Near-Field Characterization of Micro Nano-Scaled Fluid Flows

Experimental Fluid Mechanics Series Editors: Wolfgang Merzkirch, Donald Rockwell, Cameron Tropea Series Editors Prof...

Author: Kenneth D. Kihm

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Experimental Fluid Mechanics Series Editors: Wolfgang Merzkirch, Donald Rockwell, Cameron Tropea

Series Editors Prof. Dr. Wolfgang Merzkirch Brockhauserstr. 66 44797 Bochum Germany Prof. Donald Rockwell Lehigh University Dept. Mechanical Engineering & Mechanics 19 Memorial Drive W. BETHLEHEM PA 18015 USA Prof. Cameron Tropea TU Darmstadt FB 16 Maschinenbau FG Strömungslehre und Aerodynamik Petersenstr. 30 64287 Darmstadt Germany

Kenneth D. Kihm

Near-Field Characterization of Micro/Nano-Scaled Fluid Flows

123

Author Prof. Kenneth D. Kihm The University of Tennessee Dept. Mechanical, Aerospace & Biomedical Engineering Perkins Hall 313 37996-2030 Knoxville Tennessee USA E-mail: [email protected]

ISBN 978-3-642-20425-8

e-ISBN 978-3-642-20426-5

DOI 10.1007/978-3-642-20426-5 Library of Congress Control Number: 2011925384 c 2011 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typeset & Cover Design: Scientific Publishing Services Pvt. Ltd., Chennai, India. Printed on acid-free paper 987654321 springer.com

Preface

Microscopy and fluid mechanics may sound like an odd combination. This statement may have been true before the vast opening of the new research areas associated with micro- and submicro-scale fluidics. Now, however, microscopic imaging characterization has become one of the most essential tools in studying microfluidics and nanofluidics. Furthermore, the near-field fluidics phenomena that occur within the range of a few hundred nanometers from a solid interface have received unprecedented attention from diverse disciplinary areas. The importance of nearfield fluidics has been widely recognized, spanning from the frictional drag of submerged objects to the binding of probe DNAs with target DNAs. The main scope of this monograph is to provide a knowledge base for those who plan to learn and develop microscopic tools in order to characterize near-field transport phenomena themselves. This book begins with discussions on the five feasible definitions of “nearfield” in Chapter 1. The following five chapters present the working principles of five different microscopic imaging techniques and their example applications for near-field characterizations: Total Internal Reflection Microscopy (TIRM) in Chapter 2; Optical Serial Sectioning Microscopy (OSSM) in Chapter 3; Confocal Laser Scanning Microscopy (CLSM) in Chapter 4; Surface Plasmon Reflection Microscopy (SPRM) in Chapter 5; and Reflection Interference Contrast Microscopy (RICM) in Chapter 6. The working principles of these microscopy techniques are presented with an aim toward readers with a minimal background in engineering optics. Often, the lengthy derivation processes of optical theories are boldly skipped in order to prevent readers from being distracted by tedious equations and mathematics. However, adequate references are presented for those readers who are interested in pursuing the more detailed derivations and related theories. The present and practical uses of these microscopy techniques for diverse near-field fluidic phenomena, such as microfluidics, nanofluidics, as well as biofluidics (whenever available), are then demonstrated through example applications in order to promote extended insights and ideas for the reader. The contents of this monograph stem from the two graduate courses that I have developed and taught for the past two decades: (1) Back-to-Basic Engineering Optics, which I taught first at Texas A&M University and then at the University of Tennessee, and (2) Micro System Measurements, which I taught at Seoul National University in more recent years. Furthermore, most of the presentations of this monograph are based on my past research outcomes, which were achieved collaboratively with many of my former as well as current students. Without their contributions and dedications, this monograph would not have been possible. They

VI

Preface

are: Dirk Kastell, Bonghun Kim, Jinhan Kim, Glenn Doerksen, Dwayne Terracina, Satish Cheeti, Timothy Walsh, Tae Kyun Kim, Gregory Lyn, Ronald Russell, Donald Lyons, Hanseo Ko, Dongho Kim, Rajesh Athirathnam, Sang Young Son, Hyunjung Kim, Minjun Kim, Kathik Ganesan, Juned Hendrasakti, Sang Kwon Wee, Satish Cherla, Sokwon Paik, Jaesung Park, Chanhee Chon, Chang Kyung Choi, Seong Hwan Kim, Charles Margraves, Iltai Kim, Joseph Tipton, Hunju Yi, Sosan Cheon, Joshua Long, Hyung Joon Kim and Eric Kirchoff. Hunju Yi, on top of his significant research contributions, patiently formatted all of the cited references, using the computer software Endnote. My work on this monograph was greatly inspired by the eminent book Flow Visualization, which was written by Professor Wolfgang Merzkirch, my careerlong mentor. For years, I have closely interacted with him, not only to bask in his academic excellence but also to admire the natural outpouring of his heart and humor. Furthermore, for the last two years, a significant portion of my writing was facilitated during my ongoing participation in the World Class University (WCU) Program at Seoul National University. I sincerely acknowledge Professor Joon Sik Lee of Seoul National University, whom I have collaborated with as my colleague in the WCU Program as well as my lifelong friend. I am indebted to my lovely wife Jennie, who gracefully accepted my placing a high priority on my work, a priority that was sometimes higher than that of our family matters. Also, to my two lovely daughters, Grace and Christina, thank you for your sweetness in understanding and supporting your father on this book project. I am wholeheartedly grateful to Grace, who painstakingly edited the entire manuscript for me, twice. Last but not least, I am endlessly indebted to the love and care forever streaming from my mother, Mrs. Yang-Ja Park Kihm, and my father, Professor Emeritus Hong-Chul Kihm. I sincerely hope that this monograph will be of help for those who develop and share interests in microscopic characterization of near-field fluidics. March 2011

Kenneth D. Kihm The University of Tennessee Knoxville, Tennessee, U.S.A.

Contents

Contents 1

Introduction……………………………........................................................1 1.1 Definitions of Near-Field........................................................................1 1.1.1 Evanescent Wave Penetration Depth ...........................................2 1.1.2 Surface Plasmon Polariton (SPP) Penetration Depth...................4 1.1.3 Photon Penetration Skin-Depth into Metal ..................................7 1.1.4 Penetration Depth of No-Slip Boundary Conditions ...................7 1.1.5 Equilibrium Height (hm) for Small Particles under Near-Field Forces.........................................................................................10 1.2 Synopsis................................................................................................13

2

Total Internal Reflection Microscopy (TIRM)..........................................15 2.1 Principles and Configuration of TIRM .................................................15 2.2 Ratiometric TIRM Imaging Analysis ...................................................18 2.3 Near-Field Applications of TIRM ........................................................20 2.3.1 Near-Wall Hindered Brownian Motion of Nanoparticles ..........20 2.3.2 Slip-Flows in the Near-Field......................................................23 2.3.3 Cytoplasmic Viscosity and Intracellular Vesicle Sizes..............26

3

Optical Serial Sectioning Microscopy (OSSM)……..….……….……....29 3.1 Point Spread Functions (PSFs) under Aberration-Free Design Conditions.............................................................................................29 3.2 Point Spread Functions (PSFs) under Off-Design Conditions..............31 3.3 Principles of OSSM ..............................................................................35 3.4 Near-Field Applications of OSSM........................................................37 3.4.1 Three-Dimensional Particle Tracking Velocimetry (PTV)........37 3.4.2 Near-Wall Thermometry............................................................42 3.4.3 Near-Field Mixture Concentration Measurements.....................49

4

Confocal Laser Scanning Microscopy (CLSM)…………………………..55 4.1 Principles of Confocal Imaging ............................................................55 4.2 Microscopic Imaging Resolutions ........................................................57 4.3 Confocal Microscopic Imaging Resolutions.........................................59 4.4 Optical Slicing Thickness of Confocal Microscopy .............................63 4.5 Confocal Laser Scanning Microscopic Particle Imaging Velocimetry (CLSM-PIV) System ............................................................................65

VIII

Contents

4.6 Near-Field Applications of CLSM-PIV................................................68 4.6.1 Poiseuille Flows in a Microtube ................................................68 4.6.2 Microscale Rotating Couette Flows ...........................................73 4.6.3 Moving Bubbles in a Microchannel...........................................76 5

Surface Plasmon Resonance Microscopy (SPRM)…………………....…81 5.1 Surface Plasmon Polaritons (SPPs) ......................................................81 5.2 Dispersion of SPPs ...............................................................................83 5.3 Kretschmann’s Three-Layer Configuration ..........................................85 5.4 Surface Plasmon Resonance (SPR) Reflectance...................................87 5.5 Surface Plasmon Resonance Microscopy (SPRM) Imaging Systems.................................................................................................92 5.6 Selection of a Prism for SPRM.............................................................95 5.7 SPR Reflectance Imaging Resolution ...................................................97 5.8 Near-Field Applications of SPRM......................................................101 5.8.1 History and Uses of SPRM ......................................................101 5.8.2 Label-Free Mapping of Microfluidic Mixing Fields................102 5.8.3 Near-Field Mapping of Salinity Diffusion...............................104 5.8.4 Dynamic Monitoring of Nanoparticle Concentration Profiles.....................................................................................107 5.8.5 Unveiling the Fingerprints of Nanocrystalline Self-assembly...........................................................................110 5.8.6 Near-Wall Thermometry..........................................................113

6

Reflection Interference Contrast Microscopy (RICM)……...………....119 6.1 Interference of Plane Waves ...............................................................119 6.2 Principles and Practical Issues of RICM ............................................121 6.3 Near-Field Applications of RICM ......................................................123 6.3.1 Thin-Film Thickness Measurements........................................123 6.3.2 Electrohydrodynamic (EHD) Control of Thin Liquid Film .....123 6.3.3 Dynamic Fingerprinting of Live-Cell Focal Contacts..............127

References ..........................................................................................................131

Chapter 1

Introduction

The primary scope of this monograph covers the advanced optical characterization of near-field fluid flows, within a range of a few hundred nanometers from the interface. Optical imaging characterization differs from other experimental methods in that it not only provides direct access to full-field fluid properties but also allows the comprehensiveness of visual perception, or “flow visualization” [1]. Near-field fluid flows on both micro- and nano-scales are crucial in characterizing numerous important transport phenomena across pertinent interfaces, including the surface fluid drag, solid surface heat transfer, nanoparticle self-assembly on a surface, surface chemistry and electrostatics, and the surface binding of biomolecules and DNAs. Section 1.1 discusses five feasible definitions of “nearfield,” while Section 1.2 presents a list of five advanced microscopic techniques for near-field optical characterization.

1.1 Definitions of Near-Field The perception of being near or far is entirely relative to the reference scale of our choice. Thus, the definition of near-field is quite subjective, and indeed, it can span from the traditional boundary layer thickness along a solid surface [2,3] to the far smaller Debye layer thickness of electro-osmosis flows in a microchannel [4]. The definition and physical implications of near-field, therefore, varies depending on the scope and nature of the chosen length scales. Nevertheless, considering the physics of electromagnetic (EM) wave penetration associated with the virtual photon particles, a few formidable definitions of near-field are possible. The EM photon penetration is directed either into a dielectric region, having no free electrons, or just beneath it in the case of metal medium, where free electrons abound. Three length scales are elaborated herein for the three definitions of near-field in relevance to the photon penetrations: the penetration depth of the evanescent wave-field (Section 1.1.1), the surface plasmon polariton (SPP) penetration depth (Section 1.1.2), and the skin depth of photon penetration into metal (Section 1.1.3). Near-field can also be defined by interpreting the dynamics and behaviors of small physical particles, such as nanoparticles. Namely, the anisotropic free Brownian motion of a fine particle will be retarded due to the presence of a solid

2

1 Introduction

surface. Thus, near-field can be defined by the penetration depth of the no-slip boundary condition (Section 1.1.4). Lastly, near-field can also be defined as the equilibrium height of a small particle under various near-field forces, including van der Waals and electro-osmotic forces (Section 1.1.5).

1.1.1 Evanescent Wave Penetration Depth At an incident angle larger than the critical angle (Fig. 1.1-a), the incident light is completely reflected at the interface; i.e., total internal reflection (TIR) occurs. All of the incident ray energy is reflected back to the internal medium with a higher refractive index (RI), ni ; none is transmitted into the bulk phase of the external medium with a lower RI, nt . This statement is perfectly valid from the energy conservation and macroscopic points-of-view. From the microscopic perspective, however, the incident light penetrates the interface minutely into the external medium and propagates parallel to the surface in the plane of incidence, creating a standing electromagnetic wave field. Since the standing wave travels only along the interface, the reflectance remains unchanged from the incidence. This standing wave field is called an “evanescent wave field,” which decays exponentially with the z-distance from the interface [5]; i.e.:

⎛ z ⎞ I ( z ) = I 0 exp⎜ − ⎟ ⎜ z ⎟ p ⎠ ⎝

(1.1)

where I0 is the incident light intensity at the interface (z = 0), and the penetration depth (zp) that meets I / I o = e-1 = 0.368 is given by:

zp =

1 − λ0 2 2 ( ni sin θi − nt2 ) 2 4π

(1.2)

For the case of a glass ( ni = 1.515)–water ( nt = 1.33) interface with the wavelength in vacuum λ0 = 632.8 nm, Fig. 1.1-b depicts both the exponentially decaying evanescent wave field intensity I ( z ) / I 0 with the depth z and its even faster

decaying for a smaller incident ray angle θi. The penetration depth z p decreases quickly with increasing θ i beyond the critical angle of 61.38° for the glass-water interface (Fig. 1.2), ranging from 300 nm near the critical angle to below 100 nm while the incident angle is increased by less than 10°. The error bars indicate the uncertainty of penetration depth predictions based on the Kline-McClintock analysis [7]. Note that the uncertainty is dramatically increased when the incident angle is near the critical angle.

1.1 Definitions of Near-Field

z

3 External medium (nt) Evanescent wave field

θi Internal medium (ni)

(1)

(1)

(a) 100

10-1

10-2

I / Io

θi = 620 θi = 65o

10-3

θi = 680 θi = 700

10-4

θi = 750 10-5

0

100

200

300

400

500

600

700

800

900

1000

Depth (nm)

(b) Fig. 1.1 (a) A schematic illustration of total internal reflection (TIR) and the evanescent wave field, and (b) the evanescent wave field intensity I(z)/Io of Eq. (1.1) at different incident angles θ i for a glass (ni = 1.515) – water (nt = 1.33) interface [6].

The quickly-decaying evanescent wave field can effectively illuminate the fluid region (water) that is interfaced by the solid (glass), and the extremely thin penetration depth of the evanescent field can distinguish the region close to the solid surface, excluding the outer region far from the surface. Indeed, evanescent wave imaging is used to characterize the flow behaviors within the submicron range from the surface (Chapter 2), and thus the penetration depth of the evanescent wave field can be a fairly reasonable definition of near-field.

4

1 Introduction

350

Penetration Depth (nm)

300

250

200

150

100

50 61

62

63

64

65

66

67

68

69

70

71

72

Angle (degrees)

Fig. 1.2 The penetration depth

z p for different incident angles θi beyond the critical angle

θ c = 61.38 for a glass (ni = 1.515)–water (nt = 1.33) interface. The error bars represent o

the estimated uncertainties [6].

1.1.2 Surface Plasmon Polariton (SPP) Penetration Depth When a thin metal film intervenes between the internal and external dielectric mediums (Fig. 1.3), the reflectance no longer holds the conservation of intensity with the incident field. For a plane p-polarized incident wave field, the created evanescent wave field is absorbed by the abundant free electrons in the thin metal film, and the resulting reflectance is either frustrated or reduced from the TIR. In other words, the p-polarized evanescent wave is attenuated to trigger coherent fluctuations of free electrons in the metal layer, and this coherent energy conversion of the photons into free electrons is called the “surface plasmon phenomenon” [8]. “Plasmon” refers to dipole carriers, such as the free electrons oscillating in background ions typically in a metal. Oscillation of the dipole carriers creates varying charge density distributions where the oscillation takes place. “Surface plasmon” then implies a charge density wave propagation along the metal surface, which is distinguished from volume plasmon or plasma [9]. The surface plasmon can be excited by electromagnetic fields, which are carried by photons, if certain conditions are met. These entangled quasi-particles, composed of surface plasmons and photons, are called “surface plasmon polaritons” (SPPs). Note that, by definition, the term “polariton” means the “particle entangled with the electromagnetic wave” associated with the presence of free electrons [10].

1.1 Definitions of Near-Field External dielectric medium

5 Resonated/amplified Surface plasmon wave

z (1-R) Thin metal film

(1)

Internal dielectric medium

(R)

Fig. 1.3 A schematic illustration of the surface plasmon wave field composed by the free electron oscillation, which is driven by the incident electromagnetic wave field.

When the p-polarized wave-vector of the evanescent wave field matches the surface plasmon wave vector at a certain incident angle (called the “SPR angle”), a resonant excitation of free electrons will take place and create maximum amplification of the surface plasmon wave at the upper surface of the metal film contacting the dielectric medium [11,12]. The resulting reflectance R is ideally zero, or very low in actuality, and this phenomenon is called “surface plasmon resonance,” or SPR. Note that the s-polarized incident wave is not subject to SPR and is totally reflected, in contrast. The SPR excitation requires specific conditions for optical properties of the thin metal film in that the real part of its dielectric constant must be negative and that its absolute magnitude must be greater than that of the imaginary part [13-15]. There are several noble metals available for SPR applications, including silver, gold, copper, and aluminum. Among them, gold is preferred because of its stability and superior performance in various environmental conditions [16,17]. As we shall see in more detail in Chapter 5, the magnitude of the p-polarized SPR reflectance is extremely sensitive to the refractive index variation of the near-wall fluid region, where the SPP can penetrate and affect the reflectance. Indeed, the SPR reflectance is known to have the most sensitive RI detection capability on the order of 10-5 RIU [18,19] and more recently as fine as10-8 RIU [20]. The SPP penetration depth can thus define the measurement range for the dielectric or fluid medium and may well be a fair definition of near-field. Furthermore, the illuminating intensity of the SPR wave is an order of magnitude greater than that of the ordinary evanescent wave field generated by TIR under the same illumination source strength [15,21-23]. The penetration depth of the SPP into the contacting dielectric medium is defined as the depth at which the electric field strength of surface plasmon wave falls to 1/e. The SPP penetration depth is determined from the reciprocal of the absolute value of wavevector amplitude in the z-direction [12,24,25]:

λ δ SPP= 2π

1/ 2

+ε ⎛ ε' ⎞ ⋅ ⎜⎜ metal 2 dielectric ⎟⎟ ε dielectric ⎝ ⎠

(1.3)

6

1 Introduction

Table 1.1 Dielectric constants at λ = 632.8nm Medium

Dielectric constant (ε )

Refractive index (RI)

Gold

-11.649 + 1.271i

0.18593 + 3.418i

Water

1.7728

1.3315

Air

1.00054

1.00027

where the dielectric constant for metal is complex in order to account for the absorption (i.e., ε metal = ε ' metal +iε ' 'metal ), while the dielectric constant for nonmetal

ε dielectric is real because of the negligibly small absorption (Table 1.1)

[13,26,27]. For the incident ray of the helium-neon line in a vacuum (λo = 632.8 nm) onto a gold metal film, for example, the SPP penetration depth δSPP = 156 nm into a water medium and 358 nm into an air medium (Fig. 1.4). The penetration depth increases with increasing wavelength λ in the dielectric medium.

Fig. 1.4 Dependence of the SPP penetration depth on the incident wave length for a gold layer, interfaced either by water (solid line) or air (dashed line). The calculations were performed using λ–dependent dielectric constants for gold, water, and air, and their typical values at λ = 632.8 nm are shown in Table 1.1.


7

1.1.3 Photon Penetration Skin-Depth into Metal When the electromagnetic waves propagate onto a metal surface, the photon penetrates only a very shallow depth before its energy is consumed (to oscillate the free electrons) and eventually dissipates by the Joule heating. The Maxwell equations can be solved for the electric field vectors inside a metal by additionally considering the electrical conductivity term, which usually disappears for dielectric mediums, and the decaying irradiance into the metal is found to be proportional to the square of the E-field amplitude as follows [5]: ⎛ 2ωnI I ( z ) = I 0 exp ( −α z ) = I 0 exp ⎜ − c ⎝

⎞ z⎟ ⎠

(1.4)

where ω is the incident wave frequency, c is the speed of light in the metal medium, the RI of the metal is given as n = nR − in I ( n R , n I > 0 ) , and therefore, the photon penetration or skin depth occurring at I ( z ) = I 0 exp ( −1) is given by:

z = 1 / α = c / 2ωnI .

(1.5)

For a material to be transparent at a specific wave frequency ω , the photon penetration depth must be large in comparison to the material thickness. The ideal extreme is a dielectric medium with zero absorption ( nI = 0 ) and I / I 0 = 1 with an infinite penetration depth. The skin depth for most metals, however, is extremely small. For example, gold at a UV wavelength λ ~ 0.1 μm has a penetration depth of a mere 9.5 nm and is still only about 17 nm at λ ~ 10 μm. Not only is this scale range beyond the measureable resolution of optical tools in the visible spectrum, but flow characterization inside a metal is also rare at our present level of science. Henceforth, the photon penetration depth will rarely be considered for the nearfield definition of fluidics.

