable both to natural polymers like collagen or cellulose and to many synthetic polymers that come in fiber form or otherwise exhibit cylindrical rotational symmetry. The structural information to be determined in scattering experiments from such fiber systems includes both the structure of the individual structural unit and qualitative and quantitative information about the preferred orientation state of the ensemble. Existing approaches and new developments to analyze fiber scattering patterns are rigorously reviewed. Special emphasis is placed on the calculation of complete SAXS and WAXS fiber scattering patterns, and various practical examples including collagen and cellulose fibers as well as fibers based on copolymers of polyethylene and polypropylene are discussed. Keywords fiber diffraction, wide-angle x-ray scattering, small-angle x-ray scattering, collagen, cellulose, polypropylene, polyethylene

1. Introduction Structure analysis by scattering experiments can be performed on isotropic samples (powders, isotropic bulk, solutions), single crystals, and on systems that are neither isotropic nor perfectly oriented but show preferred orientation of the constituting structural units. The goal of structure analysis of powders, solutions, and single crystals usually is information about the structure itself (e.g., a crystal unit cell or a particle shape). Structure analysis of systems with preferred orientation additionally generates qualitative and quantitative information about the preferred orientation that can be linked to mechanical and other material properties. Frequently, the structure of the actual structural unit is already known and the preferred orientation information becomes the only output of such experiments. The mathematical treatment of preferred orientation in scattering experiments as lined out in this review applies equally to small-angle x-ray scattering (SAXS) and to wide-angle x-ray scattering (WAXS). Among the systems with preferred orientation, systems with cylindrical rotational symmetry, also known as “fiber symmetry” but not limited to actual fibers, play a particularly important role. On the one hand, this is because many systems of interest, e.g., synthetic and natural polymer fibers, show this type of sample geometry. On the other hand, the combination of point focused X-ray beam and 2D detector allows to record (almost) the Received October 18, 2009; accepted November 22, 2009. Address correspondence to Christian Burger, Chemistry Department, Stony Brook University, Stony Brook, NY 11794-3400. E-mail: [email protected]

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Figure 1. Schematic representation of a fiber scattering experiment, showing a calculated WAXS fiber pattern for α-isotactic polypropylene.

complete information contained in 3D reciprocal space in a single 2D detector frame, see Fig. 1, with the only limitations being a possible information loss at large angles near the meridian due to the curvature of the Ewald sphere1 and, of course, the obvious cut-off at large scattering angles due to finite detector size. The ability to capture the complete scattering information in a single detector frame allows unique time-resolved scattering experiments with polymer fibers as a function of a parameter like temperature, stretchingratio, relaxation time, etc. that would not be practicable otherwise. Figure 2 shows schematic sketches of various possible geometrical arrangements in systems with fiber symmetry. In all cases, we consider an individual structural unit (depicted as a decorated cylinder in the sketch) replicated throughout 3D real space. Under the assumption of “simple fiber symmetry,” the structural unit itself shows cylindrical symmetry about its own symmetry axis (depicted as individual arrow for each cylinder), either by its own nature (e.g., SAXS of whole semi-crystalline polymer stacks) or because of an actual rotational average (e.g., WAXS of the crystalline lamellae inside a semi-crystalline polymer fiber). The symmetry axis of each structural unit forms an orientation angle β with the main fiber axis (large vertical arrow in Fig. 2), resulting in a distribution of orientation angles known as orientation distribution function (ODF) g(β) depending a single angle β, assumed to 0 on the pole and π/2 = 90◦ on the equator. β is one the three Euler angles α, β, γ characterizing the orientation of an individual structural unit. The average over the azimuthal angle α of the fiber (cf. Fig. 5) is the condition for the presence of any kind of fiber symmetry, “simple” or otherwise, and the average over the azimuthal angle γ of the individual structural unit is a consequence of “simple fiber symmetry” as discussed above. The case of “general fiber symmetry,” see e.g. ref. 2, with a bivariate ODF g(β, γ ) is considerably more complicated but not very common in praxis, so that we limit this review to the situation of “simple fiber symmetry.” Note also that the orientation angle β of each structural unit and its position in the sample should be uncorrelated in a way not to generate any constructive interference which is usually valid in good approximation. As Fig. 2 shows, simple fiber symmetry is not limited to the prevalent case of parallel orientation depicted in

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Figure 2. Schematic sketches of various possible geometrical arrangements of individual structural units (depicted as decorated stacks), tilted with respect to the main fiber axis (vertical arrow).

Fig. 2(a) with an ODF peaked about β = 0, but other situations with ODFs centered about β = π/2 = 90◦ (Fig. 2(b)) or an arbitrary oblique angle (Fig. 2(c)) are possible. The majority of polymer fiber SAXS and WAXS reports found in the literature does not fully exploit the large amount of information contained in those fiber patterns. The data evaluation is frequently limited to obtaining Hermans’ orientation parameter P2 ,3 a single numeric parameter defined in (4·7) describing the width of the ODF, hopefully taking the limitations discussed in section 5. and, for equatorial arcs, (4·9) into account. We hope to show in this review that a complete calculation of the whole SAXS or WAXS fiber scattering pattern allowing a semi-quantitative or even quantitative comparison with the experimental data is the most satisfactory data analysis approach and discuss its technical details. As can be seen in Fig. 1, the dominant feature of preferred orientation in fiber patterns from sufficiently ordered samples, e.g., semi-crystalline polymer fibers, are characteristic arc-shaped peak profiles. One might expect that these arcs could be modelled using a factorization of radial and angular distributions both exhibiting some sort of bell-shape distribution. Under certain conditions this is correct, and the details will be discussed in section 5. It is important to note that while the radial component can often be modeled using traditional peak profiles like Lorentzians or Gaussians, this is usually not a valid approach for the angular component. Figure 3 shows a comparison of the resulting fiber averages of a tilted polar point and a tilted equatorial ring. It is clear, that the precession average of the tilted equatorial ring generates a qualitatively different type of intensity distribution, as would any precessing ring at an off-axis position. Thus, there are geometric relationships between the individual peak profiles of a fiber pattern and their ODF that need to be taken into account for a consistent description of fiber scattering. The correct mathematical treatment of preferred orientation can be difficult, as is shown by the fact that one of the most frequently cited approaches to deal with this problem was recently shown to be incorrect,4 see section 2.

2. Transformation between Axial and Equatorial Profiles The strongest density fluctuation in uniaxially oriented arrangements of polymer molecules as well as of nematic liquid crystals is due to the lateral packing of elongated structural units and results in equatorial arcs that usually dominate the fiber patterns. In this case,

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Figure 3. Tilting a polar point and an equatorial ring by an orientation angle β and performing a fiber average leads to significantly different results: the polar point generates a simple ring while the precession average of the tilted equatorial ring generates a non-uniform intensity band about the equator.

the angular profile of the equatorial arcs is related to but not identical to the ODF of the structural units. The relationship was first given by Kratky in 1933.5 In Fig. 3, the properly normalized (see section 3.) angular profile of the polar point tilted from its axial position by an angle β in Fig. 3 can be described by a δ-function: δ(φ − β) sin β

(2·1)

The corresponding intensity profile of the equatorial band extending over the interval π/2 ± β is given by the croissant function4, 5 2 π −1 Re(sin2 φ − cos2 β)−1/2

(2·2)

where taking the real part Re removes the imaginary values of the square root for angles φ < π/2 − β outside the equatorial band. The complete transformation between arbitrary axial distributions gax and equatorial distributions geq can now be pieced together as a superposition of croissant functions: π/2 δ(φ − β) gax (φ) = sin β dβ gax (β) sin β 0 π/2 geq (φ) = 2 π −1 gax (β) Re(sin2 φ − cos2 β)−1/2 sin β dβ (2·3) 0

Throughout this section, the axial profile gax can describe either a meridional peak profile of the ODF itself. When the axial profile gax is written as a function of x = cos φ and the equatorial profile geq is written as a function of y = sin φ, gax (φ) ≡ gˆ ax (cos φ) ≡ gˆ ax (x),

(2·4)

geq (φ) ≡ gˆ eq (sin φ) ≡ gˆ eq (y),

(2·5)


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they are related by an Abel transformation,6 gˆ eq (y) =

2 π

y

gˆ ax (x) (y 2 − x 2 )−1/2 dx.

(2·6)

0

(2·6) can sometimes be used to analytically calculate the equatorial profile in cases where an analytical solution for the the full transformation kernel F (φ, φ ) to be discussed in section 3. can not be found. For example, the equatorial profile (6·18) for the Maier-Saupe ODF (6·15) can be derived4 from (2·6) without knowledge of the general kernel (6·17). A particularly interesting example for an equatorial profile in a stretched polyethylene 2D fiber WAXS is shown in Fig. 4(a), with a 3D relief detail of the equatorial profile shown in Fig. 4(b). The puzzling aspect of this pattern is that the typical bell shape normally observed in such profiles is replaced by a rather flat plateau. Since the Abel transformation (2·6) constitutes a fractional integral of order 1/2, it can be conjectured that applying another Abel transform to the resulting croissant-shaped distribution leads to the desired plateaushaped distribution with flat top and smooth edges, which is indeed the case.7 A possible physical interpretation of having a croissant function as an ODF is sketched in Fig. 4(c) in terms of a continuous variation of the preferred orientation across the fiber cross-section, presumably due to internal shearing effects during fiber stretching.7 The known inversion of the Abel transformation, d gˆ ax (x) = dx

x

gˆ eq (y) (x 2 − y 2 )−1/2 y dy,

(2·7)

0

Figure 4. Experimental polyethylene fiber WAXS showing equatorial profiles with usual “box patterns” having flat plateaus rather than bell shapes, and their interpretation in terms of an axial ODF given in form of a croissant function, leading to a structural model with a continuous variation of the preferred orientation across the fiber cross-section. Reproduced with permission from ref. 7.

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could be used to determine the ODF from an equatorial peak as discussed in ref. 3 for cellulose fibers. However, the inversion (2·7) constitutes an “ill-posed problem” and its numerical treatment requires some care.8, 9 Apparently unaware of Kratky’s original work, Leadbetter and Norris in 1979 attempted to independently rederive (2·3) in the context of scattering from nematic liquid crystals,10 leading to one of the most frequently cited and practically employed approaches to analyze equatorial scattering from systems with preferred orientation. Their result differs from (2·3) for the identical problem. It was recently shown that Leadbetter and Norris’s solution was incorrect, and the exact location of the error in their derivation was pointed out.4 Unfortunately, this important correction has not attracted much attention, and the invalid Leadbetter and Norris approach appears to be in continuous and widespread use.

3. General Transformation for Arbitrary Profile As discussed in the introduction, the preferred orientation of a system in simple fiber symmetry is fully described by an ODF g(β) depending on a single angle β describing the distribution of the tilt angles of the individual structural units with respect to the fiber axis. As a probability density distribution, g(β) is normalized, and we choose the following normalization,

2π

α=0

π

g(β) sin β dβ dα = 4 π

=⇒

π/2

g(β) sin β dβ = 1,

(3·1)

0

β=0

where the simplification results from symmetry considerations. We found the normalization (3·1) to be the most convenient but note that it differs from the one chosen in ref. 11 which in turn differs from the one in ref. 12. For the isotropic case, we have g(β) = 1. Let I (s, φ ) be the intensity distribution of the individual structural unit and J (s, φ) be the resulting intensity distribution of the preferentially oriented ensemble. Here s = 2 λ−1 sin θ is the absolute value of the scattering vector s, λ is the wavelength, and 2θ is the scattering angle. Note the two different polar angles φ and φ in their own coordinate frames of the structural unit and the fiber, respectively. In order to calculate the intensity distribution J of the fiber-averaged ensemble, we need to average over the intensity distributions I of the individual structural units, properly weighted with the ODF, and correctly taking the relationships between all involved angles into account. We abbreviate I (s, φ ) as I (φ ) and J (s, φ) as J (φ) for constant s. J (φ) =

1 4π

2π α=0

π

I (φ ) g(β) sin β dβ dα

(3·2)

β=0

From the spherical trigonometric relationships cos φ = cos φ cos β + sin φ sin β cos α cos β = cos φ cos φ + sin φ sin φ cos η

(3·3)

we have the Jacobian11, 12 sin β dβ dα = sin φ dφ dη

(3·4)


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Figure 5. Spherical-trigonometric relationships between the scattering vector s and the primary axes of the intensity distribution of the structural unit I (s, φ ) and the oriented ensemble J (s, φ), respectively.12

and can substitute the integration variables in (3·2) from α and β to η and φ : 2π π 1 I (φ ) g(β) sin φ dφ dη 4 π η=0 φ =0 2π 1 1 π = I (φ ) g(β) dη sin φ dφ 2 φ =0 2 π η=0 π/2 ≡ I (φ ) F (φ, φ ) sin φ dφ

J (φ) =

(3·5)

0

where the integration kernel F (φ, φ ) is given by 1 π F (φ, φ ) = g(β) dη π 0

(3·6)

and symmetry considerations allowed to adjust the upper integration limits in both (3·5) and (3·6). It is clear from (3·3) that the transformation kernel is symmetric in φ and φ : F (φ, φ ) = F (φ , φ).

(3·7)

The kernel F (φ, φ ) has an intuitive physical meaning: A narrow peak (approximated as a δ-function) as part of the intensity distribution of the structural unit I (φ ) at a given angle φ0 transforms into a peak profile J (φ) described by this kernel: I (φ ) =

δ(φ − φ0 ) sin φ0

=⇒

J (φ) = F (φ, φ0 ).

(3·8)

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Since the kernel itself can describe a valid peak shape, it must be normalized,

π/2

F (φ, φ0 ) sin φ dφ = 1

(3·9)

0

for arbitrary φ0 , so that we also have

π/2 π/2 0

F (φ, φ ) sin φ dφ sin φ dφ = 1,

(3·10)

0

and

π/2

J (s, φ) sin φ dφ =

0

π/2

I (s, φ ) sin φ dφ ,

(3·11)

0

i.e., the preferred orientation effect only redistributes the existing intensity but leaves the invariant constant, as it should be. Setting φ = 0 in (3·6) with (3·3) restores the ODF itself, F (φ, 0) = g(φ)

(3·12)

so that the ODF could in some approximation be directly determined if a meridional peak could be experimentally observed (which is usually not the case for WAXS from most polymer fibers in typical 2θ -ranges). The relationship between F (φ, π/2) = geq (φ) and the ODF g(β) = gax (β) was discussed in section 2. For the isotropic case, we have: g(β) = 1 =⇒ F (φ, φ ) = 1.

(3·13)

Note that the integral transformation (3·5) is a linear operation, so that more complicated ODFs could be superimposed as linear combinations, ˜ g(β) =

N

fn gn (β),

n=1

F˜ (φ, φ ) =

N

fn Fn (φ, φ ),

(3·14)

n=1

where the normalization condition (3·1) requires that N n=1 fn = 1. The most frequent application of (3·14) together with (3·13) is the addition of an isotropic fraction f to an arbitrary ODF: ˜ g(β) = f + (1 − f ) g(β), F˜ (φ, φ ) = f + (1 − f ) F (φ, φ ).

(3·15)

See ref. 13,14, and Fig. 10 for examples of the application of (3·15) to WAXS from cellulose fibers.


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4. Legendre Expansions In a similar way as a convolution integral simplifies upon Fourier or Laplace transformation, the integral transformation (3·5) can be reduced to a product when all involved functions are expanded into series of Legendre polynomials.12, 15, 16 Due to symmetry constraints, only those Pnm have non-zero coefficients where m = 0 and n is even. Hence, let g be expanded as g(β) =

∞

an P2n (cos β),

(4·1)

n=0

where the coefficient an is given by

π/2

an = (1 + 4 n)

g(β) P2n (cos β) sin β dβ,

(4·2)

0

using the orthogonality relation

π/2

P2m (cos φ) P2n (cos φ) sin φ dφ =

0

δmn . 1 + 4n

(4·3)

Note that our normalization differs from the one used in ref. 12. The kernel F (φ, φ ) can now be written as12, 15 F (φ, φ ) =

∞

an P2n (cos φ) P2n (cos φ ).

(4·4)

n=0

The Legendre polynomials are the eigenfunctions of the integral operator (3·5),

π/2

P2n (cos φ ) F (φ, φ ) sin φ dφ =

0

an P2n (cos φ). 1 + 4n

(4·5)

Noting that P0 (cos φ ) = 1, we can understand the non-obvious normalization (3·9),

π/2

F (φ, φ ) sin φ dφ = a0 P0 (cos φ) = 1,

(4·6)

0

that appears to be difficult to prove by other means, as is trying to solve this integral for explicit kernels F (φ, φ ) like those in (6·13) or (6·17). Due to the normalization of g, a0 = 1. The next coefficient a1 is related to Hermans’ orientation parameter P2 ,3 also known as the nematic order parameter, P2 = 0

π/2

a1 3 cos2 β − 1 g(β) sin β dβ = , 2 5

(4·7)

which assumes the values of P2 = 1 for perfect parallel orientation, P2 = 0 for totally random orientation, and P2 = −1/2 for perfect perpendicular orientation, respectively. Setting φ = π/2 in (4·4), we obtain the expansion F (φ, π/2) =

∞ (−1)n (2 n)! n=0

4n n! n!

an P2n (cos φ),

(4·8)

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from which it can be seen that P2,π/2 = −

P2,0 , 2

(4·9)

so that an axial P2 , i.e., Hermans’ orientation parameter of the ODF, can be obtained from a P2 extracted from an equatorial arc by multiplying with −2, if the approximation (5·14) holds. When I and J are expanded into Legendre series corresponding to (4·1) with parameters bn and cn , respectively, the integral transformation (3·5) reduces to the product cn =

an bn 1 + 4n

(4·10)

which could be inverted to a division if either I for known g or g for known I is to be retrieved from a given J .12 When applied to experimental data, Legendre expansions will primarily be useful when all involved functions are broad. For high degrees of orientation and/or narrow peak widths of I , the convergence of the Legendre expansions will be poor and numerical stability problems can arise.

5. Factorizable Normalized Peak Profiles We consider WAXS or SAXS from a fiber system with sufficient translational periodic order such that discrete scattering peaks are generated. The intensity distribution I of a discrete peak of the structural unit will have certain widths based on crystallite size and disorder effects. For convenience and without significant loss of generality, we assume this intensity distribution I (but not, in general, the orientation-smeared arc-shaped intensity distribution J ) to be factorizable into a product of normalized distributions. In cylindrical coordinates, s12 = s sin φ , s3 = s cos φ , we have I (s) = I (s12 , s3 ) = Iint H12 (s12 ) H3 (s3 ) where the individual H distributions shall be normalized, ∞ H12 (s12 ) 2 π s12 ds12 = 1,

(5·2)

0 ∞ −∞

so that

(5·1)

H3 (s3 ) ds3 = 1,

(5·3)

I (s) d3 s = Iint .

(5·4)

Let H0 be a 1D normalized bell-shaped distribution of unity integral width, e.g. a Gaussian, H0 (t) = exp(−π t 2 ),

(5·5)

H0 (t) = (1 + π 2 t 2 )−1 .

(5·6)

or Lorentzian distribution,


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Figure 6. Various collagen SAXS patterns showing meridional reflections with different degrees of preferred orientation. Reproduced with permission from ref. 17.

Possible candidates for the functions H12 and H3 in (5·1) with centers a and adjustable widths b12 or b3 could be: H3 (s3 ) = b3−1 H0(s3 /b3 ) for a = 0 H3 (s3 ) = (2 b3 )−1 ± H0[(s3 ± a)/b3 ] H12 (s12 ) ∼ = (2 π b12 s12 )

−1

(5·7) for a > 0

H0[(s12 − a)/b12 ]

for a b

(5·8) (5·9)

Note that (5·9) is an approximation that tends to be very good as long as there is no significant overshoot of the shifted H0 towards the negative region of the abscissa. For an H12 centered about s12 = 0, a construct based on a 1D distribution H0 will, in general, not be applicable so that one of the following distributions could be used, 2 −2 2 H12 (s12 ) = b12 exp −π s12 b12 , (5·10) −3/2 −2 2 2 H12 (s12 ) = b12 1 + 2 π s12 b12 . (5·11) Figure 6 shows meridional SAXS of various collagen samples with different degrees of preferred orientation. The undistorted intensity distribution of a single peak is assumed to be factorizable as in (5·1). For each peak, the integrated intensity Iint , the peak position s3 = a, the lateral width b12 and the longitudinal width b3 are parameters to be retrieved. For meridional collagen SAXS, it can further be assumed, that the positions a are equidistant and that b12 is constant, reducing the overall number of parameters of interest. The orientation distribution g is taken to be peaked around β = 0. Figure 6(a) shows an example of a system with a very high degree of preferred orientation, combined with a relatively broad lateral width b12 . In this case, the effect of the preferred orientation is barely noticeable, does not lead to an appreciable curvature of the reflections, and can in general be neglected.

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Figure 7. Comparison of (a) experimental 1st order meridional fish bone collagen SAXS (the figure shows a near-beamstop detail of figure 6(b)) and (b) a calculated peak profile J , using (3·5) with (6·13), where I is given by (5·1) with (5·10) and (5·8) with (5·5), a = 1, b12 = 1.3, b3 = 0.09, p = 40. Note that the maximum of the peak distribution is not exactly located at s = (0, a −1 ) which could have implications for the use of such patterns for calibration purposes. Reproduced with permission from ref. 17.

Figure 6(b) shows the situation for an intermediate degree of preferred orientation and broad b12 . The reflections are appreciably curved but that curvature is not simply circular with its center at the origin of reciprocal space as is the case in Fig. 6(c). It appears that there is no good approximation to treat this case satisfactorily so that the exact relationship (3·5) needs to be integrated numerically, as shown in Fig. 7 using the transformation kernel based on Onsager’s ODF (6·10) and parameters as indicated.17 Note how the spine of the peak in Fig. 7 is curved between the dotted layer line (representing the situation of Fig. 6(a)) and the dashed unit circle (representing the situation of Fig. 6(c)). Note also that the center of the peak is not at the ideal position of the reciprocal period. In the limit of a very broad peak, the reciprocal period is shifted toward the point of inflection at the lower angle flank of the peak. It is also of interest to note, that the separation of preferred orientation and lateral constant width information that normally requires a sequence of peaks can here be carried out for a single peak profile. Figure 8(c) shows a nice example for the final result of an analysis of both the equidistant meridional reflections as well as the broad and diffuse equatorial butterfly pattern due to disordered mineral stacks in mineralized intramuscular herring bone.18 In Fig. 6(c), we have the combination of a low degree of preferred orientation and a lateral width b12 that is small enough to not noticeably distort the reflections from their circular arc shapes. These reflections should, in good approximation, be factorizable into their radial and angular contributions, as discussed in the next section. In view of (3·11), Iint could in principle be obtained by integration over the orientationally smeared peak profile J , but a peak fitting procedure with Iint as adjustable parameter is usually a preferable alternative, especially if non-constant backgrounds and/or overlapping peaks are present. Furthermore, when the scattering angles are large enough that the curvature of the Ewald sphere can no longer be neglected so that its correction leads to a region of missing information around the meridian,1 a peak fit will interpolate this missing region and takes its contribution to the total integral into account, as shown for the example of SAXS from intramuscular fish bone in Fig. 9. In WAXS of polymer fibers measured up to suffiently large scattering angles, the situation can occur that the missing region about the meridian due to the curvature of the Ewald sphere is not acceptable because complete reflections near the meridian are not


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Figure 8. Comparison of experimental and calculated SAXS patterns for mineralized herring bone, taking both the equidistant meridional reflections and the equatorial butterfly pattern into account. Reproduced with permission from ref. 19, see also ref. 18 for a detailed account on this analysis.

observable and not correctable in a way shown in Fig. 9. In this case, a single exposure in normal beam geometry into a single 2D detector frame is no longer sufficient; the sample needs to be tilted and multiple exposures are required. An example mapping an undistorted 2D section through the 3D intensity distribution of polyacrylonitrile (PAN) fibers using a modified fiber diffractometer in symmetric transmission with a point detector was given by Liu and Ruland.20 Consider a meridional peak in parallel orientation (g peaked around β = 0) or an equatorial peak in perpendicular orientation (g peaked around β = π/2) and assume that the lateral width b12 of I given by (5·1) is small compared to the width contributed by the

Figure 9. SAXS of unmineralized intramuscular fish bone and the effect of the curvature of the Ewald sphere. Even a small (and practically unavoidable) tilt angle of 0.83◦ leads to a significant effect in the corrected figure (b) that cannot be neglected for the higher meridional orders. The calculated figure (c) interpolates the missing region about the meridian and produces the correct integrated intensities. Reproduced with permission from ref. 17.

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orientation distribution g, as in Fig. 6(c). Under these conditions, H12 can be approximated by a δ-function, so that (3·5) can be solved to yield a factorizable function for J :

π/2

J (s, φ) = 0

δ(s sin φ ) H3 (s cos φ ) F (φ, φ ) sin φ dφ π s 2 sin φ

H3 (s) H3 (s) F (φ, 0) = g(φ). 2 π s2 2 π s2

=

(5·12)

(5·12) shows that, under these conditions, the orientation distribution g can be directly obtained as the angular part of the peak shape. Here and below in this section, the distributions J are normalized,

∞ π/2

0

J (s, φ) 4 π s 2 ds sin φ dφ = 1,

(5·13)

0

so that the integrated intensity Iint (5·4) could be obtained as a scaling parameter in a fit without the need for any integrations. Note that the information about b12 is lost in (5·12) and cannot be retrieved from a pattern like the one in Fig. 6(c). The corresponding case for an equatorial peak in parallel orientation or a meridional peak in perpendicular orientation, where I is given by (5·1) with (5·7) and b3 is small compared to the orientation width, leads to π/2 H12 (s sin φ ) δ(s cos φ ) F (φ, φ ) sin φ dφ J (s, φ) = 0

H12 (s) F (φ, π/2). = 2s

(5·14)

Note that the angular part F (φ, π/2) of such a factorizable peak is not identical to the orientation distribution g but related to it in a way, that does not require the complete knowledge of the kernel F (φ, φ ), as discussed in the previous section 2.. If an off-axis peak can be approximated by a polar factorization with negligible width in φ , the following J is obtained:

π/2

J (s, φ) = 0

=

H0 [(s − a)/b] δ(φ − φ0 ) F (φ, φ ) sin φ dφ 4 π s2 b sin φ

H0 [(s − a)/b] F (φ, φ0 ). 4 π s2 b

(5·15)

Note that the normalization condition (5·13) applied to (5·15) requires that the non-obvious (3·9) holds. The approximations (5·12), (5·14), and (5·15) are usually sufficient for the vast majority of wide-angle fiber patters, provided that 1. the assumptions of simple fiber symmetry are valid, 2. the peaks are narrow enough due to sufficient crystallite sizes and long-range order, and 3. the long-range order is 3D in nature. Under these conditions, and when the kernel F (φ, φ ) can be given in analytical form, the complete fiber pattern can be modeled without the need for numerical integrations.


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6. Analytic Transformation Kernels Analytic expressions for the general transformation kernel F (φ, φ ) are very convenient, but only a small number of empirical ODFs actually allow an analytical integration of (3·5). We will usually write the ODF as a function of cos β and substitute (3·3) in the form cos β = cos φ cos φ + sin φ sin φ cos η ≡ x + y cos η

(6·1)

so that the resulting kernel F (φ, φ ) is given as a function of x = cos φ cos φ and y = sin φ sin φ . 6.1 Poisson Kernel The classical choice for an ODF with a narrow head and long tails similar to a Lorentzian distribution is the Poisson kernel:11 gPK (β) =

p1/2 (1 + p) −1 [(1 + p)2 − 4 p cos2 β] atanh(p1/2 )

(6·2)

(6·2) describes an ODF peaked about β = 0 for p > 0 and an ODF peaked about β = π/2 for p < 0, respectively. The limits p = 1 and p = −1 generate infinitely narrow ODFs while p = 0 describes the isotropic case. Hermans’ orientation parameter P2 using (4·7) is given by: P 2,PK =

p1/2 1 3 (1 + p) 1+p− − . 4p atanh(p1/2 ) 2

(6·3)

The kernel F (φ, φ ) can be obtained in analytical form:

−1/2 p1/2 (1 + p + 2 p−1/2 x)2 − 4 p y 2 FPK (φ, φ ) = 2 atanh(p1/2 )

−1/2

, + (1 + p − 2 p−1/2 x)2 − 4 p y 2

(6·4)

which is equivalent, apart from our differing normaliztion, to the form given in ref. 11, but is more consistent within the notation used throughout this section. Note that (6·4) constitutes the rare case of an analytical kernel for both parallel and perpendicular orientation. However, the Lorentzian-like peak shape with very long tails may not be appropriate for all practically encountered systems. 6.2 Cosp and Sinp Orientation Distributions The classical choices for Gaussian-like ODFs with broad heads and short tails are11 gCP (β) = (1 + p) |cos β|p

(6·5)

for parallel and gSP (β) =

2 [(3 + p)/2] sinp β π 1/2 (1 + p/2)

(6·6)

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for perpendicular orientation. Hermans’ orientation parameters P2 are given by: P 2,CP =

3 (1 + p) 1 − 2 (3 + p) 2

(6·7)

P 2,SP =

1 3 − , 2 (1 + p) 2

(6·8)

and

respectively. For | cos β|p with integer p, a solution for the kernel F (φ, φ ) based on a binomial expansion is given in ref. 11. A previously unknown solution for arbitrary p is FCP (φ, φ ) =

i (p + 2) [f (x + y, x − y) − f (x − y, x + y)]

(p + 3/2)

π 1/2

with f (u, v) = |u|p u1/2 v −1/2 2 F1 (1/2, 1 + p; 3/2 + p; u/v),

(6·9)

where 2 F1 is a hypergeometric function. An analytical solution for the kernel F (φ, φ ) for sinp β with arbitrary p does not appear to be feasible. 6.3 Onsager’s Orientation Distribution Inspection of (3·6) with (6·1) leads to the straightforward conclusion that a simple solution of the integral could be obtained if g(β) ∼ exp(p cos β) since exp[p (x + y cos η)] can be factorized and the remaining η-dependent part can be integrated. Taking symmetry and normalization into account leads to gON (β) = p csch(p) cosh(p cos β),

(6·10)

where csch(p) = 1/ sinh(p). The ODF (6·10) was first used by Onsager21 as an empirical trial function for the hard-rod fluid. Note that (6·10) remains perfectly well behaved for broad distributions, i.e. small p, while |cos β|p develops a singularity at β = π/2. (6·10) can be expanded into a series of Legendre polynomials and modified spherical Bessel functions in (z) = [π/(2 z)]1/2 In (z) where In is the modified Bessel function of the first kind of order n, gON (β) = p csch(p)

∞

(1 + 4 n) i2n (p) P2n (cos β),

(6·11)

n=0

from which the coefficient an of the Legendre expansion (4·1) can be extracted, e.g. to use it in (4·10). Hermans’ orientation parameter P2 is given by

(6·12) P 2,ON = 1 − 3 p−1 coth(p) − p−1 . The kernel F (φ, φ ) has a particularly simple shape: FON (φ, φ ) = p csch(p) cosh(p x) I0 (p y)

(6·13)

where I0 is the modified Bessel function of the first kind of order 0. For φ = π/2, this takes the form FON (φ, π/2) = p csch(p) I0 (p sin φ).

(6·14)


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Figure 10. Comparison of experimental and calculated WAXS for two samples of dissolved and respun cellulose fibers showing predominantly a cellulose II crystal structure. Reproduced with permission from ref. 14.

Curiously, an equivalent form of (6·13) was found in ref. 22 as an approximate solution for a Gaussian orientation distribution, in our notation given by g(β) ∼ exp(−p β 2 /2), in the limit of large p, not noting its connection to Onsager’s function (6·10). The combination of a reasonable shape for the ODF (6·10) and a simple form for the kernel (6·13) makes this ODF the preferred choice when it is applicable (i.e., parallel orientation), and we have made extensive use of it to generate calculated fiber patterns for both natural and synthetic polymer fibers. Examples are shown in Fig. 10 for cellulose and in Fig. 11 for a polypropylene copolymer. In both cases, the calculation of the full WAXS fiber pattern was based on (5·15) with (3·15) and (6·13). The factorizable exp(p cos β) = exp(p x) exp(y cos η) (6·10) can, unfortunately, not be easily adapted to perpendicular orientation; trying exp(p sin β) does not lead to an analytical solution for the kernel so that other ODFs are preferred for perpendicular orientation.

Figure 11. Comparison of experimental and calculated WAXS for a sheared sample of a propylenebutylene statistical copolymer showing fiber symmetry. The lower left quadrant of the 2D WAXS pattern in the left shows a calculated WAXS pattern for pure α-iPP, the upper right quadrant shows a calculated WAXS pattern for pure γ -iPP, and the two remaining noisy quadrants show the experiment data. The 3D relief plot in the right shows calculated WAXS for a superposition of 20% α-iPP and 80% γ -iPP in the two smooth quadrants and the experimental data in the noisy quadrants. We found such quadrant plots to be very instructive for the comparison of calculated and experimental fiber patterns. Reproduced with permission from ref. 23.

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6.4 Maier-Saupe Orientation Distribution The Maier-Saupe ODF24 is defined as gMS (β) = c exp(p cos2 β) = c exp(−p sin2 β),

(6·15)

where the normalization constant c is given by c=

2 p1/2 , π 1/2 erfi p1/2

(6·16)

x erfi(x) = erf(i x)/ i is the imaginary error function, erf(x) = 2 π −1/2 0 t 2 dt, and c = c exp(p). In analogy to the Poisson kernel, (6·15) is written such that positive p describes parallel orientation (g peaked about β = 0) and negative p describes perpendicular orientation (g peaked about β = π/2). (6·15) is a fairly straightforward choice for an orientation distribution and has been used frequently before, e.g. in ref. 25 to describe the preferred orientation in system containing the tobacco-mosaic-virus, but all treatment of the general integral (3·5) has been numerical so far. While a fully closed form solution for the kernel can still not be given, the following series, which can be derived using the expansion exp(z cos φ) = ∞ n=−∞ In (z) cos(n φ), where In is the modified Bessel function of the first kind of order n, FMS (φ, φ ) = c exp[p(x 2 + y 2 /2)] I0 (2 p x y) I0 (p y 2 /2) +2

∞

I2n (2 p x y) In (p y 2 /2) , (6·17)

n=1

shows excellent convergence behavior, so that in typical situations a very small number of terms of the sum need to be evaluated, and the calculation of full fiber patterns using (6·17) becomes computationally feasible. For φ = π/2, (6·17) reduces to (6·18) F (φ, π/2) = c exp p2 sin2 φ I0 p2 sin2 φ . An example for perpendicular orientation, i.e., ODF peaked about β = π/2, that cannot be treated using Onsager’s ODF but can be treated using the Maier-Saupe ODF with negative parameter p is found for a-axis or b-axis orientation in polyethylene fibers,26 see Fig. 12.