1.1.4 Penetration Depth of No-Slip Boundary Conditions The history of published observations of Brownian motion goes back to Gray [28], who first identified the irregular motion of a small glass globule suspended in a fluid. The observation of the random motion of small particles was first reported by Jan Ingenhousz [29], and the random motion of pollen particles under a microscope was subsequently discovered by the eminent botanist Robert Brown, who noted and named it as an eponym [30]. Albert Einstein used the kinetic theory to derive the diffusion coefficient for the thermal motion of small particles in terms of fundamental parameters in his well-known doctoral dissertation [31] and a subsequent article [32]. Considering the Stokes drag of spherical particles freely suspended in the far-field fluid (Fig. 1.5), the diffusion coefficient D of the suspended particles is given by Einstein as:

8

1 Introduction

D=

kT 3π μ d p

(1.6)

where k is Boltzman’s constant (1.3805 x 10-23 J/K), T is the absolute temperature, and μ is the dynamic viscosity of the fluid. If the particles are diluted to ensure that their separation distance exceeds ten particle radii, the particle interaction effects are found to be negligible [33]. While the diffusion coefficient is a property that is difficult, if not impossible, to measure, the mean square displacement (MSD) r 2 is a readily measurable property with a specified sampling time increment δ t ; i.e.: r 2 = 2D ⋅ δ t

for 1-D Brownian motion

(1.6-a)

r 2 = 4D ⋅ δ t


(1.6-b)

= 6D ⋅ δ t


(1.6-c)

r

2

Because of the random nature of the thermal motion of fluid molecules, the diffusion coefficient D must be isotropic in the fluid, regardless of the bulk flow

Fig. 1.5 Far-field free Brownian motion versus near-field hindered Brownian motion, due to the presence of a no-slip solid wall.


9

motion [34-36]. Particles that approach the solid wall, however, are subjected to the directional influence of the no-slip boundary condition, and the isotropy of particle motion is no longer valid for these particles belonging to the near-field. Corrections to the Stokes’ isotropic resistance formula will be inevitable in characterizing particle motion in the vicinity of the solid boundary. Brenner [37] provided an analytical expression for the correction factor for the normal Brownian motion, ξ, by solving the Navier Stokes equation for a creeping flow as:

ξ

−1

⎡ ⎤ ∞ ⎢ 2 sinh( 2n + 1)α + (2n + 1) sinh 2α ⎥ 4 n (n + 1) = sinh α ⋅ ∑ − 1⎥ ⎢ 1 3 n =1 ( 2n − 1)( 2n + 3) ⎢ 4 sinh 2 (n + )α − (2n + 1) 2 sinh 2 α ⎥ 2 ⎣⎢ ⎦⎥

(1.7) where α is given as a function of the particle diameter dp and the elevation h measured from the solid surface to the suspended particle:

⎛ 2h + d p ⎞ ⎟ ⎟ ⎝ dp ⎠

α = cosh −1 ⎜⎜

(1.8)

Brenner’s finding has been supported by a number of authors who have highlighted the need for a correction to the Stokes’ Law for a particle close to a wall, or for the case where there are two or more particles close to each other [38-40]. A few years later, Goldman et al. [41] analyzed the slow viscous motion of a sphere parallel to a plane wall and used an analogy corresponding to a translational lubrication theory to derive the correction factor for the tangential Brownian motion β as:

β

−1

3 4 5 ⎡ 9 ⎛⎜ d p ⎞⎟ 1 ⎛⎜ d p ⎞⎟ 45 ⎛⎜ d p ⎞⎟ 1 ⎛⎜ d p ⎞⎟ ⎤⎥ ⎢ = 1− + − − ⎢ 16 ⎜⎝ d p + 2h ⎟⎠ 8 ⎜⎝ d p + 2h ⎟⎠ 256 ⎜⎝ d p + 2h ⎟⎠ 16 ⎜⎝ d p + 2h ⎟⎠ ⎥ ⎣ ⎦ (1.9)

which is again a function of the particle diameter dp and its elevation h. Now, the corrected Brownian motion components are given as:

D⊥ = ξ ⋅ D = ξ

D// = β ⋅ D = β

kT 3πμ d p

kT 3πμ d p

(1.10-a)

(1.10-b),

10

1 Introduction

and the corrected overall Brownian motion is given as:

DO = ψ ⋅ D =

2β + ξ ⋅D 3

(1.10-c)

Figure 1.6 shows the three correction factors ( ξ , β , and ψ ) as functions of the particle elevation h for 200-nm particles suspended in water. The effect of the noslip solid wall diminishes as h approaches 1 μm, and interestingly, this penetration depth of no-slip remains more or less the same for a wide range of submicron particles. Therefore, an order of 1 μm of the no-slip penetration depth can be considered as another possible definition of near-field for microscopic characterizations. 1.0

0.8

0.6

ξ,β,ψ 0.4

Tangential Correction Term Normal Correction Term 3 Dimensional Correction Term

0.2

0.0 0

100

200

300

400

500

600

700

800

900

1000

Depth (nm) Particle elevation (nm) Fig. 1.6 Correction factors for free (ψ ), normal ( ξ ), and tangential ( β ) diffusion coefficients as functions of the particle elevation for 200-nm spherical particles suspended in water and retarded by the no-slip solid surface condition [6].

1.1.5 Equilibrium Height (hm) for Small Particles under Near-Field Forces In addition to the hydrodynamic interaction between a suspended single sphere and the wall (Section 1.1.4), at least four additional effects can be considered in the near-field; namely, particle-to-particle interactions, sedimentation, short-range Van der Waals forces, and electrostatic and electro-osmotic forces [42,43]. These


11

factors may affect the overall hindered Brownian motion, beyond the hydrodynamic effect [44]. The extremely low volume fraction of nanoparticles usually provides an average inter-particle distance that is more than 100 times their radius, such that the resulting inter-particle effects may be considered negligible [45]. The next concern is the effect of particle sedimentation, due to the density mismatch between the suspended nanoparticles and the base fluid. The Peclet number (Pe) defines the gravitational sedimentation relative to the opposing diffusion as [46]:

Pe =

LU sed 4π a 3 Δρ g = DH 9μ DH

(1.11)

where DH represents the hydrodynamically hindered diffusion coefficient, as previously shown in Eq. (1.10), and the system length L is set to the particle diameter 2a. Again, for most experimental conditions of our present interest, the sedimentation velocity Used is negligibly small; as an example, it is on the order of 1 nm/s for the case of a 100-nm radius polystyrene particle suspended in water [47]. The time-independent interactions between a sphere located at height h and a substrate surface (h = 0) establish a potential energy U referring to the gravitational, van der Waals, and electrical double layer forces: U ( h) = U g ( h) + U vdw ( h) + U e ( h)

(1.12)

The gravitational potential energy U g (h) under a constant gravity is given by:

4 U g (h) = Fg h = π a3 g Δρ h 3

(1.13)

Assuming negligibly small particle-to-particle interactions, the van der Waals potential U vdw (h) is given by [48,49]:

U vdw = −

A123 ⎡ 1 1 ⎛ δ ⎞⎤ + + ln⎜ ⎟⎥ ⎢ 6kT ⎣ δ δ + 2 ⎝ δ + 2 ⎠⎦

(1.14)

where δ = h a and A123 represents the Hamaker constant, with the subscripts 1 for the particle, 2 for water, and 3 for the glass substrate. Based on the Derjaguin approximation for thin double layers relative to the particle size, we use a constant charge model (i.e. particles that maintain a uniform fixed surface charge density during interactions) to derive the electrostatic potential U e (h) [50,51]: ⎛ eψ 2 ⎞ −κh ⎛ eψ ⎞ ⎛ kT ⎞ U e (h) = 16εa⎜ ⎟ tanh⎜ 1 ⎟ tanh⎜ ⎟e e kT 4 ⎝ ⎠ ⎝ 4kT ⎠ ⎠ ⎝ 2

(1.15)

12

1 Introduction

where ψ1 and ψ2 are the Stern Potentials of the substrate surface and the particle surface, respectively, ε is the dielectric permittivity of the base fluid, e is the elemental electric charge, and κ is the Debye-Hückel reciprocal length parameter, which is calculated to be 15 nm-1. Following the analysis of Behrens and Grier [52], the surface Stern Potentials are calculated to be 44.4 mV for the glass substrate surface, 40.97 mV for polystyrene nanoparticles with radius a = 500 nm, 24.89 mV for a = 250 nm, 74.47 mV for a = 100 nm, and to 26.1 mV for a = 50 nm (pH = 6.5 for all cases). However, since the electromotive force can be considered to be concentrated on the bottom area within the effective radius [53], calculations of the electrostatic potential incorporate the effective radius in Eq. (1.15) while retaining a in estimating the gravitational and van der Waals potentials. The total potential for a particle located at h is given by: 4 A U ( h) = π a 3 g Δρ h + 123 3 6kT

⎡1 1 ⎛ δ ⎞⎤ ⎛ kT ⎞ ⎛ eψ 1 ⎞ ⎛ eψ 2 ⎞ −κ h ⎢ δ + δ + 2 + ln ⎜ δ + 2 ⎟ ⎥ + 16ε ao ⎜ e ⎟ tanh ⎜ 4kT ⎟ tanh ⎜ 4kT ⎟ e ⎝ ⎠⎦ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎣ 2

(1.16)

Fig. 1.7 Potential energy profiles for polystyrene spheres [diameters 100 nm, 200 nm, 500 nm and 1000 nm] levitated above a cover glass. The solid curve represents the predictions (Eq. 1.16) for the largest particles (1000 nm), and the dashed curve represents the smallest particles (100 nm). The predictions are calculated from Eq. (1.16) with Δρ = 55 kg/m3, A123= -2.095 kBT/nm, κ-1 = 15nm, a= 50 – 500 nm, and T = 293 K [47].

1.2 Synopsis

13

Differentiating Eq. (1.16) with respect to h and then equating it to zero provides local minima corresponding to the equilibrium height (hm), which is also called “separation distance” or “most probable distance” [54]. Figure 1.7 shows the potential energy profiles on a separation scale relative to hm for the tested nanoparticles, ranging from 50 nm to 500 nm in radius. Potential energy is reported on a scale relative to the minimum for each profile, which inherently occurs at hm. The most probable location of small particles under the equilibrium of the gravitational, van der Waals, and electrostatic forces in the near-field will be at the equilibrium height hm, and therefore, hm can be considered as yet another definition of near-field.

1.2 Synopsis The next five chapters present the working principles and example applications of five advanced microscopic imaging techniques for near-field characterization: Total Internal Reflection Microscopy (TIRM) in Chapter 2; Optical Serial Sectioning Microscopy (OSSM) in Chapter 3; Confocal Laser Scanning Microscopy (CLSM) in Chapter 4; Surface Plasmon Reflection Microscopy (SPRM) in Chapter 5; and Reflection Interference Contrast Microscopy (RICM) in Chapter 6.

Chapter 2

Total Internal Reflection Microscopy (TIRM)

Total internal reflection microscopy (TIRM) uses the evanescent wave field (Section 1.1.1) as an illumination light source and allows near-field characterization within the penetration depth zp of less than 1 μm of the evanescent wave field:

zp =

1 − λ0 2 2 ( ni sin θ i − nt2 ) 2 4π

(1.2)

The fundamental concept of TIRM is simple, requiring an excitation light beam traveling at a high incident angle to create the evanescent wave field [55,56]. Such a narrowly defined illumination depth is considered to be a highly effective way of overcoming the background noise that is often the biggest problem in single molecule imaging [57]. The principles and configuration of TIRM are summarized in Section 2.1 and the ratiometric TIRM imaging analysis technique is presented in Section 2.2. Finally, selected near-field applications of TIRM are discussed in Section 2.3.

2.1 Principles and Configuration of TIRM While TIRM technology has been previously used in the biomedical and biophysical fields [58-60], the first microfluidic application was not recognized until Zettner and Yoda performed near-wall flow field measurements for a rotating Couette flow [61]. Shortly thereafter, they published an experimental study of electro-osmotic flow measurements using TIRM technology [62]. Their system (Fig. 2.1) used a prism to create multiple total internal reflections, seemingly inspired by the earlier work in the colloidal studies [51,63-65]. This setup requires that the specimen be positioned between the prism and the microscope objective and that the higher order evanescent wave field must be used due to the geometrical constraint, which substantially weakens the field intensity after repeated

16

2 Total Internal Reflection Microscopy (TIRM)

internal reflection modes. In addition, because of the repeated reflection modes, more strayed rays are rendered, resulting in images with low signal-to-noise ratios. A more preferable TIRM setup has the laser illuminated through an inverted microscope, which significantly benefits from a special TIRM objective lens with a high numerical aperture (NA) [66]. The experimental setup (Fig. 2.2-a) consists of an IX-50 Olympus inverted microscope with a Plan APO 60X, 1.45 NA TIRM lens, a 200-mW CW argon-ion laser at 488-nm, and a frame grabber board (QED Imaging Inc.). The test field is placed on the upper surface of the 170-µm thick glass slip, which is viewed from below. The angle of incidence is determined by a transfer function R = fn sin θ i , which involves the off-center location of the laser beam in the optical pathway of the microscope R, the focal length of the TIRFM objective f, and the refractive index n of the cover glass, or equivalently of the index-matching oil (Fig. 2.2-b).

Fig. 2.1 A schematic of the optics used to create the evanescent wave. The evanescent waves imaged by the microscopic objective are from the fifth TIR [61].

When using yellow-green (505 nm/515 nm) carboxylate-coated fluorescent beads of 200±20 nm diameter (1.05 SG), the non-TIRM image with θ i = 60°
R

where R is the fluorescent particle radius. After substituting Eq. (2.2) into Eq. (2.1) and performing some mathematical manipulations, the normalized intensity detected by a CCD for a fluorescent particle emitter of radius R, located at h, from the interface is given by:

⎡⎛ R I N (h, R, c ) = 4 π c z 3p ⎢⎜ ⎜ ⎣⎢⎝ z p

⎞ ⎛ ⎟ cosh ⎜ R ⎟ ⎜z ⎠ ⎝ p

⎞ ⎛ ⎟ − sinh ⎜ R ⎟ ⎜z ⎠ ⎝ p

⎞⎤ − z p ⎟⎥ ⋅ e ⎟⎥ ⎠⎦ h

(2.3)

Although Eq. (2.3), in principle, can determine the particle location h by measuring I N under a given penetration depth z p , the fluorescent particle concentration c is difficult to measure and usually not accurately known. By taking the ratio of

20


I N at two different z-locations, the unknown c can be eliminated and the ratio RI determines the relative z-location Δh (Fig. 2.4); i.e.: RI ≡

⎛ Δh ⎞ I 1N ( h1 , R, c ) ⎟ = exp⎜ − 2 ⎜ zp ⎟ I N ( h2 , R, c ) ⎠ ⎝

(2.4)

If the particle emitting the brightest intensity is selected as a reference zero point (z = 0), all other particle locations can be identified from the ratio of their intensities to that of the reference particle. Note that the physical location of the brightest particle may not be exactly at the solid surface; rather, it should be at the most probable separation distance (Section 1.1.5). Since both the glass surface and the particles are negatively charged, there exists a most probable separation distance, which is equivalent to the minimum potential energy state that ensures mechanical equilibrium. Thus, z = 0 here simply indicates a reference point for the relative locations of other, less bright particles. Nevertheless, the errors associated with this reference point location are expected to be small in comparison to other uncertainties, and the ratiometric TIRM imaging analysis can provide quantitative information on particle locations in the near-field within a few hundred nanometers (a mere 1% of the diameter of a human hair) of the solid wall [72-74].

2.3 Near-Field Applications of TIRM 2.3.1 Near-Wall Hindered Brownian Motion of Nanoparticles The presence of a solid wall at a finite distance from a particle necessitates corrections to the Stokes’ resistance formula that describes isotropic free Brownian motion (Section 1.1.4). The near-wall hindered Brownian motion is attributed to the no-slip boundary condition of the solid surface, and the directional dependence of the boundary condition renders the thermal motion of small particles anisotropic [35,75]. Brenner [37] provided an analytical correction factor for the normal diffusion coefficient, and a few years later Goldmann et al. [41] provided an analytical correction factor for the parallel diffusion coefficient. While their correction factors have long been accepted by the fluid mechanics society, the ratiometric TIRM technique made it possible to experimentally verify their theories of near-field hindered Brownian motion. The three-dimensional thermal motion of a 200-nm fluorescent particle in water at 293K was tracked for 67 consecutive frames using a 60x, 1.45 NA TIRM objective imaging, and their vector displacements during successive frames show the near-field hindered Brownian motion (Fig. 2.5-a). The tested nanoparticles are yellow-green (505-nm/515-nm) carboxylate-coated fluorescent spherical beads with less than ± 5% variations in their radii, all having a specific gravity of 1.055. The novel neural network model finds the relationship among particles between pairs of images [76,77]. The anisotropic nature of the three different components (x-y, y-z, x-z) of the near-wall hindered Brownian motion becomes more apparent when they are presented separately in Fig. 2.5-b. While the x-y motion remains

2.3 Near-Field Applications of TIRM

21

nearly isotropic, both y-z and x-z motions show pronounced reductions of particle displacements in the z-direction. 600

500

Lateral movement Down movement

Depth (nm)

400

z [um] 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8

300

200

0.8 0.6 0.4 0.2 0 y [um] -0.2 -0.4 0.2 0.4 -0.6 0.6 0.8 -0.8

100

0 45.0

44.5

44.0

85 43.5

Y (μ m)

84 43.0

42.5

86

87

-0.8 -0.6 -0.4 -0.2 0 x [um]

89 88

) μm X(

83 42.0

82

(3-D)

1

1

0.5

0.5

0.5

0

z [um]

1

z [um]

y [um]

(a)

0

-0.5

-0.5

-0.5

-1

-1

-1 -1

-0.5

0 x [um]

2-D (x-y)

0.5

1

0

-1

-0.5

0 y [um]

(b) 2-D (y-z)

0.5

1

-1

-0.5

0

0.5

1

x [um]

2-D (x-z)

Fig. 2.5 (a) The evolution of three-dimensional near-wall locations of a single 200-nm particle over 67 imaging frames recorded for the duration of 2.23 s, and (b) their near-wall hindered anisotropic Brownian motion components [6].

The low volume fraction of 0.001% provides the average inter-particle distance as being greater than 100 times their radius, and the inter-particle effect can thus be considered negligible [45,50]. Individual tracking of nanoparticles determines the mean square displacements (MSDs) for four different nanoparticle sizes of 50, 100, 250 and 500-nm radii (Fig. 2.6). The measured MSDs are averaged over the different particle-wall distances that the particle is at during the measurement. The measured values of the lateral MSD components, <x2> and , agree well with the theoretical predictions. Small discrepancies are observed only for the case of the nanoparticles with 50-nm radii, but the discrepancies are within the experimental uncertainty represented by the extended bar. However, the normal component deviates significantly from the theory, showing progressively

22


substantial underestimations with decreasing particle sizes, particularly for the 50nm and 100-nm particles. These underestimated z-component MSDs beyond the hydrodynamically hindered diffusion may be attributed to the additional near-field force effects on the nanoparticles (Section 1.1.5).

Fig. 2.6 Mean square displacements (MSDs) of the variously sized nanoparticles in the near-field, measured using the ratiometric TIRM and the predictions based on the theory, which account only for the hydrodynamic hindrance of the no-slip solid wall [47].

The additional near-field interactions refer to the gravitational, van der Waals, and electrostatic forces, and the nanoparticles are subjected to a total potential energy given by Eq. (1.12). The equilibrium height is defined as the most probable location for small particles carrying the minimum potential energy and thus determined by differentiation of Eq. (1.16). The equilibrium height hm is a gradually decreasing function with increasing particle diameter (Fig. 2.7) and is located well within the evanescent wave field penetration depth. The extended bars show the zcomponent MSDs accounting only for the hydrodynamic hindrance to the particles located at hm. Since the particles cannot penetrate the solid wall, the lower portions of the extended bars are shown by dashed lines, clearly illustrating that the nearwall Brownian motion should be further reduced beyond the simple hydrodynamic hindrance. For the larger particles (250-nm and 500-nm radii), the “wallinterception hindrances” are relatively small, and this is consistent with the small


23

discrepancies between the measured and predicted MSD values for the larger particles, as shown in Fig. 2.6. Furthermore, the substantially reduced illumination intensities beyond the penetration depth zp can result in a systematic measurement bias that significantly underestimates the MSD measurements near hm. In other words, the Brownian displacements extended to the outside of zp will not be effectively detected in comparison with the displacements inside of zp, and this can underestimate the measured MSDs. Furthermore, the smaller particles are subjected to more underestimation bias because of their larger magnitudes of MSD fluctuations outside of the penetration depth (Fig. 2.7) [78].

Fig. 2.7 Predictions of the root mean squares of the MSDs (i.e., < z >≡ 2 DH Δt ) based on the near-wall hindrance by hydrodynamic slow-down [37,41] and the estimated equilibrium heights hm for the four different-sized nanoparticles [47].