7. Off-Axis Centered ODFs, Four-Point Patterns So far, we have only considered ODFs centered about β = 0 for parallel orientation (Fig. 2(a)) or ODFs centered about β = π/2 for perpendicular orientation (Fig. 2(b)). As sketched in Fig. 2(c), ODFs centered about oblique tilt-angles are also possible. SAXS from lamellar systems with such ODFs leads to characteristic four-point patterns. At first sight one might be tempted to create the ODF by shifting an existing ODF: ˜ g(β) ∼ g(β − β0 ).

(7·1)

However, it quickly becomes apparent that ODFs of the type (7·1) are difficult to normalize and in general not recommended. The correct approach is to use one of the analytic kernels


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Figure 12. Calculated WAXS fiber patterns for orthorhombic (a–c) and monoclinic (d) polyethylene with symmetry and orientation as indicated, using (5·12) and (5·15) with (5·5) and (6·17), radial integral width b = 0.15 nm−1 , axis labeling s in nm−1 , see ref. 26 for details.

discussed in section 6. as the ODF: ˜ g(β) = F (φ, β0 )

(7·2)

which, in view of (3·9), automatically ensures the correct normalization. An analytical kernel F (φ, φ ) corresponding to the ODF defined in (7·2) can usually not be found so that using Legendre expansions as discussed in section 4. becomes the most favorable approach, especially if the Legendre expansion coefficients of (7·2) can be given in analytical form which is the case for the kernel based Onsager’s ODF in view of (6·11).

8. Conclusions It was the goal of this review to show that a rigorous treatment of preferred orientation effects in SAXS and WAXS from natural and synthetic polymer fibers and other samples with fiber symmetry is possible. The preferred data analysis approach is the calculation of the complete fiber pattern, taking both the parameters of the individual structural units (crystal structures, crystallite or particle sizes and shapes) and of their orientation arrangement in the ensemble into account. Practical examples for the calculation of whole fiber patterns and their comparison to experimental scattering data were shown for natural collagen and cellulose fibers as well as fibers based on copolymers of polyethylene and polypropylene.

Acknowledgments The authors wish to thank Drs. Dufei Fang, Hongwen Zhou, and Lixia Rong for their assistance with the X-ray measurements and data analysis; Drs. Melvin Glimcher and Lila Graham of Harvard Medical School for providing the bone samples. We gratefully acknowledge financial support from the National Institutes of Health (BC) and the National Science Foundation (BH).

References 1. Fraser, R. D. B.; Macrae, T. P.; Miller, A.; Rowlands, R. J. “Digital processing of fiber diffraction patterns,” J. Appl. Cryst., 1976, 9, 81–94. 2. Plaetschke, R.; Ruland, W. “Preferred orientation of the internal structure of carbon layers in carbon-fibers,” Prog. Coll. Polym. Sci., 1985, 71, 140–144.

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3. Hermans, J. J.; Hermans, P. H.; Vermaas, D.; Weidinger, A. “Quantitative evaluation of orientation in cellulose fibres from the x-ray fibre diagram,” Rec. Trav. Chim. Pays-Bas-J. Roy. Neth. Chem. Soc., 1946, 65, 427–447. 4. Burger, C.; Ruland, W. “Evaluation of equatorial orientation distributions,” J. Appl. Cryst., 2006, 39, 889–891. 5. Kratky, O. “Zum Deformationsmechanismus der Faserstoffe, I.,” Kolloid Z., 1933, 64, 213–222. 6. Bracewell, R. The Fourier Transform and its Applications, 3rd ed., pp. 351–356 McGraw-Hill, New York, 1999. 7. Zuo, F.; Burger, C.; Hsiao, B. S.; Chen, H.; Chiu, D.; Lai, S.-Y. “Equatorial box patterns in WAXD during uniaxial deformation of olefin block copolymer fibers,” Macromolecules, 2009. submitted. 8. Seitsonen, S. “Determination of orientation distributions in fibres and sheets,” J. Appl. Cryst., 1968, 1, 82. 9. Seitsonen, S. “Calculation of orientation distributions in fibres and sheets,” J. Appl. Cryst., 1973, 6, 44–44. 10. Leadbetter, A. J.; Norris, E. K. “Distribution functions in 3 liquid-crystals from x-ray-diffraction measurements,” Mol. Phys., 1979, 38, 669–686. 11. Ruland, W.; Tompa, H. “Effect of preferred orientation on intensity distribution of (hk) interferences,” Acta Cryst. A, 1968, 24, 93–99. 12. Ruland, W. “Elimination of effect of orientation distributions in fiber diagrams,” Colloid Polym. Sci., 1977, 255, 833–836. 13. Chen, X. M.; Burger, C.; Fang, D.; Ruan, D.; Zhang, L.; Hsiao, B. S.; Chu, B. “X-ray studies of regenerated cellulose fibers wet spun from cotton linter pulp in naoh/thiourea aqueous solutions,” Polymer, 2006, 47, 2839–2848. 14. Chen, X. M.; Burger, C.; Wan, F.; Zhang, J.; Rong, L. X.; Hsiao, B. S.; Chu, B.; Cai, J.; Zhang, L. “Structure study of cellulose fibers wet-spun from environmentally friendly naoh/urea aqueous solutions,” Biomacromolecules, 2007, 8, 1918–1926. 15. Deas, H. D. “The diffraction of x-rays by a random assemblage of molecules having partial alignment,” Acta Cryst. A, 1952, 5, 542–546. 16. Lovell, R.; Mitchell, G. R. “Molecular-orientation distribution derived from an arbitrary reflection,” Acta Cryst. A, 1981, 37, 135–137. 17. Burger, C.; Zhou, H. W.; Sics, I.; Hsiao, B. S.; Chu, B.; Graham, L.; and Glimcher, M. J. “Smallangle x-ray scattering study of intramuscular fish bone: collagen fibril superstructure determined from equidistant meridional reflections,” J. Appl. Cryst., 2008, 41, 252–261. 18. Burger, C.; Zhou, H. W.; Wang, H.; Sics, I.; Hsiao, B. S.; Chu, B.; Graham, L.; and Glimcher, M. J. “Lateral packing of mineral crystals in bone collagen fibrils,” Biophysical Journal, 2008, 95, 1985–1992. 19. Zhou, H. W.; Burger, C.; Sics, I.; Hsiao, B. S.; Chu, B.; Graham, L.; and Glimcher, M. J. “Smallangle x-ray study of the three-dimensional collagen/mineral superstructure in intramuscular fish bone,” J. Appl. Cryst., 2007, 40, S666–S668. 20. Liu, X. D.; Ruland, W. “X-ray studies on the structure of polyacrylonitrile fibers,” Macromolecules, 1993, 26, 3030–3036. 21. Onsager, L. “The effects of shape on the interaction of colloidal particles,” Ann.NY Acad.Sci., 1949, 51, 627–659. 22. Holmes, K. C.; Leigh, J. B. “Effect of disorientation on intensity distribution of non-crystalline fibers. 1. Theory,” Acta Cryst. A, 1974, 30, 635–638. 23. Mao, Y.; Burger, C.; Thurman, D. W.; Tsou, A. H.; Hsiao, B. S. “Shear-induced crystallization of propylene-butylene random copolymer revealed by 2D wide-angle x-ray scattering analysis: experiment and simulation,” Macromolecules, 2009. submitted. 24. Maier, W.; Saupe, A. “Eine einfache molekular-statistische Theorie der nematischen kristallinflussigen Phase 1.,” Z. f. Naturforschung A, 1959, 14, 882–889.


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25. Oldenbourg, R.; Wen, X.; Meyer, R. B.; Caspar, D. L. D. “Orientational distribution function in nematic tobacco-mosaic-virus liquid-crystals measured by x-ray-diffraction,” Phys. Rev. Lett., 1988, 61, 1851–1854. 26. Keum, J. K.; Burger, C.; Zuo, F.; Hsiao, B. S. “Probing nucleation and growth behavior of twisted kebabs from shish scaffold in sheared polyethylene melts by in situ x-ray studies,” Polymer, 2007, 48, 4511–4519.

Polymer Reviews, 50:113–143, 2010 Copyright © Taylor & Francis Group, LLC ISSN: 1558-3724 print / 1558-3716 online DOI: 10.1080/15583721003698853

Reviews Polymeric Membranes for Chiral Separation of Pharmaceuticals and Chemicals AKON HIGUCHI,1,2,3 MIHO TAMAI,4 YI-AN KO,5 YOH-ICHI TAGAWA,4 YUAN-HSUAN WU,6 BENNY D. FREEMAN,6 JUN-TANG BING,7 YUNG CHANG,8 AND QING-DONG LING3,5 1

Department of Chemical and Materials Engineering, National Central University, No. 300 Jung da Rd., Chung-Li, Taoyuan 32001, Taiwan 2 Department of Reproduction, National Research Institute for Child Health and Development, 2-10-1 Okura, Setagaya-ku, Tokyo 157-8535, Japan 3 Cathay Medical Research Institute, Cathay General Hospital, No. 32, Ln 160, Jian-Cheng Road, Hsi-Chi City, Taipei 221, Taiwan 4 Graduate School of Bioscience and Biotechnology, Tokyo Institute of Technology, B-51 4259 Nagatsuta-cho, Midori-ku, Yokohama, Kanagawa 226-8501, Japan 5 Graduate Institute of Systems Biology and Bioinformatics, National Central University, No. 300 Jung da Rd., Chung-Li, Taoyuan 32001, Taiwan 6 Department of Chemical Engineering, The University of Texas at Austin Center for Energy and Environmental Resources, 10100 Burnet Road, Building 133, Austin, TX 78758, United States 7 Obstetrics & Gynecology Division, Li Shin Hospital, No. 77 Guang Tai Rd., Ping-Zhen, Taoyuan 32405, Taiwan 8 Department of Chemical Engineering, R&D Center for Membrane Technology, Chung Yuan Christian University, 200, Chung-Bei Rd., Chungli, Taoyuan 320, Taiwan The optical resolution or chiral separation of one specific enantiomer from others is in demand for the production of pharmaceuticals because many pharmaceuticals exist as stereoisomers, with each enantiomer having different biological activity. There is considerable demand for separation techniques appropriate for the large-scale resolution of chiral molecules. Chiral separation of racemic mixtures of pharmaceuticals through chiral or achiral polymeric membranes with or without a chiral selector represents a promising system for future commercial application. This article reviews several polymeric materials for the chiral separation of pharmaceuticals. Several chiral separation Received December 10, 2009; accepted January 11, 2010. Address correspondence to Akon Higuchi, Department of Chemical and Materials Engineering, National Central University, Jhongli, Taoyuan 32001, Taiwan. E-mail: [email protected]

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A. Higuchi et al. membranes were prepared from chiral polymers where enantioselectivity was generated from chiral carbons in the main chain. However, it is rather difficult to generate excellent chiral separation membranes from chiral polymers alone, because racemic penetrants mainly encounter the flexible side chains of the membrane polymers. Therefore, chiral separation membranes were also prepared using polymers with a chiral branch. Furthermore, several molecules have been used for specific interactions between the molecules and specific pharmaceuticals or drugs in chiral separation membranes. Cyclodextrins, crown ether derivatives, albumin, and DNA are commonly used as stereoselective ligands in chiral separation membranes. Finally, this article discusses future trends in polymeric materials for chiral separation membranes. Keywords chiral separation, optical resolution, polymeric membranes, pharmaceutical, dialysis

1. Introduction Terrestrial life utilizes only the L enantiomers of amino acids; this is known as the homochirality of life.1 The ability to optically resolve one specific enantiomer from others is important for the production of pharmaceuticals and food products2 because many pharmaceuticals, nutraceuticals, and agricultural chemicals have their stereoisomers, with each enantiomer having different biological activity. In some cases, only one of the isomers has the preferable activity, while the other chiral form may produce undesirable and/or toxic side effects. For example, it has been reported that the severe teratogenic side effects of the drug thalidomide may reside exclusively in the S-enantiomer.3 The (S,S)-diastereomer of ethambutol is effective in the treatment of tuberculosis, but the (R,R)-diastereomer can cause blurred vision, eye pain, and might result in complete blindness.4,5 The FDA and the Committee for Proprietary Medicinal Products (CPMP) now require pharmaceutical companies to produce only a single enantiomer as the therapeutic agent or to clearly demonstrate the appropriateness of using a racemic mixture.3,6,7 This requirement has resulted in considerable demand for separation techniques appropriate for the large-scale resolution (purification) of chiral molecules.3 Worldwide, the market for chiral fine chemicals sold as single enantiomers was $6.63 billion in 2000, and the market is expected to grow at a rate of 13.2% annually, reaching $16.0 billion in 2007.8 There is a growing need for separation techniques appropriate for the large-scale resolution of chiral molecules, although many single enantiomer drugs are produced by stereoselective synthesis. In particular, relatively low-cost pharmaceuticals cannot be produced by stereoselective synthesis. The most widely used methods for the separation of racemic mixtures are diastereomeric salt crystallization,9,10 column chromatography,11–15 and stereoselective enzyme catalysis.16,17 Liquid membranes with immobilized chiral ligands have also been used for chiral separation,3,18–20 although these techniques could be difficult to apply in commercial systems because of the instability of the liquid membranes. An alternative approach is to use an affinity ultrafiltration system in which a large stereoselective ligand is added to the bulk solution to selectively bind, and thus retain, one of the stereoisomers.3 Chiral separation of pharmaceuticals through polymeric membranes with an immobilized chiral selector could be very promising for commercial systems in the future. This paper summarizes polymeric materials for the chiral separation of pharmaceuticals and discusses the future trend of polymeric materials for chiral separation membranes.

2. Permeation and Selective Theory (Analysis) for Chiral Separation Chiral separation membranes preferentially allow a specific enantiomer to adsorb to or diffuse into the membrane. This specificity is generated by chiral recognition sites in the

Membranes for Chiral Separation

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membranes such as chiral side chains, chiral backbones, or immobilized chiral selectors in polymeric chiral separation membranes. These enantioselective membranes act as selective barriers in the resolution process, and they preferentially transport one enantiomer due to the stereospecific interaction between the enantiomer and chiral recognition sites.21 The transport process of enantiomers through the membranes can be categorized as filtration, dialysis, electrodialysis, and pervaporation, depending on the main driving force of the permeation of enantiomers through the membranes, i.e., pressure gradient, concentration difference, electric field difference, or vapor difference, respectively. The flux of enantiomers, J i , can be defined in the dialysis membranes and filtration membranes as follows: Ji = Qi /At,

(1)

where Qi is the mass of solute i (R-enantiomer or S-enantiomer) allowed to permeate for a given time t, and A is the effective membrane area. The permeability coefficient for the dialysis process with no electric field gradient through the membrane is defined as Pi = Ji L/(Cf − Cp ),

(2)

where Pi is the permeation coefficient of the solute i, L is the membrane thickness, and Cf and Cp refer to the concentrations in the feed solution (solution at the upstream side) and permeate solution (solution at downstream side), respectively. A solution-diffusion mechanism determines the permeation of enantiomers through the homogeneous dense membranes and is described as follows: P = DS,

(3)

where D and S refer to the diffusion coefficient and sorption coefficient (solubility), respectively. The diffusion coefficient D is a kinetically determined coefficient influenced by the membrane and enantiomer characteristics and the interaction between the two. The sorption coefficient is a thermodynamically determined parameter defined as the ratio of the concentration in the membrane (Cm ) to that in the solution (Co ), as shown in Eq. [4]. S = Cm /Co

(4)

The separation factor α is calculated from the concentration of the upstream side and downstream side, and is defined as follows: α = (Cp (R)/Cp (S)/(Cf (R)/Cf (S))

(5)

α = (Cp (S)/Cp (R)/(Cf (S)/Cf (R)),

(6)

or

where Cf (R) and Cf (S) are the concentrations of the R-enantiomer and S-enantiomer in the feed solution (solution at upstream side), respectively. Cp (R) and Cp (S) are the concentrations of the R-enantiomer and S-enantiomer in the permeate solution (solution at downstream side), respectively. The concentrations in the upstream side, Cf (S) and Cf (R),

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are the same in some cases. In this case, α reduces to; a = Cp (S)/Cp (R) or Cp (R)/Cp (S).

(7)

The enantioselectivity of transport through the membrane can be divided into two factors, solubility selectivity and diffusion selectivity. α = P (R)/P (S) = D(R)S(R)/[D(S)S(S)]

(8)

α = P (S)/P (R) = D(S)S(S)/[D(R)S(R)],

(9)

or

where D(R) and D(S) are the diffusion coefficients of the R-enantiomer and S-enantiomer, respectively. S(R) and S(S) are the solubility coefficients of the R-enantiomer and S-enantiomer, respectively. The chiral selectivity of transport through membranes is also evaluated in terms of the enantiomeric excess (ee) of permeates.21 The ee value is defined as the ratio of the concentration difference over the total concentration of both enantiomers in the permeate.22 ee = [Cp (R) − Cp (S)]/[Cp (R) + Cp (S)]

(10)

ee = [Cp (S) − Cp (R)]/[Cp (S) + Cp (R)].

(11)

or

When the concentrations in the feed side Cf (S) and Cf (R) are the same, the separation factor can be calculated from ee using the following equation: α = (1 + ee)/(1 − ee).

(12)

3. Resolution Mechanism through the Membranes The mechanism of chiral separation on polymeric membranes can be categorized as diffusion-selective membranes and sorption-selective membranes.23 Diffusion-selective membranes are usually made of an intrinsically chiral polymer without specific foreign chiral selectors, for example albumin or other proteins, chiral polysaccharide chains or segments, DNA, crown ether derivatives, and oligopeptides. Sorption-selective membranes can be made by embedding or immobilizing chiral selectors in polymer membranes or on the membrane surfaces and these membranes have less selective diffusion but show highly selective sorption. Examples of chiral selectors include crown ether derivatives,24 cyclodextrin, albumin and other proteins, and DNA. In most cases of chiral separation through polymeric membranes, there is a trade-off between diffusion selectivity and solution selectivity; the membranes showing diffusion selectivity for one chiral isomer have sorption selectivity for the opposite chiral isomer. Therefore, the permeation selectivity is determined by whichever selectivity is higher, sorption selectivity or diffusion selectivity. In general, chiral separation membranes with sorption selectivity should be designed with no diffusion selectivity, and vice versa. One method that can be used to reduce the diffusion selectivity of sorption selective concentration-driven permeation chiral separation membranes (dialysis membranes) is to apply an electrical potential that makes the concentration-driven permeation of chiral pharmaceuticals or chemicals a potential-driven permeation. Potentialdriven permeation generally results in the same diffusion coefficient for each isomer.


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The driving force for the permeation and separation of chiral pharmaceuticals and chemicals is the concentration difference between feed and permeate solutions for the dialysis method, and a pressure-driven force for ultrafiltration and nanofiltration. Most studies of chiral separation membranes have been performed in dialysis membranes. The main disadvantages of the dialysis method are that the concentration of the final product is more dilute than that of the feed solution, and that permeation is extremely slow. Due to these disadvantages, chiral separation in industrial applications may require ultrafiltration or nanofiltration through chiral separation membranes. In addition to dialysis and filtration, pervaporation via membranes is also useful for the chiral separation process, where the driving force of the permeation is a vapor pressure difference. Shinohara and Aoki et al. reported chiral separation of racemates of 1,3-butanediol, 2-butanol, and their derivatives by pervaporation through a (+)-poly{1[dimethyl(10-pinanyl)silyl]-1-propyne} membrane.25 They reported a permeation rate of 1.19 × 10−3 gm/h and 41.7%ee for racemic 1,3-butanediol. Enantioselective vapor permeation is also effective for chiral separation if the racemic compounds are more or less volatile. Only a few examples have been reported of chiral separation of pharmaceuticals and racemates using the pervaporation method25 although it is expected that this technology will be used more often in the future.

4. Chiral Separation Membranes Prepared from the Chiral Main Chain of Polymers Several chiral separation membranes were prepared from chiral polymers where enantioselectivity was generated from chiral carbons in the main chain. Poly(γ -methyl-Lglutamate),26–28 alginate,29,30 chitosan,29 cellulose,31 and their derivatives (see Fig. 1) are typically used as chiral polymers for the preparation of chiral separation membranes. Examples of chiral separation membranes prepared from a chiral polymer main chain are summarized in Tables 1 and 2, and are reviewed as follows.

Figure 1. Chemical scheme of PMLG (a), sodium alginate (b), cellulose (c) and chitosan (d) used as chiral polymers for preparation of chiral separation membranes.

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a

Tryptophan Tryptophan Tryptophan Tryptophan Tyrosine Tryptophan Tryptophane Tryptophan Tryptophan Phenylalanine Tryptophan Tryptophan Tryptophan Tryptophan Tryptophan Tryptophan Tryptophan Ac-tryptophan

Targeted molecule

Separation factor 1.4 3.0 2.6 60.0 5.0 2.6 3.4 3.4 99.0 1.1 8.0 14.0 7.0 1.4 1.9 1.1 1.2 2.0

Flux or permeability coefficient (methoda,b) J = 10−6 gm/m2h atm (UF) P = 8.4 × 10−6 g m−1/h (ED) P = 4.2 × 10−8 cm2s−1 (D) P = 4 × 10−7 mol/m2h (D) P = 10−5 mol/m2h (D) P = 2.2 × 10−8 m2s−1 (D) J = 7.5 mg/m2h (UF) J = 24.8 mg/m2h (UF) J = 6.4 mg/m2h (UF) J = 2.11 × 10−12 m2/sec (UF) (UF) (UF) (UF) P = 5.02 × 10−9 cm2/sec (D) P = 1.87 × 10−9 cm2/sec (D) P = 6.04 × 10−9 cm2/sec (D) P = 4.71 × 10−9 cm2/sec (D) P = 4.9 × 10−6 cm/sec (ED)

Method; D indicates dialysis, ED indicates electro dialysis, UF indicates ultrafiltration.

PMLG derivatives PMLG derivatives PMLG derivatives PMLG derivatives PMLG derivatives Crosslinked PMLG Crosslinked alginate Crosslinked alginate Crosslinked chitosan Crosslinked L-phenylalanine Plasma polymerized l-menthol Plasma polymerized d-camphor Plasma polymerized l-menthol Plasma polymerized terpene Plasma polymerized terpene Plasma polymerized terpene Plasma polymerized terpene Polyamide

Chiral sites of membranes

Table 1 Chiral separation through polymeric membranes having chiral main chain

27 26 26 28 28 71 29 30 72 34 73 74 74 75 75 75 75 76

Ref.


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Table 2 Chiral separation through polymeric membranes having helical structure of main chain Chiral sites of membranesa Poly(OPSPA) Poly(OPSPA) Poly(CPSPA) Poly(HPSPA) Poly(HPSPA) Copoly(CHPSPA) Copoly(CHPSPA) Copoly(PSDPA) Copoly(PSDPA) Copoly(PSDPA) Cellulose acetate butyrate MTSPOE

Targeted molecule

Flux or permeability coefficient (methodb)

Phenylalanine Tryptophan Phenylalanine Phenylalanine Phenylalanine Phenylalanine Phenylalanine Tryptophan Tryptophan Tryptophan 2-phenyl-1-propanol

P = 1.11 × 10−14 m2/h (D) P = 1.34 × 10−14 m2/h (D) P = 4.34 × 10−14 m2/h (D) P = 2.9 × 10−14 m2/h (D) P = 3.02 × 10−14 m2/h (D) P = 3.94 × 10−14 m2/h (D) P = 3.90 × 10−14 m2/h (D) P = 5.51 × 10−12 m2/h (D) P = 5.15 × 10−12 m2/h (D) P = 3.60 × 10−12 m2/h (D) J = 1.19 × 10−6 g/hr atmcm2 (UF) P = 13.72 m2h−1 (UF)

Separation factor Ref. 640 2.9 7.9 2.6 2.1 4.1 3.5 1.4 1.6 3.4 19.0

37 37 67 67 67 67 67 66 66 66 31

1.5

77

a Poly(OPSPA); Poly(p-(oligopinanylsiloxanyl)phenylacetylene), Poly(CPSPA); Poly(chiral pinanylsiloxanyl)phenylacetylene), Poly(HPSPA); Poly(hydroxylpinanylsiloxanyl)phenylacetylene), Copoly(CHPSPA); Copoly(chiral hydroxylpinanylsiloxanyl)phenylacetylene), Copoly(PSDPA); Copoly(pinanylsilyl)diphenylacetylene), MTSPOE; 1,2-bis(2-methyl-1-triethylsiloxy-1-propeny loxy)ethane derivatives. b Method; D indicates dialysis, UF indicates ultrafiltration.

Aoki et al. prepared chiral separation membranes from poly(γ -methyl-L-glutamate) (PMLG) chiral main chains with achiral side chains of 3-(pentamethyldisiloxanyl)propyl groups.27 The enantioselectivity and permeation rate through the modified PMLG membranes were higher than those through unmodified PMLG membranes by ultrafiltration. The enantioselective permeation continued for more than 160 hrs. Increasing the disiloxane side chain content increased the permeation rate while maintaining the enantioselectivity. The α-helix content of the membranes did not have a significant effect on the enantioselectivity or permeation rate. This result indicates that the higher-order structure did not affect the enantioselective permeation. The enantioselectivity was ascribed to the asymmetric carbons of the main chain rather than to the α-helix conformation of the membrane materials. The adsorption enantioselectivity of this membrane favored D(R)-tryptophan, while the diffusion and permeation selectivity favored L(S)-tryptophan. Therefore, enantioselective permeation was caused by the suppression of D-tryptophan. The authors of this study concluded that the siloxane region was small enough for the asymmetric centers in the main chain to interact with the permeating solutes and to enantioselectively recognize the permeating solute.27 Thoelen used poly(γ -methyl-L-glutamate) (PMLG) membranes transesterified with R 30 for the chiral separation of tryptophan.26 The membranes showed Igepal and Brij enantioselectivity towards tryptophan in pressure driven permeation. An initial enantiomeric excess of 20% was obtained, but a decline in selectivity was observed during the course of the permeation experiment. This decrease was ascribed to the saturation of the enantioselective recognition sites in the membrane based on the mechanism of affinity membranes.

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Changing the driving force into an electrical potential difference solved this problem, resulting in a constant separation factor of 3 for PMLG membranes in the separation of acethyl-tryptophan. Based on these results, electrodialysis with membranes showing affinity to specific enantiomers appears to be a highly promising membrane process for chiral separation, even though the membranes do not show steady state enantioseparation in conventional concentration-driven or pressure-driven membrane processes.26 Photocontrol of membrane chiral recognition has also been developed.32 Yashima et al. prepared membranes of cellulose and amylose derivatives bearing a photoresponsive [4-(phenylazo)phenyl]carbamate residue incorporated at the 2,3,6-,6-, or 2,3-positions of the glucose units.32 Enantioselective adsorption of several neutral racemates (i.e., trans2,3-diphenyloxirane, 1,2,2,2-tetraphenylethanol, hydrochloric salt of oxprenolol, and 1-(9anthryl)-2,2,2-trifluoroethanol) on the photoresponsive membranes was investigated during the course of trans-cis isomerization of the pendant azobenzene residues. The chiral recognition ability was influenced by the trans or cis content, and the trans isomers of the polysaccharide derivatives showed higher enantioselectivity than the cis isomers. The photo-responsiveness of the chiral recognition of these polymers was discussed on the basis of circular dichroism (CD) data, lH nuclear magnetic resonance (NMR) spectroscopic data, and molecular modeling.32 Tris(phenylcarbamate)s of cellulose and amylose were reported to possess the conformations of left-handed 3-fold (3/2) and 4-fold (4/1) helices, respectively, on the basis of X-ray analysis.32,33 Therefore, the photoresponsive cellulose membranes bearing the [4(phenylazo)phenyl]carbamate residue probably have similar conformations.32 According to this hypothesis, the intramolecular hydrogen bonds along the polysaccharide backbone can participate in the formation of the rigid conformations, which should only be possible for the trans isomers. From the structures of trans- and cis- photoresponsive cellulose having [4-(phenylazo)phenyl]carbamate calculated by molecular mechanics, the pendant [4-(phenylazo)phenyl] carbamate residues in the trans-conformation were arranged regularly, while those of the cis-conformation were not because of the bent structure.32 Moreover, the carbamate residues of the photoresponsive cellulose in the cis-conformation are unfavorably concealed behind the bent cis-azobenzene moieties, so that the carbamate residues are not able to interact effectively with racemates.32 These molecular modeling results explain the decrease in adsorption ability and the lower chiral recognition ability of the cis-conformation of the photoresponsive cellulose membranes. Kim et al. prepared crosslinked sodium alginate and chitosan membranes with glutaraldehyde for chiral separation of racemic tryptophan and tyrosine by ultrafiltration.29 Both crosslinked sodium alginate and chitosan membranes were found to be applicable for the chiral separation of racemic tryptophan and tyrosine by a pressure driven process. When a crosslinked chitosan membrane with a 70% swelling index was used for the chiral separation of a racemic tryptophan mixture (0.49 mmol/l aqueous solution), over 98% of enantiomeric excess (e.e.) and 6.4 mg/(m2h) of flux were obtained.29 The presence of five chiral carbons located on the ring structure of sodium alginate and chitosan seemed to induce a chiral environment in the membrane, which is similar to the function of cellulose and its derivatives, making the membrane enantioselective. With an increasing degree of crosslinking, the membrane showed higher enantioselectivity by increasing the interaction between the chiral environment of the membrane and penetrating chiral isomers.29 The other factors that could decrease the intermolecular interaction between the membrane and solutes, such as an increase in operating pressure and an increase in the concentration of the feed solution, acted against the enantioselectivity.29


121

Masawaki et al. prepared crosslinked L(S)-phenylalanine with glutaraldehyde, and UF membranes were prepared from the blend of crosslinked L-phenylalanine and polysulfone.34 The membrane showed diffusion selectivity of D(R)-phenylalanine, while sorption selectivity of L-phenylalanine was found in concentration-driven permeation. In total, the membrane showed preferential permeation of D-phenylalanine over L-phenylalanine due to diffusion selectivity, and the separation factor was reported to be 1.25 to 4.0 in both concentration-driven and pressure-driven permeation.34

5. Chiral Separation Membranes Prepared from Polymers with a Chiral Branch It is rather difficult to generate excellent chiral separation membranes from chiral polymers alone, because racemic penetrants mainly encounter the flexible side chains of the membrane polymers. Therefore, chiral separation membranes were prepared using polymers with a chiral branch. Some examples of chiral separation membranes prepared from polymers with a chiral branch are shown in Table 3 and reviewed as follows. Lee and Frank prepared polypeptide-modified poly(vinylidene fluoride) (PVDF) membranes for the separation of chiral molecules in ultrafiltration.35 Poly(γ -benzyl-Lglutamates) (PBLG) were vapor-deposited on the PVDF membranes, and the PBLG on PVDF membranes were modified through debenzylation or an ester exchange reaction to produce poly(L-glutamic acid) (PLGA) and polyglutamates with triethylene glycol monomethyl ether side chains (PLTEG). The enantioselectivities for chiral α-amino acids (tryptophan, phenylalanine and tyrosine) and chiral drugs (propranolol, atenolol, and ibuprofen) were measured by concentration-driven experiments, and were found to range from 1.04 to 1.47.35 The selectivity increased with the helical content of PLGA immobilized on PVDF membranes. The enantioselectivity was observed to be higher for chemically grafted polypeptide-modified PVDF membranes compared to polypeptidephysisorbed PVDF membranes. This difference is attributed to the higher molecular weight and density of the polypeptide chains, which enhance the interaction between the chiral compounds and the surface-bound polypeptides.35 Gumi et al. prepared chiral separation membranes from polysulfone grafted with N-dodecyl-4(R)-hydroxy-L-proline as a chiral selector.36 The membranes prepared from the chiral derivatized polysulfone showed a separation factor of 1.1 in the dialysis permeation of racemic propranol, where S-propranol preferentially permeated through the membranes.36 Aoki et al. prepared chiral separation membranes from poly[p-(oligopinanylsiloxanyl) phenylacetylene]s with a chiral helical main chain. Membranes with a high chiral helicity in the main chain showed good enantioselectivity for racemic phenylalanine, tryptophan, valine, and 2-phenethyl alcohol based on diffusion selectivity, while there was almost no sorption selectivity.37 Chiral separation of racemic amino acids through polymeric membranes with saccharide side chains was also reported. Satoh prepared chiral separation membranes of polyacrylonitrile-graft-(1->6)-2,5-anhydro-3,4-di-O-methyl-D-glucitol.38 The permeation rates of the amino acids increased in the order of phenylglycine < phenylalnine < tryptophan, according to the molecular size of the permeating solutes. The permeation rate of the D-isomer was found to be higher than that of the L-isomer for the amino acids that were evaluated, although the L-isomer was more highly adsorbed than the D-isomer. Therefore, the chiral separation by these membranes was caused by diffusion selectivity.

122 Tryptophan, tyrosine, serine Tryptophan Phenylalanine Tyrosine Propranol Atenolol Ibuprofen Glutamic acid

Tryptophan Phenylalanine 1,3-butanediol 2-butanol Tryptophan (D) Phenylalanine (D) 2-BuOH 2-BuOH 1,3-Butanediol Phenylglycine perchlorate Phenylalanine perchlorate

Targeted molecule

(D) P = 1.95 × 10−7 cm2/s (D) P = 1.35 × 10−7 cm2/s (D) P = 1.90 × 10−7 cm2/s (D) P = 1.87 × 10−7 cm2/s (D) P = 1.56 × 10−7 cm2/s (D) P = 2.39 × 10−7 cm2/s (D)

P = 1.34 × 10−14 m2/h (D) P = 1.11 × 10−14 m2/h (D) P = 1.19 × 10−3 g/mh (EV) P = 8.37 × 10−4 g/mh (EV) P = 4.72 × 10−6 gm/m2h (D) P = 1.65 × 10−6 gm/m2h (D) P = 837 × 10−6 gm/m2h (D) P = 8.37 × 10−4 gm/m2h (PV) P = 1.19 × 10−4 gm/m2h (PV) P = 4.91 × 10−7 cm2/min (D) P = 4.01 × 10−7 cm2/min (D)


1.5 1.3 1.1 1.2 1.1 1.2 1.1

2.9 640.0 2.4 2.6 2.2 3.4 2.6 2.6 2.4 1.2 1.1 1.1

Separation factor

37 37 25 25 78 78 78 25 25 38 38 38 79 35 35 35 35 35 35 36

Ref.

a Poly(DPSPP); Poly[(−)-1-p-[dimethyl(10-pinanyl)silyl]phenyl-2-phenylacetylene], Poly(DPSP); Poly{1-dimethyl(10-pinanyl)sily]-1-propyne}, PANg-D-glucitol; Polyacrylonitrile-graft-(1->6)-2,5-anhydro-D-glucitol, PMLG; Poly(L-glutamate), PSf; Polysulfone. b Method; D indicates dialysis, ED indicates electro dialysis, PV indicates pervaporation, UF indicates ultrafiltration.