2.3.2 Slip-Flows in the Near-Field The no-slip boundary condition at the solid surface is experimentally proven to be acceptable for a wide range of fluid flows. For extreme conditions, such as a rarefied gas flow [79] or a flow over a hydrophobic surface [80-83], the no-slip assumption has been challenged for its physical justifications. Indeed, a more general boundary condition was proposed by Navier nearly two hundred years ago [84]:

uslip = β

du dy

(2.5)

24


where du/dy represents the shear rate at the wall. The slip length β = 0 for a noslip condition, but β is set to a non-zero quantity for a slip boundary condition. The use of micron-resolution particle image velocimetry (PIV) [85] allows measurements of the velocity profiles and shear rates in the near-wall region within 450 nm of a 30 x 300 μm microchannel [86]. For water flows seeded by 300-nm fluorescent dyes as tracers, no measurable slip length was identified for uncoated hydrophilic glass surfaces. On the other hand, the measured data for an octadecyltrichlorosilane (OTS)-coated hydrophobic surface yielded a slip length of approximately 1 μm. This magnitude of the slip length, however, was most likely overestimated because of the experimental uncertainties, including the uncertainty in defining the solid surface location and the limitations of approaching the measurement in the near-wall region. A more straightforward method was attempted to estimate the slip length by measuring the flow rate through a micro-channel and comparing the results with the ideal Poiseuille flow rate [80]; i.e.:

Qmeasured = QPoiseuille + Qslip

(2.6-a)

Qslip = uslip ⋅ Achannel

(2.6-b)

where the increment of the velocity profile due to the slip is assumed to be uniform for the entire channel cross-sectional area. Combining Eqs. (2.5), (2.6-a), and (2.6-b) yields the slip length in terms of other measurable quantities. For the case of OTS-coated hydrophobic surfaces, the slip length is shown to increase linearly with the shear rate, with a value of approximately 30 nm at a shear rate of 105 s-1. This technique is restricted to the assumption that the velocity profiles, with or without slip, precisely follow the theoretical Poiseuille flow. The resulting slip length is shown to be less than 3% of the aforementioned PIV results. In order to alleviate the ambiguities associated with the micro-PIV measurements as well as the Poisselle flow rate comparison, TIRM-based particle tracking was attempted in order to measure the flow velocities in the near-wall region directly [87]. The velocity measurements were made for average realization in the somewhat loosely defined “observation range” as 100 ~ 150 nm in the z-direction, perpendicular to the flow direction. These averaged velocity data fall on a straight line when plotted against the shear rate but, surprisingly, show no distinction between the hydrophilic and hydrophobic surfaces. Furthermore, no discernible differences were observed between the 200-nm and 300-nm tracer particles. The slip length for the observation range was estimated as approximately 100 nm; however, the slip length would have to be an order-of-magnitude smaller if an experiment were conducted to provide data with z-directional resolution. Huang et al. [88] used ratiometrically z-resolved TIRM (Section 2.2) to study the existence and magnitude of slip velocities. Test channels of 50-μm depth by 250-μm width were fabricated using a polydimethylsiloxane (PDMS) molding technique [89]. The hydrophilic channel surfaces were created by exposing the PDMS to oxygen plasma, while the hydrophobic surfaces were made by coating


25

(a)

(b) Fig. 2.8 The apparent velocity of particles measured for 200-nm fluorescent polystyrene microspheres in a deionized water shear flow over a (a) hydrophilic surface and (b) hydrophobic surface, respectively, and the comparison to slopes of expected apparent velocities (Eq. (2.5)), if there exists a 0-, 50- or 100-nm slip length [88].

26


OTS on the glass bonded to the PDMS. The measured slip length is represented by the slope of the velocity-shear rate plot (Fig. 2.8). The slip length for the hydrophilic surface ranges from 26 to 57 nm, with a slightly increasing trend with increasing shear rate. On the other hand, for the hydrophobic surface, the slip length ranges from 37 to 96 nm, with a similar increasing trend with the shear rate. Despite the measurement uncertainties associated with the excessively large dye particle sizes and the y-locations of the measurement planes, the results indicate that the no-slip may not always be accurate and that the flow modeling may depend on the wall surface properties. Though it seems obvious that hydrophobicity induces more apparent slip, the slip length measurements using TIRM bring challenges to several sources of measurement uncertainties. For example, the seeding particle sizes on an order of 100 nm seem too large for other relevant length scales, including the evanescent wave penetration length on the same order of magnitude, the slip length itself, and the slip-flow region that may be well below 100 nm. The use of smaller seeding particles, however, would elicit additional complicating factors, such as more pronounced ambiguities associated with near-wall hindered Brownian diffusion, the generally enhanced electrokinetic interactions with the surface, the increased minimum elevation of fine particles under the electric double-layer interaction [90], and the severely reduced fluorescence emission intensity. Nevertheless, the TIRM technique carries potential as a formidable tool in quantitatively exploring the slip flow in the near-field, once the aforementioned concerns are alleviated with improving designs and technologies.

2.3.3 Cytoplasmic Viscosity and Intracellular Vesicle Sizes An important area of research involving intra-cellular protein trafficking regards the movement of proteins, from the endoplasmic reticulum to specific cellular locations through a series of membrane structures [91]. Much of the existing research has focused on the interaction of these vesicles with the plasma membrane, due to the important biological functions associated with excocytosis [92-94]. Li et al. [95] proposed the motion of these vesicles near the membrane to be divided into three categories of Brownian, directional, and caged diffusion movements. In examining biofluidic diffusion of vesicles in the near-field plasma membrane region, a number of techniques have been used to measure bulk averages over hundreds or thousands of proteins or vesicles in the field-of-view. These include stateof-the-art optical techniques such as fluorescence recovery after photo-bleaching (FRAP) [96-98], fluorescence resonance energy transfer (FRET) [99], and fluorescence correlation spectroscopy (FCS) [100]. In contrast, TIRM can simultaneously determine both the average vesicle size and the effective intracellular fluid viscosity, based on individual tracking of the fluorescently tagged vesicles. The wide-field illumination, with its relatively thick optical depth, excites all of the vesicles inside the cell and provides blurred images that do not allow for individual tracking. In contrast, the substantially thin evanescent wave illumination limits the response of the vesicles within the near-field region on the order of 100 nm from the substrate (Fig. 2.9-a). The inset photo shows an overlaid image of protein


27

z

Immersion

Objective 60X,

91 μm

(a)

(b) Fig. 2.9 (a) The TIRM (green) images of NAG-1 vesicles overlaid on the DICM image of human brain cancer cells, and (b) the vesicle diameter and cytoplasmic viscosity calculated from the regression analysis of the near-wall hindered Brownian motion of the vesicles [110].

28


vesicles (NAG-11) in green on a differential interference contrast microscopy (DICM) image of human brain cancer cells in red [102]. A total of 23,000 three-dimensional vesicle locations are recorded, and they are classified into five different bins by 50-nm increments of their z-locations. In each bin, the two-dimensional (x-y) MSDs (Eq. (1.6-b)) are determined and correlated with the Stokes-Einstein diffusion equation [31]; i.e.: MSD (δ t ) ≡

( X (δ t ) − X (0) )

2

+ (Y (δ t ) − Y (0) )

2

= 4D ⋅ δ t = 4 ⋅ β

kT ⋅ δ t (2.7) 3πμd p

where X and Y are the two-dimensional position of the center of a vesicle image location, which uses Gaussian filtering to achieve sub-pixel accuracy [103], and the brackets < > represent the average of the square of the displacement. The coefficient β is the near-wall hindrance correction factor for the tangential Brownian motion, which is given as a function of the vesicle diameter dp as well as the medium z-location of the 50-nm bin (Eq. 1.9). At a given temperature, the two unknowns dp and μ for one equation (Eq. 2.7) are determined by a nonlinear regression using the 23,000 data realizations (Fig. 2.9-b). This yields an average vesicle size of 496 nm and an effective viscosity of 0.068 N⋅s/m2 (water viscosity at 20°C is 0.001 N⋅s/m2). The cytoplasmic viscosity is substantially higher than that of water, implying that dominating restraining forces exist in the near-field region. These forces could be due to collisions of vesicles, vesicle fusions with the membrane, and/or tethering of the vesicles to a microtubule. The vesicle size and cytoplasmic viscosity historically show large scattering in their measured data. Existing literature estimate the vesicle sizes as ranging from 60 nm to 1.3 μm, and the viscosity as ranging from 0.001 to 100 N⋅s/m2 [59,104-109].

1

The non-steroidal anti-inflammatory drug-activated gene-1 (NAG-1) protein, which is believed to play an important role in anti-tumorogenesis, was tagged with a Green Fluorescent Protein (GFP) and transfected into human T98G glioblastoma brain cancer cells [101].

Chapter 3

Optical Serial Sectioning Microscopy (OSSM)

Optical serial sectioning microscopy (OSSM), also known as “deconvolution microscopy,” was originally developed in order to construct three-dimensional images of a thick biological specimen by analyzing point spread functions (PSFs) of both focused and unfocused images [111,112]. The analysis method of unfocused images was implemented to obtain three-dimensional locations of granules embedded in a thick fluidic specimen [113]. The deconvolution principle is based on the determination of the radial intensity profile of the particle diffraction images as a function of defocus. In other words, the relative line-of-sight (z) location of a particle can be determined by interpreting the radial diffraction patterns of its defocused images. This deconvolution concept can be used in velocimetry to dynamically track the three-dimensional locations of nanoparticles in the near-field fluid flows. An elaboration of PSFs is essential to understanding the deconvolution principle and is presented in Sections 3.1 and 3.2, while the principles of OSSM and its near-field microfluidic applications are summarized in Section 3.3 and Section 3.4, respectively.

3.1 Point Spread Functions (PSFs) under Aberration-Free Design Conditions When a point source or small particle is imaged through an aperture or highmagnification objective lens, the wave nature of light forms a spatially distributing diffraction pattern. This three-dimensional diffraction pattern is called a “point spread function” (PSF), or a mathematical description of the point source image [114]. Since the point source forms the basis of any complex object, superposition of individual PSFs can in principle comprise the complete image of any object. The basic principle of PSFs is based on Kirchhoff’s law of scalar diffraction [115,116]. The lengthy formulation of PSFs is not repeated here, as the detailed steps are well presented elsewhere [117]. Under the ideal design conditions of an aberration-free

30

3 Optical Serial Sectioning Microscopy (OSSM)

system1 (Fig. 3.1), the intensity distribution of a three-dimensional axi-symmetric PSF [118,119] through a circular aperture of radius a is given in terms of the dimensionless diffraction variables (u,v) as follows:

I (u, v ) ⎛ 2 ⎞ =⎜ ⎟ Io ⎝u⎠

2

2 2 1+ 2 s 2+2s ⎧⎡ ∞ ⎤ ⎫⎪ ⎤ ⎡∞ ⎪ s⎛ u ⎞ s⎛ u ⎞ J 2 + 2 s (v )⎥ ⎬ ⎨ ⎢ ∑ (− 1) ⎜ ⎟ J 1+ 2 s (v )⎥ + ⎢∑ (− 1) ⎜ ⎟ ⎝v⎠ ⎝v⎠ ⎥⎦ ⎪⎭ ⎥⎦ ⎢⎣ s = 0 ⎪⎩ ⎢⎣ s = 0

with u =

ka 2 (zd − z f ) , v = kaRd , and k = 2π 2 λ zf zf

(3.1)

(3.2)

where the subscript f refers to the focal plane, d refers to an arbitrary diffraction imaging plane, and thus (zd − z f ) indicates the axial defocusing distance. The imaging point is coordinated as ( xd , yd , zd ) with Rd = ( xd + y d )2 , and u and v are the normalized axial and radial coordinates, respectively. The design conditions of the aberration-free system stipulate that the light ray from the observation point passes directly through both the cover slip of a designed thickness (170 μm in most cases) and the immersion medium having a designed refractive index, before traveling to the detector located on the back-focal imaging plane (Fig. 3.1). The design conditions of the aberration-free system specify a cover glass of a designated refractive index (ng*) and thickness (tg*), as well as an immersion medium of a designated refractive index (ni*) and thickness (ti*). The specimen thickness (ts*) should be zero to ensure aberration-free imaging. The PSF with no aberration, as seen in Eq. (3.1), is symmetric, with respect to both the u- and v-axes (Fig. 3.2). The cross-sectional PSF at the focal plane (u = 0) is equivalent to the Fraunhofer diffraction, or Airy function [121]; i.e.: I (0, v ) ⎛ 2 J 1 (v ) ⎞ =⎜ ⎟ Io ⎝ v ⎠

2

(3.3)

The PSF along the optical axis (v = 0) is given by the sync function, which has zero intensity points at u = ±4π , ± 8π , ... , and local maxima at u = ±6π . I (0, v ) ⎛ sin (u / 4 ) ⎞ =⎜ ⎟ Io ⎝ u/4 ⎠

1

2

(3.4)

Optical aberrations are defined as the departure from the idealized conditions of Gaussian optics. Common optical aberrations may be classified as follows: spherical, chromatic, curvature of field, comatic, and astigmatic. Among these aberrations, the spherical aberration is the most serious in the monochromatic illumination for macroscopic applications. As light rays emerge from several radial points of a lens, they are not converged into a single focal plane but instead focused on different planes along the optical axis, which results in blurry images. However, for microscopic applications, several factors contributing to additional aberration must be accounted for, as described in Section 3.2.

3.2 Point Spread Functions (PSFs) under Off-Design Conditions

31

Fig. 3.1 Schematic illustration of a symmetric point spread function (PSF) formed by aberration-free design conditions [120].

Fig. 3.2 A three-dimensional point spread function (PSF) projected onto the (u,v)-plane [122].

3.2 Point Spread Functions (PSFs) under Off-Design Conditions In reality, optical aberrations must be considered, since the imaging is most likely conducted under “off-design” conditions. Aberrations are commonly caused by two variables: one, the different refraction indices (RIs) of the cover glasses and immersion media, and two, the variability in the thicknesses of the immersion media and cover glass from the specified design values. When the design conditions are not met, the refracted rays have optical pathways that deviate from the original aberration-free conditions and do not converge to the ideal focal point. Consequently, the refraction due to the index mismatching affects the optical aberration

32


Fig. 3.3 Asymmetric point spread function (PSF) under off-design conditions [120].

of an objective lens and produces asymmetric diffraction patterns, as schematically illustrated in Fig. 3.3. Since most specimens have different RIs from those of a cover glass and an immersion medium, asymmetric PSFs will prevail in practice. In contrast to Eq. (3.1), a more comprehensive PSF is given as an integral form that consists of the Bessel function and a sinusoidal complex exponential term that is derived by elaborating Kirchhoff’s scalar diffraction theorem [115]. The resulting 3-D light intensity distribution is given in terms of the radial location rd and the defocus distance Δz as:

⎡ ⎤ NA ρ rd ⎥ exp [ jW ( Δz, ρ )] ρ d ρ I ( xd , yd , Δz ) = C ∫ J 0 ⎢ k 2 2 0 ⎣ M − NA ⎦ 1

2

(3.5)

Here, k is the wave propagation number, which is equivalent to 2π/λ (with λ being the emission wavelength of the point source), NA is the numerical aperture of the objective lens, M is the total magnification of the microscopic imaging system, and ρ is the normalized radius in the exit pupil plane. The phase aberration function, W(Δz,ρ), is the product of the wave number k and the optical path difference (OPD) that is calculated with the following equation. The optical path difference (OPD) is generated from the two different optical paths connecting an identical point source and imaging end point in both design (Fig. 3.1) and off-design (Fig. 3.3) systems; i.e.:

OPD =

⎛ n t ⎞ nt ns t s nt n t + g g + i i − ⎜ g * g* + i* i* + n ⋅ RS ⎟ ⎜ ⎟ cos θ s cos θ g cos θi ⎝ cos θ g* cos θi* ⎠

(3.6)

3.2 Point Spread Functions (PSFs) under Off-Design Conditions

33

where n and t are the refractive index and thickness of each optical layer, respectively. The subscript s, g, and i indicate the respective layers of specimen fluid, cover glass, and immersion medium. The symbol ∗ signifies the design conditions of these parameters. The physical defocusing distance Δz’ is given by:

Δz ' =

t g ti ⎛ t g * ti * ⎞ t Δz ⎟ = s + + −⎜ + ni n s n g ni ⎜⎝ n g * ni* ⎟⎠

(3.7)

Combining Eqs. (3.5) - (3.7) gives general expressions for the three-dimensional PSFs, for both design and off-design conditions.

(a) A symmetric PSF under the design conditions

z

(b) An asymmetric PSF under the off-design conditions Fig. 3.4 Meridian sections of three-dimensional and axi-symmetric point spread functions (PSFs). (a) The symmetric PSF is created under the design conditions (ts = 0, ns =1.33, tg = 0.17 mm, ng = 1.522, and ni = 1.0). (b) The asymmetric PSF is created under off-design conditions (tg = 0.233 mm and ti = 0.481 mm). The red dashed lines indicate the locations of the outer-most-fringe diameter Domf at various defocusing distances Δz’ [123].

34


Aberration-free imaging is achieved when the microscope system is tuned to the design conditions (OPD = 0) that require the light ray to travel through a cover glass of a designated refractive index and thickness, an immersion medium of a designated refractive index and thickness, and a zero-thickness specimen (Fig. 3.4-a). In practice, specimens with zero thickness are unrealistic since any fluid transport requires a finite cross-section. Moreover, when the used cover glass differs from the specified glass, the resulting phase aberrations render the 3-D PSF asymmetric for the off-design conditions (Fig 3.4-b). Note that the PSFs for both design and off-design conditions remain axi-symmetric as long as the point source stays within the paraxial range of the objective lens.

Fig. 3.5 The optical serial sectioning microscopy (OSSM) setup uses an epi-fluorescent system, based on an inverted microscope equipped with a high-NA objective lens. The illumination light is filtered at 480 nm and the fluorescent emission is centered at 520 nm [124].

3.3 Principles of OSSM

35

3.3 Principles of OSSM The basic principle of optical serial sectioning microscopy (OSSM) is to analyze the sectioned fringe patterns of 3-D PSFs and to determine the fluidic properties (ns) or particle locations (ts), assuming all other parameters are given. An ordinary epi-fluorescence microscopy can be used to set up OSSM, as schematically shown in Fig. 3.5, with high NA objective lenses of mostly oil or water immersion types that make the fringe patterns more distinctive. One worthwhile remark is that a 14or higher bit CCD system is recommended to ensure high-quality PSF images. The most crucial part of the experiment is to ensure the calibration accuracy of the OSSM-measured radial intensity profiles in comparison with the calculated intensity profiles, based on Eq. (3.5). When the test particle (500 ± 16 nm diameter) is located at the top glass plate of the calibration chamber with the zero specimen thickness (Fig. 3.6), the diffraction images, taken at any Δz ' by vertically adjusting the objective lens position, will construct the symmetric 3-D PSFs (Fig. 3.4-a). On the other hand, when the test particle is located at the bottom plate, the specimen thickness of 170 μm creates a substantial aberration, and the recorded diffraction images conform to the sectional fringes of the asymmetric 3-D PSFs (Fig. 3.4-b).

Objective lens 40X, 0.75 NA, Dry

170 μm

170 μm

Cover glass (ng = 1.522)

Δ z’

Fluorescent microspheres

Water (ns = 1.33) Slide Glass

Fig. 3.6 Schematic configuration of OSSM fringe calibration, using microspheres of 500nm nominal diameter [120].

36


(a)

(b)

Fig. 3.7 Comparison between the measured and calculated PSF sectional patterns for both (a) design conditions and (b) off-design conditions.

3.4 Near-Field Applications of OSSM

37

The measured diffraction images of the inset photos of Fig. 3.7 are observed in order to determine the diameters of the outer-most-fringes along 1.33-μm intervals of Δz’. Also, a series of calculated intensity distributions, as shown beside each corresponding photo, is obtained at the same intervals of Δz’. The last peak of the calculated intensity profile is identified as the outer-most-fringe location. The aberration-free design conditions (Fig. 3.7-a) are ts* = 0 mm, tg* = 0.17 mm, ti* = 0.51 mm, ng* = 1.522, and ni *= 1.0, while the off-design conditions (Fig. 3.7-b) are ts = 0.17 mm, tg = 0.17 mm, ti ≈ 0.38 mm, ng = 1.522, and ni = 1.0. For both the design and off-design cases, the measured outer-most diameters show good agreement with the calculated values at the same defocusing distances of Δz ' (Fig. 3.8). Therefore, the line-of-sight locations of suspended particles can now be determined by optimally fitting the measured DOMF to the predicted PSF sectional profiles.

20

Symmetric PSF

DOMF (μ m)

15 10

Asymmetric PSF

5 0 0

10

20

30

Δz' (μm) Fig. 3.8 The correlation of outer-most-fringe diameters Domf with the defocusing distance Δ z ' . The symbols represent the measured data based on the PSF sectional images in Fig. 3.7 while the dashed lines represent the calculations based on Eq. (3.5) [120].

3.4 Near-Field Applications of OSSM 3.4.1 Three-Dimensional Particle Tracking Velocimetry (PTV) A three-dimensional micro-particle tracking velocimetry (micro-PTV) is made possible by using a single camera with deconvolution microscopy, based on the

38


OSSM principle. The use of multiple cameras arranged at different viewing angles, called “stereoscopic” or “multiscopic” PIV, has been mostly successful at mapping the three-dimensional velocity fields at the macrosopic level [125-128] but has been limitedly successful for microscale measurements, and only at relatively lower magnifications [129-131]. Furthermore, there remain unanswered questions regarding its cumbersome calibration procedure as well as the lowered imaging accuracy, due to the significant optical aberrations and astigmatisms. A number of studies correlating the particle image intensity with the amount of defocusing or depth-of-field for the case of the two-dimensional micro-PIV have been published [128,132-136]. Such published efforts on 3-D particle tracking include holographic PIV [137] as well as defocusing digital particle image velocimetry (DDPIV) [138-142]. OSSM velocimentry is inherently microscopic and more straightforward to use because the line-of-sight tracking of particle locations can be done based on the aforementioned sectional fringe analyses of PSFs. In order to complete the 3-D tracking, the ordinary PTV scheme tracks the planar, or x-y, locations of the same particle. Using OSSM, the feasibility of 3-D tracking of small particles has been demonstrated [143,144]. A three-dimensional microscale flow is created to flow over a 95-μm diameter polystyrene bead that is fit snugly inside a 100-μm square test channel (Fig. 3.9). 500-nm diameter fluorescent polystyrene particles (505nm absorption/515nm emission) with 1.05 SG (specific gravity) are seeded in deionized water at a 0.01%

Fig. 3.9 A test section that generates a three-dimensional flow over a 95-μm diameter polystyrene sphere that is fit inside a 100-μm square microchannel [124].


39

concentration to function as point sources of PSFs. In order to reduce the refractive index mismatching between the test channel wall (n = 1.475) and the cover glass (n = 1.522), a small amount of immersion oil (no = 1.516) is smeared into the gap. The objective lens is focused on the top inner surface of the test channel, and the defocused images of the particles in the flow are recorded within 25 μm from the top inner surface focal plane. Dynamic images of PSF sectional fringes (Fig. 3.10-a) are recorded digitally at 33 frames-per-second. The outer-most-fringe diameter Domf and its center location are simultaneously determined by newly developed image analysis software [124]. First, the recorded 8-bit images (0-255 pixel gray levels) are filtered into 1-bit images (0-1 pixel gray levels, Fig. 3.10-b). The key idea herein is the use of a “circle-fitting” concept in which a sufficiently large circle is started around a given pixel as centered and its radius is then progressively shrunk to examine if the majority of the circularly distributed pixel points fall into the “bright” category, ensuring that they are located on the fringe ring (Fig. 3.10-c). The examination is conducted continually for all of the pixels to identify all existing outer-most rings (Fig. 3.10-d), and this examination is repeated for the successive images. Once a fringe ring is identified with its diameter Domf, the corresponding interrogation point (i.e., the center of the circle) is assigned as the x-y location of the particle. The threshold filtering procedure for a binary image involves identifying the outer-most-ring from the multiple concentric fringes. This process significantly controls the accuracy of the entire image analysis. The following protocols are used to enhance filtering accuracy: a.

b.

c.