Poly(DPSPP) Poly(DPSPP) Poly(DPSPP) Poly(DPSPP) Poly(DPSP) Poly(DPSP) Poly(DPSP) Poly(DPSP) Poly(DPSP) PAN-g-D-glucitol PAN-g-D-glucitol PAN PMLG derivatives PMLG derivatives PMLG derivatives PMLG derivatives PMLG derivatives PMLG derivatives PMLG derivatives PSf having myrtenal-derived terpenoid

Chiral sites of membranesa

Table 3 Chiral separation through polymeric membranes having chiral side chain


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6. Chiral Separation Membranes with Immobilized Stereoselective Ligands as Chiral Selectors and Recognition Sites Several groups have used specific interactions between large biological molecules and specific pharmaceuticals or drugs for chiral separation. Cyclodextrins39–45 and crown ether derivatives24 (see Fig. 2) are commonly used as stereoselective ligands in chiral separation membranes. The idea of using affinity binding of specific enantiomers by large biological macromolecules such as proteins and DNA in ultrafiltration dates back to the early work by Higuchi et al.46 on the purification of a tryptophan isomer by exploiting its binding to albumin on the membrane. Chiral separation using membranes with immobilized large molecules as chiral selectors can work by three mechanisms: (1) affinity membranes, (2) selective sorption membranes, and (3) selective diffusion membranes. The chiral separation mechanism of affinity membranes is based on the selective adsorption of specific isomers compared to the other isomers. Since these membranes cannot obtain steady state chiral separation, chiral separation work using affinity membranes was not included in this review. Several examples of chiral separation membranes with immobilized stereoselective ligands as chiral selectors and recognition sites based on selective sorption and/or diffusion membranes are summarized in Tables 4 and 5, and described in detail in the following sections. 6.1 Immobilized Cyclodextrin Membranes Native cyclodextrins (CD) are cyclic oligosaccharides consisting of six to eight D-(+)glucopyranose units that provide three-point interactions for the chiral recognition of various organic molecules by hydrophobic interaction with the CD cavity and two hydrogen bonds

Figure 2. Chemical scheme of alpha-cyclodextrin (a), beta-cyclodextrin (b), gamma-cyclodextrin (c), 18-crown-6 (d), dibenzo-18-crown-6 (e), and diaza-18-crown-6 (f) used as stereoselective ligands in chiral separation membranes.

124 Flux or permeability coefficient (methoda) (ED) P = 2.94 × 10−7 cm2s−1 (D) P = 0.249 × 10−7 cm2s−1 (D) P = 2.70 × 10−7 cm2s−1 (D) (D) P = 1.53 × 10−7 cm2/s (D) P = 1.66 × 10−7 cm2/s (D) P = 0.029 mg/cm2h (D) J = 6.7 × 10−4 mol/m2h (D) (D) (D) P = 1.75 × 10−8 m/s (D)

Targeted molecule D-4-hydroxyphenylglycine Phenylalanine Tryptophan Histidine Chlorthalidone Phenylalanine Tryptophan Tryptophan Lactic acid Propranolol Propranolol Propranolol

Method; D indicates dialysis,. ED indicates electro dialysis, UF indicates ultrafiltration.

β-cyclodextrin β-cyclodextrin β-cyclodextrin β-cyclodextrin β-cyclodextrin β-cyclodextrin β-cyclodextrin β-cyclodextrin N-3,5-dinitrobenzoyl-L-alanine-octylester N-hexadecyl-L-hydroxyproline L-di-n-dodecyltartrate N-dodecyl-4(R)-hydroxy-L-proline

Chiral sites of materials in membranes

Table 4 Chiral separation through polymeric membranes having small chiral molecules

1.3 1.4 1.3 1.2 1.2 1.3 1.1 1.5 15.9 1.0 1.0 1.1

Separation factor

80 41 41 41 39 23 42 40 81 82 82 36

Ref.


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Table 5 Chiral separation through polymeric membranes having large chiral molecules Chiral sites of materials in membranesa Crosslinked BSA Crosslinked BSA Crosslinked BSA Crosslinked BSA DNA-cellulose DNA-cellulose DNA-cellulose DNA-cellulose DNA DNA DNA-chitosan DNA-chitosan D-amino acid oxidase apoenzyme a

Targeted molecule


Separation factor

Ref.

Phenylalanine Leucine Tryptophan Tryptophan Tryptophan Tryptophan Phenylalanine Phenylalanine Phenylglycine Phenylalanine Phenylalanine Phenylalanine Phenylalanine

1.5 m3/m2 day kg (UF) 1.5 m3/m2 day kg (UF) 1.5 m3/m2 day kg (UF) (UF) 6.5 × 10−3 m3/m2 day kg (UF) (UF) 6.5 × 10−3 m3/m2 day kg (UF) 6.5 × 10−3 m3/m2 day kg (UF) 6.5 × 10−3 m3/m2 day kg (UF) (UF) 1.3 × 10−3 m3/m2 day kg (UF) 1.7 × 10−3 m3/m2 day kg (UF) 2.2 × 10−5 cm2/sec (D)

1.3 1.1 1.4 8.7 1.2 1.3 1.6 1.6 1.1 1.2 2.7 1.8 3.3

48 48 48 83 2 2 2 55 2 51 56 56 49

BSA; bovine serum albumin. Method; D indicates dialysis, UF indicates ultrafiltration.

b

with the hydroxyl groups at the opening of the CD.43 Xiao and Chung prepared immobilized β-cyclodextrin (CD) membranes using commercially available cellulose (CA) dialysis membranes with a molecular weight cutoff (MWCO) of 1000 and investigated the chiral separation of a racemic tryptophan solution through the immobilized CD membranes.42 Their dialysis transport experiments showed that D-tryptophan preferentially permeated through the immobilized CD membranes, obtaining an enantioselectivity of around 1.10. Note that the L-tryptophan binds CD at a higher affinity (binding constant of 0.043 mM−1 in CD solution) than D-tryptophan (0.031 mM−1 in CD solution).42 This means that the chiral separation of tryptophan is based on diffusion selectivity in the immobilized CD membranes.42 Compared with other chiral selector-immobilized membranes, CD-functionalized membranes have a lower cost and might have wider applicability and higher tolerance in various environments. However, chiral separation through immobilized CD membranes has the disadvantage of low selectivity because native cyclodextrins have limited chiral recognition ability and limited flexibility, which are important to enable interaction with the enantiomers. Chemical modification of CD and the preparation of CD derivatives might be an interesting topic of research, and chiral separation can be performed using immobilized CD-derivative membranes. Xiao et al. prepared acetylated-β-cyclodextrinimmobilized CA dialysis membranes for chiral separation of racemic tryptophan.23 The acetylated CD-immobilized membrane exhibits enantioselectivity in the range of 1.26–1.33 depending on the acetylation time, while native CD-immobilized membranes only show an enantioselectivity of 1.11. The improvement in enantioselectivity after acetylation was mainly attributed to the improved discrimination ability of acetylated CD and the decrease

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in membrane pore size.23 From molecular modeling simulations, the acetylation of hydroxyl groups was suggested to result in a CD conformation with toroidal distortions, creating a greater steric hindrance for phenylalanine interaction. As a result, compared to the original CD, the acetylated CD has less effective binding but better discrimination of enantiomers. Molecular modeling simulations also indicated that the energy drop was only 3 kcal/mol between different enantiomers before and after the binding of phenylalanine with an unmodified CD, while the energy drop increased to 10 kcal/mol when the acetylated CD was employed as the chiral selector, which contributed to the higher recognition of L-phenylalanine as a chiral selector.23 Ishihara prepared a copolymer of acrylnitrile (PAN) and aminoethylated β-CD and used it to make chiral separation membranes.41 The membranes showed preferential permeation of L-phenylalanine over D-phenylalanine due to diffusion selectivity with a separation factor of 1.40, while the membranes showed preferential sorption of D-phenylalanine over L-phenylalanine, the opposite tendency to that of native CD and acetylated CD. Therefore, these results suggest that the selective sorption of CD to specific enantiomers such as the R-isomer or L-isomer can change depending on the chemical modification of CD. The appropriate chemical modification of CD will likely be important for the development of chiral separation membranes with immobilized CD derivatives. 6.2 Immobilized Albumin Membranes Serum albumin is reported to have a high-affinity binding site for L-tryptophan. Its binding constant was reported to be 4.4 × 104 M−1 by Kragh-Hansen,47 and weakly bound Dtryptophan has been reported to displace L-tryptophan.48 This evidence prompted Higuchi et al. to develop a method for chiral separation of racemic amino acids using ultrafiltration of solutions of various racemic amino acids through immobilized serum albumin membranes, making use of the binding site of bovine serum albumin (BSA) to the L-isomer.46,48 These authors reported that the immobilized BSA membranes efficiently demonstrated chiral separation of not only racemic tryptophan but also leucine and phenylalanine.48 The target molecule for chiral separation through the immobilized albumin membranes should be amino acids with aromatic or hydrophobic side groups because of the specific binding site characteristics of albumin. The chiral separation of low molecular weight pharmaceuticals such as ibuprofen using the immobilized BSA membranes should be an interesting research topic in the future. 6.3 Immobilized Apoenzyme Membranes Enzymes are well-known to have high substrate selectivity, understood with the lock and key model. Enzymes could be a good selection for the recognition of chiral molecules in chiral separation membranes. However, enzymes not only recognize the specific enantiomer, but also catalyze a chemical reaction on the molecule. Since apoenzyme requires a cofactor to perform the enzymatic reaction, unwanted chemical conversion of the substrate molecule in enzyme-based separation can be circumvented when using this molecular-recognition agent. Lakshmi and Martin investigated enantioseparation using apoenzymes immobilized in porous polymeric membranes.49 They found that the membranes selectively transport the specific substrate molecule without the unwanted chemical conversion of the molecule. When D-amino acid oxidase apoenzyme was loaded in the membranes, facilitated transport of D-phenylalanine relative to L-phenylalanine was observed, with the maximum D- versus L-penylalanine selectivity coefficient reported to be from 3.3 to 4.9.49


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6.4 Immobilized Antibody Membranes Antibodies can specifically bind to a variety of targets, known as antigens, depending on the variants of antibodies. The interaction between the antibody and antigen is extremely high, and allows the antibody to identify and bind only their unique antigen in the midst of the millions of different molecules from an induced fit binding.50 Recognition of the antigen by the antibody could be available for the recognition of chiral molecules in chiral separation membranes. However, the binding constants for the antibody are generally too large to bind with the specific antigen reversibly, which is undesirable because the chiral separation membrane must ultimately release the target molecules so that they can be collected in the permeate solution. Lee et al.50 solved this problem by tuning the binding constant of the antibody with the addition of dimethyl sulfoxide (DMSO) to the racemic feed solution and the permeate solution. They prepared chiral separation membranes immobilized antibody for 4-[3-(4fluorophenyl)-2-hydroxy-1-[1,2,4]triazol-1-yl-propyl]-benzonitrile, which is a drug serving as an inhibitor of aromatase enzyme activity.50 This molecule has two chiral centers and thus four stereoisomers: RR, SS, SR, and RS. The antibody used selectively binds the RS relative to the SR enantiomer, and the membranes based on the Fab fragment of this antibody were used to separate this enantiomeric pair. Nanopore alumina membranes were used as host membranes for immobilization of the anti-RS molecules. The membranes having pores with diameters of 20 and 35 nm were used for these studies.50 A sol-gel template synthesis method was used to deposit silica nanotubes within the pores of the alumina membranes. The inside walls of the silica nanotubes were then reacted with a silane that terminated in an aldehyde functional group, which reacts spontaneously with free amino sites on the antibody they used.50 An average separation factor of 2.0 was obtained for the membranes prepared from the alumina membranes with a pore diameter of 35 nm, when both the RS and SR enantiomers were dissolved in 10% DMSO-phosphate buffer saline (PBS) buffer at pH 8.5 as a feed solution. When the effect of the concentration of the enantiomers in the racemic feed solution on the flux was investigated, they observed a Langmuirian-shaped flux curve for the RS enantiomer but not for the SR enantiomer, which suggests a facilitated transport of the RS enantiomer.50 The selectivity in a facilitated transport process can be increased by shutting down the nonfacilitated (diffusional) transport of the unwanted chemical species. This can be accomplished by decreasing the pore size in the membrane in porous membranes. When Lee et al. used alumina membranes having pores 20 nm in diameter as base membranes for the immobilization of the antibody, the separation factor was reported to be increased to 4.5.50 The porous polymeric membranes immobilized antibodies could be one of the candidates for the chiral separation membranes immobilized proteins. 6.5 Immobilized DNA Membranes DNA has been discovered to have several novel functions aside from carrying genetic information, such as electron transfer and DNA enzymatic activity.51 DNA can also intercalate some enantiomers with a binding constant that depends on the stereoenantiomer.52 DNA is contained in several common protein preparations as an impurity on the order of ppb.53 Therefore, Higuchi et al. investigated the effect of the DNA in the albumin solution on the chiral separation of amino acids by ultrafiltration in 2002.54 These results generated the idea that DNA has a binding site for enantiomers, with the binding constant

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depending on the stereoenantiomer. Higuchi et al. established that DNA can be used as a biomacromolecular chiral selector in chiral separation technology.52–56 When affinity ultrafiltration experiments were performed for the chiral separation of racemic phenylalanine using DNA as chiral selectors in the feed solution with a DNA concentration less than 0.5 ppm, D(R)-phenylalanine was preferentially present in the collected permeate solution, although the separation factor fluctuated from 0.5 to 20 depending on the permeation time. This fluctuation was explained by the fact that DNA sometimes releases phenylalanine in a dilute DNA solution (i.e., 0.01–0.5 ppm) due to the conformational change of DNA over time.52 Higuchi et al. prepared immobilized DNA membranes from cellulose dialysis membranes with different pore sizes and investigated the effect of the pore size on chiral separation through immobilized DNA membranes.52,54,55 They found that D-phenylalanine preferentially permeated through the immobilized DNA membranes with pore sizes 5000) as shown in Fig. 3.55 The pore size of the immobilized DNA membranes regulated preferential permeation of the stereoenantiomer through the membranes. The immobilized DNA membranes adsorbed L-phenylalanine preferentially, independent of the pore size.52 Furthermore, in a concentration gradient and electric field, DNA was able to permeate through membranes with a pore size of 5 nm but did not permeate through membranes with a pore size of 1.5 nm. Therefore, in membranes with a pore size 2 nm, DNA was expected to be immobilized on the surfaces as well as inside the pores. Considering the above results, Fig. 4 shows the model of chiral separation by the immobilized DNA membranes.55

Figure 3. Dependence of the separation factor in the permeate (open circle) and the concentrate (closed circle) solutions through the immobilized DNA membranes on the MWCO of the base membranes and on the pore size of the immobilized DNA membranes at pH 7.0 and 25◦ C.55


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Figure 4. Chiral separation model in the ultrafiltration of racemic phenylalanine solution through the immobilized DNA membranes.2

Zhang et al. also reported that DNA can be used as a chiral selector for the chiral separation of racemic tyrosine and tryptophan by affinity ultrafiltration through dialysis membranes with MWCO = 12,000–14,000.57 They reported that D-enantiomers were preferentially present in the permeate solution while L-enantiomers were preferentially present in the feed solution.57 Higuchi and other researchers55,57 showed that the immobilized DNA membranes are potentially useful for chiral separation. Chiral separation by these immobilized DNA membranes is based on the interaction between DNA and a specific stereoenantiomer because no chiral separation was found in the cellulose membranes without bound DNA. The immobilized DNA membranes were categorized as channel-type membranes and not as affinity membranes as for affinity ultrafiltration using albumin.46,48,58 The membrane pore size and the binding affinity of the specific stereoenantiomer should be the most important factors for the preparation of channel-type membranes. The immobilized albumin membranes reported in the literature46,48,58 did not work as channel-type membranes but as affinity membranes, although the membranes have a similar pore size (e.g., MWCO = 13,000) to the membranes used in DNA immobilized membranes. This is due to the strong binding affinity of L-amino acids to albumin. When the binding affinity of the specific stereoenantiomer to the membranes is too strong, the specific enantiomer cannot permeate through the membrane, adsorbing instead. The weaker binding affinity of DNA to L-amino acids compared to that of albumin makes the immobilized DNA membranes channel-type membranes.55

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7. Chiral Separation by Non-Chiral Membranes The central dogma that chirality can only be generated from chiral molecules could be extended to predict that membranes without any chiral molecules cannot contribute to chiral separation. Therefore, most researchers have developed chiral separation membranes prepared from natural chiral polymers, synthetic chiral polymers from asymmetric synthesis, polymers with chiral branches, or immobilized chiral molecules, proteins, polysaccharides, and DNA. However, chiral separation membranes can be prepared from non-chiral polymers with “chiral memory,” accomplished with molecularly imprinted membranes or membranes with a chiral memory of the polymer helicity. Some examples of those chiral separation membranes are sumarized in Tables 6 and 7, and described in detail in the following sections. 7.1 Molecularly Imprinting Membranes A molecularly imprinted polymeric membrane is designed to mimic the recognition site of an enzyme with its shape, formed by interactions with a “template” target molecule. There are two basic methods of preparing molecularly imprinted membranes—covalent and noncovalent molecular imprinting methods. In both cases, the template molecules are chosen to allow interactions with the functional group of the imprinted polymeric membranes. In the covalent method of molecular imprinting, the imprint (template) molecule is covalently coupled to a monomer during polymerization.59,60 The imprint molecule is Table 6 Chiral separation through polymeric membranes having chiral free volume shape (molecularly imprinted membranes) Membrane materials DIDE resin Polyamide DIDE resin EEE derivatives Carboxylated polysulfone Carboxylated polysulfone Polysulfone derivatives E2 K resin (DE)2 K resin (IDE)2 K resin (DIDE)2 K resin Chitosan/GPTMS hybrid Chitosan/GPTMS hybrid a

Targeted molecules

Flux or permeability coefficient (methoda)

Tryptophan Serine Ac-tryptophan Ac-tryptophan Glutamic acid (D)

P = 0.74 × 10−4 cm2/h (D) (UF) P = 3.33 × 10−7 cm2/sec (ED) P = 6.11 × 10−5 cm2/sec (ED) P = 5.86 × 10−5 cm/sec (D)

Separation factor Ref. 1.4 9.0 4.6 5.0 1.1

61 63 84 85 86

Glutamic acid (L) P = 5.94 × 10−5 cm/sec (D)

1.2

86

Ac-glutamic acid

(ED)

1.6

87

Ac-tryptophan Ac-tryptophan Ac-tryptophan Ac-tryptophan Phenylalanine

(D) (D) (D) (D) (D)

1.5 1.7 2.1 2.5 4.5

88 88 88 88 64

Phenylalanine

(D)

2.1

64

Method; D indicates dialysis,. ED indicates electro dialysis, UF indicates ultrafiltration.


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Table 7 Chiral separation through polymeric membranes having chiral free volume shape (chiral helical memory membranes) Membrane materialsa Poly(diphenylacetylene) Poly(diphenylacetylene) Poly(diphenylacetylene) Copoly(HPA) Copoly(HPA) Poly(HPA) Poly(HPA) Poly(phenylacetylene) a

Targeted molecules


Tryptophan Tryptophan Tryptophan Phenylalanine Phenylalanine Phenylalanine Phenylalanine Phenylalanine

P = 22.5 × 10−12 m2/h (N) P = 19.7 × 10−12 m2/h (N) P = 13.4 × 10−12 m2/h (N) P = 12.6 × 10−14 m2/h (D) P = 13.1 × 10−14 m2/h (D) P = 11.0 × 10−14 m2/h (D) P = 10.7 × 10−14 m2/h (D) P = 9.6 × 10−14 m2/h (D)

Separation factor Ref. 1.2 1.4 2.9 1.3 1.4 1.2 1.1 1.5

66 66 66 67 67 67 67 67

Copoly(HPA); copoly(hydroxylphenylacetylene), Poly(HPA); Poly(hydroxylphenylacetylene). Method; N indicates nanofiltration, and D indicates dialysis.

b

chemically cleaved from the highly crosslinked polymer after copolymerization with a crosslinker. In the non-covalent method of molecular imprinting, the imprint (template) molecules are mixed with functional monomers capable of interacting non-covalently with the imprint molecules. The functional monomers are copolymerized with crosslinkers to generate a highly crosslinked and rigid polymer. The imprint molecules are subsequently removed from the polymer, leaving recognition sites complementary to the imprint species in the shape and positioning of functional groups.59 Preparation of the polymer in this way induces molecular memory, as the recognition sites are capable of selectively recognizing the imprint species. During both the imprinting procedure and the rebinding, the imprint molecules interact with the polymer via non-covalent interactions, e.g., ionic, hydrophobic, and hydrogen bonding interactions. Yoshikawa et al. applied this molecular imprinting method to develop chiral separation membranes by the non-covalent bonding method in 1995.61 Their work was the first report on chiral separation membranes prepared by a molecular imprinting method. They prepared polystyrene copolymer grafted tetrapeptide derivatives, and the molecular imprinting membranes were prepared from the polystyrene copolymer with template molecules of Boc-L-tryptophan or Boc-D-tryptophan. The imprinting molecules were extracted from the imprinting membranes by methanol. L-tryptophan permeated through the membranes imprinted with Boc-L-tryptophan. However, chiral separation using molecularly imprinted membranes has so far suffered from a relatively low selectivity. Itou and Yoshikawa et al. prepared molecularly imprinted polymeric membranes from polystyrene resin bearing a tetrapeptide of glycine (G-membranes).62 N-αtert-Butoxycarbonyl-D-tryptophan (Boc-D-Trp) or N-α-tert-butoxycarbonyl-L-tryptophan (Boc-L-Trp) were used as the template molecules to convert G-membranes into chiral separation membranes. Because the constitutional residue of the tetrapeptide, glycine, had no asymmetric carbon, both template molecules, Boc-D-Trp and Boc-L-Trp, worked as template molecules to construct chiral recognition sites within the membranes. The membrane imprinted by the D-isomer of the template molecule recognized the D-isomer of N-α-acethyltryptophan (Ac-D-Trp), while recognition sites for N-α-acethyl-L-tryptophan (Ac-L-Trp) were constructed by imprinting with Boc-L-Trp.62 Membrane separation of the racemic mixtures was investigated by adopting an applied electrical potential difference as

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a driving force for membrane transport. The two G-membranes imprinted as above showed chiral separation ability in this format as well. Permeation selectivity was reported to be ca. 2.3 at the optimum applied electrical potential difference of 2.0 V, and was based on adsorption selectivity.62 Son and Jegal prepared molecularly imprinted membranes by interfacial polymerization with a template (D-serine) of piperazine and trimesoyl chloride on polysulfone microfiltration support membranes.63 The D-serine template was removed by keeping the membrane in 50◦ C water for 50 h after interfacial polymerization to generate an active crosslinked polyamide layer. The three -COCl groups of trimesoyl chloride reacted with the two amine groups of the piperazine. Hydrogen bonding is expected to occur between the amine of piperazine and the -COOH of D-serine in the molecular cavity of the molecularly imprinted membranes. When a racemic serine solution was used for chiral resolution by pressure-driven permeation, the permeation rate of D-serine appeared to be much faster than that of L-serine. When the operating time reached 60 h, the enantiomeric excess (%ee) of the serine mixture in permeates was reported to be about 80%.63 Jiang and Wu reported on enantioselective chitosan (CS)/γ -glycidoxypropyltrime thoxysilane (GPTMS) hybrid membranes prepared in an aqueous phase by a sol–gel process using chitosan as the bulk polymer, L-phenylalanine as the imprinting molecule, and GPTMS as the crosslinking agent.64 The separation factor α D/L was reported to be as high as 4.5. These organic–inorganic hybrid CS/GPTMS materials represent promising materials for the development of sol–gel imprinting with effective crosslinking and a lower degree of swelling, and they exhibit good separation properties. The introduction of silica into the chitosan created a dense and uniform hybrid network and reduced the degree of swelling of the materials in an aqueous system, which ensured the formation and maintenance of imprinting sites. The specific interactions of imprinting cavities in the hybrid membrane with templates resulted in significantly improved chiral resolution of the imprinted membranes by improving the binding ability of the imprinting molecules, hindering their diffusion and facilitating transport of the other isomers.64 7.2 Membranes Composed of an Achiral Polymer with a One-Handed Helical Conformation The construction of controlled secondary structures in polymers has attracted a great deal of attention in recent years, with one-handed helical polymers as a typical example. The preparation of one-handed helical polymers has usually been achieved by one of the following methods: (a) polymerization of optically active monomers, (b) polymerization of prochiral monomers using optically active catalysts or initiators, (c) induction of chirality by interaction between achiral polymers and chiral additives, and (d) induction of chirality in achiral polymers with a chiral functional group followed by removal of the chiral functional group.65 Method (d) enables the construction of chiral membranes from achiral polymers. Such a “chiral memory” of the polymer helicity was first found by Yashima’s group, but they did not apply this technique for chiral separation technology.66 Teraguchi and Masuda verified enantioselective permeation through helical polymeric membranes composed of achiral poly(diphenylacetylene).65 The chiral memory of the membranes was created using poly(diphenylacetylenes) with a high content of the pinanylsilyl group, generating a chiral polymer, followed by depinanylsilylation after preparation of self-stable membranes. Depinanylsilylation of the membranes was carried out by exposure of the membranes to a mixture of hexane/trifluoroacetic acid at room temperature.65 The chiral selectivity of racemic tryptophan solutions through the membranes was found to


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be as high as 58.6%(ee), while that of the chiral poly(diphenylacetylenes) retaining the pinanylsilyl group was 80.5%(ee). These studies verify that membranes composed of achiral polymers with chiral helical memory can contribute to the chiral separation of chemicals and drugs.65 Teraguchi and Aoki et al. also prepared chiral helical poly(hydroxyl-containing phenylacetylene) and poly(phenylacetylene) with and without the chiral pinanylsiloxy group. First, they prepared poly(pinanylsiloxyl-containing) phenylacetyle membranes.67 Poly(hydroxyl-containing phenylacethylene) or poly(phenylacetylene) membranes made from an achiral polymer were then prepared by depinanylsilylation of the membranes in situ.67 The resulting membranes exhibited circular dichroism despite the absence of the chiral substituents (pinanylsiloxy group), indicating that the main polymer chains retained their chiral helicity (chiral memory in the membranes). The membrane prepared from a polymer with chiral side chains (i.e., chiral helical poly(phenylacetylene) containing the chiral pinanylsiloxy group) showed excellent chiral separation of phenylalanine in concentration-driven permeation, exhibiting 34.8–77.4 ee% depending on the chemical structure of the polymeric membranes.67 However, depinanylsiloxyed membranes (poly[hydroxyl-containing phenylacetylene] and poly[phenylacetylene]) also showed chiral separation of phenylalanine in concentration-driven permeation, with 6.05–21.1 ee% depending on the chemical structure of the polymeric membranes. Although the polymer used to prepare these membranes has no chirality, it retains its helical conformation due to the preparation method.67 Their study demonstrated that the chiral main chain is also important for chiral separation using membranes.

8. Comparison of Data Reported by Different Researchers There is an inherent trade-off, as the separation factor generally decreases with increasing permeability of solutes or gases through the membranes.68–70 This trade-off should be considered for the chiral separation of drugs and pharmaceuticals through polymeric membranes. The available data on permeability and separation factors of tryptophan and phenylalanine through chiral separation membranes was collected from the literature.2,23,25–31,34–42,48,49,51,55,56,61,63,64,66,67,71–88 The empirical upper bound relationship for chiral separation of racemic tryptophan and phenylalanine is shown in Figs. 5 and 6. The upper bound correlation is that the log of the permeability of amino acids versus the log of the higher separation factor yielded a limit for achieving the desired result of a high separation factor combined with high permeability. The upper bound correlations for the chiral separation of racemic phenyalanine and tryptophan through polymeric membranes under concentration-driven permeation (i.e., the dialysis method) were described as α = −0.333 − 0.333 ∗ log(P /cm2 sec−1 ) −1

α = −1.08 − 0.4167 ∗ log(P /cm sec ) 2

for racemic phenylalanine;

(13)

for racemic tryptophan.

(14)

This research did not clearly indicate an upper bound relationship in chiral separation through membranes, especially for the chiral separation of phenylalanine, while the upper bound relationship clearly follows P = kα n in gas separation membranes and processes,68 where P is the permeability of the fast gas, α is the separation factor, k is referred to as the “front factor,” and n is the slope of the log–log plot of the P vs kα n. Figures 5 and 6 will contribute to the evaluation of chiral separation properties for the development of improved chiral separation membranes.

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Figure 5. Relationship between permeability coefficients and separation factor of phenylalanine through several chiral polymeric membranes concentration-driven permeation. Data were cited from references (see Table 1S in Appendix A).

10. Conclusions and Future Perspectives More than 100 articles have been published on the development of polymeric membranes for chiral separation. Most chiral separation membranes have relatively low separation factors, except for affinity membranes. One of the solutions to this problem is to use a

Figure 6. Relationship between permeability coefficients and separation factor of tryptophan through several chiral polymeric membranes concentration-driven permeation (◦) and potential-driven permeation (•). Data were cited from references (see Table 2S in Appendix A).


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Figure 7. Flow diagram of a multi-stage ultrafiltration process using two types of membranes for chiral separation.27

multistage chiral separation process. Higuchi et al. proposed a multi-stage cascade in the ultrafiltration process through channel-type membranes for chiral separation in 2003.55 When two different types of membranes are used in a cascade filtration model (Fig. 7), there is no change in the concentration ratio between the R-enantiomer and S-enantiomer in the feed solution in each stage because two membranes with opposite enantiomeric selectivity are used. When there are n stages of the multi-stage process using two types of chiral membranes, the purity of the enantiomer (ee) from the racemic amino acid mixture can be estimated.55 Figure 8 shows some examples calculated with the following membrane conditions: (a) α = 1.2 and 1/1.2, (b) α = 1.6 and 1/1.6, (c) α = 2 and 0.5, and (d) α = 4 and 0.25.55 Only four stages are necessary to obtain 99% purity when membranes with α = 4 and 0.25 are used in the multi-stage process. The biggest advantage of the multi-stage process using two types of chiral membranes is the theoretical 100% product recovery.55 Several researchers have investigated chiral separation by affinity ultrafiltration using albumin as a large stereo-specific binding agent.46,48,89–92 Albumin has several chiral recognition sites for amino acids and small drugs.47 The stability and high cost of these proteins make it difficult to develop a large-scale commercial process for the chiral separation of pharmaceuticals by affinity ultrafiltration using albumin. DNA was recently discovered to have several chiral recognition sites for specific enantiomers.52–55 DNA is much more stable than proteins and is less expensive than albumin when using DNA isolated from salmon testis. The separation factors of immobilized DNA membranes and immobilized albumin membranes were both acceptable, although DNA seems to be a more promising stereo-specific binding agent than BSA or HSA. Several polymeric membranes were developed from natural chiral polymers (i.e., polyamino acids and polysaccharides) and synthetic polymers with a chiral main backbone

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Figure 8. Dependence of chiral purity (ee%) of pharmaceutical enantiomers on the number of filtrations in the multi-stage ultrafiltration process using chiral separation membranes of α = 4 and 0.25 (a), α = 2 and 0.5 (b), α = 1.6 and 1/1.6 (c), and α = 1.2 and 1/1.2 (d) from top to bottom lines.55

or chiral side chains. Molecularly imprinted membranes were also prepared from achiral monomers and/or polymers. Currently, there is no optimized membrane for the chiral separation of pharmaceuticals and chemicals because of the low separation factors and/or low permeabilities of these membranes (flux). New, intelligent designs of chiral polymeric membranes are necessary to enable the development of chiral separation membranes that can be applied to industrial pharmaceutical production. In conclusion, advanced polymeric materials are playing an important role in the development of chiral separation membranes for pharmaceutical applications.

Acknowledgments This research was supported by grants from the National Science Council of Taiwan under Grants No. 97-2221-E-008-011-MY3 and NSC97-2120-M-008-002, the VGHUST Joint Research Program, Tsou’s Foundation (98DFA0700006), and the Cathay General Hospital Project (98CGH-NCU-B1). Grants-in-Aid for Scientific Research (No. 21500436) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan are also acknowledged.

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APPENDIX A

Table 1S Relationship between permeability coefficients and separation factor of phenylalanine through several chiral polymeric membranes concentration-driven permeation. Data were cited from references No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Membranes poly(1) original Poly(2) original copoly(1/3) original copoly(2/3) original poly(3) original poly(1) depinalsilylated Poly(2) depinalsilylated copoly(1/3) depinalsilylated copoly(2/3) depinalsilylated poly(3) depinalsilylated PDSP in methanol Poly(p-PSPA) Poly(1,3-BPDSPA) Poly(3-PDSPA) Poly(1-PDSPA) Poly(1,3,5-TPTSPA) Poly(1,3-BPTSPA) PAN-bCD PAN-Glucose PAN-bCD PLGA β-cyclodextrin immobilized cellulose D-amino acid oxidase apoenzyme

Preferential permeation

alpha

Ref. No.

8.06E-14 8.39E-14 1.09E-13 1.08E-13 1.21E-13 3.06E-13 2.97E-13 3.64E-13 3.50E-13 2.67E-13 4.58E-07 3.08E-12 7.33E-13 8.78E-12 3.08E-13 3.94E-14 1.29E-13 2.94E-07 3.69E-07 2.31E-07 1.71E-07 1.53E-07

R R R R R R R R R R R R R R R R R S S S S R

2.60 2.07 4.05 3.47 7.85 1.19 1.13 1.40 1.32 1.53 3.35 640.00 20.50 1.12 6.10 1.74 1.39 1.40 1.02 1.61 1.26 1.30

67 67 67 67 67 67 67 67 67 67 78 37 37 37 37 37 37 41 41 41 35 21

2.20E-05

R

3.30

49

P (cm2/sec)

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Table 2S Relationship between permeability coefficients and separation factor of tryptophan through several chiral polymeric membranes concentration-driven permeation and potential-driven permeation. Data were cited from references No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

Membranes PPDPA-PDPA-1 PPDPA-PDPA-2 PPDPA-PDPA-3 de-PPDPA-PDPA-1 de-PPDPA-PDPA-2 de-PPDPA-PDPA-3 (+)-poly(DPSP) (+)-poly(DPSP) PMLGa supported PMLGa (+)-poly(p-PMPA) (+)-poly(p-PSPA) PAN-bCD PAN-Glucose PAN-bCD Physisorbed PLGA Chemisorbed PLGA Chemisorbed PLGA Chemisorbed PLTEG Chemisorbed PBLG β-cyclodextrin immobilized cellulose Copoly(PSDPA) Copoly(PSDPA) Copoly(PSDPA) Poly(PPDPA/PDPA) PEGDI37 PEGDI37 PEGDI37 PEGDI37Li PEGDI37Li PEGDI46 PEGDI55 PEGDI55 PEGDI55 PEGDI55 PEGDI55 PEGDI37 PEGDI37 PEGDI37


Alpha

Ref. No.

2.49E-08 4.30E-08 2.24E-08 1.78E-08 2.08E-07 2.85E-07 2.04E-07 1.42E-07 1.66E-07

R R R R R R R R R R R R S S S S S S R S R

1.39 1.60 3.38 1.22 1.36 2.88 2.64 1.41 3.04a 1.57a 1.38 2.90 1.28 1.02 1.45 1.29 1.47 1.46 1.29 1.00 1.10

66 66 66 66 66 66 78 78 26 26 37 37 41 41 41 35 35 35 35 35 42

1.53E-11 1.43E-11 1.00E-11 2.06E-08 4.10E-08 2.46E-07 5.35E-07 2.63E-07 6.32E-07 2.32E-07 1.36E-07 1.82E-07 1.84E-07 4.36E-07 1.54E-07 8.10E-09 1.20E-08 9.90E-08

R R R R R R R R R R R R R R R R R R

1.40 1.60 3.40 1.40 1.03 1.21 1.13 1.13 1.10 1.20 1.02 1.13 1.33 1.17 1.27 1.50 1.90 1.70

66 66 66 66 71 71 71 71 71 71 71 71 71 71 71 71 71 71

P (cm2/sec) 1.53E-11 1.43E-11 1.00E-11 6.25E-11 5.47E-11 3.72E-11 3.78E-07 2.72E-07 2.33E-06a 3.61E-07a


143

Table 2S Relationship between permeability coefficients and separation factor of tryptophan through several chiral polymeric membranes concentration-driven permeation and potential-driven permeation. Data were cited from references (Continued) No. 40 41 42 43 44 45 46 47

Membranes HDI55 HDI55 HDI55 HDI73 Plasma polymerized terpene Plasma polymerized terpene Plasma polymerized terpene Plasma polymerized terpene

a

Potential-driven permeation

P (cm2/sec) 1.50E-08 2.20E-08 4.10E-08 2.10E-08 5.02E-09 1.87E-09 6.04E-09 4.71E-09


Alpha

Ref. No.

R R R R R R R R

1.50 2.60 1.20 1.40 1.40 1.90 1.10 1.20

71 71 71 71 75 75 75 75

Polymer Reviews, 50:144–177, 2010 Copyright © Taylor & Francis Group, LLC ISSN: 1558-3724 print / 1558-3716 online DOI: 10.1080/15583721003698846

Dense Gas Processing of Polymers R. B. YOGANATHAN§, R. MAMMUCARI, AND N. R. FOSTER School of Chemical Sciences and Engineering, Chemical Sciences Building, University of New South Wales, Sydney NSW 2052, Australia There is a growing global awareness about environmental pollution, and many sanctions and sustainable practices have been implemented. In particular, the use of volatile organic compounds (VOCs) is a practice that is being limited and minimized world-wide. These VOCs are not only damaging to the environment, but are also an occupational hazard. The polymer processing industry is known to use VOCs extensively for polymerization, fractionation, plasticization, degradation, extraction and purification. More environmentally-friendly methods to circumvent the use of these toxic and hazardous compounds are being explored. The use of dense gases in polymer processing can respond to the need for more environmentally-friendly industrial processes. Products with high-purity, sterility, and porosity can be achieved using dense gas technology (DGT). Currently, DGT has been used for different aspects of polymer processing including polymerization, micronization, and impregnation. Due to its high solubility in polymers and diffusivity, dense CO2 can penetrate and plasticize polymers, whilst impregnating them with low-molecular weight CO2 -soluble compounds. The dense CO2 properties of inertness, non-toxicity, and affinity for various therapeutic compounds are specifically advantageous to the medical and biomedical industries. Biodegradable polymers and other medical-grade polymers have benefited from the application of DGT. The aim of this review was to show the versatility of dense CO2 for polymer processing applications, specifically polymerization, polymer blend preparation, drug loading and sterilization. Keywords polymer processing, supercritical fluids, dense gas, supercritical CO2 , dense CO2 , polymer impregnation, polymer blends, dense gas technology

1. Introduction The polymer industry expels over 20 million tons of volatile organic compounds (VOCs) each year.1 Organic solvents are used at various stages of polymer production; as reaction media and as post-polymerization processing media (extraction, purification). To avoid damaging the environment and creating unsafe working environments, alternative and sustainable media and methods to reduce organic solvent use have been sought. There are two routes to reducing the usage of organic solvents and emission of VOCs2; • develop a solvent-free method • use environmentally-friendly solvents Received July 20, 2009; accepted January 6, 2010. § Current address: Department of Pharmaceutical Sciences, Leslie Dan Faculty of Pharmacy, University of Toronto, 144 College Street, Toronto, Ontario, Canada, M5S 3M2. Address correspondence to Neil Foster, The University of New South Wales, Sydney, NSW 2052. E-mail: [email protected]

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Figure 1. Progression of dense CO2 -related polymer publications.9

Using a solvent-free method such as melt phase polymerization has the problems of high viscosity and limited mass transfer. Also, the selection of an environmentally-friendly liquid solvent may still require steps to remove the solvent after the polymerization process or post-processing stages. The use of a dense gas (DG) such as CO2 has been researched and studied for polymerization and polymer processing. A DG is a fluid with a temperature and pressure close to the critical point. The applicability of dense CO2 as a sustainable alternative to conventionally used organic solvents has been reported in the literature.2–8 Research on dense CO2 -related polymer processing is a growing field. Over the past two decades, the number of publications per year related to dense CO2 polymer processing (Fig. 1) has been steadily increasing.9 The focus of this review is the application of dense gas technology to polymer processing, with attention on the usage of dense CO2 as polymerization, blending, impregnation and sterilization media.10–13 Unlike earlier reviews on DG processing of polymers, this paper focuses on the feasibility of concurrent processes (blending, impregnation and sterilization), and on the implications of DG polymer processing for biomedical applications. Relevant published work on various dense CO2 -related polymer processing topics can be found in Table 1. 2. Dense Gas Technology Dense gas technology (DGT) optimizes the properties of fluids close to and above their critical point for applications such as purification, extraction, polymer processing, impregnation of chemical compounds, pharmaceutical processing, and sterilization of medical devices.12,111,114 A dense gas is a substance which exists at or near its critical point. The critical point of a substance is located at the termination of the phase boundary between the gas and liquid phases of a substance (Fig. 2). As pressure and temperature increase beyond the critical point the phases become indistinguishable as either a gas or a liquid, and become a supercritical fluid (SCF). Above the critical temperature and critical pressure, the substance exists as a homogeneous medium which exhibits liquid-like densities and gas-like mass transfer properties.

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R. Yoganathan et al. Table 1 Dense CO2 -related polymer processing reported in the literature

Topics

References

Polymer Phase Behavior Polymer Plasticization Polymer Foaming Polymerization Polymer Blending Polymer Impregnation Polymer Cross-linking Polymer Sterilization Polymer Micronization

12, 14–41 11, 42–51 26, 27, 52–63 10, 64–84 24, 54, 80–94 2, 26, 27, 32, 43, 65, 66, 95–104 12, 26, 27, 101 13, 105–17 27, 65, 70, 108–113

3. Physical Properties of DGs The advantages of DGs over conventional solvents include low surface tension, low viscosity, high diffusivity, and density-dependent solvent power.116 It is possible to make the transition smoothly from a gas (point A) to a liquid (point B) without exhibiting distinct phase transitions by following the A-B path outlined in Fig. 2. The path connecting point A and point B does not cross the phase boundary, but passes through the supercritical region. All substances in the supercritical region are referred to as supercritical fluids (SCFs). All SCFs, and compounds at or near the critical point, fall under the broader definition of DGs. The different physical properties of SCFs, gases and liquids are listed in Table 2. The density of a SCF is similar to a liquid; however, its viscosity is much closer to a gas. The solvent strength of a DG defines its ability to dissolve solutes. The greater the density the greater the ability of the DG to dissolve a solute. In the late 19th century, Hannay and

Figure 2. Phase diagram of a pure compound.115


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Table 2 Physical properties of a gas, a liquid and a supercritical fluid120 Property Density (gc/m−3) Diffusion Coefficient (cm2/s−1) Viscosity (cP)

Gas

SCF

Liquid

0.0006–0.002 0.1–0.4 0.01–0.03

0.2–0.9 0.0002–0.0007 0.01–0.09

0.6–1.6 0.000002–0.00002 0.2–3.0

Hogarth117, 118 reported the increased solubility of the inorganic salts, cobalt (II) chloride and iron (III) chloride, in supercritical ethanol with increments in pressure. The solvent properties of liquid CO2 for various organic and inorganic compounds have been reported by Francis.119 The solvent strength of a DG is dependent on its density, which is related to pressure and temperature. The reduced temperature (TR = T/TC ) and reduced pressure (PR = P/PC ) of a DG is between 0.9 and 1.2.120 Within the aforementioned range, the density of a DG is highly sensitive to changes in pressure (Fig. 3). At a constant temperature, a small increase in pressure causes a noticeable change in the density. A high sensitivity translates to an

Figure 3. Density vs pressure of CO2 .121

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R. Yoganathan et al. Table 3 Critical temperatures and critical pressures of dense gases120 Substance Ethylene Xenon Carbon Dioxide Ethane Nitrous Oxide Propane N-Pentane Trichlorofluoromethane Isopropanol Methanol Cyclohexane Benzene Toluene p-Xylene Water

TC (◦ C)

PC (bar)

9.3 16.6 31.1 32.2 36.5 96.7 196.5 198.1 235.2 239.5 280.3 289 318.6 343.1 374.2

50.4 58.4 73.8 48.8 71.7 42.5 33.7 44.1 47.6 81 40.7 48.9 41.1 35.2 220.5

ability to control the density and solvent strength of a DG. By tuning the solvent strength of the DG, its selectivity to dissolve various compounds can also be controlled. The properties of DGs such as tunable solvent strength and selectivity have enabled their use in various food-related industrial applications such as decaffeination,120 and the extraction of tea, hops, spices, and other flavors.122 The critical temperatures and critical pressures of selected DGs can be found in Table 3. According to Pereda et al.,116 DGs can be classified into two groups based on their TC . There are low TC gases which are condensable and high TC fluids which have a much greater solvent power, and are better for higher molecular weight compounds. The low TC gases can be applied to processes at moderate conditions, and also have a better selectivity for low molecular weight compounds. Carbon dioxide is the most used DG because it is widely available, environmentally benign, and has an easily accessible critical temperature (31.1◦ C) and critical pressure (73.8 bar). At the critical point, CO2 has a liquid-like density of 0.47 gcm−3, whereas conventional organic solvents have densities in the range of 0.8–1.0 gcm−3. In the DG region, the density of CO2 can be tuned by varying the pressure and temperature of the system. At a temperature of 35◦ C, which is above the CO2 critical temperature, it is possible to obtain a CO2 density in the range of 0.3–0.6 gcm−3 by varying the pressure between 65 bar and 80 bar. Such liquid-like densities promote the use of dense CO2 as an alternative to organic solvents.71,111,112 Dense gases also have gas-like diffusivity properties, which allow them to penetrate different materials and lower the viscosity of mixtures. These intermediary physicochemical properties allow for the use of dense CO2 for extraction, fractionation, chromatography, polymerization, micronization, and degradation.2,31,64,114,120,123–131 The physical properties of DGs greatly affect their interactions with other compounds and solvents. Processing polymers with DGs is a growing field and has been reviewed in the past.12,64,67,96,111,129,130–132 The focus of this review will be on the scope and use of DG for polymer processing.


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Figure 4. Schematic of CO2 -polymer interactions and potential applications.2

4. CO2 -Polymer Interaction The type of CO2 -polymer interaction ultimately decides its potential application, as depicted in Fig. 4. The application of dense CO2 to polymer processing depends on the solubilities of dense CO2 and the polymer in each other. A polymer swelling in the presence of dense CO2 is the first indication of an interaction. The swelling can be caused by either the polymer being CO2 -soluble, or CO2 being soluble in the polymer. Dense gas processing of polymers encompasses both types of interactions which cause swelling. Carbon dioxide on its own has a strong quadrupole moment (Fig. 5) and low polarizability, similar to methane. The aforementioned properties make dense CO2 a good solvent for both small polar and non-polar compounds,111,130,133 such as monomers, initiators, catalysts, cross-linkers, and oligomers. The majority of larger compounds such as polymers have limited or selective solubility in dense CO2 . The polymers which are CO2 -soluble possess some level of polarity and have some electronegative groups.120 Examples of CO2 -soluble polymers include polydimethylsiloxane (PDMS), polyalkene oxide (PAO), perfluorinated polypropylene oxide (PPO), polyvinyl acetate (PVAc), and polymethyl acrylate (PMA).2 The class of high molecular weight polymers most soluble in CO2 is fluorinated acrylates.38 The geometrical interaction of CO2 with various fluorinated polymers was studied.40 The

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Figure 5. Dipole and quadrupole charge distribution.2

results indicate that high solubility results from close interaction between the center of masses and an increased free volume in the polymer matrix. Within high molecular weight polymers, PVAc has been identified as the most CO2 soluble.39,41 The differences in solubility of various hydrocarbon-based CO2 -philic polymers (e.g. PVAc and PMA) can be linked to crystallinity, the presence of side chains, and accessibility of carbonyl groups.39 Spacing of the ether oxygen and carbonyl oxygen along the backbone also may affect solubility in CO2 .39,41 In general, the presence of ether oxygens in the polymer structure results in higher solubility in CO2 .41 Polymer solubility is dependent on polymer molecular weight and polydispersity.21 The solubility of a polymer in dense CO2 can be increased by the addition of co-solvents. The behavior of polymers in the presence of dense CO2 , with and without co-solvents has been reported in the literature.21 The other type of CO2 -polymer interaction occurs when CO2 is soluble in a polymer. For this type of interaction, the physical and chemical structure of the polymer affects the solubility of CO2 into its matrix. Extra polar groups and increased free volume in the polymer matrix increases the CO2 solubility in the polymer.43,104,132,134 The spectroscopic evidence of the chemistry behind the CO2 -polymer interaction was first obtained by Kazarian and co-workers43,104,132,134 while observing polymer plasticization with IR spectroscopy.

5. Chemical Processing 5.1 Polymerization Dense CO2 is an attractive alternative to conventional polymerization media because it is widely available, and most importantly, it is environmentally-friendly. The use of dense CO2 as a medium can help overcome some of the problems faced by the conventional polymerization media, such as high viscosity, low solubility, and rigorous purification processes. The DG polymerization field is gaining more interest because dense CO2 is a proven alternative to organic solvents and can readily solubilize various organic compounds. The interactions between certain polymers and dense CO2 are favorable to polymerizations in dense CO2 . Conventional polymerization methods commonly employ high temperatures to overcome the activation energy, break bonds, and make the monomer reactive.135 A suppressed glass transition temperature (Tg ) translates to a lower activation energy required to initiate the polymerization reaction. With its growing popularity over the past two decades, books and many reviews have been written on dense CO2 polymerization, where its use as a reaction medium and reactant have been discussed.2,67,126


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Carbon dioxide in the DG region provides better mass transfer properties than liquid CO2 , but maintains similar solvent behavior to liquid CO2 .124 Dense CO2 behaves like hydrocarbon solvents because it has an affinity for low molecular weight non-polar molecules. The interactions between CO2 and regularly insoluble high molecular weight polymers have been researched over the past two decades.62,64,102,108,114,124,130, 131 Many researchers have reported that in the presence of dense CO2 the Tg of polymers become suppressed.62,67,68,81,111,131,135–139 Polymerizations conducted at high temperatures in the melt phase are highly viscous processes. The high viscosity of the melt reduces the diffusive ability of compounds through the melt, thus restricting polymerization rates, thereby only allowing for the production of low molecular weight polymers. One way to alleviate the viscosity of melt polymerizations is to conduct it in dense CO2 . A reduced viscosity means a lower mass transfer resistance, which allows compounds to move more freely within the medium. Dense CO2 has good mass transfer and diffusivity properties. Many researchers have undertaken studies to develop new polymerization methods involving dense CO2 to help the polymer industry circumvent the use of environmentally hazardous and biologically toxic organic solvents.140, 141 Dense CO2 polymerizations are either homogeneous or heterogeneous. Homogeneous polymerizations in dense CO2 are polymerizations where all reactants/monomers are completely CO2 -soluble, and thereby form a homogeneous phase at the beginning of the polymerization. A heterogeneous polymerization in dense CO2 polymerization involves the use of surfactants and other additives to form a multi-phase reaction medium. The surfactants and other additives are used to create colloids and/or micelles. The classification scheme in Fig. 6 is different from the classification of CO2 -polymer interactions found in Fig. 4. The classification entitled “Polymer soluble in DG” in Fig. 4 encompasses the same class of polymers found under the classification “CO2 -philic” (Fig. 6). The CO2 -phobic classification is given to polymers that undergo swelling when

Figure 6. Classification of polymer behavior in CO2 in relation to dense CO2 polymerization.71

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dense CO2 is used as the polymerization medium. Polymers that are CO2 -phobic will exhibit hydrophilic or lipophilic properties, a characteristic which is used to find a suitable stabilizer/surfactant for heterogeneous polymerizations. 5.1.1 Homogeneous Polymerization. The use of dense CO2 as a homogeneous reaction medium has been discussed in the literature and the solubilities of high molecular weight polymers in dense CO2 have been reported.67,111,142 Studies show that fluorinated polymers are soluble in dense CO2 whereas polymers with only hydrocarbon backbones have limited solubility.2,111,124,126,130 The dense CO2 polymerization of fluorine containing co-polymers has been documented by Desimone et al.102 and Wood et al.10,129,142 Fluoropolymers are synthesized using free-radical chain growth and cationic chain growth polymerization. Conventional synthesis of fluoropolymers involves the use of chlorofluorocarbons (CFCs), a solvent subject to strict environmental regulations. Free-radical polymerization in dense CO2 is applicable because the initiator, azobisisobutyronitrile (AIBN) is CO2 -soluble. Also, AIBN creates free radicals efficiently and exhibits limited decomposition in dense CO2 compared to its behavior in other conventional solvents.111 The inertness of CO2 makes it unreactive to free radicals, making it an ideal reaction medium for free radical polymerization.67 Homogeneous polymerizations in dense CO2 have been limited to fluoropolymers because no other polymers have shown strong affinity for CO2 . Heterogeneous polymerizations in dense CO2 are applicable to a wider range of polymers and do not require both the monomer and polymer to be CO2 -soluble. 5.1.2 Heterogeneous Polymerization. Heterogeneous polymerizations in DG employ a continuous dense CO2 phase and one or more other phases where the polymerization reaction takes place. Dispersion, emulsion, precipitation, and suspension polymerizations are the main forms of dense CO2 heterogeneous polymerizations. These four types of heterogeneous polymerizations are differentiated by;77 1. initial state of the reactants 2. particle formation mechanism 3. size and shape of the formed particles Precipitation and dispersion polymerization are the most frequently used.71,77,111 At the beginning of the precipitation polymerization process, the monomer and the initiator are soluble in the continuous phase (dense CO2 ), and as the polymer forms and exceeds a certain Mw , it precipitates out of the continuous phase. Precipitation polymerization in dense CO2 uses free-radical or cationic chain growth as the reaction mechanism, and is popular because the product can be extracted immediately after the reaction in a dry state. Upon depressurization and added flushing with dense CO2 , a dry solvent-free product can easily be collected. Studies have shown that the morphology of the product from a precipitation polymerization was not as consistent as polymer particles produced using dispersion polymerization.77,101 In one case, Cooper had synthesized relatively uniform microspheres using precipitation polymerization (void of stabilizers); however, it was under very specific reaction conditions.101 According to Cooper, the uniform microspheres were produced because of the nature of the polymer (divinylbenzene (DVB)) rather than the properties of the process. Dispersion polymerizations have similar starting conditions to precipitation polymerizations because the initiator and monomer are also CO2 -soluble. The resulting product is coated by amphipathic molecules (surfactants, stabilizers) as it precipitates out of the CO2


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phase.71 The amphipathic coating is a colloid stabilizer which is used to help produce uniform particles ( Et(Ind)2 ZrCl2 > Cp2 ZrCl2 . ii. Me2 Si(Cp)(NtBu)TiCl2 showed the maximum activity and p-MeSt incorporation. The average p-MeSt content, as a function of the structural variation of the experimental metallocenes, ranged from 1.3 to 40 mol%. iii. In the copolymer backbone, p-MeSt, instead of end-capping the chain, was randomly distributed. This result particularly differs from what Pellechia et al.16,17 noted for styrene using Cp∗ TiMe3 -B(C6 F5 )3 . iv. Et(Ind)2 ZrCl2 , unlike Cp∗ TiMe3 -B(C6 F5 )3 , produced high molecular weight ethylene/styrene and ethylene/p-MeSt copolymers. No cooligomers were obtained. Me2 Si(Cp)(NtBu)TiCl2 synthesized ethylene/propylene)/p-MeSt and ethylene/1octene/p-MeSt terpolymers. The molecular weight distributions were narrow, PDI = 2–3. Chung and Dong,24 and Dong and Chung25 also copolymerized ethylene with pMeSt; however, in the presence of hydrogen—the conventional chain-transfer agent. The following metallocenes were used: Cp∗ 2 ZrCl2 , (nBuCp)2 ZrCl2 , Cp2 ZrCl2 , Et(Ind)2 ZrCl2 , and Me2 Si(Cp)(NtBu)TiCl2 . The objectives were to study the influence of (a) opening at the active sites on the catalyst performance and product properties; and (b) hydrogen on the resulting copolymer backbone. The openings at the active sites increase in the order the above metallocenes have been reported. Cp∗ 2 ZrCl2 with the most closed active site did not incorporate p-MeSt. On the other hand, the constrained geometry Me2 Si(Cp)(NtBu)TiCl2 with the most open active site exhibited a very high level of copolymerization activity. The effect of hydrogen was found to depend on the structure of the experimental metallocenes. For Me2 Si(Cp)(NtBu)TiCl2 , hydrogen did not affect the resulting copolymer backbone, which means that the insertion of p-MeSt as the pendant side groups was retained. However, for Cp2 ZrCl2 and (nBuCp)2 ZrCl2 , corresponding to a given p-MeSt

Synthesis of Functional Polyolefins using Metallocenes H2

CH2 CH2 CH M

181

CH2 CH3

p-MeSt CH2 CH2 CH2 CH Ph

H2 CH2 CH2 CH2 CH2

CH3

CH3

Scheme 2.1. The chain transfer mechanism of copolymerization of ethylene with p-MeSt in the presence of hydrogen.25

feed concentration, the increase in hydrogen concentration increased the catalyst activity, and decreased the molecular weights. The resulting copolymer chain showed Me or p-MeSt end groups. This is opposite to what happened with Me2 Si(Cp)(NtBu)TiCl2 . See Scheme 2.1. The p-MeSt mol% in the copolymer, and the PDI did not significantly vary.24,25 2.2.2 Synthesis of Polypropylenes with Phenyl or Substituted Phenyl End Groups. From the chemical and structural viewpoint, propylene differs from ethylene. Propylene, unlike ethylene, is prochiral. Therefore, it copolymerized with styrene and p-MeSt in a different fashion.26–29 Et(Ind)2 ZrCl2 synthesized isotactic polypropylene backbone containing a terminal phenyl (styrene) or p-MeSt group. This is a spectacular difference from what happens when ethylene is copolymerized with styrene or p-MeSt. See Section 2.1.1. Hydrogen served as the external chain transfer agent while styrene or p-MeSt acted as an in-situ one. With the increase in styrene feed concentration, the catalytic activity, styrene conversion, and the number average molecular weight Mn decreased. Mn ranged from 23,500 to 10,000 g/mol. However, the average styrene content in the copolymer showed the opposite trend. Also, an increased amount of hydrogen was needed to maintain high catalyst activity and styrene conversion. Me2 Si[2-Me-4-Ph(Ind)]2 ZrCl2 , like Et(Ind)2 ZrCl2 , evidenced similar results but Mn ranged from 4,600 to 1,800 g/mol.27,28 It further demonstrated the following:24,25 i. The Mw of the resulting polymers was proportional to [propylene]:[p-MeSt]. ii. Corresponding to a given p-MeSt feed concentration, the increasing concentration of hydrogen increased the catalyst activity and the conversion of p-MeSt. The p-MeSt mol% in the polymer backbone remained fairly unaffected. However, it increased with the increase in p-MeSt feed concentration. iii. Hydrogen was necessary to complete the chain transfer reaction to p-MeSt. Scheme 2.2 illustrates the mechanism of copolymerization of propylene with p-MeSt using Me2 Si[2-Me-4-Ph(Ind)2 ]ZrCl2 in the presence of H2 . During the polymerization of propylene (with 1,2 insertion), the propagation Zr–C site (II) can also react with p-MeSt (with 2,1 insertion) to form p-MeSt-terminated PP (III). The catalytic Zr–C site in compound (III) becomes inactive to propylene and p-MeSt due to (a) the steric hindrance between the active site (Zr–C) and the incoming monomer (propylene with 1,2 insertion), and (b) the formation of a complex with the adjacent phenyl group. However, in the presence of H2 the dormant Zr–C (III) species can react with H2 to form PP–t–p-MeSt (V) and regenerate a Zr–H species (I) that can reinitiate the polymerization

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Scheme 2.2. The mechanism of copolymerization of propylene with p-MeSt using Me2 Si[2-Me-4Ph(Ind)2 ]ZrCl2 in the presence of H2 chain transfer agent.30

of propylene to continue the cycle. Overall, this whole process resembles sequential chain transfer reactions first with p-MeSt, next with H2 . 2.2 Co- and Terpolymerization of Olefins with 1,4-Divinylbenzene Chung and Dong30–32 copolymerized ethylene with 1,4-divinylbenzene (DVB) using Cp2 ZrCl2 , Ind2 ZrCl2 , Et(Ind)2 ZrCl2 , Me2 Si(Ind)2 ZrCl2 , and (C5 Me4 )Me2 Si(Cp) (NtBu)TiCl2 . Et(Ind)2 ZrCl2 turned out to incorporate maximum 1,4-DVB (7.2 mol%). This product showed Tm = 88.2◦ C and Mw = 34,000 g/(g mol). They and also Dong et al.33 conducted the following terpolymerization reactions: Polymerization systems i. (Ethylene + 1-octene)/divinyl benzene [EO-DVB] ii. (Ethylene + propylene)/divinyl benzene [EP-DVB]

Zirconocene catalyst type Et(Ind)2 ZrCl2 , Me2 Si(Cp)(NtBu)TiCl2 , and Cp2 ZrCl2 Et(Ind)2 ZrCl2 and Me2 Si(Cp)(NtBu)TiCl2

They noted that the catalyst type influenced the incorporation of divinyl benzene. For the (ethylene + 1-octene)/divinyl benzene system, the divinyl benzene incorporation capability varied as follows: Me2 Si(Cp)(NtBu)TiCl2 >Et(Ind)2 ZrCl2 >Cp2 ZrCl2 (poor incorporation). However, for the (ethylene + propylene)/divinyl benzene system, Et(Ind)2 ZrCl2

Synthesis of Functional Polyolefins using Metallocenes

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and Me2 Si(Cp)(NtBu)TiCl2 showed comparable incorporation capability. Each catalyst produced a high molecular weight product for either of the terpolymerization systems. However, Et(Ind)2 ZrCl2 showed balanced properties with an effective incorporation of comonomers and monoenchainment of DVB. The resulting terpolymers were completely soluble in common organic solvents such as toluene or hexane. The following selected properties were reported:

Terpolymer type

DVB (mol%)

Properties Mw (g/mol)

Tg (◦ C)

EP-DVB EO-DVB

1.1−21.1 2.0−8.0

86,000−138,000 69,000−136,000

–22 to –51 –50 to –60

2.3 Copolymerization of Olefins with Allylbenzene Byun et al.34 first copolymerized ethylene with allylbenzene using Et(Ind)2 ZrCl2 . A random copolymer containing the reactive pendant phenyl group was obtained. This result can be compared with what was obtained during the copolymerization of ethylene with pMeSt using the same metallocene.18–23 In a subsequent study, they investigated the effect of metallocene structural variation on this copolymerization system by using Cp2 ZrCl2 , (nBuCp)2 ZrCl2 , (2-MeInd)2 ZrCl2 , and Cp∗ 2 ZrCl2 .35 The results can be summarized as follows: i. The catalytic activity, compared to homopolymerization of ethylene, increased with the increasing allylbenzene feed concentration. This shows a positive comonomer effect. ii. The incorporation of allylbenzene in the copolymer decreased in the following order: Cp2 ZrCl2 > (nBuCp)2 ZrCl2 > (2-MeInd)2 ZrCl2 > Cp∗ 2 ZrCl2 , and Mw as: Cp2 ZrCl2 > (2-MeInd)2 ZrCl2 > (nBuCp)2 ZrCl2 > Cp∗ 2 ZrCl2 ; 2.2 ≤ PDI ≤ 2.8. iii. The metallocene structure influenced the chain transfer mechanism. The following two mechanisms—β-H elimination and chain transfer to Al (due to the presence of trimethyl aluminum in MAO)—mostly prevail in metallocene-catalyzed olefin polymerization. For Cp2 ZrCl2 and (nBuCp)2 ZrCl2 , the former was predominant while for (2-MeInd)2 ZrCl2 and Cp∗ 2 ZrCl2 , the latter showed to be the major one, which was attributed to the incorporation of the allylbenzene in the propagating chain end. However, exceptions to what has been stated above have also been reported in the literature. For example, in propylene polymerization using metallocenes such as Cp∗ 2 ZrCl2 , chain transfer takes place predominantly via β-Me rather than β-H elimination.36,37 Zheng et al.38,39 used the work of Byun et al.,34 and Byun and Kim35 to incorporate various anhydrides and chlorosulfonic acid group at the para-postion of the pendant phenyl ring of the ethylene-allylbenzene copolymer (that served as a reactive intermediate precursor). See Section 3.3.2 for further discussion. 2.4 Copolymerizationof Olefins with Allylanisole Byun et al.40 copolymerized 4-allylanisole with ethylene using the following zirconocenes—Et(Ind)2 ZrCl2 , (nBuCp)2 ZrCl2 , Cp2 ZrCl2 , Cp∗ 2 ZrCl2 , and (2-MeInd)2 ZrCl2 . The comonomer 4-allylanisole was randomly incorporated as a pendant group in

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the backbone; however, it dropped the catalytic activity. The subsequent transformation of the anisole methoxy (−OCH3 ) group using AlCl3 into a hydroxyl group produced phenolcontaining polyethylenes. This means that ethylene-co-4-allylanisole acted as a reactive intermediate precursor for this final product. The functional group transformation was confirmed using the 1H and 13C NMR assay of the copolymers. The following results were obtained: i. All the metallocenes, except Cp∗ 2 ZrCl2 , despite structural variation formed cooligomers without using any conventional chain-transfer agent (2,900 ≤ Mw ≤ 7,700). ii. The ligand structure of the zirconocene significantly affected the copolymerization of ethylene with 4-allylanisole. The catalyst having bridged or less substituted ligands favored the incorporation of the anisole than the unbridged analogues. Et(Ind)2 ZrCl2 incorporated more allylanisole (6.4 mol%) than the remaining experimental metallocenes. Probably, the accessibility of the comonomer to the catalyst active center affected its insertion. iii. Cp∗ 2 ZrCl2 showed the highest catalytic activity, but the lowest incorporation of the anisole. This indicates that the polymerization activity is affected by the accessibility of the polar functional group (Lewis base) to the metal center. iv. The catalytic activity increased with the increase of the MAO concentration. However, this markedly reduced the incorporation of the anisole and the molecular weight of the resulting copolymer. v. Pretreating the anisole with MAO did not significantly change the activity or the comonomer incorporation, regardless of the pretreatment time. On the other hand, the activity of the catalyst and comonomer incorporation depended on the MAO concentration. vi. The molecular weight of the copolymers decreased with the increase of the MAO concentration. The end group analysis of the products revealed that the chain transfer to aluminum was the dominant chain transfer reaction. vii. The final copolymer was characterized with pendant phenol groups. viii. The activity and Mw varied as a function of the metallocene structures as follows: Activity: Et(Ind)2 ZrCl2 > (nBuCp)2 ZrCl2 , Cp2 ZrCl2 > (2-MeInd)2 ZrCl. Molecular weight: (2-MeInd)2 ZrCl > Et(Ind)2 ZrCl2 > (nBuCp)2 ZrCl2 > Cp2 ZrCl2 . The above order fairly established an inverse relation between activity and molecular weight. For Et(Ind)2 ZrCl2 , the activity of the catalyst and molecular weight of the copolymer decreased as the concentration of the anisole in the feed increased. This deactivating effect was attributed to the complexation between the polar anisole and the catalytic active site. Atiqullah et al.41 copolymerized propylene with allylanisole using Me2 Si(Ind)2 ZrCl2 and Et(Ind)2 ZrCl2 . The weight-average molecular weight Mw decreased linearly as the concentration of allylanisole (AA) in the feed increased. This happened with both metallocenes. Therefore, allylanisole acted as an in-situ chain transfer agent. The chain transfer constant ktr /kp was determined through kinetic modeling. This turned out to be 0.33 and 0.40 for Et(Ind)2 ZrCl2 and Me2 Si(Ind)2 ZrCl2 , respectively. The characterization of the resulting products by 1H NMR demonstrated that allylanisole end-capped the isotactic polypropylene chains which showed to be low molecular weight oligomers; 4.96 × 103 ≤


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Scheme 2.3. Propagation and chain transfer (termination) mechanisms of cooligomerization of allylanisole with propylene.41

Mw ≤ 9.80 × 103. This finding matches what was observed with styrene and p-MeS.26–29 Scheme 2.3 shows the proposed chain propagation and termination mechanisms. During the chain propagation step, propylene gets incorporated into the isotactic backbone through 1,2 regioselective insertion.42 On the other hand the chain termination step involves protonolytic chain transfer by allylanisole (AA). The latter aspect may be attributed to the 2,1 insertion by AA into the propagating Zr+−C site followed by proton transfer, or a four-centered σ –bond metathesis transition state.43,44 The regenerated Zr+−H species is capable of (a) reinitiating the polymerization of propylene, and (b) continuing the polymerization cycle. The 1H NMR spectra of the products did not evidence vinylic chain end resonance (at δ (ppm) = 4.65−4.73),36 suggesting that chain termination (transfer) by β-H elimination (that is, formation of a –CH=CH2 ) did not occur. In a typical 1H NMR spectrum of a typical AA-PP cooligomer, the end-capping by an AA unit is manifest by the resonances at: δ (ppm) = 3.5786 → –OCH3 ; δ (ppm) = 5.8032 → –CH=CHCH2 −Ph (allylic structure). The suppression of β-H elimination may be attributed to the unfavorable β-agostic interaction at the propagating active site with an allylbenzene end unit.24 The representative peak due to the allylic unsaturation supports Scheme 2.3. An eventual consequence of the above terminal chain transfer mechanism is the following. The inserted bulky phenyl group of AA (with the π –electrons therein) is likely to exert steric hindrance and interact with Zr+. See Scheme 2.3. Consequently, the catalytic activity

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of Et(Ind)2 ZrCl2 and Me2 Si(Ind)2 ZrCl2 will decrease with the increasing concentration of AA. This was supported by the cooligomerization trials.