For an interrogation section containing a maximum normalized gray level greater than 0.9, the number “1” is assigned to all pixels with gray levels higher than 0.75, to be identified as the fringe ring image, and “0” is assigned to all of the remaining pixels with gray levels below 0.75, to be considered as background noise. If an interrogation section does not satisfy protocol (a) AND shows the differential between its maximum and minimum gray levels as being less than 0.15 (i.e., for the case of a relatively blurry interrogation section), “0” is assigned to all of the pixels in the section. If an interrogation section does not satisfy either protocols (a) or (b), “1” is assigned to all of the pixels falling below the section-average gray level and “0” is assigned to those with gray levels above the average.

For a given pixel point, the circle-fitting starts with a sufficiently large circle of 45-pixel radius and 24 angular circumferential pixel points. If the average value of all 24 pixels is higher than a specified threshold, the circle is recognized as a fringe ring; otherwise, the circle is reduced to the next 44-pixel radius and thereafter until either a ring is identified or the radius reduces to zero, with no ring identified.

40


x y 576 pixels (93 μm)

(a)

1024 pixels (165 μm)

(b)

(c)

(d)

D

A

B

C

44 pixels 90 pixels

Fig. 3.10 (a) A raw diffraction image captured with an 8-bit intensity resolution and a 30ms shutter speed. The dashed line indicates the 95-μm diameter polystyrene sphere. (b) The 8-bit gray scale image is converted to a one-bit binary image. (c) An identification of a 3-D particle position is conducted. (d) Identified 3-D particle locations and the corresponding outer-most rings [124].


41

The algorithm is summarized in the flow chart shown in Fig. 3.11. Figure 3.10c shows an identification of the Domf of a 22-pixel radius as an example, and Fig. 3.10-d shows a few identified rings at different locations (x, y, Domf(Δz’)). Once all particle locations (x, y, Domf(Δz’)) are identified for successive frames, the use of the nearest-neighbor-search method for particle tracking determines the threecomponent velocity vector fields. To eliminate erroneous vectors, a threedimensional median filtering procedure with 3 x 3 x 3 surrounding vectors performs post vector processing. Furthermore, incorrectly directed vectors are eliminated. If the center vector deviates beyond a tolerable range from the median of the surrounding 26 vectors, the center vector is replaced by an average of both

Divide an image by a section of 16× 16 pixels

Read 256 pixel intensities in each section

Find a maximum, a minimum, and an average intensity out of 256 intensities

Maximum >0.9

Each pixel >0.75

yes

yes

no

The pixel = 1.0

Max-Min < 0.15

yes

no

All pixels = 0.0

Each pixel < Average

no

no The pixel = 0.0

yes The pixel = 0.0

The pixel = 1.0

Go to the next 16× 16 pixel section

Fig. 3.11 A detailed flowchart for the digital image processing to identify Domf and its center location for sectional PSF fringes [124].

42


the center and median vectors. The tolerance is ranged from 0.1 to 0.5, depending on the image quality. Additionally, any empty interrogation sections identifying no vector are filled with the median of the surrounding vectors, in order to smooth out the flow field without affecting the flow field magnitudes and directions. The resulting three-dimensional vector fields for the creeping flow (Re = 0.003) over a snugly fit 95-μm diameter sphere inside a nominal 100-μm square channel are shown in Fig. 3.12. The presented vector fields cover the near-field of 20-μm depth from the top inner surface of the microchannel, and 2,304 vectors are shown with a volumetric spatial resolution of 5.16 μm × 5.16 μm × 5 μm. The flow acceleration is displayed in the gap region between the sphere and the square channel wall, and the two different vertical motions of ascending and descending are clearly identified at the front and rear regions of the sphere, respectively. The measurement accuracy of micro-PTV depends on several factors, and one nontrivial factor associated with the small length scale comes from the rendering effect of Brownian diffusion of seeded particles. The associated errors can be estimated by considering the three-dimensional mean square displacement (MSD) of Brownian motion; i.e.:

εB =

r2

1/ 2

Δx

=

1 u

6D Δt

(3.8)

where 〈r2〉 denotes the three-dimensional MSD (Eq. (1.6)), Δx denotes the average displacement of the seeded particles, u denotes the corresponding characteristic velocity, D denotes the Brownian diffusion coefficient of the suspended particles in the fluid, and Δt denotes the time interval between observations. For an estimated characteristic velocity of 60 μm/s and a given time interval of 0.033s, the error due to the Brownian motion is estimated to be approximately 21% in the case of a single particle detection. For an ensemble-averaged realization, this error dramatically decreases by ε B N , where N is the number of independent samples. An example case of N = 200 thus yields a reduced uncertainty of approximately ± 1.48 %.

3.4.2 Near-Wall Thermometry In 1946, Lawson and Long [145] presented a feasibility study that examined how Brownian motion can be used to devise low temperature thermometry. The Brownian motion of tracer particles in micro-PIV is known to diminish the crosscorrelation signal peak and to negatively affect the image depth of correlation [146]. Conversely, this cross-correlation broadening has been used to measure the thermal motion of small particles [147,148].


43

0

20

Y 40 (μm) 60

80

0

Z 10 (μm) 20 0

25

50

75

100

125

150

X (μm)

(a)

Reference vector: 100 μm/s

X

Y Z

0 10

0

20 0

50

Z

20 40

x

100 X (μm)

60 150

Yy(μm)

80

(b) Fig. 3.12 Full-field mapping of vector profiles: (a) orthogonal projections onto the x-y and x-z planes, and (b) a three-dimensional view [124].

44


Brownian motion refers to the motion of small particles caused by the random bombardment by surrounding fluid molecules. The three-dimensional mean square displacement (MSD) of the particle is given by: n

MSD = r

2

=

∑r

i

i =1

n

n

2

=

∑ ( Δx

2 i

+ Δyi2 + Δzi2 )

i =1

n

= 6 D Δt

(3.9)

where D is the Brownian thermal diffusivity (or equivalently, a diffusion coefficient) of the particle and Δt is the observation time interval of each incremental displacement. The observation time interval may be equated to the image frame interval of a CCD camera as long as the frame rate is sufficiently high to discern the minutely changing displacements of the random walk of the particles. Following the Stokes-Einstein equation, the diffusivity is known to be a function of the fluid parameters: D=

κT 6πμrp

(3.10)

where κ is Boltzmann's constant (1.3805 x 10-23 J/K), T is the absolute temperature of the fluid, μ(T) is the dynamic viscosity of the fluid [149], and rp is the particle’s radius. Perrin [150,151] verified the Stokes-Einstein theory by painstakingly measuring the time dependence of one- and two-dimensional MSDs of microscale grains of a known size in a fluid. More recently, the use of video microscopy has allowed two-dimensional tracking of the Brownian motion of suspended particles with substantially shorter time intervals than in Perrin’s experiment. The resulting MSDs have shown good correlation with Einstein’s theoretical values [34,152]. The viscosity of liquid, on the other hand, is a decreasing function of temperature and is expressed as [153]:

μ = A ⋅ 10

B T−C

(3.11)

where A, B, and C are constant variables that depend on the fluid. For example, for water, A, B and C are known to be 2.414 ×10-5, 247.8, and 140, respectively. Combining Eqs. (3.10) and (3.11) gives the diffusivity of particles with a known diameter as a function of just the suspension liquid temperature; i.e.: D=

κT B ⎤ ⎡ 6π ⎢ A ⋅ 10T − C ⎥ rp ⎦ ⎣

(3.12)

The solid curve in Fig. 3.13 shows the temperature dependence of viscosity in Eq. (3.11) as well as of diffusivity in Eq. (3.12). The diffusivity data are normalized


45

by Do at T = 0°C so that the particle size dependency is not apparent. The intermediate dashed curve shows the noticeably weaker temperature dependence of the diffusivity when the temperature dependence of viscosity is ignored. Therefore, the unique D-T correlation of Eq. (3.12) allows the use of OSSM as thermometry by measuring the MSD of small particles suspended in a fluid. The instantaneous diffraction patterns of fairly monodispersed polystyrene fluorescent particles (500-nm±16 nm) suspended in water (Fig. 3.14-a) can be digitally analyzed to determine their depth-wise locations, using the Domf - Δz’ correlation under the off-design conditions (Fig. 3.14-b). The resulting depth-wise locations of the individual particles are marked in microns in Fig. 3.14-a. The measured trajectory of an arbitrarily selected single particle over three seconds (90 frames) represents the typical isotropic and random walk of free Brownian motion in water at 25°C (Fig. 3.14-c). The solid line segments correspond to upward movements, while the dashed line segments correspond to downward movements. The directions and magnitudes of the three-dimensional displacements confirm the isotropic nature of Brownian motion (Fig. 3.14-d). The corresponding probability histogram of the measured displacements (Fig. 3.14-e) fits well with the Gaussian 10

D/Do 9

D/Do, with constant viscosity μ/μο

8 7 6

D/Do ,

5

μ/μ o 4 3 2 1 0 0

20

40

60

80

100

o

Temperature [ C]

Fig. 3.13 The normalized diffusion coefficient (D/Do) and fluid viscosity of water (μ/μo) as functions of temperature. The reference diffusivity and viscosity values for normalization are taken at T = 273K, which prevents the particle size dependence from being apparent [120].

46


(b)

(a)

(c)

(d)

(e) Fig. 3.14 (a) Measured diffraction patterns of 500-nm diameter polystyrene fluorescent particles suspended in water at 25°C, with numeric values indicating the depthwise zlocations in µm, (b) the Domf - Δz’ correlation, (c) the measured three-dimensional Brownian motions of a single particle at 33-ms time intervals (solid lines indicate upward movement while dashed lines indicate downward movement), (d) the random and isotropic Brownian motions recorded over 203 time steps, and (e) the PDF of the Brownian MSD fitted to the Gaussian or random probability distribution [120].


or

random

(

probability

)

distribution

47

p (r , Δt ) =

2 4π r 2 e − r / 4 DΔ t , 3/ 2 8 (πD Δt )

where

r ≡ Δx 2 + Δy 2 + Δz 2 , with Δx, Δy, and Δz being elementary one-dimensional displacements, respectively. As an example, the x-y measurement resolution is estimated to be 0.16-μm for the case of a 40X magnification imaging with the CCD pixel resolution of 6.45 μm. The line-of-sight z resolution is estimated by accounting for the sensitivity of the outer-most ring diameter to the defocus distance; this is also estimated to be about 0.16-μm. Substituting Eq. (3.12) into Eq. (3.9) gives the correlation between MSD and T as: (3.13) κΔt ⋅T MSD = B ⎡ ⎤ π ⎢ A ⋅ 10 T −C ⎥ rp ⎣ ⎦ where the fluid temperature T is determined from the measured MSD data for a given particle size rp. The temperature correlations of the measured MSDs are presented for 500-nm particles suspended in water, with the temperature ranging from 5°C to 70°C (Fig. 3.15). The test chamber is geometrically similar to the calibration chamber (Fig. 3.6) but provides a steady temperature condition by having an embedded copper exchanger block connected to a constant temperature bath. To abate the initiation of natural convection, this chamber was designed to provide a Rayleigh number (= gβΔTL3/αν) of approximately 22 (β = 595.4 × 10-6 K-1, ΔT = 50K, L = 170 μm, α = 1.63×10-7 m2/s, and ν = 3.98 × 10-7 m2/s), which is much less than the critical value of 1708 for the onset of natural convection [154]. A thermo-couple probe is flush-installed at the inner bottom surface to monitor the fluid temperature. The test chamber intentionally uses an off-design cover glass of 223-μm thickness so that the visibility of the asymmetric PSFs may be more pronounced and the signal-to-noise ratio of the fringe detection can be further enhanced. Each symbol represents an ensemble-averaged MSD for seven arbitrarily selected particles that are tracked for one second at each temperature condition (i.e., a total of 210 data realizations at 30 fps). The error bars indicate a 95% confidence range of the measured MSDs, assuming a Gaussian distribution, as previously shown in Fig. 3.14-e. The three primary curves represent theoretical predictions for the 3-D MSDs of 6 DΔt as a function of T (as shown in Eq. (3.13)), 2-D (x-y, x-z, or y-z) MSDs of 4 DΔt , and 1-D (z) MSDs of 2 DΔt . The average discrepancies between the measurements and predictions are 5.55%, 4.26%, and 3.11% for 1-D (z), 2-D, and 3-D, respectively.

48


0.6

3D Theory 3D(XYZ) Experiment 2D Theory 2D(XY) Experiment 2D(XZ) Experiment 2D(YZ) Experiment 1D Theory 1D(z) Experiment

0.5

2

MSD (μm )

0.4

0.3

0.2

0.1

0 0

10

20

30

40

50

60

70

80

o

Temperature ( C)

Fig. 3.15 The theoretical and experimental mean square displacements (MSDs) of 500±16 nm diameter nanoparticles, as functions of the fluid temperature. Each symbol represents 210 data realizations of 7 individual particles. The dashed lines surrounding the theoretical curves of each dimension represent a range of MSDs that is caused by the uncertainty (3.2%) of the particle’s diameter. The error bars indicate a 95% confidence interval of the measured MSDs [120].

The pair of dashed curves for the primary curve shows the measurement uncertainty range, based on the single-point detection estimation [7]. For the tested temperature span of 5 to 70°C, 1-D MSD measurement uncertainties range from ±4.33% to ±2.11%, which is slightly higher than the 3-D MSD uncertainties that range from ±2.61% to ±1.23% for the same temperature span. The uncertainty gradually decreases with increasing temperature, and a more detailed analysis


49

shows that the elementary uncertainty contribution associated with the particle diameter (500±16 nm) is predominant over the other uncertainty contributors. Without sacrificing much accuracy in comparison to the 3-D MSD measurements, the single z-component detection of MSD using the OSSM may well be considered as an effective method of thermometry for nanofluids. This would negate the need of the cumbersome two-dimensional MSD detections, which are based on the traditional particle tracking method. A priori to the OSSM thermometry is the knowledge of the temperature dependency of the fluid viscosity and the known particle sizes.

3.4.3 Near-Field Mixture Concentration Measurements Another use of OSSM is in implementing a nonintrusive measurement tool for fluid mixture concentrations in the near-field. A novel approach for detecting mixture concentrations is made possible by detecting the test fluid RI directly from the corresponding sectional PSF fringe patterns of the nanoparticles. When all other geometrical (t) and optical (n) parameters are set constant for Eq. (3.6), the optical path length differential (OPD) can be a function solely of the test fluid RI (ns). All ray angles θ will remain unchanged once the focal plane remains fixed, and the 3-D diffraction patterns of the PSF in Eq. (3.5) will change only with ns. The key idea is that the nanoparticles are fixed outside the wall of the mixing chamber, so that the test fluid can be free from intrusion by any physical probes (Fig. 3.16). Fluorescently labeled 500-nm polystyrene microspheres with excitation/emission wavelength maxima at 505/515 nm [155], respectively, are self-assembled by evaporation onto the top cover glass. Plasma treatment of the glass surface as well as addition of surfactant helps to disperse the microspheres as evenly as possible, with minimal aggregation. The off-design PSFs with immersion oil (n = 1.516), glycerol (n = 1.477), and water (n = 1.337) are geometrically similar, except for their defocusing distances Δz. Note that the OSSM system is set for off-design conditions and that the immersion oil is arbitrarily selected as a reference condition with Δz = 0. Both measured and calculated sectional fringe patterns represent the RI differences of the three different fluids. Δz increases with increasing deviations of RI from the selected reference of the immersion oil, and the outer-most-fringe diameter Domf at the back focal plane also increases with the deviation. Comparison of the measured Domf with the calculated Domf shows good agreement, and the extended bars represent the RMS variations of the measured diameters for ten (10) realizations. In the case of the immiscible interface of immersion oil and water, both at 22°C, the sectional fringe patterns of 3-D PSF go through a distinct transition from the oil region to the water region inside a microchannel of a 92μm x 124 μm cross-section (Fig. 3.17). The experimental conditions are fine-tuned to generate well-focused images (Δz = 0) for immersion oil (Fig. 3.17-a), and the spherical waves emitted from the fluorescence particle schematically illustrate the in-phase propagation through the homogeneous oil phase. When the interface is approached

50


Fig. 3.16 The three-dimensional PSF patterns for OSSM and their projections onto the reference focal plane of the immersion oil. Both Δz and Domf increase with a decreasing RI of the test fluids [123].


51

Fig. 3.17 Sectional PSF images of spatially fixed fluorescent nanoparticles outside the glass wall for the region near the stationary interface of immiscible water and immersion oil inside the 92 μm–high microchannel. The spherical waves emitted from the nanoparticles experience off-phase propagation due to the optical path length difference of the second fluid (water). The resulting fringe patterns are a hybrid of the focused image, which represents the oil region, and the diffracted fringes, which represents the water region: (a) the oil region more than 150 μm away from the interface, (b) the oil side, approximately 80 μm from the interface, (c) directly at the interface, (d) the water side, approximately 80 μm from the interface, and (e) the water region more than 150 μm away from the interface [123].

52


Fig. 3.18 Formation of the time-dependent mixing region for the case of glycerin penetrating water inside a microchannel (92 μm high and 2 mm wide). (a) The glycerin concentration in the interfacial region increases with time, showing a decrease of the outer-mostfringe diameter Domf, and (b) the measured Domf and the refractive index changes from 17.6 μm (PR = 1.337; 100% water at t = 0) to 8.3 μm (RI = 1.477; 100% glycerol at t = 5s) [123].


53

(Fig. 3.17-b), the spherical waves experience an off-phase propagation, due to the optical path length difference of the second fluid (water). The resulting fringe patterns are thus a hybrid of the focused image, which represents the oil region, and the diffracted fringes, which represents the water region. The “fan” angle of diffracted fringes provides a good indication of the relative measurement location with respect to the interface location, showing progressively increased fan angles as the waves enter the water region (Figs. 3.17-b, c, and d). When completely inside the water region, the spherical waves propagate in-phase, and complete diffraction images are extracted (Fig. 3.17-e). The precise location of the interface of two immiscible fluids can be detected when the fan angle approaches 180°, as closely shown in Fig. 3.17-c, assuming that the interface is flat or its curvature is negligibly small. As an example, two miscible fluids, such as glycerin and water, create a diffusive mixing region with continuously varying mixture concentrations (Fig. 3.18a). When a small amount of glycerin smears into the water filled microchannel (92 μm high and 2 mm wide), the glycerin quickly diffuses into water, and eventually the entire microchannel volume will be filled with glycerin. The time-dependent diffusion process, monitored at a fixed location of the channel, shows the gradual concentration change from 100% water to 100% glycerin. The outer-most-fringe diameter (Domf) shows a change from 17.6 μm for 100% water (t = 0) to 8.3 μm for 100% glycerin (t = 5s). The solid curve in Fig. 3.18-b shows the theoretical correlation of Domf with the mixture RI values. The symbols present the measured Domf, and the error bars indicate the RMS variations of the measurements. Since the mixture RI is known to increase linearly with glycerin concentration [139], the glycerin concentration can be determined from the mixture RI. Historically, optical tracking of intrusive seed fluorescent particles has been widely used to characterize micro-mixing [156], but the seeded particles physically interfere with the mixture and the measurement results will never precisely depict the mixing, which is essentially a molecular diffusion process. Furthermore, most seed particles are tens of nanometers large and thus several orders larger than molecules. It is impossible to imagine that both the seed particles and fluid molecules move precisely together, where the molecular diffusive mixing prevails. In contrast, OSSM can serve as a nonintrusive and full-field tool for the precise mapping of molecular diffusion in the near-field mixing process.

Chapter 4

Confocal Laser Scanning Microscopy (CLSM)

Confocal microscopy, which was patented by Dr. Marvin Minsky [157] at Harvard University in 1957, dramatically improves the optical imaging resolution to unprecedented levels. The unique feature of confocal microscopy is its ability to deliver extremely thin, in-focus images by a true means of depth-wise optical slicing. This also allows for the gathering of three-dimensional reconstructed information from the line-of-sight depth-wise resolved imaging without the need for any invasive slicing of the specimens [158-160]. The confocal microscopy has been widely used in the biological, pharmaceutical, medical, and material science research areas and is often associated with laser-induced fluorescence (LIF) imaging, which allows microstructures to be more clearly visible [161,162]. Fluidic applications, however, were not realized until the optically sliced microscopic particle imaging velocimetry (PIV) was developed by Park et al. of the author’s group [163]. This innovation is named “confocal laser scanning microscopic-PIV” (CLSM-PIV). The basic principles of confocal imaging are discussed concisely in Section 4.1. General discussions on microscopic imaging resolutions are presented in Section 4.2. In-depth and mathematical discussions for the confocal imaging resolutions and optical slicing are presented in Sections 4.3 and 4.4, respectively. Finally, the CLSM-PIV system is discussed in Section 4.5, and its applications to flow measurements are presented in Section 4.6.

4.1 Principles of Confocal Imaging The basic ‘confocal’ concept is described as the point scanning of the laser excitation and a spatially filtered fluorescence signal emitting back from the focal point onto the confocal point (Fig. 4.1). The pinhole aperture, located at the confocal point, exclusively allows the emitted fluorescent light from the focal point to pass through the detector (solid rays). At the same time, the pinhole aperture filters out the fluorescent light emitted from outside the focal point (dashed rays). This spatial filtering is the key principle in enhancing the depth-wise optical resolutions by optical slicing.

56

4 Confocal Laser Scanning Microscopy (CLSM)

Fig. 4.1 The principles of confocal microscopy, using a pinhole as the spatial filter [163].

In conventional wide-field microscopy (WFM), a specimen is completely illuminated by an excitation light and emitted back to the detector with no spatial filtering, so that the entire specimen is fluorescing or emitting simultaneously. It is of no doubt that this excitation light has its highest intensity at the focal point of the objective lens, but nevertheless, the parts of the specimen other than at the focal point absorb some of the excitation light as well and thus also fluoresce. This phenomenon contributes to a background haze in the captured image. The spatial filtering using a pinhole aperture constructs one point-wise image at a time. The illuminating laser scans rapidly from point to point on a single focal plane in a synchronized manner with the aperture, completing a full-field image on the detector (Fig. 4.2). This scan may be repeated for multiple depth-wise focal planes in order to reconstruct three-dimensional images when needed.

Fig. 4.2 A schematic illustration of galvanometric scanning in order to conform to a fullfield image [163].

4.2 Microscopic Imaging Resolutions

57

The depth discrimination capability of confocal microscopy has been analytically characterized for a range of fluorescence wavelengths, and the simulation results have been compared with the corresponding experimental results [164]. A theoretical analysis for standard confocal microscopy, along with 3-D fluorescence correlation spectroscopy, has been developed using a point-spread function in conjunction with a collection efficiency function [165]. Aberration compensations for confocal microscopy were discussed regarding the spherical aberrations that occur when one is focused deep within the specimen [166], and for additional aberrations induced by mismatches in the refractive index values across or inside the specimen [167]. An extensive study [168] showed that the signal-tobackground ratio1 of an optimized confocal microscope can be more than 100 times greater than the signal-to-background ratio available with a conventional microscope.

4.2 Microscopic Imaging Resolutions When the Fraunhofer condition2 is satisfied, microscopic particle imaging can be depicted by Fraunhofer diffraction rings (Fig. 4.3), also called an “Airy function”, which is equivalent to a 2-D projection of the 3-D point-spread function (PSF). If multiple point sources emit rays of an identical wavelength λem, all of their Airy disks3 have the same diameter, as long as they are constructed by the same objective with a specified numerical aperture (NA)4. Two neighboring objects are said to be “marginally resolved” when the center of one Airy disk falls on the first minimum of the other Airy pattern, the so-called Rayleigh criterion for monochromatic imaging. The Rayleigh criterion is generally accepted as the lateral resolution for conventional microscopic imaging and is used to estimate the minimum resolvable distance between two point sources of light generated from a specimen. The Rayleigh criterion, or equivalently, the lateral microscopic imaging resolution, is equal to the Airy disk radius; i.e., 0.61λem / NA [5]. 1

2

3 4

Here, the “signal” refers to the detected light that originates from the resolution volume defined by confocal microscopy, and the “background” refers to the light that originates outside of the resolution volume. This is also called a “far-field” diffraction condition, which is defined as R > a 2 / λ , where R is the smaller of the two distances from the particle to the objective lens and from the objective lens to the imaging detector, a is the particle radius, and λ is the wavelength in the medium. For typical conditions of micro-PIV ( R ~ 1 mm, a ~ 200 nm, and λ ~ 500 nm), for instance, the inequality is amply satisfied by more than 12,000. An Airy disk is defined as the first dark ring of the Airy function and is shown in Fig. 4.3. The numerical aperture (NA) is defined as NA ≡ ni sin θ max , where ni is the refractive index of the immersing medium (air, water, oil, etc.) adjacent to the objective lens and θ max is the half-angle of the maximum cone of light collimated by the lens. Since sin θ max < 1.0 , NA never exceeds the refractive index of the immersing medium. The use of immersion oil can effectively increase NA and therefore increase the imaging resolution as well.

58


Airy disk diameter

Fig. 4.3 The Fraunhofer diffraction rings are called an “Airy function,” which is a footprint of the three-dimensional point-spread function (PSF) [169].

Unlike the lateral Fraunhofer diffraction, the axial diffraction pattern of a point source does not constitute a disk shape but rather an hourglass, or “flare” of the PSF (Fig. 4.4). Similar reasoning can be used to draw the axial Rayleigh criterion, which is defined by taking the distance from the maximum intensity location at the focal plane to the first location of the minimum intensity along the optical axis, or equivalently, nλem / NA 2 [5]. Note that this axial resolution increases with the increasing medium RI (n), whereas the aforementioned lateral resolution is independent of n. Both the axial and lateral resolutions decrease with increasing NA. In the usual sense, the depth-of-field (DOF) or axial resolution is referred to as the “defocusing range” between the two minimum intensity points on both sides of the focal plane, implying that the images are “unacceptably” blurred beyond this range. Thus, the conventionally defined microscopic axial resolution is equivalent to 2nλem / NA 2 .

Microscopic axial resolution

Fig. 4.4 An hour-glass shaped point spread function (PSF) along the optical axis [169].

4.3 Confocal Microscopic Imaging Resolutions

59

4.3 Confocal Microscopic Imaging Resolutions The point spread function (PSF), as presented in Sections 3.1 and 3.2, describes the image of a point source that is constructed via an ordinary microscope, which is referred to as wide-field microscopy (WFM):

I (u, v ) ⎛ 2⎞ =⎜ ⎟ I o WFM ⎝ u ⎠

2

2 2 2+2s 1+ 2 s ⎧⎡ ∞ ⎤ ⎫⎪ (3.1) ⎤ ⎡∞ ⎪ s⎛ u ⎞ s⎛ u ⎞ J 2 + 2 s (v )⎥ ⎬ ⎨⎢ ∑ (− 1) ⎜ ⎟ J 1+ 2 s (v )⎥ + ⎢ ∑ (− 1) ⎜ ⎟ ⎝v⎠ ⎝v⎠ ⎪⎩⎣⎢ s = 0 ⎦⎥ ⎪⎭ ⎦⎥ ⎣⎢ s = 0

The pinhole in confocal microscopy (CM) is viewed as a second point source located in the middle of the optical path before reaching the detector (Fig. 4.1). So, the confocal microscopic image of a point source is described by the square of the PSF of the illuminating light source onto the real point source by the PSF of the emitted fluorescent light onto the pinhole; i.e.: 2

2 2 2+ 2s 2⎧ 1+ 2 s ⎡ ⎤ ⎫⎪⎤ ⎤ ⎡∞ I (u, v ) ⎛ 2 ⎞ ⎪⎡ ∞ s⎛ u ⎞ s⎛ u ⎞ ⎢ = ⎜ ⎟ ⎨⎢∑ (− 1) ⎜ ⎟ J 1+ 2 s (v )⎥ + ⎢ ∑ (− 1) ⎜ ⎟ J 2 + 2 s (v )⎥ ⎬⎥ I o CM ⎢⎝ u ⎠ ⎪⎣⎢ s = 0 ⎝v⎠ ⎝v⎠ ⎦⎥ ⎪⎭⎥⎦ ⎦⎥ ⎣⎢ s = 0 ⎩ ⎣ (4.1)

with u =

ka 2 (zd − z f ) , v = kaRd , and k = 2π 2 λ zf zf

(3.2)

where the subscript f refers to the focal plane, d refers to an arbitrary diffraction imaging plane, and thus (zd − z f ) refers to the axial defocusing distance. The im-

aging point is coordinated as ( xd , y d , zd ) with Rd = ( xd + y d )2 , and u and v are the normalized axial and radial coordinates, respectively. The maximum image intensity at the focal plane (Δz = 0) of CM is substantially higher than that of WFM because of the multiplication (Fig. 4.5). This shows that focused CM can provide more distinctive and brighter images than WFM. Furthermore, the modulation intensity of CM images diminishes far more quickly with increasing defocusing distance Δz, in comparison to that of WFM images. This describes the key advantages of focused CM: the abilities to provide a distinctive optical slicing capability and to rapidly eliminate the ambiguity associated with the unfocused images. Table 4.1 summarizes the lateral and axial resolutions of CM imaging, as well as the optical slice thicknesses, which were developed theoretically but with experimental corrections by multiple contributors [114,162,164,165,168,169,171175]. The pinhole diameter is an important parameter for confocal microscopy and plays a decisive role in determining image resolutions. When the modified pinhole

60


Fig. 4.5 PSF profiles of a single point by (a) wide-field microscopy (WFM) and (b) confocal microscopy (CM) [170].

diameter5, PD, is greater than one (1) Airy Unit6 (AU) - i.e., PD > 1.0 AU - a geometric-optical analysis is used, while for PD < 0.25 AU, a wave-optical analysis is used [169]. Either analysis may be used in the case of the intermediate range of 0.25 AU < PD < 1.0 AU.

5 6

Modified pinhole diameter PD = Pinhole diameter (μm)/Magnification. Airy unit AU = 1.22 λex/NA with λex being the fluorescent excitation wavelength.

4.3 Confocal Microscopic Imaging Resolutions

61

Table 4.1 Lateral and axial imaging resolutions and optical slice thicknesses for both widefield microscopy (WFM) and confocal microscopy (CM). Conventional microscope

Lateralresolution

Axial resolution

NA ≥ 0.5

0.61λem NA

2

n ⋅ λem NA 2

NA < 0.5

Geometric-optical (PD > 1.0 AU)

Wave-optical confocal microscope (PD < 0.25 AU)

0.51λex NA

0.37λ NA

0.88λex

0.64λ

n − n 2 − NA 2 1.67n ⋅ λex NA 2

n − n 2 − NA 2 1.28n ⋅ λ NA 2

2

Optical slice thickness

No definition

⎛ ⎞ ⎛ 2n ⋅ PD ⎞ 0.88λem +⎜ ⎟ ⎜ 2 2 ⎟ ⎝ n − n − NA ⎠ ⎝ NA ⎠

2

0.64λ n − n 2 − NA 2

The geometric-optical CM analysis uses a criterion based on full width at half maximum (FWHM) of two neighboring PSFs at the confocal plane, somewhat analogous to the Rayleigh criterion for WFM (Section 3.1). Likewise, the axial resolution of CM is based on the FWHM of the PSF constructed along the optical axis. For the wave-optical CM, given a sufficiently small PD, the FWHM of the illuminating PSF and that of the emitting PSF are comparable in their magnitudes and both PSFs are needed to determine the total PSF imaged on the recording plane. Therefore, both the lateral and axial resolutions of the wave-optical confocal microscope are specified by the functions of the mean wavelength λ 7 of λem and λ ex . On the other hand, for the geometric-optical confocal microscope with a relatively large PD, the FWHM of the emitting PSF is larger than that of the illuminating PSF, and the deterministic resolutions can be specified solely by the smaller PSF; i.e., the illuminating PSF. Consequently, both lateral and axial resolutions of the geometric-optical CM are specified by the functions of just the excitation wavelength, λ ex . Note that the image resolutions of conventional microscopy depend only on the emission wavelength λem . The comparison of imaging resolutions under typical fluorescence conditions of λex = 488 nm, λem = 515 nm, and n = 1.0 (Fig. 4.6) shows that CM resolutions are consistently better than WFM for the same NA, and that both lateral and axial resolutions decrease with increasing NA. As expected, the smaller PD of the wave optical CM allows for a better imaging resolution for all NAs in comparison to the geometrical CM with a relatively larger PD.

7

The mean wave length λ is defined as λ ≡ 2

λex ⋅ λem 2 λ2ex + λem

.

62


10

Conventional Microscopy

Lateral resolution (μm)

Geometrical Confocal Wave Optical Confocal

1

0.1 0.1

0.3

0.5

0.7

0.9

NA (a)

1000

Conventional Microscopy

Axial resolution (μm)

Geometrical Confocal Wave Optical Confocal

100

10

1

0.1 0.1

0.3

0.5

NA

0.7

0.9

(b) Fig. 4.6 (a) Lateral and (b) axial imaging resolutions, as functions of the objective NA for n = 1.0 (air), λex = 488 nm, λem = 515 nm, and λλ = 500.96 nm for both wide-field microscopy (WFM) and confocal microscopy (CM) [163].

4.4 Optical Slicing Thickness of Confocal Microscopy

63

4.4 Optical Slicing Thickness of Confocal Microscopy A more exclusive feature of confocal microscopy is its optical slicing capability, as shown by the PSF comparison in Fig. 4.5. For WFM, most photons from

Geometrical-Optical Confocal Microscopy

Optical Slice Thickness ( μm)

1000

Pinhole Diameter=150 Pinhole Diameter=100 Pinhole Diameter=75 Pinhole Diameter=50 Pinhole Diameter=30

100

Unit: μm

10

1 0.1

0.2

0.3

0.4

0.5

NA

0.6

0.7

0.8

0.9

1

(a) n = 1.0, λem = 515 nm, 40X Nominal, 37.6X Confocal magnifications

Wave-Optical Confocal Microscopy 100 Optical Slice Thickness ( μ m)

Index of refraction =1.516 (Oil) Index of refraction=1.33 (Water) Index of refraction=1.0 (Air)

10

1

0.1 0.1

0.3

0.5

0.7

0.9

1.1

1.3

1.5

NA

(b) 40X Nominal, 37.6X Confocal magnifications Fig. 4.7 Optical slice thicknesses (Table 4.1) for (a) a geometric-optical confocal microscope and for (b) a wave-optical confocal microscope [163].

64


off-focused images reach the recording plane, and the effective range or depth-offield is determined by the objective NA. An objective lens with a high NA can reduce the depth-of-field; however, the total number of photons more or less remains the same because of the lack of spatial filtering restrictions, and the resulting images are blurred due to obscured focusing [135,176,177]. In contrast, the spatial filtering by a pinhole of confocal microscopy actively controls the accepted number of photons. This spatial filtering is minimal at the focal plane but quickly increases with the defocusing distance. This allows for true “optically sliced” images with greatly improved focusing via confocal microscopy. Table 4.1 also lists the CM optical slice thicknesses for both geometricaloptical CM (for finite size pinholes) and wave-optical CM (for extremely small pinholes). The optical slice thickness of geometrical-optical CM decreases with an increasing NA and also decreases with a reduced pinhole diameter (Fig. 4.7-a). The arrows show the comparison of two optical slice thicknesses corresponding to NA = 0.3 and NA = 0.75, respectively. The optical slice thickness of the CM with a sufficiently small pinhole (wave-optical) corresponds to the ideal case of a pinhole diameter tending to zero (Fig. 4.7-b). This optical slice thickness shows a substantial reduction with an increasing RI of the measurement environment of air (n = 1.0), water (n = 1.33), and silica glass or a special immersion oil (n = 1.516). Note that the use of water or oil immersion increases the corresponding NAs, due to their high RIs in comparison to air’s, and that the resulting optical slice thicknesses can thus be significantly reduced from that of an air environment.

Fig. 4.8 Comparison of the confocal microscopic image quality between (a) the sharp but requiring four times more lighting when using a 0.5 AU pinhole and (b) less sharp but brighter image at lower lighting when using a 1.0 AU pinhole [178].

4.5 Confocal Laser Scanning Microscopic Particle Imaging Velocimetry

65

Similar to the principle of a camera aperture opening, a smaller pinhole certainly provides clearer images, maximizing the benefit of CM imaging, but at the cost of reduced brightness or the requirement of more power for the illumination light (Fig. 4.8). 4.5 Confoca l La ser Scanning Microsco pic Particle I maging Velocimetry

4.5 Confocal Laser Scanning Microscopic Particle Imaging Velocimetry (CLSM-PIV) System The galvanometric steering of the focal point of traditional confocal microscopy (Fig. 4.2) limits its scanning speed to approximately one (1) frame-per-second (FPS), which is too slow for most flow measurements. The essential innovation of the confocal laser scanning microscopy [173] is the implementation of dual highspeed spinning disks (Fig. 4.9). The upper disk is a rotating scanner that consists of 20,000 micro-lenses, and the lower one is called a “Nipkow” disk and consists of 20,000 matching pinholes of 50-μm diameter. The incident light is focused by the micro-lens of the upper scanning disk through the pinholes onto the lower Nipkow disk. A dichroic mirror, located between the two disks, reflects the returning confocal fluorescence signal to the CCD.

Fig. 4.9 The dual-spinning Nipkow disk design and its operation principles [163].

The use of the spinning disks [179,180] replaces the single pinhole and makes it possible for confocal microscopy to scan full-field images at substantially higher frame rates. For example, the disk rotation at 30-rps allows a scanning rate of 360 full-images per second, or 12 images per revolution of the disk. Then, by

66


averaging three sweeps per single field for statistical enhancement, a full field imaging of up to 120-FPS can be achieved. Such a high-speed confocal laser scanning microscopy (CLSM) has been used in biomedical applications of realtime 3-D imaging of single molecular fluorescence [181]. Confocal laser scanning microscopy can accommodate the use of particle image velocimetry [128,182,183] to provide optically-sliced microfluidic velocity field measurements. Combining CLSM with PIV was first attempted at the Microscale Fluidics and Heat Transport Laboratory of Texas A&M University in 2003, and the first CLSM-PIV (Figs. 4.10-a and -b) was completed as a geometricoptical type (PD > 1.0AU) in 2004 [163]. Since then, several studies have used a similar configuration for different biofluidic and microfluidic applications [184,185]. The CLSM-PIV system essentially consists of a dual-Nipkow disk confocal module (CSU-10; Yokogawa, Japan), an upright microscope (BX-61; Olympus, Japan), a 50-mW CW argon-ion laser (tuned at 488-nm; Laser Physics, U.S.A.), a frame grabber board (QED Imaging, U.S.A.), and PIV analysis software (DaVis; LaVision, Germany). The lower inlet port of the confocal head unit is attached to the ocular port of the microscope, and the upper outlet port is connected to the CCD camera (QED Imaging UP-1830, UNIQ, 1024 x 1024 pixels at 30 FPS).

CCD Camera (UP-1830, UNIQ) Confocal Unit (CSU-10, Yokogawa)

Confocal

Fiber Optic Circular Microtube

Micro Syringe Pump (55-2111, Harvard Apparatus)

(a)

Ar-ion laser (50 mW, 488 nm, LaserPhysics)

(b)

Fig. 4.10 (a) A schematic layout of the CLSM-PIV, and (b) the confocal head unit at the Microscale Fluidics and Heat Transport Laboratory of Texas A&M University (photo by K.D.K).

4.5 Confocal Laser Scanning Microscopic Particle Imaging Velocimetry

67

Table 4.2 presents further details on the CLSM-PIV system in Fig. 4.10. Note that nominal magnifications are specified for WFM, while the optical paths for CM are routed through the confocal unit before the detector, resulting in slightly reduced actual magnifications. So, the actual CM magnification needs to be experimentally calibrated using a precise length scale. The numbers shown in parentheses are the actual CM magnifications, which are slightly lower than the nominal magnifications. The optical slice thicknesses shown in Table 4.3 are estimated to be smaller than 3-μm for the 40X-0.75NA objective and less than 27-μm for the 10X-0.3NA objective for the present CM system. Also, note that since most of the optical considerations for confocal microscopy have been made for relatively higher NA values, the derived formula may not be accurate in predicting the slice thickness for the case of 10X-0.3NA. 4.5 Confoca l La ser Scanning Microsco pic Particle I maging Velocimetry

Table 4.2 The optical parameters for the CLSM-PIV system, as shown in Fig. 4.10.

λex, excitation wavelength (μm)

0.488

λem, emission wavelength (μm)

0.515

λ , mean wavelength (μm)

0.500879

Refraction Index

1.0

NA

0.75

0.3

Overall Magnification

40 (37.6)

10 (9.4)

Airy Unit (AU)

0.793

1.984

Pinhole Diameter (μm)

50

50

PD (μm)

1.329

5.319

Table 4.3 The optical imaging resolutions and slice thicknesses of the CLSM-PIV system, as shown in Fig. 4.10. Conventional microscope 40X 10X Lateral resolution Axial resolution Optical Slice Thickness

WaveGeometric-optical confocal microscope optical confocal microscope 40X 10X 40X 10X

0.418

1.047

0.331

0.829

0.247

0.617

1.831

11.444

1.268

9.323

0.946

6.959

2.820

26.701

0.946

6.959

Not Defined

68


The standard cross-correlation scheme based on FFT, developed by LaVision, Inc., was used to process the PIV images in order to obtain the raw vector field. This scheme implements a multi-pass interrogation process with an adaptive offset algorithm to enhance the signal-to-noise ratio. The first-pass cross-correlation is calculated for a 64×64-pixel interrogation volume by FFT without any volume offset, and then the interrogation volume is divided into four sub-areas of 32×32pixels for the second-pass calculations. The estimated displacement value obtained from the first pass calculations is used as the volume offset value for the secondpass calculations. The displacement values of the four highest cross-correlation peak locations, corresponding to the four interrogation volumes of the second-pass calculation, are stored for presentation.

4.6 Near-Field Applications of CLSM-PIV 4.6.1 Poiseuille Flows in a Microtube Fully developed laminar Poisseulle flows are imaged for the 510-μm ID microtube at 9.4X CLSM (10X nominal magnification, NA = 0.3) as well as for the 99-μm ID microtube at 37.6X CLSM (40X nominal magnification, NA = 0.75). The raw PIV images (Fig. 4.11) are shown for the two selected planes of y/R = 0 (at the center-plane) and y/R = 0.98 (near the top end of the microtube’s inner surface). The laminar flow entrance, or developing length, is estimated to be L/D = 0.65 [186], which is equivalent to L = 64.3-µm and L = 335-µm respectively, for the two tubes, and thus the fully developed Poiseuille flow is ensured for the test section. The CLSM images demonstrate spatially filtered images with clear definition of individual seed particles (200-nm nominal diameter) that are located within the optical slicing thickness. For WFM images, in contrast, both the internally reflected rays from the microtube inner surface and the external rays coming through the microtube wall enter the detector without spatial filtration. The resulting WFM images are thus largely blurred, making the particles are poorly defined. The apparent image diameter8 of the stationary 200-nm seed particles is estimated to be 2.10-μm, or 0.42% of the 510-μm ID microtube, and 0.86-μm, or 8

The actual recorded image diameter of a seed particle on the CCD is given by [114]: 2 2 d e = ⎡⎣ M 2 d p + d s ⎤⎦

1

2

where d e is the imaged particle diameter in CCD, M is the nominal magnification of the objective lens, d p is the seed particle diameter, and

d s is the characteristic diameter of

the point spread function (PSF). For magnifications much larger than one, the diameter of the diffraction-limited PSF in the image plane is given by:

d s = 2.44 M

λ .