3. Copolymerization of Olefins with Oxygen-Containing Functional Groups 3.1 Graft Copolymerization of Olefins with MMA Methylmethacrylate (MMA) is very important from the application viewpoint; therefore, in this section, it will be discussed first. The copolymerization of an olefin with MMA using transition metal complexes can proceed via 1,2 insertion or 2,1 insertion. During 1,2 insertion, the potential copolymerization could be inhibited by back chelation of the penultimate carbonyl group with the transition metal atom. Consequently, the olefin and the comonomer may be prevented from access to the vacant coordination sites of the transition metal. However, in case of 2,1 insertion, a metal-oxygen enolate bond is formed. Consequently, olefin will not insert due to endothermicity of the insertion step. The metal-oxygen bond (BDEM-O ) dissociation energy is much higher than that of the metal-carbon bond (BDEM-C ) dissociation energy. See Scheme 3.1 and Fig. 3.1.6

Scheme 3.1. Copolymerization of an olefin with MMA.6

An exception to the above occurs when the metal-oxygen enolate species can rearrange to form another carbon-bonded intermediate. Such a system has been discovered in late transition and rare earth metal complexes.6 The research group of Chung5,45–57 have extensively worked on the copolymerization of α-olefins with MMA using the reactive polyolefin intermediate (precursor) approach. The reactive polyolefin was prepared by copolymerizing an α-olefin with a selected “reactive”

Figure 3.1. Bond energy diagram.6


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comonomer such as 5-hexenyl-9-BBN and p-MeSt. Here, the key factor is to select a functional comonomer which should meet the following criteria: i. It should not complex with the metallocenes and be soluble in hydrocarbon polymerization media; ii. It should have good copolymerization reactivity with α-olefins; and iii. It should be facile and subsequently effective to form a stable in-situ intiator to polymerize MMA. By far the most effective reactive comonomers used for preparing PE-g-MMA are boranes5,45–57 and p-MeSt.18–23 The graft copolymerization of α-olefins with MMA proceeds stepwise. The first step synthesizes PE-containing borane and p-MeSt side groups whereas the next step converts the resulting product to PE-g-PMMA. 3.1.1 Synthesis of Polyolefins with Borane Side Groups. The copolymerization of α-olefins and 5-hexenyl-9-BBN (a higher α-olefin-containing borane moiety) is a convenient way to prepare borane-containing polyolefin.5,45–57 The borane moiety does not pre-complex with metallocene and dissolves well in organic solvents used in polymerization.58 The reactivity ratio of the two monomers governs the structure of the resulting copolymer. The bigger the size of the monomer, the lower is usually the activity. Ethylene is generally five times more reactive than propylene. Therefore, the copolymerization of the borane monomer with ethylene59 will be more difficult than with propylene,51–53 or with an α-olefin (1-butene or 1-octene).60 However, the metallocene catalyst offers better reactivity for copolymerization of borane monomer with ethylene. Chung et al.61 copolymerized ethylene with 5-hexenyl-9-BBN using Et(Ind)2 ZrCl2 and Cp2 ZrCl2 . The borane was incorporated as the pendant side group (Scheme 3.2). The resulting product served as a reactive polyolefin intermediate. See Section 3.1.2. Other findings can be summarized as follows: i. Et(Ind)2 ZrCl2 showed overall satisfactory copolymerization performance at the ambient temperature. ii. The concentration of the borane in the resulting copolymer turned out to be proportional to that in the feed. About 50 to 60 wt% of borane monomer was incorporated into the copolymer in about half an hour. iii. The catalytic activity increased with the increase of borane in the initial feed concentration. iv. Cp2 ZrCl2 incorporated less borane than Et(Ind)2 ZrCl2 . v. The presence of the borane moiety made the copolymer air-sensitive. vi. The molecular weight was high with PDI < 3.

Scheme 3.2. Reaction of ethylene with 5-hexen-9-BBN.20

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Scheme 3.3. Synthesis of polyethylene-g-MMA copolymer from borane side groups.63,64

Chung and Xu62 copolymerized the olefin such as ethylene with a borane dimer (9-BBN) using Cp∗ 2 ZrMe2 in the presence of methyltri(pentafluorophenyl)borate [MeB(C6 F5 )3 ] cocatalyst. The borane dimer got incorporated into the growing polyethylene chain as a terminal reactive functional group. This finding differs from what was observed with Et(Ind)2 ZrCl2 and Cp2 ZrCl2 . However, the product backbone is comparable with what Pellechia et al.16,17 noted in the copolymerization of ethylene with styrene using Cp∗ TiMe3 -B(C6 F5 )3 . The above was the first step. In the next step, the resulting borane-terminated copolymer PE-t-B was oxidized by NaOH/H2 O2 to the corresponding hydroxyl-terminated PE-t-OH copolymer. Increasing the concentration of the dimer decreased the catalytic activity and the molecular weight Mw of the PE-t-OH copolymer. Therefore, the dimer acted as an in-situ chain-transfer agent. 3.1.2 Synthesis of Polyolefin-g-MMA Copolymer from Borane Side Groups.. The alkyl-9BBN side groups in polyethylene can be spontaneously oxidized even at very low temperature (–65◦ C) to a peroxide species as shown in Scheme 3.3. The insertion of oxygen increases the unfavorable ring strain into the C–B bonds of the bicyclic ring of 9-BBN. This destroys the stable double chair-form structure. The oxidation reaction selectively takes place at the C–B bond in the linear alkyl group.63,64 This produces the peroxyborane (C–O–O–B) (I) species. The peroxy borane (I) behaves differently from regular benzoyl peroxides. It decomposes by itself even at ambient temperature. The decomposition reaction follows the homolytical cleavage of peroxide to generate an alkoxy radical (C–O∗ ) and a borinate radical (B–O∗ ). The alkoxy radical (C–O∗ ) generated in this way is highly reactive; it initiates radical polymerization with methylmethacrylate. The borinate radical (B–O∗ ) is stabilized by the empty p-orbital of boron by back donating electron density. The growing chain (II) then reacts with MMA to extend the polymer chain to form a graft copolymer. The graft length of (PMMA side chain) is basically controlled by the MMA concentration and reaction time. The PE-g-MMA copolymerization results are listed below:57 i. Oxygen affected the graft efficency. Even though the final stoicheometry of oxygen to boron should be 1:1, the best result was obtained when oxygen was introduced slowly so that O B at any time. An excess of oxygen not only poisoned the free radical polymerization but also overoxidized to boronates. Borates are poor free-radical initiators at room temperature.


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Scheme 3.4. Synthesis of PE-g-MMA graft copolymer from p-MeSt side groups.61

ii. The polarity of the solvent played an important role in the graft reaction. THF was found to be a better solvent than the nonpolar benzene which slowed the reaction probably due to low solubility of oxygen. iii. The FTIR spectrum of PE-g-PMMA showed a strong adsorption band at 1,730 cm−1 corresponding to the ester groups. A high concentration (>65 mol%) of PMMA can be incorporated into PE by a small quantity (0.5 mol%) of borane groups. 3.1.3 Synthesis of Polyolefin-Graft-MMA Copolymer from p-MeSt Side Groups. First we shall review the synthesis of PE-g-MMA, then that of PP-g-MMA. The p-MeSt side groups in polyolefins [Section 2.1.1] can be converted into a polyolefin graft copolymer via anionic polymerization. See Scheme 3.4. Generally, a low concentration (< 1 mol%) of p-MeSt in the copolymer is preferred to prepare the graft copolymer because the resulting graft copolymer will have low graft density and long graft length. The p-MeSt side groups in PE can be effectively metallated at ambient temperature.65 The lithiated PE-p-MeSt copolymer contains several polymeric anions that are homogenously distributed in the polymer chain. The lithiated PE-p-MeSt initiates graft copolymerization of methylmethacrylate which is separated from the homopolymer by solvent fractionation. In most cases, less than 10 wt% homopolymer was obtained. A polar solvent like THF gave poor yield at 0◦ C and 25◦ C, while a nonpolar solvent such as cyclohexane gave better yield. The polar solvent may increase the nucleophilicity of the carbanion, which results in more side reactions. It is interesting to note that the anionic polymerization of polar monomers using butyl lithium as an initiator cannot achieve high yields at ambient temperature. Usually very low reaction temperature (< –20◦ C) is required. In lithiated PE-p-MeSt case, the formed polymeric benzylic lithium is much more stable; therefore, it minimized the side reactions. The graft polymerization of MMA in nonpolar cyclohexane is fairly effective and a sufficiently long graft length can be achieved even at ambient temperature. Lu and Chung66 carried out polypropylene-g-MMA copolymerization using poly(propylene-co-p-MeSt) as starting material. The polypropylene copolymer containing p-MeSt was synthesized using a supported Ziegler-Natta catalyst system: (MgCl2 /TiCl4 /ED [external donor]/AlEt3 . The PP-co-p-MeSt was lithiated similar to PE-co-p-MeSt. However, the reaction was conducted at 70◦ C. The anionic graft polymerization of MMA took place at room temperature without any side reaction. The MMA incorporation was obtained in the range of 23 to 49 mol% having Tg 71.8 to 96.2◦ C and Tm 155.8 to 156.8◦ C.

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3.2 Block Copolymerization of Olefins with MMA The block copolymerization of ethylene with MMA is an important subject. These copolymers have excellent properties as diverse as adhesion, dyeability, printability, printability, gas permeability, and compatibility with other functional polymers. An established technique for improving the interfacial interaction between polymers is to use block and graft copolymer as compatibilizer. The diblock copolymer structure is known to be the most effective of compatibilizers. Usually the compatibility of polymer blends can be improved by adding a small quantity ( 1×106) with narrow polydispersity (PDI < 1.05) was obtained. (C5 Me5 )2 LnR showed excellent ethylene polymerization activity.90–92 Ethylene was copolymerized with MMA in two steps.88 It was first homopolymerized using SmMe(C5 Me5 )2 -THF or [SmH(C5 Me5 )2 ]2 at 20◦ C in toluene under atmospheric pressure. Next, MMA was added. The reaction is shown in Scheme 3.8. Ethylene initially polymerized very rapidly and the reaction completed in 2 min. The polymer properties were as follows: Mn = 10,000, and PDI ∼ = 1.43. However, the subsequent copolymerization with MMA proceeded rather slowly. The reaction was carried out for 2 h at 20◦ C. The resulting polymer was soluble in 1,2,4-trichlorobenzene at 100◦ C but was insoluble in THF or CHCl3 , indicating conversion to the desired block copolymer.

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Scheme 3.7. Reaction showing the formation of PE-b-PMMA.82,89

Scheme 3.8. Copolymerization of ethylene with MMA using SmMe(C5 Me5 )2 catalyst.82

Repeated fractionations of the block copolymer in hot THF did not change the molar ratio of polyethylene to PMMA though PMMA-PE blend is easily extracted with THF. The molar ratio of PE to PMMA blocks could be controlled by feeding MMA in the range of 100:1 to 100:103, when Mn of the initial PE was ∼10,000. However, this ratio of PE:PMMA decreased with an increase of Mn of the initial PE, especially when Mn exceeded 12,000. These findings can be attributed to the encapsulation of the active sites by polyethylene, thus inhibiting the diffusion of MMA to the active sites. As a result further copolymerization was suppressed. Desurmont et al.93–95 synthesized a hydrogenated complex of samarocene [Me2 Si(C5 H3– 3-Me3 Si)2 SmH(THF)2 ] having a binuclear µ-H structure (See Fig. 3.3). The above complex showed high ethylene polymerization activity (2.7 × 104 g PE/mol Sm h). Polyethylenes with Mn = 3 × 104 to 5 × 104 and PDI ∼ = 1.65 were obtained. This complex also exhibited block copolymerization of ethylene with MMA [PMMA:PE 19:81 mol:mol, Mn = 6 × 104 to 7 × 104, PDI ∼ = 1.68] when ethylene was first polymerized and next MMA was added. However, the reverse order of addition induced no block copolymerization. It produced only PMMA homopolymer. Desurmont et al.93–95 also carried out block copolymerization of 1-pentene or 1-hexene with MMA using the following bridged complexes of yttrium and samarium (See Fig. 3.4).

Figure 3.3. Structure of [Me2 Si(C5 H3– 3-Me3 Si)2 SmH(THF)2 ] catalyst.95


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Figure 3.4. Structure of yttrium and samarium complexes.95

The block copolymerization was carried out in two steps. The first step homopolymerized 1-pentene or 1-hexene at 20◦ C in toluene under atmospheric pressure. In the second step, MMA was added to accomplish block copolymerization. Unlike ethylene, 1-pentene or 1-hexene polymerized rather slowly and the polymerization reaction was completed in 24 to 32 h to give poly(1-pentene) (Mn = 2.8 × 104 and PDI = 1.51) and poly(1-hexene) (Mn = 5.3 × 104 and PDI = 2.46, 90% yield) using the yttrium complex. The activity of the samarium complex was much lower than that of the yttrium one. The as-synthesized polymer showed bimodal MWD. However, when this was washed with hot hexane, a unimodal diblock copolymer was obtained. Desurmont et al.93–95 also prepared tri-block copolymers (ABA type) using ethylene and MMA. Here, two different samarium complexes were used. See Fig. 3.5. Compared to Catalyst 4, Catalyst 3 showed both lower catalytic activity and MMA incorporation, and produced polyethylene of higher molecular weight. However, Catalyst 4 synthesized MMA-co-Ethylene-co-MMA triblock polymer with molecular weight much greater than that obtained by using Catalyst 3.

3.3 Copolymerization of Olefins with Alcohols, Acids, and Ethers Olefins have been copolymerized with alcohols, acids, ethers, and oxazolines using metallocenes, according to the following three routes:

Figure 3.5. Structure of two different samarium complexes.95

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The polar groups can be protected by either silane or alkylaluminum compounds before polymerization and later on can be converted back to alcohols by washing with a suitable acid. 3.3.1 Direct Copolymerization of Olefins with Alcohols. Aaltonen and Loefgren96 copolymerized ethylene with the methylene spacer-containing 10-undecen-1-ol using (nBuCp)2 ZrCl2 . They found the following: i. Spacer effect: The longer methylene spacer group in the comonomer protected the catalyst from poisoning. ii. Temperature effect: At 60◦ C, an alcohol concentration of 9.9 wt% was incorporated in the product, whereas at 80◦ C, this was 1.2 wt%. Either temperature showed bimodal molar MWD as the alcohol feed concentration was increased. This indicates the formation of two or more active catalyst species. The polymer yield at both temperatures decreased with the increase in the alcohol feed concentration. iii. Reaction time effect: The consumption of ethylene increased with time because of its continued copolymerization with 10-undecen-1-ol. iv. 10-undecen-1-ol effect: The catalyst is deactivated; the Mw decreased; and the MWD broadened with the increase in concentration of 10-undecen-1-ol. When the concentration of 10-undecen-1-ol was increased, its –OH group reacted more with the Me of MAO and its associated/free AlMe3 . As a result, the alkylation of (nBuCp)2 ZrCl2 suffered which affected the generation of the active metallocenium cation; hence, the catalyst deactivated. The latter two phenomena may be attributed to the chain transfer effect of the alcohol as its concentration increased. The bimodal MWD indicates that at least two active species were present. The bimodality was also observed during DSC analysis. Aalotonen et al.97 copolymerized ethylene and propylene with 10-undecen-1-ol using Et(Ind)2 ZrCl2 , Et(Ind)2 ZrCl2 , Me2 Si(Ind)2 ZrCl2 , Me2 Si(2-MeInd)2 ZrCl2 and Me2 Si(2Me-4,5-BenzoInd)2 ZrCl2 . They studied the influence of (a) pretreating the metallocenes with MAO and (b) their structural variation on the above copolymerization reaction. The copolymerization of ethylene with 10-undecen-1-ol showed the following: i. The pretreatment of 10-undecen-1-ol with MAO before initiating polymerization increased the ethylene polymerization rate. ii. The copolymerization activity decreased as Me2 Si[Ind]2 > Me2 Si[2-MeInd]2 > Et[Ind]2 > Me2 Si[2-Me-4,5-BenzoInd]2 ∼ = Ind2 . Me2 Si(2-MeInd)2 ZrCl2 showed almost half the activity of the non-substituted catalyst probably due to sterically more crowded coordination sphere. However, the bulky Me2 Si(2-Me-4,5BenzoInd)2 ZrCl2 showed much higher ethylene homopolymerization activity. This may be attributed to the presence of the electron-donating substituent (Me and Benzo groups). iii. The alcohol incorporation varied as Me2 Si[2-Me-4,5-BenzoInd]2 > Me2 Si[2MeInd]2 > Me2 Si[Ind]2 > Ind2 . The overall incorporation of the alcohol ranged from 0.8 to 13.4 wt%.


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iv. In terms of activity, conversion, and alcohol incorporation, the performance of Me2 Si[2-MeInd]2 and Me2 Si[Ind]2 was better than the remaining ones. v. The Mw can be rated as Ind2 > Me2 Si[2-MeInd]2 > Me2 Si[2-Me-4,5-BenzoInd]2 > Et[Ind]2 . Each metallocene produced high molecular weight polyethylene homopolymer (Mw > 100,000) which significantly decreased upon addition of 10undecen-1-ol. The non-bridged metallocene offered a little broader molecular weight distribution (PDI = 5.0) than the bridged analogues (PDI = 2.0–2.5). vi. The PDI for all the zirconocenes except Ind2 ZrCl2 showed to be comparable and characteristic of single-site catalysts. On the other hand, for copolymerization of propylene with 10-undecen-1-ol, the following findings can be reported: i. The copolymerization activity decreased as Me2 Si[2-MeInd]2 > Me2 Si[2-Me-4,5BenzoInd]2 > Me2 Si[Ind]2 > Et[Ind]2 . ii. The alcohol incorporation varied as Me2 Si[Ind]2 ∼ = Et[Ind]2 > Me2 Si[2-MeInd]2 ∼ = Me2 Si[2-Me-4,5-BenzoInd]2 . iii. In terms of activity, conversion, and alcohol incorporation, the performance of Me2 Si[2-MeInd]2 and Me2 Si[2-Me-4,5-BenzoInd]2 was better than the remaining ones. The overall incorporation of the alcohol ranged from 2.7 to 3.8 wt%. iv. The Mw can be rated as Me2 Si[2-Me-4,5-BenzoInd]2 > Me2 Si[2-MeInd]2 > Me2 Si[Ind]2 > Et[Ind]2 . The addition of a Me substituent in the α–position of each C5 ring dramatically increased Mw . This was attributed to the steric influence of the substituents making chain termination more difficult. v. The PDI for all the zirconocenes showed to be comparable and characteristic of single-site catalysts. Hakala et al.98 and Seppälä et al.99 copolymerized several oxygen-containing olefins—alcohols, ketones, ester, and carboxylic functionalities—with propylene using Et(Ind)2 ZrCl2 . See Fig. 3.6. They noted the following: i. All the comonomers significantly decreased the propylene polymerization activity. ii. The structure of the comonomer markedly affected its polymerizability and the catalyst deactivation. The steric protection of the functional group diminished the deactivating influence of the comonomer. The comonomers containing keto or weakly shielded ester groups poisoned the catalyst to the largest extent. The tertiary alcohols were found less detrimental to the catalyst than the primary and secondary ones. Also, the tert-butyl derivative of 10-undecenoic acid was tolerated better than the methyl ester due to the better protective effect of the bulkier tert-butyl group. iii. The structure of the comonomer chain (straight or branched) affected the activity of the metallocene. The deactivation of the catalyst is due to the interaction between the Lewis acid catalyst components and the free electron pairs of oxygen atoms in the comonomer structures. The interaction leading to catalyst deactivation will weaken if the oxygen atom is shielded by substituents added to the adjacent carbon atoms. Therefore, the activity of the metallocene, demonstrated in Fig. 3.7, was found to be more detrimentally affected by straight-chain alcohols than by the branched ones, reflecting the effect of steric hindrance of oxygen-containing group. Also, of the two esters, the tert-butyl derivative was tolerated better than the methyl ester, evidently again due to the better protective effect of the bulkier tert-butyl group (Fig. 3.6).

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Figure 3.6. Structures of oxygen-containing functional comonomers copolymerized with propylene.98, 99

iv. The longer was the spacer group the better was the incorporation of the comonomer (Fig. 3.7). The highest comonomer content (2.7 wt%) was achieved with 10undecen-1-ol and the highest conversion (12.1 wt%) with 10-undecenoic acid. v. The incorporation of the functional comonomers decreased the melting temperature of the polymer. vi. The molecular weight of the copolymers was slightly lower than that of the propylene homopolymer and the polydispersity index of all the copolymers was typically narrow, as usually evidenced by metallocene catalysts. The aforesaid findings are explained as follows. The interaction between the Lewis acid catalyst components and the free electron pairs of oxygen atoms in the comonomer structures is responsible for deactivating the catalyst. Thus, shielding the oxygen atom by bulky substituents weakens this interaction, which reduces the deactivation. In addition, a longer spacer between the polymerizable double bond and the oxygen atom favored the copolymerizability of the functional comonomer.

Figure 3.7. The effect of shielding and spacer in alcohols on (a) catalyst deactivation and (b) comonomer incorporation.99


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Scheme 3.9. Copolymerization of propylene with 6-t-butyl-2-(1,1-dimethylhept-6-enyl)-4methylphenol using Me2 Si(H4 Ind)ZrCl2 .101

The catalyst deactivation may not be totally avoided when oxygen-containing polar comonomers are added. However, functional groups (such as alcohols and to some extent carboxylic acids) capable of forming stable, protected aluminates are less deactivating than the less acidic and/or less polar groups such as esters.98,99 Also, a selected study on ester groups revealed that the steric protection is important as well. For example, tert-butyl ester deactivated the catalyst to a lower extent than the methyl ester. Kaya et al.100 copolymerized propylene with 10-undecen-1-ol using Et[Ind]2 ZrCl2 . At 30◦ C, they obtained a copolymer that incorporated 0.18 mol% 10-undecen-1-ol, and showed Mw = 16,800 and Tm = 138.2◦ C. Using Me2 Si(H4 Ind)ZrCl2 , Wilen and Nasman101 copolymerized propylene with 6-tbutyl-2-(1,1-dimethylhept-6-enyl)-4-methylphenol, which is a thermooxidative stabilizer. The reaction is shown in Scheme 3.9. The findings can be summarized as follows: i. The synthesized copolymers incorporated 1.3 to 5.5 wt% phenolic units and showed high thermooxidative stability even after prolonged extraction with a mixture of refluxing 2-propanol:cyclohexane (50:50). ii. The addition of the phenolic stabilizer significantly increased the polymerization rate. Thus, the sterically hindered phenolic monomer was found as a polar activator and an effective comonomer to copolymerize with propylene. The initial polymerization rate, compared to that of the homopolymerization of propylene, increased almost 6 times when the phenolic comonomer was added. An increase in activity was also observed when 2,6-di-tert-butylphenol was added during propylene polymerization. The activity enhancement can be attributed to the ability of the phenolic stabilizer to scavenge the free AlMe3 present in MAO.102 iii. The products showed narrow molecular weight distribution, PDI ∼ = 2.0. iv. The incorporation of the comonomer decreased the crystallinity and melting point. Wilen et al.103,104 also copolymerized ethylene with 6-tert-butyl-2-(1,1-dimethylhept6-enyl)-4-methylphenol (a sterically hindered phenolic stabilizer) using Cp2 ZrCl2 , Me2 Si(H4 Ind)2 ZrCl2 , Et(H4 Ind)2 ZrCl2 in the presence of MAO. See Scheme 3.10. The copolymerization was conducted at 20◦ C and 1.6 bar in toluene. This approach of the copolymerization of a stabilizer with an olefin using metallocene proved to be unique for tethering stabilizers on the polyolefin backbone. The following results were obtained: i. The hindered phenol increased up to 3 times the initial rate of copolymerization over that of ethylene homopolymerization for Me2 Si(H4 Ind)2 ZrCl2 and

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Scheme 3.10. Copolymerization of ethylene with 6-tert-butyl-2-(1,1-dimethylhept-6-enyl)-4methylphenol.103

ii.

iii.

iv. v. vi. vii. viii. ix.

Et(H4 Ind)2 ZrCl2 . On the contrary, the non-bridged Cp2 ZrCl2 showed no such increase in activity. The enhancement in catalyst activity was more for propylene (5-fold increase) than ethylene (2- to 3-fold increase). This finding can be attributed to the prochiral nature of propylene and the removal of AlMe3 via reaction with the phenolic comonomer. The level of comonomer insertion depended on the chirality of the metallocenes used. The comonomer insertion level (0.6–6.7 wt%) differed for Cp2 ZrCl2 . It was 2 to 3 times lower than that obtained with the bridged metallocenes. The phenol incorporation by Cp2 ZrCl2 is lower presumably because it is a poor catalyst for prochiral monomers. This is also reported by Kaminsky et al.105 The molecular weight distribution was well below 3 indicating single site catalysis. The Mn of the products synthesized by the above metallocenes ranged from 20,000 to 28,000 with PDI less than 2.6. The melting point and crystallinity of the resulting copolymers decreased with the increase in phenolic content as a result of increased branching. The thermo-oxidative stability of the copolymers produced was very high. The synthesized product was a random copolymer, which contains phenolic longchain branches. Polymerizations conducted at 20◦ C and 80◦ C produced copolymers with very high molecular weight and lower molecular weights, respectively. All the homo- and copolymer pairs showed fairly similar molecular weights and molecular weight distributions. The overall molecular weight was not influenced by the presence of the phenolic comonomer.

Mullins et al.106 copolymerized ethylene and propylene with an hindered allyl phenol (4-allyl-2,6-di-t-butyl phenol) using Me2 SiCp∗ (NtBu)TiMe2 and B(C6 F5 )3 cocatalyst. Hydrogen was used as a molecular weight regulator. Terpolymerization was also carried out using 1-octene. The molecular weight dropped more with ethylene than with propylene. The resulting polymers were reported to show improved coatability and blending characteristics.


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3.3.2 Copolymerization of Olefins with Acids, Andyrides, and their Derivatives. Maleic anhydride (MA)-modified polyolefins are one of the most important classes of functionalized polyolefins in commercial applications. The reason is that they combine low cost, high activity, and good processibility. They are generally chosen to improve compatibility, adhesion, and paintability of polyolefins. Lu and Chung66,107 synthesized maleic anhydride-modified polypropylene having a well-defined molecular structure using borane-terminated PP as an intermediate. The borane terminated PP was prepared by hydroboration reaction of chain end unsaturated PP (u-PP). The u-PP was suspended in THF and a slight excess of 9-BBN was added to initiate the reaction by stirring the whole mixture at 55◦ C for 5 h. The resulting 9-BBN terminated PP was oxidized in presence of maleic anhydride at room temperature by slowly adding stoichiometric quantity of oxygen (vs borane) for ∼4 h. Hydroboration converted this functionalized chain end-unsaturated polypropylene to the borane-terminated polypropylene. The borane group at the end of the polymer chain was selectively oxidized using oxygen to form a stable polymeric radical. This reacted in-situ with maleic anhydride (MA) to produce maleic anhydride-terminated PP (PP-t-MA) having a single MA unit. However, the polymeric radical also copolymerized with styrene (St) and maleic anhydride to produce the PP-b-StMA di-block copolymer. Because of the low tendency of homopolymerization by MA, the PP structure incorporated a low concentration of MA to form the final PP-b-MA copolymer. However, the addition of a small amount of styrene in the PP-B-MA mixture significantly increased the incorporation of MA into the copolymer backbone. The addition of styrene extended the PP chain end, forming an alternating styrene and MA (St-MA) copolymer. In other words, a diblock copolymer of PP-b-(St-MA) was obtained, containing both PP and St-MA segments. The reaction is shown in Scheme 3.11. Kaya et al.100 copolymerized propylene with the methylene spacer-containing 10undecenoyl chloride and 10-undecenoic acid using Et[Ind]2 ZrCl2 . The incorporation of the functional copolymers was 0.14–0.20 mol% while the melting point ranged from 136.2 to 138.7◦ C. The copolymerization with the undecenoyl chloride R-COCl is of interest for the synthesis of polymers with different functionalities through post-modification. The addition of an appropriate polymerization termination agent can incorporate different functional groups in the copolymer. For instance, the addition of water, amines, or alcohols to the polymer solution after the completion of polymerization results in copolymers with carboxylic acid, amide, or ester functionalities, respectively. In the above study, the 1H NMR spectra analysis of the copolymer obtained with R-COCl revealed that free carboxyl acidic groups formed in the polymer backbone during the termination of the polymerization by adding water to the system.

Scheme 3.11. Reaction scheme showing the synthesis of PP-b-(St-MA) copolymer.107

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The synthesis of highly soluble reactive intermediate precursor and functional polyolefins without degradation or crosslinking is a challenge. Zheng et al.38,39 found that ethylene-allylbenzene copolymer originally prepared by Byun et al.34,40 can overcome this situation. They incorporated glutaric anhydride (GA), succinic anhydride (SA), phthalic anhydride (PA), and chlorosulfonic acid at the para-postion of the pendant phenyl ring of the ethylene-allylbenzene copolymer. Friedel-Crafts (FeC) acylation reaction, in the presence of anhydrous aluminum chloride in carbon disulfide introduced the aforesaid anhydrides. The melting temperatures (Tm s) of the acylated copolymers with GA first decreased slowly; then increased significantly with the increase of the amount of carboxyl acid groups.38 The reaction of the ethylene-allylbenzene copolymer with chlorosulfonic acid in 1,1,2,2-tetrachloroethane followed by hydrolysis introduced the acid functionality. The melting temperature increased with the degree of sulfonation. The sulfonated copolymers increased the degradation temperature from 444 to 460◦ C and the surface hydrophilicity compared to the base copolymer.38 3.3.3 Copolymerization of Olefins with Ethers. The copolymerization of olefins with ethylene oxide synthesizes amphiphilic copolymers. Amphiphilic copolymers contain hydrophobic and hydrophilic blocks and show interesting surface properties. They are ideal candidates for many applications such as emulsifiers, dispersants, stabilizers, antifoaming agents in aqueous solutions, and compatibilizers in polymer blends and composites. Lu et al.108 carried out diblock copolymerization of ethylene oxide with polyethylene, syndiotactic polystyrene, poly(ethylene-co-1-octene) and poly(ethylene-co-styrene). The copolymerization was done in two steps; in the first step, borane-terminated polyolefin was synthesized using metallocenes and borane chain transfer agents. In the second step, the borane terminal group was converted to an anionic (—O−K+) terminal group for the subsequent ring-opening polymerization of ethylene oxide. The reactions are detailed in Scheme 3.12. The yield and incorporation of ethylene oxide mildly increased with the initial feed concentration. However, the molecular weight increased far greater. 3.3.4 Copolymerization of Olefins with Oxazolines. Kaya et al.100,109 used Et[Ind]2 ZrCl2 and Me2 Si[2-Me-4,5-BenzoInd]2 ZrCl2 to copolymerize propylene with the following functional comonomers: 2-(9-decene-1-yl)-1,3-oxazoline, 2-(9-decen-1-yl)-4,4-dimethyl-1,3oxazoline, and 2-(4-(10-undecene-1-oxo)phenyl)-1,3-oxazoline. The structures of these comonomers are given in Fig. 3.8. Up to 0.52 mol% oxazoline was incorporated into the polypropylene backbone. The Mn values (8.0 × 103 to 12.0 × 103) evidence the formation

Scheme 3.12. Diblock copolymerization of ethylene oxide with polyethylene, syndiotactic polystyrene, poly(ethylene-co-1-octene) and poly(ethylene-co-styrene).108


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Figure 3.8. Structures of the comonomers: 2-(9-decen-1-yl)-1,3-oxazoline (R- Ox1), 2-(9-decen1-yl)-4,4-dimethyl-1,3-oxazoline (R-Ox2), 2-[4-(10- undecene-1-oxy)phenyl]-1,3-oxazoline (ROx3).100

of approximate cooligomeric products. The acid-functionalized copolymer was obtained by hydrolyzing the 10-undecenoyl chloride copolymer solution. The steric hindrance in the oxazoline ring of the comonomer R-Ox2 potentially reduced catalyst poisoning compared to other oxazolines. An increase in the polymerization temperature decreased the molecular weight, crystallinity, and the melting point of the resulting copolymers.

4. Nitrogen-Containing Polar Functional Groups Nitrogen-containing polar functional groups cover amines, acryl amides, imides, and so on. Polymers containing amino groups have been widely studied and are useful functional polyolefins. This may be attributed to the chemical and structural versatility of the amino functional group. The reactions of amines include those of bases and nucleophiles. 4.1 Copolymerization of Olefins with Amines The structural and functional versatility of amines leads to diverse applications that range from polymer precursors for other functional polymers to ion exchange resins, analytical and preparative chromatography, solid phase synthesis and catalysis, drug delivery, metal ion extraction (hydrometallurgy), light harvesting, and chemical sensors. Amines can enhance adhesion and miscibility in polymer blends and composites, thereby improving the physicalmechanical properties of the polymer. Amines are introduced to the polyolefin backbone either by copolymerization of aminecontaining monomers,110,111 or post-functionalization of polyolefins.112 Stehling et al.110 copolymerized α-olefins such as propylene or 4-methylpentene with alkene-substituted alkoxy amines using [Et(H4Ind)2 ZrMe2 ]/[HNPhMe2 ]+[BPh4 ]−. The copolymerization of propylene with the alkoxyamine offered a product with Mn = 28,000, and PDI = 1.8. The incorporation of the alkoxy amine into the copolymer was well correlated to the feed ratio. The reaction is detailed in Scheme 4.1. The alkoxy amine pendant group in polyolefin backbone was used to initiate free radical polymerization. The above copolymer was also heated at 123◦ C with styrene in presence of acetic anhydride to form graft copolymer. The resulting graft copolymer showed Mn of 210,000 and PDI of 2.0.