2NA

4.6 Near-Field Applications of CLSM-PIV

69

Crown glass (n = 1.544)

170μm

Borosilicate microtube (n = 1.475) 170μm

Water (n = 1.33)

Cyanoacrylate glue (n ~ 1.33)

CLSM Images

WFM Images Center-plane y/R = 0.98

(a) 99 μm ID Center-plane y/R = 0.98

(b) 510 μm ID Fig. 4.11 Particle images taken at the two different sectional planes of y/R = 0 (centerplane) and y/R = 0.98 (near the top inner wall), by CLSM (left column) and by WFM (right column): (a) ReD = 2.75x10-3 for the 99 μm ID microtube, and (b) ReD = 2.1x10-2 for the 510 μm ID microtube.

70


0.87% of the 99-μm ID microtube. Note that the relatively larger particle image size for the smaller ID microtube makes it essential to accommodate the reduced particle number density. The scale velocity of the 99-μm microtube (Vmax = 54μm·s-1) is more than three times greater than that of the 510-μm microtube (Vmax = 79.7-μm·s-1), and this further blurs the images in the case of the smaller microtube. The mean particle image streaks associated with the finite exposure time (33.3ms) are calculated to be 1.8-μm for the 99-μm microtube (more than two times larger than the stationary particle image size) and 2.7-μm for the 516-μm microtube (25% larger than the stationary particle image size). Because of the lens effect [166] of the microtube walls and the refractive index mismatching of the multiple layers of different materials9 (Fig. 4.11), the actual imaging plane (curved lines in Fig. 4.12) deviates from the planar focusing plane (dashed lines) for a circular microtube. Based on the geometrical ray analysis with the paraxial imaging assumption, it is shown that the actual imaging points match with those of the flat imaging plane only along the vertical centerline, and the deviations progressively increase with the radial distance from the center point. The curved imaging plane also tends to negatively bias the inner wall locations, and the amount of the bias is estimated to be 2.4-µm for the 99-µm microtube and 12.6-µm for the 510-µm microtube. Standard PIV analysis [134,187], without exhaustive efforts for artificial validation and vector improvement schemes, provides velocity profiles at different y-planes for the Poiseuille flows in the two microtubes (Fig. 4.13). The solid symbols represent the CLSM-PIV data, the regular symbols represent the WFM-PIV data, and the parabolic curves represent the theoretical Poiseuille flow profiles that have been depth-corrected by, accounting for the aforementioned refractive index mismatching. The error bars represent 95% of the standard deviations of the averaged data of thirty axial locations per image and for all twenty-nine PIV image pairs processed; i.e., an average of 870 velocity profiles altogether. In comparison with the Poiseuille predictions, the most pronounced deviations of the WFM-PIV data occur at the center plane for the 99-μm microtube flows. Because of the lack of optical slicing, inclusion of the slower moving foreground as well as background particle images substantially lower the center-plane flows. While the optically sliced CLSM imaging can effectively minimize the biasing associated with the foreground and background noise, the WFM images can still be substantially biased by them. The magnitude of this negative bias is notably diminished at y/R = 0.2 because of the compensation effect by the positive bias from the flow at the center-plane (background) against the negative bias by the flow at the larger y-locations (foreground), and thus the negative bias becomes minimal at y/R = 0.4 as a compensation of the positive and negative bias is supposedly reached. Further away at y/R = 0.6 and 0.8, a transition from the negative to positive bias is observed, since the magnitude of the negative bias decreases as the no-slip tube wall is approached. The spatially-filtered CLSM-PIV data agree with the calculated profiles at all y-planes. 9

The tested fluid of water (n = 1.33 at λ = 500 nm); the Borosilicate micro-tube wall (n = 1.475); the Cyanoacrylate glue layer (n ~ 1.33); the Crown glass cover slip (n = 1.544 at λ = 515 nm and n = 1.547 at λ = 488 nm); and air (n = 1.0).


71

y

R

Fig. 4.12 Consideration of the curved imaging planes (solid lines) to compensate for the refractive index mismatching through the multiple material layers, as shown in Fig. 4.11, versus the uncorrected flat imaging planes (dashed lines) for the case of the 99-μm ID microtube [163].

For the 510-μm ID microtube, the level of the negative bias of the WFM-PIV results at the center plane is noticeably reduced in comparison with the smaller 99-μm microtube. The advantageous feature of the CLSM-PIV is less pronounced for the objective lens with a relative low NA = 0.3 for the lower magnification of 10X, and the WFM-PIV data agrees fairly well with the predicted profiles for most of the flow. When the tube wall is approached for y / R ≥ 0.8 , however, the positive biasing begins to override, while the CLSM results stay in close agreement with the theoretical Poiseuille profiles. As the microtube wall is approached, the WFM-PIV image quality degrades further because of the dramatically increased image distortions, due to the lens effect as well as the more severe image obscurations by internal reflection. Consequently, the WFM-PIV becomes more severely biased in the near-wall region, whereas the CLSM micro-PIV results show consistently good agreement. Note that CLSM imaging in general shows more distinctive improvements with higher magnifications and with higher NA objectives, and should be even more pronounced with oil-immersion based objectives with even larger NAs, mostly larger than one.

72


y/R = 0

y/R = 0.2

y/R = 0.4

y/R = 0.8

(ID = 99 μm)

(ID = 510 μm)

y/R = 0.9

Fig. 4.13 Comparisons of the Poiseuille velocity profiles measured by the CLSM-PIV (solid symbols) and by the WFM-PIV (regular symbols). Two different microtubes of 99 μm ID and 510 μm ID are imaged by two different objectives with 40x (NA = 0.75) and 10x (NA = 0.3), respectively [188].


73

4.6.2 Microscale Rotating Couette Flows Couette flow provides a linear velocity distribution in a viscous fluid between two parallel flat walls when one wall remains stationary and the other moves at a constant speed [2]. If the moving wall is replaced by a rotating disk, the flow confined between the disk and the stationary wall is called a “rotating Couette flow.” Figure 4.14 illustrates an experimental configuration to develop microscale rotating Couette flows in the 180-μm gap region between the rotating upper disk and the stationary bottom surface. A precision DC motor provides a constant disk rotating speed of 17.0 rpm. 200-nm yellow-green (505/515 nm) fluorescent microspheres (SG = 1.05) at 0.002% volumetric concentration are used as PIV tracers in water. The advantage of CLSM-PIV in achieving optically-sliced images is clearly seen in Fig. 4.15-a, as Fig. 4.15-b shows blurred and obscured images from the unfocused foreground and background images from WFM-PIV. The velocity contours from the WFM-PIV poorly display the concentricity and accuracy of the Couette flow, whereas CLSM-PIV substantially improves the concentric features. The WFM data show more irregularities and deviations from the CLSM data with increasing h; i.e., as the rotating disk surface is approached. This is attributed to the more complicated flow profiles associated with the possible initiation of threedimensional secondary flows as the flow rotation increases.

h

r

Fig. 4.14 A schematic illustration of the setup for a microscale rotating Couette flow experiment.

74


(h = 35 μm)

85.1

57 .8

(h = 88 μm)

167 .3

(h = 142 μm)

23 5 .7

112 .5

153.6

5 7 .8

85.1

.7

16 .7

30.4 16 3 .0

400.0 386.3 372.6 358.9 345.2 331.6 317.9 304.2 290.5 276.8 263.1 249.4 235.7 222.0 208.3 194.7 181.0 167.3 153.6 139.9 126.2 112.5 98.8 85.1 71.4 57.8 44.1 30.4 16.7 3.0 (μm/s)

640 μm

57 30

.8

.4

16.7

167.3 .8 98 57.8

19

4.

7

126 .2

71.4 16 .7

1 6 .7

3.0

(a) CLSM-PIV

(b) WFM-PIV

Fig. 4.15 Particle images and their velocity contours by (a) CLSM-PIV and (b) WFM-PIV at three different heights (h), measured from the stationary bottom wall [170].

The rotational velocities along h at three different r-locations (50, 100 and 200 μm) are presented in Fig. 4.16, where each symbol represents the average of the total data realizations taken at 16 different angular locations per image for a total of 30 PIV images. The error bars represent the fluctuation ranges of the measured velocity vector magnitudes with a 99% confidence range. The confidence ranges of the WIF-PIV data are always wider than the corresponding CLSM-PIV data


Theory CLSM WFM

100 Velocity(micron/sec)

75

75

50

25

r = 50 μm

0 0

50

100

150

200

Height(micron)

Velocity(micron/sec)

200

Theory CLSM WFM

150

100

50

r = 100 μm

0 0

50

100

150

200

Height(micron)

Velocity(micron/sec)

400 Theory CLSM WFM

300

200

100

r = 200 μm

0 0

50

100

150

200

Height(micron)

Fig. 4.16 Comparison of tangential velocity distributions as functions of h at three different radial locations (r). The symbols represent the average data from 480 measurement realizations, the solid extended bars represent the data-scattering range measured by CLSM, and the dashed extended bars represent the data-scattering range measured by WFM [170].

76


because of the larger fluctuations in the former data. Furthermore, the deviations of the WFM-PIV data from the ideal linear profiles increase with increasing radial locations, particularly as the upper rotating disk is approached at a greater h. The gradually progressing underestimation of the CLSM data reflects the threedimensional secondary flow initiation with an increasing radius in the vicinity of the rotating disk, where the rotational speed slows down and the flows do not precisely follow the two-dimensional Couette patterns. The rapidly increasing deviations of the WFM data are attributed to the obscurities created by the unfocusedplane imaging of the complicated three-dimensional secondary flows.

4.6.3 Moving Bubbles in a Microchannel The movement of gas bubbles in a liquid [189], which is called “Taylor bubbles” [190-193], is common to numerous fluidic and energy transport devices, including such capillary-dominated systems as heat pipes [194] and thermosyphons [195]. Proton-exchange membrane (PEM) fuel cells [196] are also capillary flow devices, the performance of which is directly affected by two-phase flow phenomena [196]. As the product water accumulates in the form of liquid film on the walls of the gas flow channels of the cathode, perturbations disturb the liquid film such that the channel becomes completely blocked by liquid - a phenomena known as “liquid holdup.” This disrupts the flow of oxygen through the channel and, subsequently, to the membrane electrode assembly. Thus, fuel cell performance is degraded. An important dimensionless group characterizing the bubble behavior in liquid is the capillary number (Ca), which is given by:

Ca =

μU b σ

(4.2)

When the capillary number is sufficiently small, the flow may be considered under capillary-dominated conditions. However, if Ca exceeds a critical value in a confined microchannel, the gas bubble does not wet the channel surface and starts forming an entirely suspended “lobe” shape that is detached from the channel surfaces [197-200]. The capillary number of 0.1 is generally accepted as the critical value [201]. The Bond number scales the effect of gravity to that of capillarity of a static liquid surface as follows: Bo =

ρgd 2 σ

(4.3)

When the Bond number is less than 1, capillary forces prevail as the shape of a liquid surface. In order to ensure that the systems are in the capillary-dominated flow regime, the channels should be scaled so that the Bond number, Bo, remains small (10-4 < Bo < 10-2).


77

Ca = 0

Ca = 0.04

Ca = 0.12

Ca = 0.21

Fig. 4.17 The movement of an air bubble (dark images) in SAE-30 oil (μ = 0.20 N⋅s/m2, σ = 0.03 N/m, ρ = 9,200 kg/m3 at 20°C) at different speeds inside a 1-mm square channel [202].

78


200-nm seed particles suspended in water

Objective lens

Z Air Bubble

U-velocity 0.000356 0.0003 0.000244 0.000188 0.000132 7.6E-05 2E-05 -3.6E-05 -9.2E-05 -0.000148 -0.000204 -0.00026 -0.000316 -0.000372 -0.000428 (m/s)

Fig. 4.18 An optically-sectioned flow field map in front of the air bubble that is advancing into the water in a 500-μm square microchannel, using the CLSM-PIV technique (Ca = 6.11 x 10-6, Bo = 0.034) [188].


79

When a long air bubble moves at various advancing speeds into the SAE-30 oil inside a 1-mm square channel, the backlit illumination produces dark images for the air bubbles because of the strong attenuation by refraction through the curved air-oil interface (Fig. 4.17). When the air bubble contacts the channel inner surface, the backlit illumination largely transmits because of no refraction, as shown by the bright areas in the middle of the dark air bubble images. The flushcontacted area of the air bubble decreases with increasing capillary number, since the bubble tends to detach from the channel walls when the capillary number increases and approaches the critical value of 0.1. The Bond number is estimated to be approximately 0.3, regardless of the capillary number, and all air bubbles are under the capillary-dominated condition. The illustration in Fig. 4.18 represents the flow field in front of the advancing air bubble in a square microchannel. The CLSM micro-PIV enables opticallysectioned flow field measurements with an extremely shallow field-of-depth of less than 1.0-μm and a lateral resolution of better than 0.5-μm [2,188]. Hollow, spherical, 200-nm fluorescent particles are used as tracers to achieve a full-field, optically-sectioned flow velocity vector map inside a 500x500-μm square micro-6 channel, with Ca = 6.11x10 and Bo = 0.034. Note that this ensures the capillarydominating flow conditions, so that the bubble never detaches from the channel walls. The moving coordinates of the velocity vectors are transformed to the stationary frames by subtracting the bubble speeds, so that the resulting flow vectors present the relative motion of the flow with respect to the moving bubbles.

Chapter 5

Surface Plasmon Resonance Microscopy (SPRM)

As a label-free visualization tool, surface plasmon resonance (SPR) reflectance imaging can characterize near-field fluidic transport properties within 100 nm from the solid surface. The key idea is that the SPR reflectance intensity varies with the nearfield refractive index (RI) of the test fluid, which in turn depends on the micro- and nano-fluidic scalar properties, such as concentrations, temperatures, and phases. Flow visualization techniques based on RI detection have been extensively well documented for macro- and meso-scale fluidic applications by Wolfgang Merzkirch and his collaborators [1,203-207]. The SPR imaging technique is a recent development for micro- and nano-scale fluidic applications and is primarily promoted by the author’s groups, who are working at both The University of Tennessee of the United States and Seoul National University of South Korea. Understanding the basic principles of SPR requires knowledge of fundamental quantum physics and classical electrodynamics. The first part of this chapter (Sections 5.1 to 5.7) presents a step-by-step approach to the basics of surface plasmon polaritons (SPP), surface plasmon resonance (SPR), the implementation of an SPR imaging system, and the imaging resolution, with the goal of providing the necessary understanding and guidelines to those who plan to implement their own SPRM systems. The second part of this chapter (Section 5.8) presents brief discussions on selected applications of the SPR reflectance imaging for various micro- and nanoscale fluidic scalar properties in the near-field.

5.1 Surface Plasmon Polaritons (SPPs) In quantum physics as well as solid physics, “quasi-particles” are known to exhibit quantum phenomena; i.e., the wave effect accompanied by quantized observables. Photons and phonons are two typical terms that exhibit this wave-particle duality. “Surface plasmons” and “polaritons” are two other types of quasi-particles. These latter two exist primarily on the surface of substances containing abundant free electrons, or metals. A substance that contains little or no free electrons, on the other hand, is called a dielectric medium. Plasmon refers to dipole carriers, such as free electrons oscillating in the background ions of a metal. The oscillation of the dipole carriers creates varying

82

5 Surface Plasmon Resonance Microscopy (SPRM)

charge density distributions. Surface plasmon, then, implies that the charge density wave propagates along the metal surface [9]. When the metal surface is illuminated by photons, the surface plasmon becomes excited by the electromagnetic (EM) fields. These entangled quasi-particles, composed of both surface plasmons and photons, are called “surface plasmon polaritons” (SPPs). Note that, by definition, the term “polariton” means “a (virtual) particle entangled with an electromagnetic wave” associated with the presence of free electrons [208]. Henceforth, further understanding of these SPPs requires the solving of the Maxwell wave equations by incorporating the appropriate boundary conditions at the metal-dielectric medium interface. The dielectric constant is the key property here. The dielectric constant, also known as a relative electrical permittivity, is the measure of electrical conductivity that acts to diminish the electric field strength formed in a medium.1 The dielectric constant in a vacuum is set to be a reference value of one (1), and the dielectric constants of most other mediums are larger than one because of their higher conductivity or electrical permittivity than that of a vacuum. The dielectric constant ε is more commonly known as [210]:

n= ε

(5.1)

where ε takes a complex function to account for the phase relationship of the complex electric field; i.e.:

ε = ε ' + iε "

and

n = nR + inI

(5.2)

The real part of RI, nR , is the refractive index, which decides the speed of the EM wave inside the medium c = co / n , where co is the speed of light in vacuum and

nI is the extinction coefficient of the EM wave, which determines the absorption when propagating into the medium. The magnitude of n I for most optically transparent dielectric mediums (i.e. air, water, glass etc.) is negligibly small, while the magnitude of n I for most metals is significant, allowing the EM waves to be quickly absorbed within the extremely thin skin depths of metals (Section 1.1.3). Combining Eqs. (5.1) and (5.2) gives:

1

ε ' = nR2 − n I2

(5.3-a)

ε " = 2n R n I

(5.3-b)

An alternate, or more physically correct, explanation requires the concept of electrical susceptibility, based on a fundamental understanding of classical electrodynamics [209]. Nevertheless, perceiving the permittivity concept with electrical conductivity will be sufficient to properly grasp the presented scope of SPPs herein.

5.2 Dispersion of SPPs

83

n R2 =

ε' 2

nI =

+

1 ε ' 2 +ε "2 2

(5.3-c)

ε"

(5.3-d)

2n R

These are four important expressions that describe either electromagnetic waves inside any medium or the SPPs on the interface of two mediums. They determine the optical propagation, decay, reflection, transmission, as well as refraction of light.

5.2 Dispersion of SPPs Dispersion is the phenomenon in which the propagation wavelength λ of quasiparticles depends on its oscillation frequency ω ( = 2πν ). The dispersion relation of photons, also known as a “photon line,” is given by the fact that their oscillation frequencies, or in our perception color, remain unchanged but their wavelengths vary with the speed of light or refractive index n in the medium; i.e.:

λ=

c

ν

=

2πc ,

ω

or equivalently,

β=

2π

λ

=

ω

(5.4)

c

where the wave propagation number β represents the reciprocal of the wavelength. Likewise, the dispersion of SPPs relates the propagation wavelength of SPPs along the interface with their oscillation frequency. The most simple geometry sustaining SPPs is that of a single flat interface (Fig. 5.1) between (1) a metal and (2) a dielectric medium with dielectric constants (or relative permittivities) of ε 1 (complex) and ε 2 (real). The darker arrows represent the electric field oscillation, while the lighter arrows indicate the magnetic field oscillation. This EM field is

Fig. 5.1 A single flat interface between (1) a metal and (2) a dielectric in the transverse magnetic (TM) mode ( p-polarization) in order to sustain SPPs.

84


consistent with the transverse magnetic (TM) mode, or p-polarized electric field, which creates SPPs, whereas the transverse electric (TE) mode (s-polarization) cannot sustain SPPs [9]. When the x-axis is set parallel to the SPP propagation direction with the E-field parallel to the incident plane, as in Fig. 5.1, the magnetic field carries only the ycomponent; i.e.: i ( β x − ω t ) − k2 z e yˆ ( z > 0) ⎪⎧ H e , H (r, t ) = ⎨ 2 i ( β x −ωt ) + k z e 1 yˆ ( z < 0) ⎪⎩ H1e

(5.5)

where β is the wave propagation number and the real parts of k1 and k2 must be positive, in order to prevent the field from diverging as it moves away from the interface. This field should satisfy Maxwell’s wave equation: ∇2 H −

ε ∂2H

= 0,

(5.6)

⎛ω ⎞ k2 2 = β 2 − ⎜ ⎟ ε 2 2 ⎝c⎠

(5.7-a)

⎛ω ⎞ k12 = β 2 − ⎜ ⎟ ε12 ⎝c⎠

(5.7-b)

c 2 ∂t 2

leading to: 2

2

Using two additional Maxwell equations: ∇ × E = − μ0 μ

∂H , ∂t

∇ × H = ε 0ε

(5.8-a) ∂E , ∂t

(5.8-b)

together with the appropriate interfacial boundary conditions for both the electric and magnetic fields, the following three results are given (the derivation details are omitted here, as they are available in most textbooks on classical electrodynamics, such as the one by Jackson [209]): H1 = H 2

(5.9)

k2 ε =− 2 . k1 ε1

(5.10)

5.3 Kretschmann’s Three-Layer Configuration

β=

ω c

85

ε1ε 2 ε1 + ε 2

(5.11)

The first expression, Eq. (5.9), shows the continuity requirement for the magnetic field across the interface. The second, Eq. (5.10), requires that the real part of ε 2 / ε1 must be negative because the real parts of both k1 and k2 should be positive, as previously mentioned. This implies that the two interfacing mediums must have real parts of their dielectric constants with opposite signs. This can be satisfied by metal and dielectric interfaces, since most metals have negative real parts of their dielectric constants for the optical frequency ranges. Lastly, the final dispersion relation, Eq. (5.11), implies that the propagation wavelength of SPPs along the interface ( β = 2π / λx ) is related to the oscillation frequency of SPPs via the two dielectric constants of the interfacing metal-dielectric medium, ε 1 and ε 2 , for a given incident photon frequency ω . Note that this provides the dispersion relationship for SPPs at the interface, while Eq. (5.4) provides the dispersion relationship for incoming photons.

5.3 Kretschmann’s Three-Layer Configuration The dispersion relation between the real part of β and ω for SPPs for a gold-air interface is shown by the solid curve (red) in Fig. 5.2; the photon line is presented by the dashed line (black). The normalized variable ω p is called the “plasma frequency,” or the natural oscillation frequency of the free electrons and positive ions within a metal, and it is given by: 1/2

⎛ 2 ⎞ ω p = ⎜ ne e ε m ⎟ e 0 ⎝ ⎠

(5.12)

where ne, e, and me are the density of electrons, elementary electric charge, and the mass of a single electron, respectively. The SPP wave propagation in the x-direction along the interface is represented by k x = 2π / λSPP ≡ Re {β } . In conx

trast, the (incoming) photons radiate and propagate isotropically, so that the photon wave propagation number is represented by k x = k y = k z = 2π / λ photon . Considering the simplest possible metal-dielectric medium interface (Fig. 5.1), the black dashed line represents the dispersion of photons propagating in the dielectric medium onto the metal surface; i.e., the photon line in air, given by Eq. (5.4) [26]. The SPP dispersion curve (red) does not intersect the photon line, as graphically shown, and the SPP wavelength k x does not match the photon

86


medium Prism

metal/medium (1-2) interface

Fig. 5.2 The dispersion relation for SPPs on the metal-dielectric medium interface, as shown by the red curve, and the photon lines in the dielectric mediums of air and a BK7 glass prism, as shown by the black and blue lines, respectively.

frequency ω . Therefore, for the simplest metal-dielectric medium interface, SPPs cannot be excited by the incident photons because the surface plasmon cannot “tangle” with the photons. In order to provide matching between the SPP dispersion curve and the photon line, the photon line should be rotated clockwise. A simple way to achieve this would be to let the photons propagate in a denser medium in comparison with the aforementioned dielectric medium (air), sustaining a shorter wavelength and thus a higher β , as shown in Eq. (5.4). It would then be possible for the resulting photon line (blue) to intersect the metal-medium dispersion curve, thus allowing SPP excitation. If a glass prism is selected to be the denser medium, then the interfacing dielectric medium can be air or water (or any other medium with a lower refractive index than glass). The most popular configuration used to achieve this arrangement is called “Kretschmann’s three-layer configuration” [211], named after its inventor who certainly deserves the eponym (Fig. 5.3). The surface plasmon line defines the maximum photon frequency allowing for SPP excitation and is given by:

ωS 1 = ωp 1 + ε2

(5.13)

5.4 Surface Plasmon Resonance (SPR) Reflectance

87

z y E x

E

② ① ③

(b) Fig. 5.3 Kretschmann’s three-layer configuration, which allows the excitation of SPPs by the incident photons, is composed of (1) a metallic film, (2) a dielectric test medium, and (3) a dielectric prism.

We now see that Kretschmann’s configuration allows for SPP excitation as long as the incident light photon frequency ω / ω p matches the x-directional SPP propagation number k x c / ω p and does not exceed ωS .

5.4 Surface Plasmon Resonance (SPR) Reflectance Surface plasmon polaritons (SPPs) decay quickly when far from the interface, and the SPP excitation itself is confined to the near-field. A direct examination of SPPs would enhance our understanding of the nanoscale sciences and near-field optical phenomena to an unprecedented degree [212]. The direct characterization of SPPs and their excitation, however, is not yet possible, due to the fact that no available measurement tool can be brought so close to the interface without disturbing the near-field opto-electrical and physical phenomena. At present, the most feasible way of characterizing SPPa seems to be through analyzing the far-field outcomes, which originate from the SPP excitation associated with the near-field phenomena. When SPPs are excited, they propagate along the surface with the wave propagation number β . This means that they absorb the energy from the incident light. The remaining energy, if any, is reflected, and the resulting reflectance (R) is less than 1. The absorbed energy by the SPPs is dissipated inside the metal in the form of Joule heating by the damping of electrons. Furthermore, the magnitude of absorption (1-R) depends on the optical, material, and physical conditions imposed in the near-field. This near-field dependence of the absorbed energy forms the basis of using surface plasmon resonance (SPR) reflectance as a highly sensitive measurement tool for observing micro- and nanoscale transport phenomena occurring in the near-field.

88


If the illuminating light source on the metal layer is monochromatic, there exists a specific angle at which SPPs can be excited and resonated; this is called the “SPR angle.” When all other optical and material conditions are fixed, the SPR angle depends only upon the index of refraction of the medium (or dielectric constant). The refractive index of the contacting dielectric medium is the most sensitive parameter commonly associated with near-field phenomena, such as mixing, temperature changes, evaporation, chemical reactions, ligand-receptor binding, and DNA binding, just to name a few. The SPR reflectance R, which is based on Kretschmann’s three-layer configuration (Fig. 5.3) of a metal film (1) - dielectric medium (2) - prism substrate (3), is given by:

R = R

(n 1 , n 2 , n 3 , d , ω , θ )

(5.14)

where ni (i = 1, 2, 3) is the refractive indices for the three mediums, d is the metal layer thickness, ω is the incident photon frequency, and θ is the incident ray angle. When monochromatic light is illuminated at a fixed angle onto a metal layer through a specific glass prism, the SPR reflectance R is determined solely from the refractive index of the dielectric medium n2 , which is associated with the microand nano-scale fluidic transport phenomena in the near-field. For p-polarized incident light, the reflectance R can be calculated by applying the Fresnel theory to the aforementioned three-layer configuration [213,214]. The resulting Fresnel equations are given as [5,15,215]:

R = |rp|2 rp =

r31 =

Zi =

(5.15-a)

[r31 + r12 exp( 2ik z1d)] [1 + r31r12 exp( 2ik z1d)]

Z3 − Z1 Z − Z2 ,r12 = 1 Z3 + Z1 Z1 + Z 2

0.5 εi 2 , k zi = ⎡ε i (ω / c ) − k x23 ⎤ , i = 1,2,3 ⎣ ⎦ k zi

k x 3 = ε 31/2 ⋅

ni = ε i

ω c

sin θ

(5.15-b)

(5.15-c)

(5.15-d)

(5.15-e)

(5.15-f)


89

where rp is the reflection coefficient2 for the p-polarized incident light, ω is the angular frequency ( 2πν ), c is the speed of light in a vacuum, k is the wave propagation number ( 2π / λ ), and ε is the dielectric constant. The SPR reflectance R can be readily determined as a function of the pertinent variables by numerically solving the above Fresnel equations, either by constructing a short MATLAB program or by downloading one of the user-friendly programs from http://www.mathworks.com/matlabcentral/fileexchange/13700 [216]. For example, when a d = 47.5-nm gold layer is illuminated by light with 632.8-nm waves (vacuum) at 20°C through a BK7 glass prism (n = 1.515), the calculations carried out by setting R = 0 provide the SPR angle for zero reflectance as 43.8° for an air test medium, 72.1° for a water test medium, 74.9° for ethanol, and 69.0° for glycerin3 (Table 5.1). Figure 5.4 shows R from the gold-water interface, via a BK7 prism, as functions of the incident angle for three different gold-layer thicknesses. For the optimal thickness of 47.5 nm obtained from the resonant condition (R = 0)

Fig. 5.4 The calculated SPR reflectance R for water medium with gold film thicknesses of 20, 47.5 and 60 nm, when illuminated by p-polarized incident waves at λ = 632.8-nm through a BK7 glass (n1 = 1.515) prism at 20°C ( θ sp = 72.1°).

2

3

The reflection coefficient is defined as the magnitude of the ratio of the reflection electric field to the incident electric field. Because of the relatively high refractive index of glycerin, the SF10 prism (n = 1.723) is used for the calculation.

90


Table 5.1 Thermophysical [217] and optical [218] properties of tested dielectric fluids [219].

Fluids

Density (g/cm3)

Refractive Index (20° C)

SPR angle (degrees) for 100% concentration with a 47.5-nm gold film

Air

0.0012

1.0008

43.8

Water Ethanol

1.0 0.7893

1.3321 1.3604

72.1 74.9

Glycerin

1.261

1.4730

69.0

Prism (RI) BK7 (1.515) BK7 BK7 SF10 (1.723)

Surface Tension (mN/m) 71.99 21.97 63.30

1.0

Reflectance R

0.8 0% 0.6

20% 40%

0.4

60% 80%

0.2

100% 0.0 50

55

60

65

70

75

80

85

Incident Angle (degree) (a) Fig. 5.5 Calculated SPR reflectances as functions of the incident angles for different glycerin concentrations in pure water. The test mixture temperature is constant at 20°C, and a glass prism with a 47.5-nm gold (Au) metal layer is illuminated by p-polarized and bandpass-filtered white light at 632.8 nm. (a) For the BK7 prism (n1 = 1.515), the SPR angle progressively increases from 70.7° for pure water to 86.1° for a 60% glycerin concentration; thereafter, no resonant SPPs are possible. (b) For the SF10 prism (n1 = 1.723), the SPR angle ranges from 56.3° for pure water to 69.0° for 100% glycerin concentration. (c) The nearly linear dependence of RI on the glycerin mass concentration is shown for the glycerin-water mixture.


91

1.0 0.8 0%

0.6

R

20%

0.4

40% 60%

0.2

80% 100%

0.0 50

55

60

65

70

Incident Angle(degree)

75

80

(b) Glycerin concentration (mass %)

(c) Water/glycerin mixture

SPR Angle (° ) (a) BK7 (b) SF10

0

70.7

56.3

10

72.5

57.3

20

74.4

58.2

32

77.2

59.5

40

79.5

60.4

52

84.1

61.8

60

86.1

62.9

72

-

64.5

80

-

65.7

92

-

67.6

100

-

69.0

(c)

Fig. 5.5 (continued)

in Eq. (5.15), the reflectance varies from nearly one to zero at the SPR angle before increasing thereafter. For a 20-nm gold layer, because of the reduced population of free electrons, less of the evanescent wave is absorbed, resulting in a greater SPR reflectance in comparison with that of the optimal 47.5-nm layer. Further, for a 60-nm layer, the SPR transmission is less attenuated in the z-direction due to the inefficient, non-optimal absorption by the SPPs, and the resulting reflectance is thus even greater. As another illustrative example, the SPR reflectances of water-glycerin mixtures with a BK7 prism are shown in Fig. 5.5-a and with an SF10 prism in Fig. 5.5-b. The refractive index of water–glycerin mixture linearly increases with an increasing glycerin mass concentration (Fig. 5.5-c). The test mixture temperature remains constant at 20°C, and a 47.5-nm gold (Au) metal layer is illuminated by

92


p-polarized and band-pass-filtered light at 632.8 nm. When the resonance condition is met, the incident photons are completely absorbed by SPPs, and the reflectance thus is zero. The SPR resonant angle increases with an increasing glycerin concentration. The BK7 prism (n = 1.515) limits the resonance to only approximately 60% glycerin concentration, whereas the SF10 (n = 1.723) prism allows resonance for the whole range, from pure water to 100% glycerin. In general, a prism with a higher refractive index will provide lower SPR angles and more importantly, allow a wider measurement range for SPR resonance, in comparison to a prism with a lower refractive index.

5.5 Surface Plasmon Resonance Microscopy (SPRM) Imaging Systems While a variety of SPR detection systems are commercially available, virtually all of them are designed for very specific purposes, mostly for biomedical applications; none of them allow enough flexibility to be modified for near-field fluidic applications. In contrast, the SPRM configuration is basically straightforward, but requires a delicate alignment for SPR angle adjustments and imaging. In essence, an SPRM imaging system can be readily assembled and aligned for near-field fluidic characterization. The optical train is relatively simple in that either a white light source (Fig. 5.6-a) or LED source (Fig. 5.6-b) is arranged to be p-polarized, narrow band-pass filtered, and collimated in order to conform to an incident beam. These two systems are essentially identical, except for the type of light source and the method of beam steering. The white light system uses a rotating mirror for beam steering while the LED-system rotates the entire incident optical train in order to align the SPR angle. Although both systems work equally well, the latter system, which has been recently developed at Seoul National University of South Korea [220], requires fewer optical elements. Thus, its SPR angle alignment is relatively easy when compared with the original SPRM system, which was implemented at the University of Tennessee, Knoxville of the United States [221]. The bandpass filter narrows the white light spectra of a tungsten-halogen lamp to be centered at 632.8-nm, with a full width half maximum (FWHM) of 10-nm. The bandpass filtering must make the bandwidth narrow enough to minimize the diffraction interference noise but also wide enough to prevent coherent diffraction ring noises [23,222]. Because of this, a highly monochromatic laser is not recommended for the SPRM imaging system. Most LED sources, on the other hand, generate sufficiently narrow spectrums, and additional band-pass filters are not necessary. Both light sources should be plane (p)-polarized, the E-field of which should be parallel to the incident plane. A 14-bit cooled EM-CCD camera (Hamamatsu Model C9100-02) uses a long focal distance lens of M Plan APO 5x (NA = 0.14, f = 40 mm by Mitutoyo) to record SPR images at a high spatial resolution.

5.5 Surface Plasmon Resonance Microscopy (SPRM) Imaging Systems

93

White Light

(a)

(b) Fig. 5.6 The layout of the SPRM imaging system: (a) the first system, using a filtered white light source at 632.8 nm at the University of Tennessee [223] and (b) the improved and integrated system, using an LED light source at 625 nm at Seoul National University [220].

94


The incident ray illuminates the 47.5-nm thick gold film deposited on the 2.5nm thick titanium adhesion layer that coats the 160-μm thick cover glass substrate. The cover glass RI matches the prism RI, and the two are interfaced by a thin

ε 2 = -13.198 + 1.245i; θSPR = 69.47° [224] 0.9

ε 2 = -10.270 +1.024i; θ SPR = 72.47° [227]

ε 2 = -12.290 + 1.470i; θSPR = 70.27° [225] 0.7

ε 2 = -10 + 1.3i; θSPR = 72.87°

Normalized R

[226]

ε 2 = -11 + 1.7i; θ SPR = 71.60° [229]

0.5

ε 2 = -11.6 + 2.205i; θ SPR = 71.049° [228] 0.3

ε 2 = -11.594 + 2.426i; θSPR = 71.096° [24]

0.1

20

30

40

50

60

70

80

-0.1 Water Temp. (Celsius)

Fig. 5.7 Normalized SPR reflectance (R) versus the medium (water) temperature (T) for seven different dielectric constants, which were measured by seven different research groups, for similar thin gold films of approximately 47.5-nm thickness deposited on the top surface of a BK 7 prism (n = 1.515) [230].

5.6 Selection of a Prism for SPRM

95

index-matching oil layer. The dielectric constant of a thin metal layer varies because of varying uncertainties from different measurement techniques, differences in surface roughness, dimensional uncertainties of the film thickness, and differences in the fabrication process. The use of different dielectric constant values generates different SPR reflectance (R) correlations with the medium temperature (T), as evidenced in Fig. 5.7. The measured data from seven different studies [24,224-229] show that the real part of the dielectric constant of a 47.5-nm thick gold film deviates up to 15% over the averaged dielectric constant [224] and that the imaginary part deviates up to 50% [24]. In contrast, and perhaps more optimistically, the SPR optimum angle θ SPR shows a mere ±2.5% deviation among the seven results, and this can be at least partially attributed to the dominating dependence of θ SPR on the real part of the dielectric constant.

5.6 Selection of a Prism for SPRM The refractive index (RI) of a prism (n3) varies widely, depending on the choice of the material, such as BK7 (n3 = 1.515), LF (1.575), topaz (1.61), SF10 (1.723), SF11 (1.779), diamond (2.417), and iodine crystal (3.34). Thus, the selection of the prism material can significantly alter the SPR reflectance’s dependency on the test fluid RI; i.e. the R-n2 correlation. An illustrative example would be a waterglycerin mixture, the RI of which increases linearly with the glycerin mass concentration (Fig. 5.5-c). When the SPR angle is tuned to water (0% glycerin), the reflectance R of Eq. (5.15) rapidly increases with a glycerin concentration (n2) increase by up to 50% in mass; this increase of the reflectance slows down until 75% of the glycerin concentration is reached. Thereafter, the reflectance slightly decreases for all seven prism materials (Fig. 5.8-a). Note that when the SPR angle is tuned to water, the SPR imaging can be used to determine the glycerin concentrations for up to a 50% concentration. Alternatively, when the SPR angle is tuned to 100% glycerin, R shows a drastically different dependency on n2 (Fig. 5.8-b). For prism materials with RI values below 1.605, either the SPR phenomenon does not occur (BK7) or a nonmonotonic dependence of R (LF) is exhibited. The main reason for this ambiguity is that the lateral component of incident ray’s wave vector (kx) is smaller than the surface plasmon wave vector magnitude (ksp); i.e., the photon line does not intersect the SPP dispersion line, as in Fig. 5.2. For prism RIs above 1.605, R shows monotonic decreases with an increasing glycerin concentration. Therefore, these prisms (topaz, SF10, SF11, diamond, and iodine crystal) are appropriate for the full dynamic range of the glycerin concentration measurements. In summary, care should be taken in selecting a proper prism material, as well as the correct SPR angle, depending on the measurement purpose.

96


R

(a)

R

(b) Fig. 5.8 SPR reflectance R, calculated based on the three-layer Fresnel modeling for seven different prism materials and aqueous glycerin mixtures contacting a 47.5-nm thick gold film illuminated by p-polarized light of wavelength λ = 632.8 nm: (a) R vs. n2 for the SPR angle tuned to 0% glycerin, and (b) R vs. n2 for the SPR angle tuned to 100% glycerin [221].

5.7 SPR Reflectance Imaging Resolution

97

5.7 SPR Reflectance Imaging Resolution In the case of a BK-7 prism (n = 1.515) with a water medium, the SPR reflectance is calculated as a function of the incident angle at four different excitation wavelengths for both a gold (Au) layer (Fig. 5.9-a) and a silver (Ag) layer (Fig. 5.9-b). The thicknesses of both metal layers are 47.5 nm, and the selected vacuum wavelengths λ = 488 nm for the argon-ion laser blue line, 632.8 nm for the helium-neon laser red line, and 1000 nm and 1500 nm for the near-IR lines. The dispersions, or wavelength dependencies, of the dielectric constants as well as of the refractive index values, are summarized in Tables 5.2 and 5.3, respectively. In both the Au and Ag layers, the “dip” becomes sharper with increasing wavelength. A sharper dip provides better sensitivity in measuring the refractive index of the dielectric medium, since the sharper dip can detect smaller SPR angle changes near the SPR angle. On the other hand, the dip becomes wider when wavelengths become shorter. It can be said that the wider curve is caused by the increased damping for the SPR propagation along the interface with a decreasing wavelength [16,17,25,231-233]. Thus, the sharper dip implies less damping of SPPs, meaning that SPPs excited at one place can travel further along the metal surface and leave longer trails, possibly deteriorating the spatial image resolution [234,235]. The IR sensors receive important attention, particularly from the biomedical immunosensor applications, because of a number of beneficial effects of IR over the visible spectra [231,236]. The longer IR wavelengths allow deeper penetration depths of interrogation in the dielectric side, and the sharper dip can enhance measurement sensitivity. The SPPs associated with IR, however, carry less damping, which can deteriorate the spatial resolution of SPR images, particularly at the boundary of the two different materials laid on the metal layer. Consider a 125- long SiO2 pattern in the x-direction, laid on a 50-nm thick Ag film that is coated on a BK-7 glass prism (Fig. 5.10). As a resonant SPP with wave vector κ0 propagates along x from the uncovered Ag metal (exposed to air) layer to the dielectric SiO2-covered area, the resonant condition is no longer met and the incoming SPP decays to a new SPP with wave vector κ1, which corresponds to the wave vector for resonant excitation of the SiO2 dielectric medium. This transmitted wave will inevitably interfere with the excitation light source, which carries the same wave vector κ0 as the incoming SPPs, but with far less amplitude because of no resonant excitation. The series of the SPR reflectance profiles show the damping dependence on the wave length, which is identified by the oscillating interference regions of wave vectors κ0 and κ1. It is now clear that the smaller damping of the longer wavelength allows for a deeper penetration of the SPPs into the uncovered area. As a result, the image of the boundary region is more deteriorated, with a larger blurred interference area.

㎛

98


(a)

(b) Fig. 5.9 The SPR reflectance “dip” for a 47.5 nm thick (a) gold and (b) silver layer, respectively, with water on the low-index side and a BK-7 prism on the high-index side for four different excitation wavelengths.

5.7 SPR Reflectance Imaging Resolution

99

Table 5.2 Wavelength dependence of dielectric constants of metal layers [13,14]. (nm)

Au layer (47.5 nm)

Ag layer (47.5 nm)

488

-2.2756 + 3.8672i

-7.8985 + 0.7362i

632.8

-11.6491 + 1.2711i

-15.8742 + 1.0728i

1000

-41.6510 + 2.9284i

-45.6106 + 2.8967i

1500

-106.421 + 1.0166i

-81.0370 + 8.1241i

Table 5.3 Dispersion of refractive index values for different materials [13,27]. λ (nm)

water

BK-7

Au layer (47.5 nm)

1.33548

1.52224

nR = nI =

632.8

1.33169

1000 1500

488

nR =

Ag layer (47.5 nm)

1.051547 1.838832

0.13083 2.81347

1.51509

0.185931 3.418136

0.13455 3.98651

1.327

1.5075

0.226734 6.457737

0.21435 6.75696

1.319

1.50127

0.492182 10.327842

0.45067 9.01333

100


㎛ long SiO

Fig. 5.10 The calculated and measured SPR reflectance profiles for a 125pattern laid on a 50-nm thick Ag film, which is coated on a BK-7 prism [235].

2

5.8 Near-Field Applications of SPRM

101

5.8 Near-Field Applications of SPRM Section 5.8.1 summarizes the history of SPR applications, for the majority excluding fluidic uses, while the remaining sections present applications of the implemented SPRM to different near-field fluid flow characterization problems, including microfluidic mixing fields (Section 5.8.2), salinity diffusion mapping (Section 5.8.3), nanoparticle concentration profiles (Section 5.8.4), nanocrystalline self-assembly (Section 5.8.5), and near-wall thermometry (Section 5.8.6).