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Scheme 4.1. Copolymerization of α-olefins such as propylene or 4-methylpentene with alkenesubstituted alkoxy amines using [Et(H4 Ind)2 ZrMe2 ]/[HNPhMe2 ]+[BPh4 ]−.112

Stehling et al.111 also polymerized functionalized α-olefins such as 5-amino-1-pentenes and 4-amino-1-butenes using dimethyl zirconocenes [(Me5 C5 )2 ZrMe2 , Et(Ind)2 ZrMe2 , (Ind)2 ZrMe2 , Et(H4 Ind)2 ZrMe2 , iPr(tBuCp)(Flu)ZrMe2 ] activated with anilinium borate [HNMe2 Ph]+[B(C6 F5 )4 ]−. The polymerization was done in toluene at room temperature for 1 h. (Me5 C5 )2 ZrMe2 /borate showed the highest polymerization activity for 5-(N,Ndiisopropylamino)1-pentene. (Me5 C5 )2 ZrMe2 /borate was 4 times more active than the (Me5 C5 )2 ZrMe2 /MAO system. The polymer product was characterized by 1H and 13 C NMR spectroscopy. 5-(N,N-diisopropylamino)-1-pentene polymerized to isotactic polyaminopentene by [Et(Ind)2 ZrMe2 ], syndiotactic polymer by [iPr(tBuCp)(Flu)ZrMe2 ], and atactic polymer by (Ind)2 ZrMe2 . The Mn varied from 800 to 8,000. Shiono et al.113,114 synthesized the atactic and isotactic polypropylenes having terminal vinylidine groups using Cp2 ZrCl2 and Et(H4 Ind)2 ZrCl2 . Et(H4 Ind)2 ZrCl2 synthesized isotactic PP in toluene at 20◦ C whereas Cp2 ZrCl2 prepared atactic PP at 0◦ C. The products having vinylidene end groups were first treated with excess borane in benzene, then with excess 1-hexene. The interaction of borane with vinylidine end groups alkylated the borane. The resulting trialkylborane was disproportionated with boron trichloride in xylene at 110◦ C to obtain alkyldichloro borane. This was reacted with 1-butylazide to synthesize polypropylenes having a 1-butylamino group at the end of the polymer chain. The yield was over 80%. The polymer was characterized using FTIR and 1H and 13C NMR spectroscopy. The Tm varied from 115.6 to 116.4◦ C. Shiono et al.,115 in another study, first produced atactic polypropylene macromer (PPM) which was later copolymerized with propylene using Me2 Si[2-Me-4,5-BenzoInd]2 ZrCl2 . The objective was to synthesize isotactic PP with an atactic side chain by copolymerization of propylene with the atactic PPM. The atactic PPM was synthesized using Cp∗ 2 ZrCl2 /MAO and liquid propylene. Here, Cp∗ 2 ZrCl2 /MAO produced vinyl-terminated PP via β-Me transfer, which in contrast to vinyledene-terminated PP, acted as the desired PPM for copolymerization with propylene. It showed a number average molecular weight of 630 and polydispersity index of 2.4. The PPM content in the final copolymer was up to 1.3 mol%. The Mn of the copolymer varied from 45,000 to 48,000. Dong et al.29 synthesized isotactic polypropylene with terminal amine groups using Me2 Si[2-Me-4-Ph(Ind)]2 ZrCl2 . Propylene was copolymerized with an amino-substituted


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styrene [4-{2-[N,N-bis(trimethylsilyl)amino] ethyl}styrene] which also acted as a chain transfer agent. The amino substituent was protected by trimethyl silane. Therefore, the first product was PP-t-St-NSi2 which was finally converted into amine styrene-terminatedpolypropylene, PP-t-St-NH2 , by reacting with hydrochloric acid. The polymer produced showed Mn in the range of 24,000 to 59,000 with PDI 2.1 to 2.5. The Tm varied from 156 to 159◦ C. Hackman et al.116 copolymerized propylene with isocitronellene using Et[Ind]2 ZrCl2 . The lower temperature (30◦ C) favored isocitronellene incorporation more than the higher temperature (60◦ C) however converse was the effect on the activity. The higher temperature lowered the molecular weight. The isocitronellene content in the resulting copolymer varied from 7.8 to 15.6 mol%. 4.2 Copolymerization of Olefins with Acrylonitrile Chung et al.61 copolymerized polyethylene with acrylonitrile using PE-co-p-MeSt as an intermediate. The p-MeSt in PE was effectively lithiated at ambient temperature. The details are given in Section 2.1.1. The resulting lithiated PE-p-MeSt copolymer contained several polymeric anions that were homogenously distributed in the polymer chain. See Scheme 4.2. The lithiated PE-p-MeSt initiated graft polymerization of acrylonitrile. The resulting polymer products were solvent fractionated to separate the homopolymer. In most cases, less than 10 wt% of the homopolymer was obtained. Hexane mildly increased the yield; the incorporation of acrylonitrile was more with hexane than THF. Overall the graft copolymerization of acrylonitrile is less efficient than that of styrene. Polar THF gave poor yield while the nonpolar cyclohexane improved the results. The polar solvent may increase the nucleophilicity of the carbanion, which causes more side reactions. The anionic polymerization of acrylonitrile using butyl lithium as an initiator could not offer high polymer yield at ambient temperature. Usually very low reaction temperature (< –20◦ C) is required. In lithiated PE-p-MeSt, the formed polymeric benzylic lithium is much more stable and therefore, it minimizes the side reactions. The acrylonitrile content varied from 15.0 to 51.2 mol%. Lu and Chung66 graft copolymerized polypropylene with acrylonitrile using poly(propylene-co-p-MeSt) as the starting material. The synthesis of PP-co-p-MeSt and its lithiation is already detailed in Section 2.2.2. The anionic graft copolymerization of acrylonitrile took place at room temperature without any side reaction. The acrylonitrile incorporation reached up to 50 mol%.

Scheme 4.2. Copolymerization of polyethylene with acrylonitrile using PE-co-p-MeSt as an intermediate.61

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4.3 Copolymerization of Olefins with Carbazole Mustonen et al.117 copolymerized ethylene with 9(bicycle[2,2,1]hept-5-en-2-ylmethyl)9H-carbazole (BHMCZ) using Ph2 C(Flu)CpZrCl2 and Ph2 C(Ind)(Cp)ZrCl2 . The polymerization conditions and the π -carboxylic ligand type influenced the formation of the cooligomers. The Flu and Ind ligands produced Mw of 6,250 and 70,200, respectively.

5. Copolymerization of Olefins with Halogen-Containing Polar Functional Groups Shiono and Soga87,118 synthesized terminally halogenated isotactic polypropylene. First, propylene was homo-polymerized using Et(H4 Ind)2 ZrCl2 . The product having terminal C C groups was hydroaluminated by di-isobutylaluminum hydride (isoBu2 AlH) to produce polypropylene having aluminum at one end. This aluminum-terminated polypropylene was next halogenated to produce halogen-terminated polypropylene. See Scheme 5.1. Bruzaud et al.119 carried out homo-, co- and terpolymerization of 11-chloro undec-1ene with ethylene, propylene, and 1-hexene using Et(Ind)2 ZrCl2 . The homo-polymerization of 11-chloroundec-1-ene was done in various solvents. Polymerization did not occur in CH2 Cl2 solvent; however, in toluene or heptane it proceeded to complete conversion. The copolymerization of 1-hexene was also done with 11-chloroundec-1-ene in heptane at molar ratio of 50:60. The copolymer obtained showed Mn of 9,000 with PDI ≈ 2.0. The homo and copolymerization of 5-chloropent-1-ene was also tried. No polymerization occurred, indicating that the catalyst was poisoned. The terpolymerization of 11-chloroundec-1-ene with ethylene and propylene in heptane was conducted at 20◦ C by keeping the ethylene pressure at 1.5 bar while that of propylene at 3.5 bar. The concentration of 11-chloroundec-1-ene was increased up to 0.15 mol/l. The incorporation of the above-chlorinated monomer was maximum 2.0 mol% with Mn of 66,000. The polymers produced in this way contained chlorine pendant groups. These chlorocontaining polymers were first treated with potassium benzoate under phase transfer condition to produce esterified polymer which was further hydrolyzed with potassium hydroxide to produce polymers having hydroxyl pendant groups.

6. Copolymerization of Olefins with Silane-Containing Functional Groups Fu and Marks120 polymerized ethylene with PhSiH3 using (Me5 C5 )2 LnH and Me2 Si(Me4 C5 )2 LnH lanthanocenes. The Mn of the resulting polymers varied from 400 to 98,000 with PDI ranging from 1.8 to 4.9. This shows the promise of lanthanocenes to synthesize oligomeric to polymeric products.

Scheme 5.1. Synthesis of halogen-terminated polypropylene.87,118


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Scheme 6.1. Synthesis of silyl-caped polyolefins either (Me5 C5 )2 LnH or Me2 Si(Me4 C5 )2 LnH.120,121

Fu and Marks120 and Koo et al.121 have reported efficient and selective silanolytic (PhSiH3 , nBuSiH3 , and PhCH2 SiH3 ) chain transfer in organo-lanthanide-catalyzed homogeneous ethylene polymerization and ethylene copolymerization with several α-olefins. A series of silyl-capped polyolefins were produced. In case of homo- and copolymerization of ethylene with 1-hexene using either (Me5 C5 )2 LnH or Me2 Si(Me4 C5 )2 LnH, the primary aryl silane (PhSiH3 ) and the alkyl-silanes (nBuSiH3 , PhCH2 SiH3 ) functioned as efficient chain transfer agents. The Mn ranged from 1,100 to 3,200. The reaction mechanism is shown in Scheme 6.1. Marks and Koo122 copolymerized propylene, 1-hexene, and styrene with PhSiH3 using Me2 SiCp∗ (NtBu)TiMe2 and borate cocatalyst [Ph3 C]+[B(C6 F5 )]−. The objective was twofold: a. Synthesize silyl-terminated polymer; and b. Evaluate the chain transfer capability of the experimental silane. The chain transfer capability of PhSiH3 was affected by the monomer type as follows: propylene (Mw = 43,000), 1-hexene (Mw = 2,500), and styrene (Mw = 72,000). It appears that 1-hexene also acted an in-situ chain-transfer agent. Makio et al.123 copolymerized ethylene with n-hexyl-SiH3 using the supported catalyst system SiO2 /MAO/Cp2 ZrCl2 . The activity and molecular weight decreased with the increase of the silane amount in the fresh feed. The product molecular weight varied from 6,000 to 7,000. Arriola et al.124 cooligomerized propylene with allyldimethylsilane in the presence of hydrogen. They used Me2 Si(Me4 C5 )(tBuN)Ti(1,3-pentadiene) and (PhF5 )3 B cocatalyst. The molecular weight of the resulting product varied from 78,000 to 232,000.

7. Copolymerization of Olefins with Dienes and Cyclic Olefins The copolymerization of ethylene or α-olefins with cyclic olefins produces cycloolefin copolymers (COC), a new amorphous thermoplastic material. COC polymers are characterized by excellent transparency and very high, long-life service temperatures. They are solvent resistant and can be melt-processed.

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Marathe and Sivaram125 copolymerized ethylene with 5-vinyl-2-norbornene (VNB) using Cp2 ZrCl2 . The copolymer produced showed pendant vinyl groups, which were oxidized to epoxy functional groups. See Scheme 7.1. The VNB content in the synthesized copolymer ranged from 6 to 14 mol%. The EVNB copolymer was then oxidized using m-chloroperbenzoic acid to produce the epoxy functional groups. The pendant vinyl groups of the resulting copolymer were also oxidized to hydroxyl functional groups as follows. The copolymer was first hydroborated with 9-BBN, then oxidized using NaOH and H2 O2 . See Scheme 7.2. Radhakrishnan and Sivaram126 copolymerized ethylene with a symmetrical diene namely 2,5-norbornadiene (NBD) using Cp2 ZrCl2 , (nBuCp)2 ZrCl2 , Et(Ind)2 ZrCl2 and Me2 Si(Cp)2 ZrCl2 . See Scheme 7.3. Ethylene readily copolymerized with NBD by Cp2 ZrCl2 through one of the double bonds. Copolymers with as high as 19 mol% NBD were synthesized without any cross linking which was evidenced by the solubility of the resulting copolymers in toluene at room temperature. (nBuCp)2 ZrCl2 increased the catalyst activity as well as the copolymer molecular weight, maintaining the same level of NBD incorporation. In case of Et(Ind)2 ZrCl2 , the catalyst activity as well as the incorporation of NBD with increase in molecular weight was observed. Me2 SiCp2 ZrCl2 produced an insoluble copolymer of ethylene and NBD.

Scheme 7.1. Copolymerization of ethylene with 5-vinyl-2-norbornene which was subsequently oxidized to epoxy functional groups.125

Scheme 7.2. Copolymerization of ethylene with 5-vinyl-2-norbornene which was subsequently oxidized to hydroxyl functional groups.125

Scheme 7.3. Copolymerization of ethylene with a symmetrical diene namely 2,5-norbornadiene.135


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The insoluble copolymer showed no unsaturation in FT-IR spectrum, indicating the participation of both endocyclic double bonds in copolymerization that cross-linked the various polymer chains. Monkkonene and Pakkanen127 also copolymerized ethylene with 2,5-norbornadiene using Cp2 ZrCl2 and [Ph2 C(Ind)(Cp)ZrCl2 ]. Cp2 ZrCl2 offered higher activity and molecular weights with less incorporation of NBD than [Ph2 C(Ind)(Cp)ZrCl2 ]. Ethylene copolymerized with NBD in the presence of Cp2 ZrCl2 through one of the double bonds. This produced only one type of copolymer structure with unsaturation on the incorporated NBD. However, [Ph2 C(Ind)(Cp)ZrCl2 ]-catalyzed copolymerization proceeded through both the double bonds. As a result a mixture of copolymers having saturated as well as unsaturated NBD was obtained. The activity of both the catalysts dropped with the increase in the NBD:ethylene feed ratio. The polymers with high NBD content were amorphous and transparent. Uozumi et al.128,129 copolymerized ethylene with 1,9-decadiene using Me2 Si(Flu)2 ZrMe2 . They noted that the combined increase of the diene and the polymerization time increased the copolymer yield and the weight average molecular weight which ranged from 328,000 to 450,000. Schiffino and Crowther130 synthesized an elastomeric terpolymer that consisted of ethylene, propylene, and a diene (ethylidene-norbornene, ENB, using Me2 Si(2, 4Me2 C5 )(Flu)ZrCl2 . The Mn of the resulting products ranged from 15,853 to 19,314; however, the PDI varied from 10.27 to 12.17. The EBN and PP content varied from 2.71−3.15 wt%, and 10.52−11.64 wt%, respectively.

8. Application of Protection and Deprotection Concepts to Synthesize Functional Polyolefins The copolymerization of olefins with polar comonomers encounters several difficulties. The polar groups partly deactivate the catalyst. The transition metals in the metallocene catalysts are often killed by the protic functionality and/or poisoned by heteroatoms such as N, O, etc. High incorporation level of polar monomers usually decreases the molar mass of the polymer.99 However, efforts to prevent deactivation of metallocenes during copolymerization with polar monomers are in progress.131–134 In general, the synthesis of functional polyolefins has involved modifying the catalyst or protecting the monomer itself. The polar comonomers successfully copolymerize with olefins when the Lewis base feature of the comonomer is reduced by masking them with aluminum alkyls, or silanes before copolymerization.134 This step is called protection. After copolymerization, the copolymer is treated with a suitable acid or other chemicals which regenerate these oxygen functional groups. The latter step is called deprotection. The functional groups of polar comonomers have been protected using pre-treatment of the comonomers with alkylaluminum and alkylsilyl compounds. What follows summarizes these protection methods.

8.1 Protection of Functional Groups through Pretreatment with Alkylaluminum Compounds Here, the polar monomers are pretreated with excess trialkylaluminum compounds such as (TIBA) or methylaluminoxane (MAO). However, this approach lowers effective comonomer incorporation into the polymer chain.

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Scheme 8.1. Copolymerization of ethylene with TMA-protected 5-Norbornene-2-methanol using Cp2 ZrCl2 , Et(Ind)2 ZrCl2 and Me2 SiCp2 ZrCl2 .135

Radhakrishnan and Sivaram135 copolymerized ethylene with TMA-protected bicyclo [2.2.1]hept-5-enen-2-methanol (5-Norbornene-2-methanol) using Cp2 ZrCl2 , Et(Ind)2 ZrCl2 and Me2 SiCp2 ZrCl2 . The reaction is shown in Scheme 8.1. The addition of acidic methanol to terminate the polymerization also acted as a deprotection reagent and converted the attached aluminum to alcohol. Me2 Si(Cp)2 ZrCl2 incorporated the maximum comonomer (6.2 mol%) which decreased the catalytic activity. However, the higher Al:Zr ratio increased the activity as well as comonomer incorporation. This observation is quite opposite to the ethylene/bicyclic olefin copolymerization, where the comonomer incorporation decreased with the increase in Al:Zr ratio. The increase in copolymerization temperature also increased the activity. The DSC curve showed two separate melting peaks, indicating a mixture of copolymer with the homopolymer of ethylene. Marques et al.136 synthesized co- and terpolymers of ethylene, propylene, and TMA-protected polar vinyl comonomers having OH and COOH functional groups using Et(Ind)2 ZrCl2 (1), Me2 Si(Me4 Cp)(NtBu)TiCl2 (2), and (2-MeBenzoInd)2 ZrCl2 (3), all activated by MAO. The vinyl comonomers comprised 5-hexen-1-ol and 10-undecen-1-ol and 10-undecenoic acid. TMA and MAO were used to protect the respective functional groups. The above catalysts produced functionalized co- and terpolymers by direct polymerization of ethylene/propylene/hydroxyl-α-olefins. However, Et(Ind)2 ZrCl2 showed appreciable activities for direct polymerization of ethylene, propylene, and carboxy-α-olefins. (2-MeBenzoInd)2 ZrCl2 exhibited better tolerance toward hydroxyolefins. MAO was not as effective as TMA to protect the alkoxy groups by preventing them from binding to the active site. The overall findings can be summarized as follows: i. The presence of the hydroxyl olefins did not significantly decrease the molecular weight of the resulting co- and terpolymers. ii. The molecular weight of the polymers obtained with Me2 Si(Me4 Cp)(NtBu)TiCl2 were slightly lower (Mn = 17.5 × 103 to 54 × 103) than those obtained with Et[Ind]2 ZrCl2 (Mn = 24.7 × 103 to 197 × 103). However, the polydispersities remained in the same range (from 2.0 to 3.9). iii. The molecular weight of the polymers obtained with (2-MeBenzoInd)2 ZrCl2 were, in general, higher than those obtained with the other two catalysts (Mn = 92.8 × 103 to 309.8 × 103). The increasing trend of Mn Me2 Si(Me4 Cp)(NtBu)TiCl2 ) < Et[Ind]2 ZrCl2 < MeBenzoInd)2 ZrCl2 may be attributed to the decreasing space available around the metal center, which is imposed by the ligand architecture. The less space that is available, the less susceptible is the metal center to β-hydrogen elimination; hence, a higher Mn is achieved. Goretzki and Fink132 copolymerized ethylene with 10-undecen-1-ol and 5-norbornene2-methanol protected by trimethyl and triisopropyl silyl groups using homogenous as well as supported Me2 Si(Ind)2 ZrCl2 and iPr(Cp)(Ind)ZrCl2 .


Figure 8.1. A terpolymer backbone of an terpolymer—significance of the carbon atoms.138

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ethylene/norbornene/norbornene

derivative

Protection by trimethyl silane decreased the catalyst activity whereas triisopropyl silane showed good catalyst activity and comonomer insertion. The incorporation of 10-undecen1-oxytriisopropyl silane in the copolymer by the supported catalysts was significantly lower than that by the homogeneous analogues. Goretzki and Fink133 copolymerized ethylene with 10-undecen-1-ol, 5-(N,Ndiisopropylamino)-1-pentene [a sterically hindered amine], and 5-norbornene-2-methanol using homogenous as well as supported Me2 Si(Ind)2 ZrCl2 , iPr(Cp)(Ind)ZrCl2 and iPr(3Me-Cp)(Flu)ZrCl2 ). Here, the functional groups were protected by triisobutyl aluminum (TIBA). This produced alkoxy aluminum alkyls which maintained the polymerization activity and introduced good comonomer insertion. At the end of polymerization, the free hydroxyl groups were regenerated using acidic methanol. The following was observed: i. Pretreating the comonomers with triisobutylaluminum (TIBA) prevented rapid catalyst deactivation. ii. 5-(N,N-diisopropylamino)-1-pentene could be copolymerized without previous complexing with TIBA, because the basic nitrogen of the amino group is mainly protected by the isopropyl groups. iii. The molecular weight of the resulting copolymers varied as a function of the comonomer and catalyst type. See below. Comonomer

Catalyst

10-undecen-1-ol Me2 Si(Ind)2 ZrCl2 /MAO/SiO2 i Pr(3-Me-CpFlu)ZrCl2 5-norbornene-2-methanol 5-(N,N-diisopropylamino)-1-pentene Me2 Si(Ind)2 ZrCl2 Me2 Si(Ind)2 ZrCl2 /MAO/SiO2

Mw 54,200 78,200 to 111,400 21,000 to 146,000 269,000 to 290,000

Alexander and Fink137 copolymerized and terpolymerized ethylene with norbornene having polar groups of alcohol and acid using iPr(Cp)(Ind)ZrCl2 . The polar groups of norbornene were passivated by reacting with triisobutyl aluminum (TIBA). The polar groups were incorporated in the range of 5–12 mol%. In addition to TIBA, trialkyl silanes were also used as protecting agents. The silanes incorporated 5–6 mol% polar groups. Wendt and Gerhard138 synthesized functionalized copolymers and terpolymers of ethylene with TIBA-protected functional comonomers using iPr(Cp)(Ind)ZrCl2 (Fig. 8.1). Protection using TIBA prevented the catalyst from deactivation. The functional comonomers included the norbornene derivatives, 5-norbornene-2-methanol, and 5-norbornene-2carboxylic acid.

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Scheme 8.2. Copolymerization of ethylene with 5-hexene-1-ol pretreated with trimethyl aluminum (TMA) using Et(Ind)(Flu)ZrCl2 .139

The overall findings are summarized below: i. Pre-treatment (protection) of 5-norbornene-2-carboxylic acid with TIBA increased the copolymerization activity with ethylene. However, this increase depended on the feed pressure of ethylene. Molecular weight in the cooligomeric product range was obtained. The average copolymer composition was about 4.5 mol%. ii. Pre-treatment (protection) of 5-norbornene-2-carboxylic acid with TIBA also increased the activity of the above system during terpolymerization with norbornene. Here, norbornene was incorporated more than the acid analogue. It also increased Mw . iii. In ethylene/norbornene/5-norbornene-2-methanol terpolymerization, the activity of the catalyst system was not markedly reduced with the increasing content of 5norbornene-2-methanol in the feedstock. Norbornene was incorporated more than the methanol analogue. iv. Ethylene/norbornene/5-norbornene-2-methanol terpolymerization offered higher activity than the corresponding terpolymerization with the norbornene acid analogue even without protection by TIBA. Mw increased by about two-fold depending on the feed composition. What follows summarizes the copolymerization of 5-norbornene-2-methyleneoxytriethylsilane (TES) and 5-norbornene-2-methyleneoxy-tert-butyldimethylsilane (TBDMS) with ethylene. The protection group was removed by treating the resulting copolymer with a dilute solution of hydrochloric acid in methanol. TBDMS offered higher Mw than TES. The terpolymerization of ethylene/norbornene/5-norbornene-2-methyleneoxyTBDMS using iPr(Cp)(Ind)ZrCl2 can be listed as follows:138 i. TBDMS offered higher activity and molecular weight than TES. ii. In either case, norbornene was incorporated more than norbornene methanol. However, when incorporating both of these two monomers the trialkyl silanes showed a comparable performance independent of the structure. Hagihara et al.139 copolymerized ethylene with 5-hexen-1-ol that was pretreated with TMA which effectively masked the hydroxyl group. Et(Ind)(Flu)ZrCl2 was used as the catalyst. The reaction is shown in Scheme 8.2. The copolymerization activity highly depended on the ratio of [5-hexene-1-oxyl group]:[TMA]. The resulting copolymer incorporated 5-hexen-1-ol up to 50 mol% with almost an alternating sequence. This catalyst system has also been reported to copolymerize ethylene with α-olefins in an alternating manner. The copolymer was insoluble in hot


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toluene; however, it dissolved in polar THF, indicating the presence of a polar group in the copolymer backbone. The PDI was in the range of 1.4 to 2.0. The increasing concentration of TMA lowered the molecular weight of the resulting copolymers due to chain transfer to the Al atom.

8.2 Protection of Functional Groups through Pretreatment with Alkylsilyl Compounds Kesti et al.132 polymerized silyl-protected alcohols, amines, and nonconjugated dienes using selected cationic Group IV zirconocene catalysts. They found that silyl ethers more easily poisoned [(H4 Ind)ZrMe]+X− than [Cp2 ∗ ZrMe]+X−. The chiral [(H4Ind)ZrMe]+X− actively polymerized 4-(tert-butyldimethylsilyloxy)-1,6-heptadiene and 5-(diisopropylamino)-1-pentene but not 4-(trimethylsilyloxy)-1,6-heptadiene or 4(tert-butyldimethylsilyloxy)-1-pentene. Steric effect may protect the polar group. However, the high steric interactions between the protected monomer and the catalyst ligand may decrease the insertion of the polar comonomer into the polymer chain.132,134 Where special trialkylsilyl compounds were utilized as alternative protection groups for norbornenemethanol with lower steric demand to evaluate this effect and to investigate alternative protection groups allowing for higher incorporation rates. The importance of sterical contribution of the protecting group to limit the accessibility of oxygen atom (catalyst poisoning moiety) to the metallocene metal was investigated by copolymerizing ethylene with the polar norbornene derivatives.140,141 The experimental metallocenes were iPr(Cp)(Ind)ZrCl2 , iPr(3-iPrCp)(Ind)ZrCl2 , and iPr(3t BuCp)(Ind)ZrCl2 . Using various trialkylsilyethers with high sterical demand, Fink et al.140 reported high activities and comonomer incorporation (up to 12 mol%) in co- and terpolymerization of these norbornene derivatives with ethylene and norbornene. Figure 8.2 shows the various trialkylsilyl-protected norbornene derivatives that were used in this study. The use of metallocenes with differently substituted Cp ligands affected the polymerization activity due to the various steric interactions between the ligand and the polar norbornene derivatives. The hindering of the formation of 3 (Scheme 8.3) is envisioned to be the key to prevent the catalyst from deactivation. The increasing sterical demand by the protection groups as well as the catalysts formed the inhibited Zr-O-complex and made the norbornene-olefin insertion more favorable. A relationship between the catalyst activity and the steric demand of the protecting group was observed. The kinetic investigations point to a reversible deactivation reaction, during which a bond between the oxygen atom of the polar norbornene derivative and the center of the active catalyst is formed that competes with the olefin coordination and the subsequent insertion. What follows summarizes the results of copolymerization of ethylene with norbornenemethanol protected by iso-propyldimethyl (IPDMS), trialkylsilyl (TES), tertbutyldimethylsilyl (TBDMS), thixyldimethylsilyl (TDMS), and triisopropylsilyl (TIPS), catalyzed by iPr(Cp)(Ind)ZrCl2 . The protecting silyls decreased the activity as follows:141 IPDMS (1a) < TES (1b) < TBDMS (1c) < TDMS (1d) < TIPS(1e) The above order shows that the degree of catalyst deactivation depended on the structure of the protection group. The activity also decreased with the increasing content of norbornene derivative feed composition. The Mw ranged from 1,600 to 12,000.

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Figure 8.2. The structure of alkyl silanes used to protect norbornenemethanol.140, 141

Hakala et al.134 copolymerized ethylene with oxygen-containing comonomers such as 10-undecen-1-ol (I), 10-undecenyl methyl ether (II), 10-undecenyl triethyl silyl ether (III), and 1-undecene (IV) using Et(Ind)2 ZrCl2 . Figure 8.3 shows the structures of these comonomers. The objective was to investigate how the molecular structure around the oxygen atom influences the comonomer incorporation. The comonomer with hydroxyl (I) or ether (II) functionality copolymerized with ethylene under mild conditions offering moderate catalyst activity. However, this activity was much lower than the ethylene

Figure 8.3. Structures of the long-chain oxygen-containing comonomers: (I) 10- undecen-1-ol, (II) 10-undecenyl methyl ether, (III) 10-undecenyl trimethyl silyl ether, and (IV) 1-undecene.134


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Scheme 8.3. Insertion mechanism including deactivation reaction between polar norbornene derivative (comonomer 1) and the metallocene catalyst system 2.140,141

homopolymerization activity. The conversions of the functional comonomers (I and II) were up to 40% whereas that of IV was up to 75%. The catalytic activity for all the comonomers was almost comparable indicating that the trimethyl silyl groups did not act as effective protective groups. The NMR characterization of the final polymer revealed that final functional group in the copolymer of silyl ether was hydroxyl; however, in methyl ether it remained unchanged. The substitution of the hydroxyl group with a trimethylsilyl or methyl ether group did not affect the copolymerization behavior of the comonomers. Similar observations were reported by Goretzki and Fink.132 The copolymerization of functional vinyl comonomers by metallocene catalysts is possible when their Lewis basicity is reduced by masking the functional moiety with alkylaluminums or by adding silyl or other protecting groups to the heteroatom.112,131,132,136 In the copolymerization with 10-undecenyl methyl ether

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(II), the methyl group remained unreacted. This demonstrates that the protection of the oxygen atom via the formation of aluminum alkoxide is not a prerequisite for comonomer incorporation. The oxygen-functionalized comonomers significantly decreased the polymerization activity. Substituting the hydrogen atom of the hydroxyl group of comonomer I with larger methyl or trimethylsilyl groups did not affect the magnitude of catalyst deactivation. MAO did not show any noteworthy differences in the ability of the alcohol I and ethers II and III to copolymerize. As the comonomer copolymerized and even the methyl ether group remained unreacted in the polymerizations reveal that the protection of the oxygen atoms via the formation of aluminum alkoxides, as in the reaction between the hydroxyl group and MAO, is not necessary for comonomer incorporation. The addition of nonfunctionalized IV to the reaction medium was found to increase the polymerization activity. The molecular weights of all the functionalized copolymers were markedly lower than that of the ethylene homopolymer. This effect was more pronounced with the functional comonomers (I, II, and III) than with the nonfunctional analogue (IV). The melting point of the copolymers also decreased. This indicates lower crystallinity due to the incorporation of the side chains. Some of the copolymers with higher amounts of hydroxyl functionality were not completely soluble in 1,1,2,2-tetrachloroethane or 1,2,4-trichlorobenzene. In contrast, all the copolymers with ether functionality were completely soluble. Goretzki and Fink132 used (a) Me2 Si(Ind)2 ZrCl2 and Me2 Si(Ind)2 ZrCl2 /MAO/SiO2 to copolymerize ethylene with 10-undecene-1-oxytrimethylsilane and 10-undecene1-oxytriisopropylsilane, and (b) iPr(Cp)(Ind)ZrCl2 and iPr(Cp)(Ind)ZrCl2 /MAO/SiO2 to copolymerize ethylene with 5-norbornene-2-methyleneoxytrimethylsilane and 5norbornene-2 methyleneoxytriisopropylsilane. They found the following. The trimethylsilyl (TMS) protecting group could not prevent the catalyst from deactivation caused by the addition of the above polar comonomers. The steric effect of TMS was considered not large enough to protect the catalytic active species against the coordination of these polar comonomers. However, protection with the triisopropyl (TIPS) group, which has a higher steric effect, retained good catalyst activity and comonomer content. Therefore, the steric effect of the protecting group strongly influences the polymerization activity and effective comonomer incorporation. The copolymers of ethylene and 5-norbornene-2-methyleneoxytriisopropylsilane, symthesized by iPr(Cp)(Ind)ZrCl2 and the supported iPr(Cp)(Ind)ZrCl2 /MAO/SiO2 , showed two melting points. This can be attributed to the bimodal molecular weight distribution of the resulting copolymers. Novak and Tanaka142 copolymerized methacrylates with ethylene using metallocenes by masking the functional group of the acrylate through preparing nonenolizable forms of this comonomer. This means that the comonomer was prevented in this way from forming enol or enolate intermediates which are of lower energy and are incapable of inserting olefins. This was achieved by converting the acrylate to the corresponding carboxylate salt, which was complexed with Ti(III) as shown in Figure 8.4. Ethylene was copolymerized at room temperature with acrylic acid-titanocene complex and with methacrylic acid-titanocene complex (0.5–37%) in the presence of [Cp2 TiMe]+[MeB(C6 F5 )3 ]− to give titanocene-complexed products (55–98% yield relative to ethylene homopolymerization rated as 100%). The acrylic monomers did not decrease the catalyst activity. The titanocene protective groups were removed by washing with aqueous acid to synthesize copolymers with carboxyl groups.142 See Scheme 8.4. Kesti et al.131 surveyed the copolymerization of olefins with nitrogen-containing polar groups using zirconocenes. Tert-amine-functionalized olefins can be copolymerized in the


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Figure 8.4. Structures of the metallocene–acrylate complexes.142

presence of steric hindrance around the nitrogen atom. As in the case of alcohols,134 the amine can be protected by trimethylsilyl groups.142 Schneider et al.143 copolymerized ethylene with N,N-bis(trimethylsilyl)-1-amino-10undecene using Me2 Si(Benz[e]Ind)2 ZrCl2 which, upon hydrolysis of the silylated amines, synthesized short-chain branched linear low-density polyethylene (LLDPE) having pendent aminoalkyl groups. The incorporation of 1-amino-10-undecene varied between 6 and 19 wt%, which significantly influenced the properties of the resulting LLDPEs. Bis-silylation overcame poisoning of the catalyst because bis-silylated amines are much weaker Lewis bases. The effect of substituents on amines on the copolymerization activity showed that the comonomer where the nitrogen atom was surrounded by the most bulky groups such as tBu and Bz less deactivated the catalysts. However, the comonomer incorporation dropped.99 Dong et al.29 copolymerized propylene with styrene derivatives carrying Cl, OH and NH2 functional groups using Me2 Si(2-Me-4-Ph-Ind)2 ZrCl2 in the presence of hydrogen as a chain transfer agent. The polar OH and NH2 groups on styrene were passivated by trialkyl silane groups before copolymerization. The silane group effectively protected –OH and –NH2 functional groups and was easily deprotected by washing with an acid.

Scheme 8.4. Ethylene/acrylate copolymerization using metallocene catalyst complex.142

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9. Conclusions and Recommendations From the application viewpoint, the catalytic activity and the product properties (average molecular weight, polydispersity index (PDI), and level of comonomer incorporation) are important determinants. In this conclusion, we summarize the advantages and limitations of metallocenes to synthesize functional polyolefins. The advantages are as follows. Metallocenes, depending on their types and structures, as well as those of the comonomer, can synthesize products having varying molecular weights, with 2.0 < PDI < 3.0. The molecular weights can range from macromeric/oligomeric to high values. The macromeric/oligomeric products are potentially suitable for the development of additives whereas the high molecular weight products may add to the application profile of commodity polyolefins, including the synthesis of compatibilizers. On the other hand, the limitations concern significant decrease in the catalyst activity (much below that of homopolymerization); low comonomer incorporation (up to 15 mol%); requirement of at least an equimolar quantity of an Al alkyl to pretreat an OH-containing comonomer, which make the process less economical and pose the problem of Al removal and other residues from the polymer; widespread implementation in existing processes that require heterogeneous (immobilized) catalysts, etc. To overcome these limitations, research continues in parallel using the less oxophilic late-transition metal catalysts. However, comprehensive work, particularly with respect to a wide range of comonomers, remains to be done in this area as well. Finally, we observe the lack of adequate research in the following areas—synthesis of easily soluble functional cooligomer/copolymer; products with a uniform distribution of the comonomer; establishment of relation among catalyst structure, and the various steps of copolymerization (initiation, propagation, and chain termination); degradation and stabilization study of the functional copolymer and correlation of the same with the metallocene structure; and application of supported metallocenes to synthesize the resulting polymers. Therefore, we recommend that the future research on this subject be directed toward these areas, as well as to the minimization of multi-step synthesis, and the development of MAO cocatalyst formulation to improve the activity and comonomer incorporation.

Acknowledgement The authors thankfully appreciate the support provided by the Research Institute and the Center of Research Excellence in Petroleum Refining & Petrochemicals (CoRE-PRP, established by the Saudi Ministry of Higher Education), King Fahd Univeristy of Petroleum & Minerals, Dhahran, Saudi Arabia. The financial support provided by Ciba Plastic Additive Segment at Basel, Switzerland, under Project Number CRP 2219, is gratefully acknowledged. The technical assistance of Mr. Anwar Hossaen is appreciated.

Glossary of Symbols AA Al:Zr ATRP 9-BBN B(C6 F5 )3 B(C6 F5 )4

Allyanisole Aluminum to zirconium ratio Atom transfer radical polymerization 9-borabicyclononane Tri(pentafluorophenyl)borane Tetra(pentafluorophenyl)borane

Synthesis of Functional Polyolefins using Metallocenes BDEM−C BDEM−O BHMCZ BR2− O∗ (nBuCp)2 ZrCl2 s

Bu-Li Bu-SiH3 −CH=CHCH2 -Ph (SiMe2 )(C5 Me4 )(NtBu) (SiMe2 )(C5 Me4 )(NtBu)TiCl2

C6 H5 CH2 SiH3 −CH2 -CH3 CH2 Cl2 [(SiMe2 )(C5 Me4 )(NtBu)TiMe]+[MeB(C6 F5 )3 ]−

13

C NMR C-O∗ COC C-O-O-BR2 C-O-O-B Cp∗ 2 ZrCl2 Cp∗ 2 ZrMe2 [Cp2 ∗ ZrMe]+[B(C6 F5 )4 ]−

[Cp2 ∗ ZrMe]+[MeB(C6 F5 )3 ]−

[Cp2 ∗ ZrMe]+X− Cp∗ TiMe3 Cp2 ZrCl2

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Bond dissociation energy of metalcarbon bond Bond dissociation energy of metaloxygen bond 9-(bicycle[2,2,1]hept-5-en-2ylmethyl)- 9H-carbazole Borinate radical Bis(n-butylcyclopentadienyl) zirconium dichloride Secondary butyl lithium Butylsilane Phenyl propylene Dimethylsilyl tetra methyl cyclopentadienyl-tertiary butyl ammonium Dimethylsilyl tetra methyl cyclopentadienyl-tertiary butyl ammonium titanium dichloride Benzyl silane Ethyl end group Dichloromethane Ion pair of dimethylsilyl tetra methyl cyclopentadienyl (tertiary butyl ammonium) methyl titanium cation and methyl tri(pentafluorophenyl) borate anion Carbon-13 nuclear magnetic resonance Alkoxy radical Cycloolefin copolymers Peroxyl borane group Peroxy borane Bis(pentamethyl cyclopentdienyl) zirconium dichloride Bis(pentamethyl cyclopentdienyl) dimethyl zirconium Ion pair of bis(pentamethylcyclopentadienyl) methyl zirconium cation and tetra (pentafluorophenyl) borate anion Ion pair of bis(pentamethylcyclopentadienyl) methyl zirconium cation and methyl tri (pentafluorophenyl) borate anion Ion pair of bis(pentamethylcyclopentadienyl) methyl zirconium cation and an anion Pentamethyl cyclopentdienyl trimethyl titanium Bis(cyclopentdienyl) zirconium dichloride

220 DSC 1,4-DVB EP-DVB EO-DVB Et(Ind)2 ZrCl2 Et(Ind)2 ZrMe2 Et(Ind)(Flu)ZrCl2 Et(H4 Ind)2 ZrCl2 Et(H4 Ind)2 ZrMe2 Et2 AlCl EVNB FeC FT-IR GC-MS H2 O2 HB(Mes)2 HB(Trip)2 11 B NMR 1 H NMR [HNPhMe2 ]+[B(C6 F5 )4 ]− [HNPhMe2 ]+[BPh4 ]− HOMO Ind2 ZrCl2 [(H4 Ind)2 ZrMe]+X− [(Ind)2 ZrMe]+[MeB(C6 F5 )3 ]−

IPDMS Pr(3-Me-Cp)(Flu)ZrCl2

i

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Pr(Cp)(Ind)ZrCl2

M. Atiqullah et al. Differential scanning calorimeter 1,4-Divinyl benzene Ethylene propylene and 1,4-divinylbenzene Ethylene 1-octene and 1,4-divinylbenzene Ethylene bis(indenyl) zirconium dichloride Ethylene bis(indenyl) dimethyl zirconium Ethylene (indenyl) (fluorenyl) zirconium dichloride Ethylene bis(tetrahydroindenyl) zirconium dichloride Ethylene bis(tetrahydroindenyl) dimethyl zirconium Diethyl aluminum chloride Ethyl-5-vinyl-2-norbornene copolymer Friedel Crafts Fourier transform infrared Gas chromatograph with mass spectrometer Hydrogen peroxide Dimesityl borane Bis(2,4,6-triisopropylphenyl) borane Boron 11 nuclear magnetic resonance Proton nuclear magnetic resonance Ion pair of dimethyl anilinium cation and tetra (pentafluorophenyl) borate anion Ion pair of dimethyl anilinium cation and tetra phenyl borate anion Highest occupied molecular orbital Bis(indenyl) zirconium dichloride Ion pair of bis(tetrahydroindenyl) methyl zirconium cation and any anion Ion pair of bis(indenyl) methyl zirconium cation and methyl tri (pentafluorophenyl) borate anion Isopropyldimethyl silane Isopropylidine (3-methylcyclopentadienyl) (fluorenyl) zirconium dichloride Isopropylidine (cyclopentadienyl) (indenyl) zirconium dichloride

Synthesis of Functional Polyolefins using Metallocenes i

Pr(tBuCp)(Flu)ZrMe2

isoBu2 AlH kp ktr LLDPE LnR(C5 Me5 )2 LUMO MA MAO Me [MeB(C6 F5 )3 ]− (2-MeInd)2 ZrCl2 (2-MeBenzoInd)2 ZrCl2 (Me5 C5 )2 ZrMe2 Me2 Si(Cp)(NtBu)TiCl2

Me2 Si(Cp)2 ZrCl2 Me2 Si(2-Me-4,5-benzoInd)2 ZrCl2

Me2 Si(2-Me-4-Ph-Ind)2 ZrCl2 Me2 Si(Ind)2 ZrCl2 Me2 Si(2-MeInd)2 ZrCl2 Me2 Si(C5 H3– 3-Me3 Si)2 SmH(THF)2

Me2 Si(C9 H6 )2 ZrCl2 Me2 Si(Cp∗ )(NtBu)TiMe2

Me2 Si(Flu)2 ZrMe2 Me2 Si(Ind)2 ZrCl2

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Isopropylidine (tertiary butyl cyclopentadienyl) (fluorenyl) dimethyl zirconium Di-isobutylaluminum hydride Rate of propagation constant Rate of termination constant Linear low-density polyethylene Bis(pentamethylcyclopentadienyl) alkyl lanthanum Lowest unoccupied molecular orbital Maleic anhydride Methyl aluminoxane Methyl Methyl tri(pentafluorophenyl)borate anion Bis(2 methylindenyl)zirconium dichloride Bis(2-methylbenzoindenyl) zirconium dichloride Bis(pentamethylcyclopentadienyl) dimethyl zirconium Dimethylsilylene (cyclopentadienyl) amido tertiary butyl titanium dichloride Dimethyl silylene bis(cyclopentadienyl) zirconium dichloride Dimethyl silylene bis(2-methyl-4,5benzoannelated indenyl) zirconium dichloride Dimethyl silylene bis(2-methyl-4phenyl indenyl) zirconium dichloride Dimethyl silylene bis(indenyl) zirconium dichloride Dimethyl silylene bis(2methylindenyl) zirconium dichloride Dimethylsilylene bis(3-trimethylsilyl cyclopentadienyl) samarium hydride adduct with tetrahydrofuran Dimethylsilylene bis(indenyl) zirconium dichloride Dimethylsilylene (pentamethyl cyclopentadienyl) (tertiary butyl ammonium) dimethyl titanium Dimethylsilylene bis(fluorenyl) zirconium dichloride Dimethylsilylene bis(indenyl) zirconium dichloride

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Me2 Si(H4 Ind)2 ZrCl2 Me2 Si(Me4 C5 )(NtBu)Ti(1,3-pentadiene) Me2 Si(Me4 Cp)(NtBu)TiCl2

(Me5 C5 )2 LnH Me2 Si(Me4 C5 )2 LnH MgCl2 MMA Mn Mw MWD NaOH NBD n BuSiH3 NH2 NMR −OCH3 PDI PE-b-PMMA PE-g-MMA PE-p-MeSt PE-t-B PE-t-OH PhCH2 SiH3 Ph2 C(Flu)(Cp)ZrCl2 Ph2 C(Ind)(Cp)ZrCl2 Ph3 C (PhF5 )3 B PhSiH3 PMMA p-MeSt PP u-PP PP-b-MA PP-B-MA PP-b-MMA

Dimethylsilylene bis(tetrahydroindenyl) zirconium dichloride Dimethylsilylene (tetramethyl cyclopentadienyl) (tertiary butyl ammonium) 1,3-pentadiene titanium Dimethylsilylene (tetramethyl cyclopentadienyl) (tertiary butyl ammonium) titanium dichloride Bis (pentamethyl cyclopentadienyl) lanthanium dihydride Dimethylsilylene bis(tetramethyl cyclopentadienyl) lanthanum dihydride Magnesium dichloride Methylmethacrylate Number average molecular weight Weight average molecular weight Molecular weight distribution Sodium hydroxide 2,5-Norbornadiene n-butylsilane Amine group Nuclear magnetic resonance Anisole methoxy Poly dispersity index Polyethylene block polymethylmethacrylate Polyethylene graft methylmethacrylate Polyethylene para methylstyrene copolymer Borane terminated polyethylene Hydroxyl terminated polyethylene Benzylsilane Diphenyl methyl (fluorenyl) (cyclopentadienyl) zirconium dichloride Diphenyl methyl (indenyl) (cyclopentadienyl) zirconium dichloride Triphenyl carbon Tri(pentafluorophenyl)borate Phenyl silane Polymethylmethacrylate Para methylstyrene Polypropylene Chain end unsaturated polypropylene Polypropylene block maleicanhydride Borane terminated propylenemaleicanhydride copolymer Polypropylene block methylmethacrylate

Synthesis of Functional Polyolefins using Metallocenes PP-b-StMA PP-g-MMA PPM PP-t-MA PP-t-p-MeSt PP-t-St-NH2 i-Pr(Cp)(Ind)ZrCl2 Pst-b-PMMA PSt-t-B PSt-t-OH PVA RAFT R-COCl R-COOH ROH R-Ox SiO2 SMA [SmH(C5 Me5 )2 ]2 SmMe(C5 Me5 )2 -THF

TBDMS TDMS TES Tg THF TIBA TiCl3 TiCl4 TIPS Tm TMA TMEDA UV VNB Zr-H Zr-C –ϕ-CH3

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Polypropylene block styrene maleicanhydride Polypropylene graft methylmethacrylate Polypropylene macromer Maleicanhydride terminated polypropylene Paramethylstyrene terminated polypropylene Amine styrene terminated polypropylene Isopropylene cyclopentadienyl indenyl zirconium dichloride Polstyrene block polymethylmethacryle Borane-terminated polystyrene Hydroxyl-terminated polystyrene Polyvinyl alcohol Reversible addition fragmentation chain transfer Alkyl acid chloride Carboxylic acid Alcohol Alkyl-1,3-oxazoline Silica Styrene maleicanhydride Bis(bis(pentamethylcyclopentadienyl) samarium hydride) Bis(pentamethylcyclopentadienyl) methyl samarium adduct with tetrahydrofuran Tertiarybutyldimethylsilane Thixyldimethylsilane Triethylsilane Glass transition temperature Tetrahydrofuran Triisobutyl aluminum Titanium trichloride Titanium tetrachloride Triisopropylsilane Melt temperature Trimethyl aluminum N,N,N ,N -tetramethyl ethylene diamine Ultraviolet 5-vinyl-2-norbornene Zirconium hydrogen bond Zirconium− carbon bond Para methyl phenyl end group

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125. Marathe, S.; Sivaram, S. “Regioselective copolymerization of 5-vinyl-2-norbornene with ethylene using zirconocenes-methylaluminoxane catalysts: A facile route to functional polyolefins,” Macromolecules, 1994, 27, 1083–1086. 126. Radhakrishnan, K.; Sivaram, S. “Copolymerization of ethylene with 2,5-norbornadiene using a homogeneous metallocene/MAO catalyst system,” Macromol. Chem. Phys., 1999, 200, 858–862. 127. Monkkonene, K.; Pakkanen, T. T. “Synthesis and characterization of poly(ethylene-conorbornadiene),” Macromol. Chem. Phy., 1999, 200, 2623–2628. 128. Uozumi, T.; Miyazawa, K.; Sano, T.; Soga, K. “Alternating copolymerization of ethylene and 1-octene with meso-[dimethylsilylbis(2-methyl-1-indenyl)]zirconium dichloridemethylaluminoxane as catalyst system,” Macromol. Rapid Commun., 1997, 18, 883–889. 129. Uozumi, T.; Tian, G.; Ahn, C.-H.; Jin, J.; Tsubaki, S.; Sano, T.; Soga, K. “Synthesis of functionalized alternating olefin copolymer and modification to graft copolymer by hydrosilylation,” J. Polym. Sci. Part A: Polym. Chem., 2000, 38, 1844–1847. 130. Schiffino, R. S.; Crowther, D. J. (Exxon Mobil Chemicals Patents Incorporated). “Ethylene copolymerization process”, March, 2004, US Patent No: 6,713,574. 131. Kesti, M. R.; Coates, G. W.; Waymouth, R. M. “Homogeneous Ziegler-Natta polymerization of functionalization monomers catalyzed by cationic Group IV metallocenes,” J. Am. Chem. Soc., 1992, 114, 9679–9680. 132. Goretzki, R.; Fink, G. “Homogeneous and heterogeneous metallocene/MAO catalyzed polymerization of trailkylsilyl-protected alcohols,” Macromol. Rapid Commun., 1998, 19, 511–515. 133. Goretzki, R.; Fink. G. “Homogeneous and heterogeneous metallocene/MAO-catalyzed polymerization of functionalized olefins,” Macromol. Chem. Phy., 1999, 200, 881–886. 134. Hakala, K.; Helaja, T.; Lofgren, B.. (2000). “Metallocene/methyl aluminoxane-catalyzed copolymerizations of oxygen-functionalized long-chain olefins with ethylene,” J. Pol. Sci., Part A: Polym. Chem., 2000, 38, 1966–1971. 135. Radhakrishnan, K.; Sivaram, S. “Copolymerization of ethylene with bicyclo[2.2.1]hept-5-ene2-methanol: a facile route to hydroxyl functional polethylenes,” Macromol. Rapid Commun., 1998, 19, 581–584. 136. Marques, M. M.; Correia, S. G.; Ascenso, J. R.; Ribeiro, A. F. G.; Gomes, P. T.; Dias, A. R.; Foster, P.; Rausch, M. D.; Chien, J. C. W. “Polymerization with TMA-protected polar vinyl comonomers. I. Catalyzed by Group 4 metal complexes with d-diimine-type ligands,” J. Pol. Sci., Part A: Polym. Chem. 1999, 37(14), 2457–2469. 137. Alexander, R.; Fink, G. “Homogeneous metallocene/MAO catalyzed polymerizations of polar norbornene derivatives: copolymerization using ethene and terpolymerizations using ethene and norbornene,” Macromol. Chem. Phy., 2000, 201, 1365–1373. 138. Wendt, R. A.; Gerhard, F. “Homogeneous metallocene/MAO-catalyzed polymerizations of polar norbornene derivatives: copolymerizations using ethene, and terpolymerizations using ethene and norbornene,” Macromol. Chem. Phy., 2000, 201, 1365–1373. 139. Hagihara, H.; Murata, M.; Uozumi, T. “Alternating copolymerization of ethylene and 5-Hexen1-ol with [Ethylene(1-indenyl)(9-fluorenyl)]-zirconium dichloride/methylaluminoxane as the catalyst,” Macromol. Rapid Commun., 2001, 22, 353–357. 140. Fink, G.; Wendt, R. A.; Angermund, K.; Jensen, V. R.; Thiel, W. “2: copolymerizations using ethene, and terpolymerizations using ethene and norbornene,” Polym. Mat. Sci. Eng., 2001, 84, 255–256. 141. Wendt, R.; Angermund, A., K.; Jensen, V.; Thiel, W., Fink, G. “Ethene copolymerization with trialkylsilyl protected polar norbornene derivates,” Macromol. Chem. Phy., 2004, 205(3), 308–318. 142. Novak, B. M.; Tanaka, H. “The “if you can’t beat them, join them” approach to olefin-polar comonomer polymerization using metallocene catalysts”, Polym. Mat. Sci. Eng., 1999, 80, 45–55. 143. Schneider, M. J.; Schafer, R.; Mulhaupt, R. “Aminofunctional linear low density polyethylene via metallocene-catalysed ethene copolymerization with N,N-bis(trimethylsilyl)-1-amino-10undecene,” Polymer, 1997, 38, 2455–2459.

Polymer Reviews, 50:231–234, 2010 Copyright © Taylor & Francis Group, LLC ISSN: 1558-3724 print / 1558-3716 online DOI: 10.1080/15583724.2010.493625

Perspective Polymer Microscopy: Current Challenges 2 ¨ LAWRENCE F. DRUMMY1 AND CHRISTIAN KUBEL 1

Materials and Manufacturing Directorate, Air Force Research Laboratory, Wright Patterson AFB, Ohio 2 Karlsruhe Institute of Technology, Institute of Nanotechnology, Eggenstein-Leopoldshafen, Germany

Keywords polymer, microscopy, atomic force microscopy, transmission electron microscopy

The growing demand for lightweight and multifunctional materials systems is pervasive across a multitude of technologies and applications. These systems invariably contain polymeric or organic components, which, through intricate synthetic control and processing techniques, are tailored for optimized properties by tuning the structure from the molecular level to the nano- and bulk scale. The need for an improved morphological understanding across length scales will grow as materials systems become increasingly complex and with that, the need for a sustained investment in education, research, and technology for morphology tools such as microscopy in the field of polymer science and engineering will grow.1 Microscopy has played a leading role in the development of several polymeric material classes such as semicrystalline polymers,2 block copolymers,3 polymer nanocomposites,4 and rigid rod polymers.5 Currently, polymers and macromolecules are used for an incredibly diverse set of materials applications ranging from structural to electrical, both in synthetic and natural materials systems. Microscopy is critical for understanding the structure of these materials, and although significant steps forward have been made in polymer microscopy, there are several major challenges that limit future prospects. This introduction article briefly outlines current challenging areas in polymer microscopy, and the articles in this special issue provide significant steps forward in addressing these challenges.

1. Challenge 1: Preserving Sample Structure The nature of all microscopic techniques is such that it is necessary to perturb the sample in order to characterize it. In scanning force microscopy, for example, the tip can damage the Received May 7, 2010; accepted May 11, 2010. Address correspondence to Lawrence Drummy, Materials and Manufacturing Directorate, Air Force Research Laboratory, 2941 Hobson Way, Wright Patterson AFB, OH 45433. E-mail: [email protected]

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sample, effectively changing the material that is being imaged or characterized. The article by McConney et al.6 in this issue examines this effect in the context of characterizing the elastic modulus of polymeric materials using surface force spectroscopy (including force–distance curves, elastic modulus measurements, and adhesion measurements). Preparation of representative materials surfaces and cross sections or generation of ultrathin films from complex structures such as devices and bulk multicomponent polymeric materials is a major challenge. Preserving the original structure throughout the sample preparation chain can be as much of a limitation as resolution, sample stability, contrast, and the optics of the microscope itself. Focused ion beam (FIB) would allow us to study selected interfaces directly, examining the effects of constraints on polymers and structural changes at surfaces and interfaces (organic–inorganic), which would be a significant advance, although the effect that ion beam damage in the FIB has on the polymer structure is not known in detail.7 Cryomicroscopy is an invaluable tool for nanostructured liquids, hydrated materials, and other macromolecular-based materials not stable in vacuum. A wide range of soft materials systems have been investigated using this technique, with a wealth of morphological information extracted, and this will continue to expand as more laboratories get access to the equipment and hands-on experience with cryopreservation techniques. Current challenges in cryomicroscopy include distortion or collapse of some structures due to confinement in a thin, electron transparent liquid layer, generation of contrast from typically low-Z materials, as well as beam damage. The article by Zhong and Pochan8 in this issue discusses these challenges, as well as techniques such as cryo-TEM tomography and the multitude of polymeric architectures that have been imaged using cryo-TEM in recent years.

2. Challenge 2: Generating Interpretable Contrast In scanning probe microscopy,6 numerous signals can be extracted from a single material/experiment to obtain information about the mechanical, electrical, chemical, and magnetic properties. In electron microscopy, contrast generation from organics and light elements (without the use of staining) has undergone incremental improvements based on control of the electron energy9 and thus the electron–sample interaction and the image formation method: Defocus,10 Zernike phase-plate,11 energy filtered transmission electron microscopy (TEM),12 and Z-contrast high angle annular dark field transmission electron microscopy (HAADF-STEM).13 By increasing the scattering contrast between two phases, the necessary illumination intensity can be reduced while maintaining the same detectability. Thus, the total number of electrons that pass through the sample can be reduced, preserving the structure or allowing for higher electron optical magnification to be used.14 The most significant leaps forward in polymer electron microscopy may be a combination of a phase-plate with Cs -corrected optics. Other approaches to improve contrast while managing sample damage include improvements in detector efficiency, where a lower electron dose could be used to achieve a certain signal level in the image. Also, the actual critical dose of the polymer or the electron dose a certain material can withstand without significant detectable damage can actually be increased by certain methods. These include a reduction in temperature, changing the dose rate, varying the incident electron energy, averaging over many structures (single-particle analysis), and possibly using a pulsed electron beam15 in which the pulse time is shorter than the associated time scale for material damage.16 As is discussed in the articles by Libera and Egerton,17 Martin et al.,18 and Kolb et al.,19 generating interpretable contrast in organic materials is intimately coupled with beam damage challenges, and improvements

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in one or both can significantly increase the amount of directly interpretable microstructural information that can be extracted.

3. Challenge 3: Image Segmentation and Quantitative Microscopy Once detectable contrast between features is generated, for quantitative analysis in most cases those features must be segmented. Image segmentation is the key challenge currently limiting the accessibility of quantitative information from microscopy, and although materials scientists are beginning to use advanced techniques, most of the mathematics and algorithm development has come from the field of signal processing. Modern algorithms minimize the need for user supervision and can extract features from images without the loss of resolution or introduction of artifacts typically associated with traditional image processing. For example, anisotropic or stabilized inverse diffusion equations have been successfully used to detect boundaries in images while maintaining sharpness and definition there.20,21 The set of equations acts as an unstable inverse intensity diffusion near edges and as a stable linear diffusion in regions without edges. This has the effect of both noise removal and edge enhancement in the image. In addition, alternative noise reduction and segmentation techniques based on the watershed algorithm and curvature/energy methods are currently being actively explored. Nevertheless, for complex materials with varying composition and irregular features, automated image segmentation in two dimensions and three dimensions is still the main limiting factor for a full quantitative analysis. In summary, though microscopy has directly contributed to many of the most significant advances in polymer science and engineering, significant barriers remain for the development of the field. As research in general becomes more interdisciplinary, and polymeric materials become increasingly complex, development of microscopy tools will be critical for developing the next generation of polymeric materials.

References 1. Ober, C. K.; Cheng, S. Z. D.; Hammond, P. T.; Muthukumar, M.; Reichmanis, E.; Wooley, K. L.; Lodge, T. P. “Research in macromolecular science: Challenges and opportunities for the next decade,” Macromolecules, 2009, 42, 465–471. 2. Tsukruk, V. V.; Reneker, D. H. “Surface morphology of syndiotactic polypropylene singlecrystals observed by atomic force microscopy,” Macromolecules, 1995, 28, 1370–1376. 3. Spontak, R.; Fung, J. C.; Braunfeld, M. B.; Sedat, J. W.; Agard, D. A.; Ashraf, A.; Smith, S. D. “Architechture-induced phase immiscibility in a diblock/multiblock copolymer blend,” Macromolecules, 1996, 29, 2850–2856. 4. Drummy, L. F.; Wang, Y. C.; Schoenmakers, R.; May, K.; Jackson, M.; Koerner, H.; Farmer, B. L.; Maruyama, B.; Vaia, R. “Morphology of layered silicate- (NanoClay-) polymer nanocomposites by electron microscopy and small-angle X-ray scattering,” Macromolecules, 2008, 41, 2135–2143. 5. Martin, D. C.; Thomas, E. L. “Ultrastructure of poly(para-phenylenebenzobisoxazole) fibers,” Macromolecules, 1991, 24, 2450–2460. 6. McConney, M. E.; Singamaneni, S.; Tsukruk, V. V. “Probing soft matter with the atomic force microscope: force spectroscopy and beyond,” Polymer Reviews, 2010, 50(3), 235–286. 7. Brostow, W.; Gorman, B. P.; Olea-Mejia, O. “Focused ion beam milling and scanning electron microscopy characterization of polymer plus metal hybrids,” Materials Letters, 2007, 61, 1333–1336. 8. Zhong, S.; Pochan, D. “Cryogenic transmission electron microscopy for direct observation of polymer and small molecule materials and structures in solution,” Polymer Reviews, 2010, 50(3), 287–320.

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9. Drummy, L. F.; Yang, J.; Martin, D. C. “Low-voltage electron microscopy of polymer and organic molecular thin films,” Ultramicroscopy, 2004, 99, 247–256. 10. Handlin, D. L.; Thomas, E. L. “Phase contrast imaging of styrene-isoprene and styrene-butadiene block copolymers,” Macromolecules, 1983, 16, 1514–1525. 11. Tosaka, M.; Danev, R.; Nagayama, K. “Application of phase contrast transmission microscopic methods to polymer materials,” Macromolecules, 2005, 38, 7884–7886. 12. Du Chesne, A. “Energy filtering transmission electron microscopy of polymers—benefit and limitations of the method,” Macromolecular Chemistry and Physics, 1999, 200, 1813–1830. 13. Loos, J.; Sourty, E.; Lu, K.; de With, G.; Bavel, S. V. “Imaging polymer systems with highangle annular dark field scanning transmission electron microscopy,” Macromolecules, 2009, 42, 2581–2586. 14. Yakovlev, S.; Libera, M. “Dose-limited spectroscopic imaging of soft materials by low-loss EELS in the scanning transmission electron microscope,” Micron, 2008, 39, 734–740. 15. Shorokhov, D.; Zewail, A. H. “4D Electron imaging: Principles and perspectives” Physical Chemistry Chemical Physics, 2008, 10, 2879–2893. 16. Grubb, D. T. “Radiation damage and electron microscopy of organic polymers,” Journal of Materials Science, 1974, 9, 1715–1736. 17. Libera, M.; Egerton, R. “Advances in the transmission electron microscopy of polymers,” Polymer Reviews, 2010, 50(3), 321–339. 18. Martin, D. C.; Wu, J.; Shaw, C. M.; King, Z.; Spanninga, S. A.; Richardson-Burns, S.; Hendricks, J.; Yang, J. “The morphology of poly(3,4-ethylenedioxythiophene),” Polymer Reviews, 2010, 50(3), 340–384. 19. Kolb, U.; Gorelik, T. E.; Mugnaioli, E.; Stewart, A. “Structural characterization of organics using manual and automated electron diffraction,” Polymer Reviews, 2010, 50(3), 385–409. 20. Dong, X.; Pollak, I. “Multiscale segmentation with vector-values nonlinear diffusions on arbitrary graphs,” IEEE Transactions on Image Processing, 2006, 15, 1993–2005. 21. Frangakis, A. Noise Reduction and Segmentation Techniques Developed for Multidimensional Electron Microscopy of Biological Specimens; Ph.D. thesis, Technical University Munich, 2001.

Polymer Reviews, 50:235–286, 2010 Copyright © Taylor & Francis Group, LLC ISSN: 1558-3724 print / 1558-3716 online DOI: 10.1080/15583724.2010.493255

Reviews Probing Soft Matter with the Atomic Force Microscopies: Imaging and Force Spectroscopy MICHAEL E. McCONNEY, SRIKANTH SINGAMANENI, AND VLADIMIR V. TSUKRUK School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia The development of atomic force microscopy has evolved into a wide variety of microscopy and characterization techniques well beyond conventional imaging. The focus of this review is on characterization methods based on the scanning probe and their application in characterizing physical properties of soft materials. This consideration is broken into three major categories focusing on mechanical, thermal, and electrical/magnetic properties in addition to a brief review of high-resolution imaging. Surface spectroscopy is discussed to great extent and consideration includes procedural information, common pitfalls, capabilities, and their practical application in characterizing soft matter. Key examples of the method are presented to communicate the capabilities and impact that probe-based characterization techniques have had on the mechanical, thermal, and electrical characterization of soft materials. Keywords atomic force microscopy, force spectroscopy, scanning thermal microscopy, kelvin probe force microscopy, scanning probe microscopy, polymers

1. Introduction to Atomic Force Microscopy Imaging The invention of scanning tunneling microscopy (STM) in early 1980 by Rohrer and Binnig at the IBM Zurich Laboratories led to a fast establishment of a new class of microscopy known as scanning probe microscopy (SPM) over the past three decades.1–6 Overcoming the limitations of STM in their application to nonconductive materials, atomic force microscopy (AFM) was introduced as a logical next step in SPM techniques, thereby greatly expanding the imaging and probing capabilities.7 The ongoing development of SPM and nanotechnology remain deeply intertwined and mutually augmented. SPM techniques have several common components, including an ultrasharp probe, sensing elements (Figure 1A), a piezo scanner tube, and a computer-controlled feedback

Received January 20, 2010; accepted April 21, 2010. Address correspondence to Vladimir V. Tsukruk, School of Materials Science and Engineering, Georgia Institute of Technology, 771 Ferst Dr., Atlanta, GA 30332-0245. E-mail: [email protected]

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Figure 1. (a) Schematic depicting the AFM tip interacting with the sample surface and the most common optical technique employed to detect the deflection of the microcantilever. (b) Interaction force–separation distance plot showing the long range attractive regime (noncontact) and short-range repulsive regime (contact). (c) Schematic showing the microcantilever interaction with the sample in the three basic imaging modes of operation of AFM.

loop. One key feature that set SPM-based techniques apart from other microscopy techniques is the use of ultrasharp probes. Apart from imaging the properties with nanoscale resolution, one of the important developments is the manipulation of matter on the surface using a scanning probe. Furthermore, as natural succession to their application as force transducers in AFM, microcantilevers are being extensively investigated as a new platform for transduction in sensing technology in chemical, biological, and thermal sensing.8–13 The unprecedented lateral and vertical resolution offered by SPM techniques enables the visualization of micro-, nano-, and molecular-scale structure of polymer surfaces and interfaces. Under special conditions, atomic resolution is even attainable with SPM.14 Other outstanding advantages of SPM include true three-dimensional (3D) topology, minimal sample preparation, and imaging under a wide variety of environments, including ambient conditions, fluidic conditions, gases, and under different temperatures. Various SPM techniques enable simultaneous probing of the different properties, such as structural, mechanical, electrical, thermal, or magnetic properties with nanoscale resolution. These microscopy methods continue to provide invaluable insight into the understanding structure–property relationship of these materials at nanoscale. SPM can be used to manipulate and pattern soft matter by applying normal and shearing forces and modifying surface topography by repeated scanning.15,16

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Based on cantilever dynamics, AFM operation can be generally divided into static and dynamic modes as shown in Figure 1C. Dynamic modes involve oscillating the cantilever, usually near its resonance frequency. Under dynamic modes, the resonant frequency, amplitude, and phase of the oscillation change due to the interaction between the tip and the sample. Dynamic modes can be carried out in several variations including amplitude modulation (AM-AFM) and/or frequency modulation (FM-AFM). The most common type of dynamic mode AFM, called tapping mode or intermittent contact, is a simple and robust amplitude-modulated AM-AFM technique. On the other hand, in the static mode, the tip is raster-scanned across the surface and the deflection of the cantilever is maintained constant by the feedback control. The readers are referred to several reviews for detailed information regarding AFM-based imaging and discussion of static and dynamic modes.17,18 Under ambient conditions the magnitude of the tip-to-sample force in the contact mode is typically between 1 and 100 nN. This force for a regular tip (radius of few nanometers) results in a pressure of few GPa, which is on the order of yield stress of glassy polymers, thus often causing plastic deformation. On the other hand, the forces are greatly reduced to 0.1–1 nN by performing the scanning in fluid (water, organic solvents, etc.) because the capillary forces are significantly minimized. Overall, imaging in contact mode involves relatively large shear forces, frequently resulting in the damage and distortion of soft surfaces, making it unfavorable for polymeric and biological samples and it is thus employed only in some special cases (e.g., for friction force microscopy, see below). In order to prevent surface damage caused by contact imaging, noncontact modes were developed.19,20 Generally, noncontact modes operate with the probe scanning about 5–40 nm above the sample surface, perturbed by the attractive van der Waals forces between the tip and the sample; see Figure 1B. In order to overcome the limitation of the relatively weak tip–sample interaction force observed under static noncontact mode, the cantilever is set to oscillate at or slightly off of the resonance frequency of the cantilever. The lateral resolution of the dynamic mode is typically limited to 0.5 nm for topography and around 10 nm for other properties. Dynamic modes can reduce the typical operational forces by at least one order of magnitude compared to the contact mode (usually well below 1 nN). It virtually eliminates the shear force associated with the lateral raster scanning and reduces the tip sample contact duration by two orders of magnitude. Noncontact modes have been applied for studying a wide variety of materials such as metals, semiconductors, polymers, and biological materials. These modes offer unique advantages for probing the soft polymeric and biological samples compared to contact AFM. Although in a practical version of noncontact mode, so-called tapping mode, forces are considered minimal, they are nonetheless substantial and might result in surface modification and damage, especially in hard tapping.21 In general, the phase shift at modest tapping forces is proportional to the stiffness of a material, but stiffness is dependent on the contact radius, which is generally larger for softer materials under the same forces. On the other hand, these tip–surface contact area issues are less important under medium-tapping forces, compared to hard tapping forces. Furthermore, because the tip–surface contact area can significantly affect the phase shift angle, it is important to consider the effects of topography when interpreting phase images.22 To date, tapping mode has been extensively employed for imaging a wide variety of polymer surfaces such as hard, glassy polymers; crystalline polymers; rubbers; gels; polymer fibers; polymer blends; block copolymers; and polymer composites. Apart from tracking the surface topography using the weak van der Waals forces, noncontact dynamic mode is employed for probing other weak forces such as electrostatic and magnetic, as discussed later.

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Figure 2. AFM images revealing the conformations of adsorbed P2VP chains: (a) pH 3.89, extended coils; (b) pH 4.04, intermediate state; (c) pH 4.24, compact coils. Plots depicting the (d) RMS end-to-end distance and (e) RMS radius of gyration of P2VP single molecules adsorbed on mica surface versus pH. (Obtained from Roiter and Minko29 with permission from the American Chemical Society.)

One common approach to using lift mode involves a special raster scan where each line is scanned twice before the next line is scanned. In the first line scan, the topography is scanned in a conventional manner, such as tapping mode, and then the probe is lifted by a set amount (several nanometers) and the probe retraces the previous topographic line scan, which thereby effectively eliminates the topographical contributions to these other signals. For comprehensive review of the basic AFM modes of imaging and their application to the various classes of polymers the readers are referred to corresponding reviews and books on the subject.6,17,18,23–28 One very recent notable study was the use of AFM for revealing the conformation of a single polymer chain directly in fluid.29 Using light tapping mode (98% free amplitude) imaging under controlled pH, Minko et al. observed the conformation change in poly(2vinylpyridine) (P2VP) chains adsorbed on atomically flat mica substrates (Figures 2A–C). The P2VP chains exhibited a sharp globule to coil transition with a change in the pH from 4.0 to 3.8. Analysis of the AFM images clearly revealed that the protonation of the P2VP chains (with change in pH) dramatically altered the RMS end-to-end distance and the radius of gyration (Figures 2D and E).29 Tsukruk and coworkers have performed ambient and in-fluid tapping mode imaging of the surface morphology of the mixed covalently grafted brush layer about 5 nm thick composed of Y-shaped binary molecules polystyrene (PS) and poly-(acrylic acid) (PAA; Figure 3).30,31 The surface topography images revealed the nanoscale network-like surface morphology formed by coexisting stretched soluble PAA arms and collapsed insoluble PS chains in water. Exposure to different fluids (selective solvents for individual or either


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Figure 3. Top: Schematics of molecular transformations and AFM images of Y-shaped amphiphilic brushes combining two dissimilar hydrophobic and hydrophilic polymer chains (polystyrene [PS] and poly-(acrylic acid) [PAA]). Bottom: AFM images collected in light tapping mode in different solvents. The images clearly reveal the switching surface morphology depending on the quality of the solvent for individual components of the mixed brushes (adapted from Lin et al.32 Copyright American Chemical Society).

blocks) resulted in dramatic reorganization of the Y-shaped brushes. The structural organization of the brushes ranged from a soft repellent layer covered by swollen PS arms in toluene to an adhesive, mixed layer composed of coexisting swollen PAA and collapsed PS arms in water (Figure 3).32 The motion of macromolecules, polymers, and biomolecules can be observed in real time with AFM.33–37 This technique has been particularly useful in observing the molecular motion mechanisms of proteins. This technique has also been used to observe the reputation of polymers. The reptation of isolated isotactic poly(methyl methacrylate) (it-PMMA) chains deposited on a mica substrate was imaged in the tapping mode (Figure 4). The thin water layer (0.1 nm) adsorbed on the substrate accelerated the reptation movements. The reptation movements were also observed in the noncontact mode (frequency modulation

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Figure 4. 2D (top row) and 3D (bottom row) time-lapse AFM images showing the movements of an isotactic-PMMA chain on mica at lower humidity (34% RH). The arrow indicates movements of a loop along the chain. (Obtained from Kumaki et al.38 with permission from the American Chemical Society.)

mode) in which the tip force acting on the chains is smaller compared to that in the tapping mode.38 Figure 4 shows the detailed conformational changes of it-PMMA chains at 34% RH. The loop indicated by the arrow in the AFM image moved along the chain as shown by the 2D (top) and 3D (bottom) AFM in Figure 4. Though conventional AFM microscopy modes offer unprecedented vertical and lateral resolution, these techniques provide no information about subsurface features, except in the case of features very shallowly buried below the surface. Subsurface features (defects, fillers, and the like) can be nondestructively imaged using methods based on acoustic microscopy in which an acoustic (ultrasonic) wave is transmitted through the sample and


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the amplitude and phase of the acoustic wave are monitored to image the subsurface features. Ultrasonic force microscopy (UFM) is a robust technique developed for subsurface imaging and can be considered as a modification of the standard contact mode of AFM where the sample is oscillated at a high frequency (compared to the resonance frequency of the cantilever) by an additional piezo-resonator.39,40 The microcantilever exhibits nearly 102–104 times higher dynamic stiffness at frequencies much higher than the primary resonance frequency. The fundamental principle involves working in the inertial regime (high dynamic stiffness) of the cantilever and sensing the nonlinearity of the tip surface interaction. The sample oscillating at these higher frequencies exerts a constant additional force on the apparently stiff cantilever, elastically indenting itself into the tip. The modulation of ultrasonic waves passing through the sample thickness due to the varying local stiffness and buried features are detected as modulation of the cantilever deflection. Apart from subsurface imaging, UFM has been employed to probe the local mechanical properties of thin polymer films and composites, especially materials with high elastic moduli.41,42 A major issue with UFM for imaging the subsurface features is the nonlinear tip–sample interaction, which is extremely sensitive to the elastic and viscoelastic properties of the surface. Furthermore, the method is not ideal choice for soft polymeric and biological samples due to the relatively large forces of interaction between the tip and the sample. Overcoming these limitations, scanning near-field ultrasound holography (SNFUH) has been developed in which two ultrasonic waves are setup one from underneath the sample (2.1 MHz) and the other from the cantilever (2.3 MHz), forming a standing wave.43 The phase and amplitude of the sample scattered ultrasound wave, manifested as perturbation to the surface acoustic standing wave, are mapped to unveil the subsurface features.

2. Mechanical Characterization of Polymer Surfaces The AFM is capable exerting and detecting forces orders of magnitude lower than that of the chemical bonds.44 The photodetector has sub-Angstrom sensitivity, resulting in the theoretical ability to measure forces down to 0.1 pN, but noise from thermal, electronic, and optical sources limits the force sensitivity in ambient conditions to about 1 pN, with practical limits closer to 5 pN.44 Therefore, it should be should be quite evident that AFM has the potential to address materials and molecules with minimal forces over minimal surface areas. This part has a major section dedicated to force spectroscopy due to the ubiquitous nature of this method and because there are several techniques that use common fundamentals related to force spectroscopy. 2.1. Probes for Characterizing Mechanical Properties Regular AFM probes are fabricated from silicon or silicon nitride with typical radii of 10–20 and 20–30 nm, respectively. Silicon nitride probes are preferred for very stiff surfaces (the elastic modulus higher than 3 GPa). For these probes, at regular forces exerted during probing mechanical properties the diameter of the contact area usually does not exceed 1–3 nm and thus mechanical or adhesive properties can be probed with near-molecular resolution.45 However, the use of these highly hydrophilic tips is generally feasible for relatively stiff materials (usually with the elastic modulus higher than 1 MPa) with nonhydrophilic and low-adhesive surfaces. In the case of hydrophilic, highly compliant materials (e.g., hydrogels) with sticky surfaces, regular tips are prone to contamination and easy piercing. In these cases, colloidal probes and chemically modified tips should be used.

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Colloidal probes are fabricated by carefully gluing microspherical particles onto the end of a tipless cantilever.46,47 The microparticles are available through several commercial sources and colloidal probes themselves are commercially available as well. Microparticles with a diameter of a few micrometers from silica and borosilicate glass are most commonly used and have roughness below 1 nm for a square micrometer area, acceptable for most measurements of soft materials. Force spectroscopy performed with such probes is usually called colloidal force spectroscopy (CFS). The colloidal probes have several advantages over conventional probes for very compliant materials. A major advantage is that the applied forces per a unit area are significantly lower than conventional probes, thus allowing for probing very compliant materials such as hydrogels with the elastic modulus well below 1 MPa and down to a fraction of kPa and even few Pas.48 By applying less force per unit area, the total applied force can be much higher without plastically deforming the surface or damaging the probe, which provides higher resolution in force/area per a force curve by sacrificing lateral spatial resolution. It is very important to note that probing depths are highly dependent on the probe radius, and therefore colloidal probes are inappropriate for characterizing the stiffness or elastic modulus of ultrathin compliant films. Furthermore, the microparticle radius quoted by the manufacturer is generally quite accurate compared to conventional probes and can be easily verified with SEM. The preservation and well-defined tip shape allow for very good analysis with contact mechanics models that assume spherical shape of the probe, such as the Hertzian approximation (see below). However, care should be taken in preparation to ensure good particle–cantilever contact and that the probing particle surface is not covered with glue. It is also possible that the mechanical properties of the glue between the sphere and cantilever can be sampled instead of the sample itself when measuring stiff samples, such as reinforced polymers. Chemical modification of probes is generally used to enhance or reduce tip–sample interactions, which can be useful for a variety of applications including chemical force microscopy and chain-pulling experiments.49 Probes are usually modified with self-assembled monolayers (SAMs) with thiol chemistry on gold precoated tips or silane chemistry on native silicon oxide surface. Thiol-based surface modification involves coating tips with an adhesion layer followed by a gold coating. Silane modification can be done directly on silicon and silicon nitride tips after thorough cleaning.50 Thiol modification involves noncovalent bonding, which leads to a limited lifetime.50 Though thiol SAMs are an important tool for surface scientists, they are poor surface modifiers for applications involving relatively high forces, such as contact mode technique. On the other hand, silane-based modifications involve covalent bonds, which are quite robust and long-lasting.50 Unfortunately, silane modification involves relatively stringent reaction conditions and is somewhat difficult to initially optimize to achieve single monolayer coverage. The reaction is very sensitive to water presence, so the relative humidity has to be limited to a few percent and dry solvents must be used. On the other hand, thiol modification is relatively straightforward and can be conducted under ambient conditions. The ease of thiol tip modification has led to its extensive use even in contact mode and friction modes, causing widespread characteristic artifacts to be generated. 2.2. Force Spectroscopy 2.2.1. Principles of Force Spectroscopy. Surface force spectroscopy (SFS) is a powerful method to probe the nanomechanical and adhesive properties of surfaces, such as


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quantification of the elastic modulus, adhesion, chemical binding, inter-/intramolecular forces, resilience, elasticity, and more. Modified SFS techniques are also quite useful for electrical and thermal characterization of materials. The so-called pulling-off version of SFS is widely utilized for investigation of protein unfolding, brush stretching, and other tensile-related mechanical properties of individual molecules and requires usually special tip modification with selectively binding groups. Discussion of this approach can be found in some recent papers and reviews and will be not discussed in this review.49,51–57 AFM-indentation based methods that involve plastic deformation can be used to investigate material properties and material failure mechanisms. Indentation methods offer an alternative to elastic SFS measurements, thereby avoiding the difficulty arising from minimizing applied loads. Although AFM indentation-based measurements are an invaluable tool in polymer material analysis, this subject will not be discussed in this review; the reader is referred to relevant papers and reviews.58–61 As a surface-based technique, SFS is well suited to study the effect of free surfaces and confined surfaces on polymeric properties, which can be quite different from bulk properties. Force spectroscopy measurement is a multistep process, which should be done with great care to ensure accurate results and avoid misleading results. Therefore, it is quite important to fully understand the process and the sources of error. Furthermore, like many experimental methods, practice and experience with known samples is invaluable. Every sample behaves somewhat differently and therefore there is usually a learning curve associated with each new sample.62,63 A single force–distance curve is a plot of tip–sample force vs. piezoelement movement (Figure 5A). In Figure 5A is an ideal force–distance curve plotted in the conventional trace–retrace manner. The x-axis can be generally understood as the distance between the tip and the surface. First, the vertical piezoelement is moved in the extension direction, which is depicted in the solid line in Figures 5A and B. In the curve, line 1–2 is called the extension zero-line, which corresponds to the region when the sample is not in contact with the tip but is moving toward the probe. Line 2–3 corresponds to the “jump to contact” region (also known as the snap-to region), when the probe is initially attracted to the sample surface, thereby bending the cantilever downward. The surface is also deformed slightly toward the tip in the snap-to section of the curve. This snap-to section corresponds to an unstable displacement of the tip, where the movement of the free end of the cantilever cannot be directly related to the movement fixed end and therefore the sample penetration is not directly measured. The deflection of the cantilever, when in contact with the sample surface, is indicated by line 3–4. In this region, as the piezoelement moves the sample surface closer toward the cantilever, the cantilever passes from being bent downward through the zero deflection to being bent upward. This region is linear for purely elastic deformation with a slope directly related to surface stiffness. For infinitely stiff substrates that are utilized for sensitivity calibration, the slope is 1, which reflects the fact that the cantilever deflection is exactly equal to the piezoelement displacement. In the case of time-dependent surface deformation (viscoelasticity), nonuniform deformation, or plastic deformation this region becomes highly nonlinear. Point 4 indicates the end of the tip extension sequence and the beginning of the tip retraction sequence. Ideally, lines 3–4 and 4–5 will partially overlap and have the same slope during extension and retraction. Generally, the line 5–6 region represents the force of adhesion, “pulling forces,” or the “snap from contact” event. It is vertical in ideal cases but can display complex shapes in special cases (e.g., “sawtooth” shape for multiple chain unfolding events). Piezoelement hysteresis can be noticeable in this region at high

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Figure 5. (a) An ideal force–distance curve as explained in the text. (b) The deflection data from (a) plotted with respect to time. (c) A schematic explaining the different regions of the force curve. Note that all the numbers in a–c correspond to each other. It is also important to carefully note that in the schematic, the laser spot, cantilever deflection and sample height (piezoelement position) correspond to their positions of the force curve.

frequencies (tens of Hz) appearing as a small initial upward deflection upon the start of retraction. Line 6–7 is again a region where the cantilever is free from the contact with the surface. It is important to note that the applied force is indirectly measured by the AFM by relating the photodiode signal to cantilever deflection and relating cantilever deflection to the applied force. The cantilever spring constant must also be calibrated for each set of force measurements. Force spectroscopy mapping (sometimes referred to as force–volume mode) is a spatial map of force–distance curves collected across a selected surface area. This force–distance curve matrix can be used for sampling statistics, as well as relating surface features to mechanical properties. Calibrating the photodiode sensitivity involves obtaining force curves on a material with a stiffness that is much greater than the cantilever stiffness and therefore can be considered “infinitely hard.” Typically, a freshly cleaned piece of silicon wafer using piranha solution is employed.50 Silicon substrates are immersed for 30 min, followed by several washings under deionized water and then drying under filtered dry nitrogen gas. It is important to be stringent with cleaning of the calibration sample, to ensure that no surface contaminants interfere with the accuracy of the photodiode calibration. Error in the photodiode sensitivity


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causes a shift in all of the data introducing systematic error which can be very significant and requires postmeasurement verification. The photodiode sensitivity calibration is based on relating the known movement of the vertical piezoelement to the cantilever deflection on stiff substrates (e.g., glass or silicon with the elastic modulus of 170 GPa). Several common pitfalls are related to calibrating the photodiode sensitivity, which are mentioned here. Firstly, it is important to have a freshly cleaned sample to prevent surface contaminants common under conventional lab conditions, which can invalidate the assumption that the penetration is zero. Another common pitfall is related to the thermal drift of the piezoelement. As measurements are performed, the piezoelement warms and the response of the piezoelement will drift. The piezoelement movement is calibrated when the scanner is warm and therefore the photodiode calibration should also be performed when the scanner is warm. Thermal drift is not a problem for z-closed loop scanners because the piezoelement movement is independently measured. For scanners without z-closed loop, the scanner can be warmed by “exercising” the piezoelement. In order to prevent tip damage the scanner can be exercised in free air by false engaging. To warm the head, one can perform force curves with relatively large ramps in air for 20–30 min to warm the head. There are several well-developed methods for measuring cantilever spring constants: the most common methods are the added-mass method,64 geometry-based methods,65–68 the spring-on-spring method,69 and the thermal tuning method.70 Special developments in the form of calibration plots and modified equations have been suggested for more complicated cases such as gold-sputtered silicon nitride cantilevers.67,71 Although the developed equations are quite good at expressing the spring constant based on the cantilever geometry, there is usually a significant difference between theoretical spring constants and experimentally measured spring constants.68 The spring-on-spring method can be used to measure cantilever spring constants by performing force curves on a previously calibrated cantilever. This method has good accuracy and can be estimated as roughly 10% when performed with care; it is also relatively easy to perform and is useful in the case when thermal tuning sweep cannot cover the resonance frequency of cantilevers. The thermal tune is generally easier to perform but is not available on all microscopes and for a whole range of relevant frequencies.72,73 It is well known that the finite tip-end dimensions (usually within 5–30 nm) distort the feature sizes of images within nanoscale features because of shape convolution (sometimes called dilation or convolution). Furthermore, tip shape is often the source of common scanning artifacts, such as doubled features or asymmetric tip. Although this is a common imaging problem, in this section we are concerned with tip dimension measurements regarding the tip–sample contact area during force spectroscopy measurements. The size and shape of the SPM tip must be known to quantify the applied force per area. Several methods have been used to measure the tip size and shape. SEM has been used with relatively good success, although the resolution is practically limited to 2–3 nm. Often the imaging should be performed on conductive tips and the accelerating voltage should be limited to avoid charging. It should also be noted that SEM can often lead to the formation of carbon-based structures on the surface from surface contaminations. Another common method involves calculating tip dimensions from images obtained by scanning samples with known dimensions under tapping mode (Figure 6). Often the nanoparticles are embedded in a poly-lysine coating or attached to amine-terminated SAM, which when scanned appears to help to remove tip contamination and prevent nanoparticle rolling and detachment. Scanning standard gold nanoparticles of diameters from 5 to 30 nm that are tethered to a modified atomically flat mica or silicon surface has proven to be quite

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Figure 6. AFM tip deconvolution and dilated image of gold nanoparticle (bottom); AFM image of gold nanoparticles with diameter 20 nm (top).

accurate at characterizing the very end most portion of the tip. The tip can also be characterized with transmission electron microscopy, by measuring the shadow created by the tip with higher resolution. Another method, so-called direct tip imaging, involves scanning microfabricated calibration samples with sharp features available commercially.74,75


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2.2.2. Elastic Modulus via Force Spectroscopy. A common misconception is that accurate (usually better than ±50%) quantitative elastic modulus data cannot be obtained from force spectroscopy. This belief comes from the inability to measure the tip surface contact radius in real time and a cumbersome, extremely time-consuming experimental routine that is rarely followed properly without devastating shortcuts. Furthermore, the unstable nature of the snap-to region prevents the exact knowledge of the contact point and creates a certain discrepancy in the initial penetration thus affecting a long chain of calculation. Ease of damaging soft surfaces is a common problem for these materials. Fortunately, for all practical purposes this problem is not as critical or devastating as perceived. Overall, when all steps are performed with care, the resulting data have shown very good agreement with known elastic modulus data for known materials. Overall, quality SFS results should be considered pretty accurate within 20% deviation beyond initial engagement instabilities, as has already been demonstrated for a number of soft materials.24,76,77 There are many tasks for which SFS elastic modulus measurements with nanoscale resolution are the only viable option, but other options should always be considered when high spatial resolution is not required, such as buckling-based metrology (BBM).78 BBM is much less time consuming and has about the same accuracy as SFS. BBM is very appropriate for ultrathin polymeric samples. Furthermore, generally buckling is used for homogenous samples, although in certain cases can be used to measure the modulus of individual components.79 Freely suspended films can also be characterized using the socalled bulging approach.80 However, every technique has its own set of limitations and issues to consider. Nonetheless, if one must use SFS for elastic modulus measurements there are several critical things to do in order to get high-quality quantitative results, including using a cantilever with an appropriate stiffness, stringently avoid tip damage, preventing sample damage, performing calibrations carefully, and analyzing data properly. Although technical steps for these measurements are well known and documented in multiple notes and manuals, here we will list major steps and offer critical evaluations of uncertainties, issues, and important details that are rarely discuss in casual texts. These subjects will be discussed in detail in the following subsections, except for photodetector and sensitivity calibrations, routines that have already been discussed. 2.2.2.1. Choosing Appropriate Cantilever Spring Constants. In order to properly probe the relative stiffness or quantify the elastic modulus of a surface it is imperative to use a probe with an appropriate spring constant–tip radius combination for the sample with particular stiffness. This strict requirement is a product of inherent nature of cantilever-based transduction; specifically, the fact that the applied force (deflection) sensitivity is inversely proportional to the surface deformation (penetration) sensitivity. Relative stiffness and elastic modulus are measures of the penetration versus deflection; therefore, the implication of this seesaw relationship between the sensitivities is that the ideal ratio of deflection to penetration is 1. Furthermore, measurements with deflection-to-penetration ratios of less than 1 or more than 10 results in the stiffness or modulus going to zero or infinity, respectively, because of instrument limitations. Figure 7 is a generalized graph that indicates the appropriate range of spring constants vs. sample elastic moduli if a standard AFM tip is utilized. This graph is based upon aforementioned criteria verified with actual measurements and is a crude guide for initially choosing the appropriate cantilever spring constants when the elastic modulus can be estimated. This graph is inappropriate for probes with large tip radii, colloidal probes. An

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Figure 7. A graph indicating the upper and lower limits of appropriate cantilever spring constants as a function of sample elastic modulus. The top inset shows that the unstable region above the upper limit corresponds to probing where the cantilever deflection is much larger than the sample penetration. The bottom inset shows that the unstable region below the lower limit corresponds to probing where the cantilever deflection is much larger than the sample penetration. (Adapted from Tsukruk et al.90 Copyright Wiley-Blackwell.)

estimation of the samples’ elastic modulus is required to choose an appropriate probe, which adds to the learning curve associated with measuring new samples. 2.2.2.2. Avoiding Tip Damage. Avoiding tip damage is extremely important to obtaining robust quantitative elastic modulus data, because tip–sample contact models typically require hemispherical (or paraboloid) tip shape and the tip radius. Therefore, when small indentation depth and lateral resolution are not critical and specimens are compliant, colloidal probes should be used. Silicon nitride tips are still sharp but much more resilient than silicon tips. To preserve the tip shape, first, great care should be taken when engaging on surfaces, especially stiffer ones. Engaging in contact mode requires properly setting the difference between the deflection offset and deflection setpoint. The deflection offset is the difference between laser light shined on the top half and bottom half of the quadrant photodiode, measured in units of voltage. The deflection setpoint is a user-defined value, which when engaging is used to define the relative amount of cantilever deflection until the system considers itself engaged. In other words, when engaging, the microscope will continue to move the cantilever toward the sample until the deflection offset matches or exceeds the value of the deflection setpoint. It is important to not engage too hard, or one will destroy the tip. Therefore, the safest approach is to set this difference to be fairly small, which will


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likely falsely engage the tip at first. Then systematically slightly increase the difference, until the probe properly engages on the surface. Usually the deflection setpoint is kept at zero and the deflection offset is altered, which helps to ensure that the laser spot is near the center of the photodetector when the cantilever is engaged. Ensuring that the laser spot is in the center of the photodetector is important. Checking for a false engagement is relatively easy, by changing the deflection setpoint by a small amount (∼0.02 V) in contact scanning mode with the x-y range set to zero and checking for a noticeable change in the z-piezoelement position. It should be noted that this check will not work when the tip has been engaged too hard. Proper engagement on the sample should result in the ability to reach the sample with the piezoelement during extension and pull off the surface of the sample during retraction. It is most common to crack and destroy the tip when calibrating photodetector sensitivity when performing SFS measurements on a hard substrate (elastic modulus above 10 GPa). Unfortunately, it is even more common that the tip shape will not be exactly hemispherical after performing sensitivity, even with utmost care. It is quite difficult to accurately calibrate the photodetector without destroying the tip, especially when using ultrasharp tips with small radius of curvature. A good alternative in avoiding tip damage from sensitivity calibration is offered in a recent method developed involving thermal tuning to estimate sensitivity, without the need to perform force curves.81 This is a little less of an issue for adhesion measurements because typically relatively soft cantilevers can be calibrated with minimal forces, but nonetheless tip shape is just as critical in this case. This problem is much less critical when microscopic colloidal probes are used, where the contact area is much larger. After carefully engaging, the calibration force curves must be obtained extremely carefully. The scanner should be set to take individual curves as opposed to continuously taking curves. The trigger should be extremely small to avoid excessive deformation. That said, the trigger is directly dependent on the photodetector sensitivity. Therefore, initially one should assume a value slightly higher than typical sensitivity to avoid large forces in the first few curves. Typically, triggers should be set to 5–10 nm or less for relatively stiff surfaces and even below 1 nm for very stiff cantilevers. Relatively small ramp sizes should be selected to increase the number of data points in the contact region of the curve and to help prevent tip damage. The number of performed force curves should be minimized; a few (5–10) repeatable measurements at given location is usually sufficient. The engagement and sensitivity measurement should be performed at least several times in different locations to ensure accuracy and eliminate site-specific deviations. It is common to destroy a tip or two in order to estimate the parameters to get force curves in a safe manner. It should be stated that much of these problems can be avoided by performing the sensitivity after the force curves are obtained, but there are some disadvantages to this approach, which are discussed in detail in the section on issues regarding the execution of these measurements. 2.2.2.3. Avoiding Surface Damage. To measure the linear elastic modulus it is imperative to avoid plastically deforming the sample surface. Trigger values should be set by keeping in mind the applied force, which ideally should not exceed a few nN. It is critically important that the sample should be imaged in tapping mode before and after (should be zoomed out prior to scanning) the force curves are obtained. If plastic deformation occurs it will appear in the zoomed-out image as an array of indentation marks. Furthermore, plastic deformation can often be recognized in the force curves as a leveled-off slope at a fairly uniform deflection and from hysteresis between approaching and retracting portions of force–distance curves.

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2.2.2.4. Execution of Measurements. The order of execution that the elastic modulus measurements are performed is critically important. A common procedure execution can be described by the following steps: 1. Clean silicon immediately before measurements as described in sensitivity calibration. 2. Warm scanner head for at least 15 min, depending on the system; always ensure that the head is warm before taking any SFS data. 3. Perform sensitivity calibration, verify linearity, and optimize photodiode signal. 4. Characterize tip shape and radius. Proceed if tip shape is hemispherical. 5. Estimate initial cantilever spring constant (e.g., by using manufacturing data). 6. Image sample surface at several locations and magnifications. 7. Perform force curves and examine deflection–penetration ratio to ensure that cantilever spring constant is appropriate (note that, without measuring sensitivity first, this is just a gross estimation). 8. Scan surface again in zoom-out mode to verify absence of indentation marks. 9. If appropriate, repeat the tip calibration and check the tip shape again. 10. If there is any change in the total photodetector sum, repeat the photodetector calibration. 11. Measure the exact value of cantilever spring constant. 12. Conduct data processing and analysis of the results. An alternative to the execution listed above would be to perform the sensitivity at the end of the measurements, which prevents tip damage to great extent. But without knowing the sensitivity before the SFS measurements, the trigger and the deflection–penetration ratio can only be roughly estimated by doing sensitivity on a tip from the same box before the measurements and being careful to put the laser spot on the same part of the cantilever. As mentioned earlier, an alternative sensitivity calibration method developed by Higgins et al., which involves thermal tuning, can be used to avoid tip damage.81 The trigger, penetration–deflection ratio, and total penetration are very important and so by not knowing sensitivity one is essentially going at it blind, hoping for the best. So, there is a trade-off, because significant time can be wasted when inappropriate experimental conditions are used due to a lack of knowledge of the sensitivity. When the sensitivity is obtained after the measurements, data processing is required to apply the correct sensitivity. If the sensitivity is performed after the measurements to ensure tip preservation, then steps 1–3 should be moved and can replace step 9. It is important to note changes in the laser spot, typically observed as a change in the detector sum, because this is an indication that the sensitivity calibration changed over the course of the experiments and thus the measurements are void. There are several other things to note when performing measurements, including that the scanner warming is not critical for scanners with a z-closed loop. The order of the cantilever spring constant calibration is not too critical, although often knowledge of the sensitivity is required depending on the calibration method, and one may damage the tip performing the tip-on-tip method of calibration. A second tip size calibration may be necessary in the case of a mistake leading to larger forces, if the sample is very stiff or if there is an indication of tip contamination. If the tip size noticeably changes in the course of probing, everything should be redone with a new probe. 2.2.2.5. Tip–Surface Contact Models for Elastic Modulus. Calculating elastic moduli from applied loading force and sample penetration data involves applying a model to account for the tip–surface contact area. Here, the most basic and common models are


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presented briefly, specifically the Hertzian model, Sneddon model, and Johnson-KendalRoberts. These models are inappropriate for materials with nonlinear elasticity, such as certain gels and biological materials. The reader is referred to several reviews for detailed information regarding nonlinear elastic contact models.82,83 Typically, equations are derived from a quasi-static spring-on-spring model or force balance approach as expressed by zdefl k = P (h)

(1)

where P is the applied force and h is the sample penetration as already defined.84 Assuming a spherical tip, flat surface, and no plastic deformation, one can define an effective spring constant or stiffness for a material as: E ∂P = 2r (2) kM = ∂h 1 − ν2 where r is the tip–surface contact radius, E is the material elastic modulus, and ν is the material Poisson’s ratio.85 Unfortunately, even after determining the tip radius, there is currently no known way to measure the contact radius at nanoscale in real time as the measurements are performed. Instead, contact mechanics models are used for fair estimation, which generally differ in the approaches on considering tip–surface interaction’s contribution to the contact area.62,63 The most popular Hertzian contact mechanics model is applicable for small deformation and it assumes that the adhesion forces are zero and that at zero applied load the contact area is also zero, all of those being far from true in most SFS measurements. However, in the vast majority of practical cases these contributions can be ignored or proper corrections can be made. The force as a function of penetration depth described by the Hertzian model is P =

4 1/2 3/2 R h E 3

where R is the tip radius and E is the composite modulus defined as 1 3 1 − νS 1 − νT = + E 4 ES ET

(3)

(4)

where the subscript S and the subscript T refer to sample- and tip-related variables, respectively. The modulus associated with the probe is generally assumed to be much larger than the elastic modulus of the surface, which is surely true for all polymeric surfaces. Therefore, a simplified equation for the elastic modulus based on the Hertzian approximation can be expressed as: dP 3 1 − ν2 (5) E= 4 R 1/2 d(h3/2 ) When plotting the penetration raised to the 2/3 power versus the deflection (or the applied force) a straight line should result from data taken with a spherical tip and little to no surface–tip interaction. Poisson’s ratio is usually taken as known bulk values typically ranges between 0.3–0.5 (about 0.5 for most of elastic materials/scenarios) are modest considering overall minor contribution in Eq. (5). The Sneddon model is another popular model that can be utilized to describe tips with an elliptic paraboloid shape and for significant deformations. In this approach, the

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paraboloid function Z = bX2 is utilized to describe the contact area as:

a=

(6)

h 2b

(7)

where R in Eq. (5) can be replaced with 1/(2b) to calculate the elastic modulus. The Johnson-Kendal-Roberts (JKR) model includes an adhesive contribution, which can be expressed in terms of a reduced load, PJKR . The elastic modulus from the JKR can be described by the modified Hertzian relationship between the load and the contact area as: dPJKR 3 1 − ν2 (8) E= 4 R 1/2 d(h3/2 ) where the reduced load, PJKR , is defined as: POff 3/2 PJKR = √ P1 3

(9)

where POff is the force associated with the snap-from portion of the force curve, line 5–6 in Figure 5, and P1 is defined as: P1 = (3P2 − 1)

1 9

13 (P2 + 1)

(10)

where P2 is defined as: P2 =

Zdefl +1 Zadh

12 (11)

where Z adh is the cantilever deflection associated with the snap-from, line 5–6 in Figure 5. As mentioned earlier, there is a discrepancy regarding the initial deformation at snap in, or the zero contact point. This point is usually taken as either the snap-to point (the minimum deflection point in the extension curve) or the zero deflection point after the snap-to in the deflection curve, the imaginary intersection point between line 1–2 and line 3–4 in Figure 5. The initial penetration overestimates the modulus and as the penetration depth increases the measured modulus will steadily decrease to the “true value.” If the total deformation well exceeds (two to three times) the initial contact penetration, the true value of the elastic modulus can be obtained anyway. This is a usual case for elastic materials where overall elastic deformation of 10–100 nm utilized for data analysis is much higher the initial deformation of 0.5–3 nm. 2.2.3. Examples of SFS Measurements. There are many different ways to utilize the elastic modulus and surface stiffness measurement capabilities of SFS. Choi et al. demonstrated the variation of the elastic modulus in periodic polymer structures fabricated by multi–laser beam interference lithography.86 The variation in the elastic modulus of the SU8 microstructures was believed to be to due to the periodic variation in the cross-linking density resulting from the light intensity distribution. These measurements avoided effects of geometry by careful control of the probed depth. On the other hand, macroscopic deformation measurements (tensile test and peel test) were performed to reveal the ductile failure


253

Figure 8. Rubber microphase inclusion in glassy polymer matrix for PS-PB blend (AFM topography slice, top, left) along with examples of force mapping (3-D topography, middle; topography, top; modulus, bottom) and surface histograms for adhesion (right, top) and modulus (right, bottom). Temperature variation of the elastic modulus for glassy and rubbery phases are presented as well (left, bottom). (Adapted from Tsukruk et al.91 Copyright Elsevier.)

and necking of the thin nanoscale struts.87,88 SFS measurements can also be very useful to probe phase transitions by performing measurements with varying probing frequencies and/or sample temperatures as demonstrated in several cases.89,90 For instance, we studied the surface distribution of the adhesive forces and elastic moduli for heterogeneous glassy–rubbery polymer films.91 Micromechanical properties of polystyrene–polybutadiene (PS-PB) thin films were probed in the range of temperatures. We demonstrated that for heterogeneous films fabricated from polymer blends, the micromapping of surface properties can be obtained concurrently for glassy and rubber phases as well as across the interface with a lateral resolution better than 100 nm (Figure 8). Histograms of the surface distribution display two very distinctive maxima for both adhesive forces and the elastic moduli, which allows concurrent measurements of micromechanical properties of glassy and rubber phases. Glass transition temperature of glassy matrix and flow temperature of the rubber phase can be also detected by this technique by measuring the surface distribution of elastic modulus in a range of temperatures. Both temperatures (glassy and rubbery phases) derived from these mapping were demonstrated to be close to the known values (Figure 8). The nanomechanical behavior of molecularly thick (8–10 nm) compliant polymeric layers with the nanodomain microstructure from grafted block copolymer, poly[styreneb-(ethylene-co-butylene)-b-styrene] (SEBS or Kraton), was probed with micromechanical surface analysis based on scanning probe microscopy.92 The micromapping with high lateral resolution (below 8 nm per pixel) revealed the bimodal character of the nanomechanical response with different elastic moduli shown by the rubber matrix and the glassy nanodomains (Figure 9). High-resolution probing showed virtually constant elastic response for the compliant layer compressed to 60% of its initial thickness followed by a sharp increase of the resistance when the tip reached within 3 nm from a stiff solid substrate.

254


Figure 9. Top: AFM images (topography and phase of SEBS layer). Bottom: Surface distribution of apparent elastic moduli for the polymer layer collected with 64 × 64 resolution, size is 500 × 500 nm, lighter areas correspond to higher moduli along with histogram of the elastic modulus obtained from micromapping. (Adapted from Luzinov et al.92 Copyright Elsevier.)

Application of the double-layer deformational model allowed the estimation of the actual elastic moduli of different nanophases within the grafted polymer monolayer: 7 ± 3 MPa for the rubber phase and 20 ± 7 MPa for the glassy domains (Figure 9). Relatively high elastic modulus of the rubber matrix is caused by a combination of chemical crosslinking/branching and spatial confinement within

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