5.8.1 History and Uses of SPRM As early as the beginning of the twentieth century, Wood [237] described surface plasma waves as the excitation source for anomalous diffractions on diffraction gratings. In the late sixties, Otto [238] demonstrated excited surface plasma waves in silver by attenuated total internal reflection. Soon afterward, today’s most popular three-layer configuration for SPR excitation was proposed by Kretschmann [211]. Furthermore, in the past two decades, remarkable research progress and development activities have been achieved regarding surface plasmon waves, primarily for optical sensors detecting chemical and biological quantities. Various techniques utilizing the SPR principle are currently applied to research, which is rapidly expanding to comprise a variety of interests, including the biochemical, biomedical, pharmaceutical, chemistry, and polymer engineering fields. One of the most active areas of research is in biomedicine, which is exploring protein-protein interactions, substrate-DNA/cell/protein/enzyme joining, receptorligand attractions, and several other matters of health-wise importance [15,226,227,239-248]. The most important distinction of SPR is its label-free detection capability of such aforementioned binding interactions, without the need for fluorescent or radioscopic labeling of these biomolecules [249,250]. Other essential applications outside the field of biomedicine include measurements of thin polymer film thicknesses [225,251-253], the sensing of specific gas or liquid components [254-257], point-wise temperature measurements, theoretical modeling for such materials as hydrogenated amorphous silicon, silver film, titanium dioxide layer (TiO2), and a mixture of ethanol and glycol [254,258-260], and finally, the nanoscale optics in the near-field, using localized surface plasmon polaritons [261-265]. In addition, diverse techniques employing surface plasmon’s optical characteristics are currently being developed and tested in the form of the following: classical SPR sensors [11,12,211,227,232], SPR interferometry [18,19], SP coupled emission [15,266], SP fluorescence spectroscopy [21,22,241-243], SPR microscopy [23,222,267], the nano-optics of SP polarization [261-265], and nanoparticle characterization [268,269]. Despite SPR’s rich development history and numerous applications, its use as a fluidic characterization sensor has been scarce, and only a few studies using the SPR imaging technology for the label-free characterization of near-field fluidic properties have been published. The following sections present applications of the SPRM imaging technique for near-field fluidic characterizations.

102


5.8.2 Label-Free Mapping of Microfluidic Mixing Fields Micromixing has received great attention in several areas of microfluidic applications, including biomedical studies [270]. The most popular and traditional method of characterizing micromixing has been to seed and track tracer particles, such as fluorescent dyes, assuming that the particles represent the mixing behaviors [156]. The intrusive, foreign particles of finite size, however, will never be able to perfectly follow the molecular mixing phenomena because of their aforementioned traits. Fortunately, the SPR reflectance imaging technique allows for a label-free detection of microfluidic mixing fields, based on the refractive index variations associated with the advancement of mixing different fluids with different RIs. 1.0

R e fle c ta n c e R

0.8

0% 20%

0.6

40%

0.4

60% 80%

0.2

100%

0.0 60

65

70

75

80

85

Incident Angle(degree)

(a)

(b)

Normalized Uncertainty of SPR Refelctance ( wR/R )

0.15

0.10

0.05

0.00 10

20

30

40

50

60

70

80

Ethanol Mass Concentration (%)

(c)

(d)

Fig. 5.11 (a) The refractive index variation of an ethanol-water mixture [217], (b) the SPR reflectance R as a function of the various incident angles θ for different ethanol mass concentrations in water, (c) the normalized pixel gray level correlation of R with ethanol’s mass concentration, and (d) the overall measurement uncertainties for SPR reflectance, ωR / R . The SPR system parameters are: a BK7 glass prism (n1 = 1.515), a 47.5-nm gold (Au) metal layer, and a p-polarized white light that is bandpass-filtered at 632.8 nm [223].


103

In the case of mixing ethanol in water, the mixture RI increases with an increasing ethanol concentration to up to 80% in mass before gradually decreasing (Fig. 5.11-a). The corresponding SPR angle also increases progressively from 70.7° for water (20°C) to 75.6° for the 80% ethanol by mass before gradually decreasing to 74.9° for 100% or pure ethanol (Fig. 5.11-b). If the SPRM system is optimized for water (the dashed vertical line), the SPR reflectance increases with an increasing ethanol concentration to up to 80%; this is presented by the solid curve in Fig. 5.11-c. The symbols represent the measured SPR intensity data, and the error bars span the 95% confidence levels of pixel-by-pixel variations for the recorded images. The overall measurement uncertainties (Fig. 5.11-d) decrease with an increasing ethanol concentration. The elementary uncertainties associated with the complex dielectric constant and the thickness of the gold layer are the two most crucial factors in determining the overall uncertainties [223]. mass %

Pixel Gray Level

t=0

y

91μm

425μm t = 60 ms

t = 150 ms

t = 210 ms

t = 300 ms

t = 330 ms

(a)

(b)

Fig. 5.12 The near-field development of ethanol penetrating water by capillary phoresis in a microchannel. The left column (a) shows the recorded SPR images in gray level contours, while the right column (b) shows the corresponding ethanol concentration distributions determined by the calibration curve in Fig. 5.11-c [273].

104


The time-progressive SPRM images of ethanol penetrating a 91-µbm wide water microchannel (Fig. 5.12) were converted into contour maps of the corresponding concentration distributions, using the correlation shown in Fig. 5.11-c. The primary drive for ethanol penetration into water is attributed to diffusive mixing and capillary phoretic suction [271,272]. The ethanol-water interface in the near-field is progressively broadened because of the molecular diffusion occurring with the advancing interface. The unique RI characteristics of the ethanol mixture limit the concentration measurements to a maximum of 80%. In contrast, the RI of a water-glycerin mixture, for example, increases with an increasing glycerin concentration all the way up to 100% (Fig. 5.5-c). Henceforth, if the SPR angle is tuned to 100% glycerin and if the prism material RI is selected to be larger than 1.6, then the SPR intensity decreases with an increasing glycerin concentration, and thus complete mapping of the glycerin concentration will be possible. Figure 5.13 shows the SPR images taken via an SF10 prism of glycerin penetration into water and the time-dependent glycerin concentration profiles in the near-field.

5.8.3 Near-Field Mapping of Salinity Diffusion There have been various methods developed for the measurement of salinity. Among these, three stand out for practical considerations: the gravimetric, inductive electrical, and conductivity detection methods. The gravimetric method is essentially the direct weighing of the specific gravity of a saline solution; however, this method has the shortcoming of a single-valued representation for a stationary situation. The induced electrical method is fast and considered to be acceptably precise. For a high precision measurement of salinity, however, the last method of conductivity is preferred because of its superior measurement stability. However, this conductivity measurement technique provides only point-wise detection at any given time and features invasive electrode probes. The RI of saline solution increases linearly with an increasing saline mass concentration (Fig. 5.14-a). Fu et. al [274] used wavelength-tunable SPR microscopy to detect the point-wise RI changes of saline solution, but their technique lacked full-field capability. SPRM can measure spatially as well as temporally resolved salinity distributions from the correlations of the SPR reflectance intensity with salinity (Fig. 5.14-b), which uses the SPR angle θSPR = 73° tuned to a 10% saline solution with a 47.5-nm thick gold film coated on a BK-7 prism. In the figure, the solid curve shows the Fresnel predictions of a normalized R for the range of salinity up to 10%. The symbols represent the measured normalized pixel gray levels, which show an average RMS deviation of 0.062 from the Fresnel predictions. Finally, the error bars represent the 95% confidence interval for the pixel-by-pixel variations of a single SPR image.


Pixel Gray Level

105

Glycerin mass %

t = 0 1s

t = 0 2s

t = 0 3s

t = 0 4s

t = 0 5s

t = 1s

t = 2s

(a)

(b)

Fig. 5.13 The full-field mapping of glycerin mixture concentrations penetrating water contained in a 132-μm wide microchannel that rapidly drives gravity-driven spreading of glycerin from the right entrance. The left column (a) shows the recorded SPR images via the SF10 prism (n = 1.732), while the right column (b) shows the contour maps of glycerin concentration determined by using the calibration curve in Fig. 5.8.

106


(a)

(b) Fig. 5.14 (a) The refractive index of the saline solution as a function of salinity [217] and (b) the experimental calibration results for the normalized pixel gray levels [275].


107

The time-dependent and full-field detection of near-field salinity of an aqueous drop of 0.8-mm diameter that contains 10% saline mass falling into a 3-mm deep water bath is shown in Fig. 5.15 [275]. The slightly heavier saline drop (SG = 1.02) falls naturally by gravity toward the gold layer surface and undergoes a convective (driven by gravity and inertia)-diffusive (driven by viscous and concentration gradients) process into the surrounding water. Note that the SPR images and their corresponding salinity distributions are vertically contracted by a factor of 3.42 because of the skewed imaging associated with the inclined SPR angle. The schematic drawings illustrate the dynamic convective-diffusive process: multiple satellite saline droplets are generated (t ~ 0), one of which reaches the bottom before the main drop and starts to diffuse (0.1s < t < 0.5s); the ‘ring-vortex’ shaped main drop reaches the bottom and diffuses with the satellite droplets (0.97s < t < 6.5s); lastly, all of the saline solution diffuses into the surrounding water (t = 45s). The formation of the ring-vortex shaped saline drop is attributed to its high viscosity relative to that of water (the dynamic viscosity of a 10% NaCl aqueous solution is approximately 20% higher than that of pure water). It is well-documented that the ring vortex occurs when the intruding liquid is more viscous than the surrounding fluid; a classical example would be the falling of sulfuric acid (1.84 SG, dynamic viscosity = 26.7 cP) into water (1.0 SG, 1.0 cP) [276]. According to Korteweg’s theory [277], stresses due to the gradients of concentration and/or density could conceivably give rise to capillary phenomena, which are called “capillary-like phenomena.” It is worthwhile noting that the near-field evolvement of the saline drops on the gold surface demonstrates capillary-like phenomena for the two miscible fluids of saline and pure water.

5.8.4 Dynamic Monitoring of Nanoparticle Concentration Profiles Nanofluids are mixtures of nanoparticles (Au, CuO, Al2O3 etc.) with base fluids, such as water or ethylene glycol, and their thermo-fluidic properties increase significantly as the nanoparticle concentration increases [279-281]. Suspended nanoparticles raise the effective refractive index (ERI) of the nanofluids [282,283], and in turn, the changing ERI values affect the corresponding SPR reflectance intensities with an extremely high sensitivity [20,284-287]. Therefore, the nanoparticle concentrations can be nonintrusively determined by correlating the SPR reflectance with the nanofluidic ERI. A laboratory-assembled Abby type reflectometer [288-290] measures the critical angles for total internal reflection ( θc ) and determines the ERIs from Snell’s law neff = n p sin θ c . The measured ERIs for nanofluids containing aluminum oxide particles (Al2O3; 47-nm average diameter) consistently increase with increasing nanoparticle loadings (Fig. 5.16). Regression of the measured data provides the extrapolation as: neff = 1.332 + 0.327ν

(5.16)

108


Salinity Mass Concentration (%)

4.1

t~0

14

9 6 3 0 0.0 1.0 2.1 3.1

0.1 s

9 6 3 0

0.5 s

0. 0

9 6 3 0

0.97 s

0. 0

9 6 3 0

0. 0

2.27 s 9 6 3 0

6.5 s

0. 0

9 6 3 0

45 s

0. 0

9

Sketch by Thomson & Newall 3 Schematic of saline (1885) 0 Centerline drop formation and Salinity diffusion salinity profiles distributions 6

0. 0

SPRM images

Fig. 5.15 The progressive mapping of near-wall salinity when a drop of 0.8-mm diameter with 10% saline mass concentration falls into a 3-mm deep water pool. The elliptical shape of the SPR images are due to the skewed SPR angle (θSPR = 73°); the spreading saline drops are actually circular in the physical domain [278].


109

Concentration of Nanoparticles (Volume %)

Effective Refractive Index (ERI) neff

Normalized Uncertainty ωn/neff (%)

0

1.332

±0.38

0.5

1.333

±0.73

1

1.335

±0.75

2

1.340

±0.87

4

1.345

±1.44

8

1.357

±1.21

12

1.373

±1.31

Fig. 5.16 Experimental determination of the effective refractive index (ERI) of nanofluids containing Al2O3 nanoparticles of 47-nm diameter, using an Abby type reflectometer that measures the critical angle for total internal reflection [291].

where v is the volume fraction of the nanoparticles. The measurement uncertainty of neff associated with the broadening of the critical angle was estimated from ωn = ( ∂neff / ∂θ ) Δθ = (n p cos θ c )Δθ , showing a gradual increase with increasing particle loadings. The measured correlation of the normalized SPR intensity R with neff also provides an extrapolation function, as shown by the dashed curve in Fig. 5.17: neff = 1.332 exp(-0.000253R) + 7.854×10-5 exp(6.093R)

(5.17)

The vertical error bars in the figure below represent the measurement uncertainties of the Abby type reflectometer, while the horizontal error bars represent the rootmean-square (RMS) variations of the SPR reflectance intensities. The SPR measurement uncertainties are estimated to be less than ±7%, using the Klein-McClintock analysis [7], and the lateral imaging resolutions are estimated to be approximately 4 μm, based on the evaluation of the surface plasmon decay lengths [267]. When a nanofluid drop (47-nm Al2O3 in 1.0 μl at t = 0) slowly evaporates, a 1.6 mm wet-diameter spot is observed using SPRM (Fig. 5.18). The darkest SPR image corresponds to the lowest nanoparticle concentration of 0.25% at t = 0; thereafter, the SPR reflectance intensity increases with an increasing nanoparticle concentration. As the evaporation progresses, a region of dense nanoparticles forms along the outer edge, as evidenced by the bright ring in the SPR image at t = 283s. With further evaporation, the outer region is solidified as a self-assembly of nanoparticles, and the central fluidic region shrinks, becoming thinner and denser (t = 326s). This solidification rapidly penetrates inward into the thin film region, and a complete dry-out is reached in less than one second (t = 327s). The

110


neff − R correlation (Eq. 5.17) provides the near-field, time-resolved nanofluidic ERIs (third column); combining Eqs. (5.16) and (5.17) provides the R-v correlation, which allows the determination of the volume fraction of the nanoparticles (fourth column).

neff = 1.332 exp(-0.000253R) + 12 % 7.854× 10-5 8% 4% 2% 0.5 %

(b)

0%

0.25 %

1%

Fig. 5.17 An experimental correlation of the effective refractive index (ERI) versus SPR reflectance R for 47-nm diameter Al2O3 nanofluids for different nanoparticle loadings. The vertical error bars represent the measurement uncertainties of the broadened critical angles associated with the Abby type reflectometer, while the horizontal error bars represent the RMS variations of the SPR reflectance intensities [291].

5.8.5 Unveiling the Fingerprints of Nanocrystalline Self-assembly How nanoparticle crystalline structures assemble themselves has been a largely unknown process, whereas the existence of internal cavities has been conjectured with partial observation of evidence [292-294]. Dynamic and quantitative characterizations of nanocrystalline processes can benefit many areas involving selfassembled nanostructures, nanoscale manufacturing, and bioprocesses [295-303].


111 ERI

Concentration (%)

t=0

12+

0.25% Al2O3 nanofluid

SPR Image t = 283s

t = 326s

t = 327s

SPR Images

Effective RI Fields

Self-finned nanofluidic area with dense nanoparticles

Self-assembly solidified region

Thin layer of nanofluid of high concentrations

Schematic of evaporating nanofluid

Solidified regions (c > 12%, n > 1.38)

Effective RI Concentration Fields Fields

Fig. 5.18 Dynamic monitoring of the nanoparticle (Al2O3, 47-nm diameter) volume concentration distributions of an evaporating nanofluid. The nanofluid sample (0.25 vol.% in 1.0 μl at t = 0) leaves a spot with a size of 1.6-mm diameter, and evaporation progresses until the self-assembled dryout is reached [291].

The evaporative nanofluidic (47-nm Al2O3) self-assembly (Fig. 5.19) will experience the phase changes from liquid nanofluid (l) to cavity space (g) and self-assembled nanoparticles (s). Since the corresponding RIs change significantly with the phase changes, SPRM imaging can dynamically fingerprint the nanocrystalline self-assembly process. Figure 5.19 schematically shows the

112


cross-sectional view of a nanofluid droplet undergoing evaporation: (1) anchoring of the nanoparticles starts to form the contact line, which is pinned to the substrate [304-307], (2) evaporation lowers the surface temperature, resulting in a higher surface tension, and consequently, a thermocapillary phoretic Marangoni flow is induced toward the dorsal peak region [308-310], (3) the “replenishing” flow is provided from the bottom to the stagnant point [303], and this lifting of liquid creates a vacuum and conceives a cavity in the bottom area, (4) the downward forces of the attracting van der Waals interactions of nanoparticles with the substrate surface result in multiple inside anchorings and conform to complex hidden cavity structures, (5) the surface tension on the cavity interface continually expands the cavity areas as evaporation progresses, (6) aquatic evaporation also decreases the interparticular distance and increases the attractive van der Waals forces, enhancing the congregation of the nanoparticles [49], and finally, (7) the thermophoretic flow driven by the temperature gradients from the cavity ceiling to the droplet peak expedites evaporation [311]. Evaporative water

(2) (1)

(3)

(2) (4)

(7) (4)

(5)

(6)

Hollow cavities in gas

g-phase

t

l-phase

t + 5s

s-phase

t + 10s

Fig. 5.19 This sketch schematically represents the cross-sectional view normally erected along the dashed lines on the SPR images and shows the transport mechanism for the complex cavity formations. SPR fingerprinting identifies the existence and layout of hidden cavity structures by distinguishing s-l-g phase regions [312].


113

The final self-assembled nanocrystalline structure is achieved after 2 minutes of evaporation, after a 2-µl nanofluid droplet containing a 10% volume loading of aqueous Al2O3 nanofluid is allowed to evaporate. The crystallized glassy crust (Fig. 5.20-a) conforms to a half-toroidal shape, 2 mm in diameter and 160 μm in maximum height, with a number of radial crack lines [313-316]. The two-dimensional fingerprints of the three-dimensional cavity structure are evidenced by the SPRM images (Fig. 5.20-b). The dark image areas identify crystallized nanoparticles while the bright background represents the air interface, both inside and outside of the crust. The noncircular formation of the central crystallized spot is due to the non-axisymmetric competition of surface tension pulling associated with the multiple and distributed inner cavity growths. The open view (Fig. 5.20-c), taken after destruction of the crust, concurs with the nondestructive SPR image for the overall locations, shapes, and sizes of the crystallized inner structures, but with noticeably reduced details, for example, not revealing the detailed structure of the peripheral edge regions. The interferometric fringe image (Fig. 5.20-d) is taken by using reflectance interference contrast microscopy (RICM; Chapter 6). These RGB fringes (635 nm, 535 nm, and 465 nm, respectively) are constructed by interference of the rays reflected from the substrate surface (gold) and the rays reflected from the ventral cavity inner-surface, and they present quantitative information on the three-dimensional details of the cavity. Two neighboring fringes of an identical color represent the locations where the cavity height differential is equal to λ/4. In addition, the spectral sequence of the fringes determines the slope of the inner cavity walls; this slope increases when the fringes are seen in the order of …-B-G-R-B-G-R-…, and decreases when the fringes are seen as …-B-R-G-B-R-G-…[317]. Therefore, a full three-dimensionally reconstructed layout of the cavity structure is made possible by digitally analyzing the fringes (Fig. 5.20-e). The maximum cavity height is approximately 720 nm, which occupies approximately 0.5% of the crystallized crust’s total thickness of 160 μm. Note that the vertical scale of the reconstructed topography is magnified 400 times in comparison to the horizontal scale for clarity. This outcome provides a potential method of both better understanding and feasible control of the formation of nanocrystalline inner structures. It is notable that the topography of the crystallized cavity structures of these nanofluids remarkably resembles the earth’s formation of the much larger mountains and valleys. The formation of the complex inner structure was found to be attributable to multiple cavity inceptions and their competing growth during the aquatic evaporation.

5.8.6 Near-Wall Thermometry Among the many available means of temperature detectors, it is still safe to say that the thermocouple (TC) is the most rigorous temperature measurement tool, given

114


(a)

(b)

(c)

(d)

(e)

1.0 μm

0.5

d

Cavity height 400 μm Fig. 5.20 Anatomy of a self-assembled nanocrystalline structure, revealing the hidden hollow complex cavities formed when a 2-μl aqueous droplet (initially) containing a 10% volume of 47-nm diameter Al2O3 nanoparticles is allowed to evaporate and crystallize at an ambient temperature (21±0.5°C) and humidity (40%) on a gold surface: (a) WFM dorsal image, (b) SPRM ventral image, (c) opened view, (d) RICM image, and (e) the threedimensional reconstruction of the cavity structures from the RICM image [291].


115

a wide temperature range [318]. The limitations of TC probes, however, are their relatively large spatial resolution, physical intrusiveness in flow, and the limited point-wise detection of temperature. Alternatively, the more recent laser induced fluorescence (LIF) technique uses the temperature dependence of fluorescent emissions from seeded dyes; however, the presence of dye molecules may influence the characteristics of the test medium [317,319]. The RI values n1, n2, and n3 in Eq. (5.14) vary with temperature. The refractive index of the prism, n3, is specified by the prism material, and its temperature dependence is generally negligibly small [259]. The temperature dependence of the thin metal (Au) film n1(T), on the other hand, is small but not completely negligible. More importantly, the measured data for n1(T) scatter, and consequently, the R-T correlation varies, as previously discussed in Section 5.5. The gradient of the R-T correlations shown in Fig. 5.7 represents the sensitivity of the SPR reflectance change corresponding to a unit temperature change; thus, the steepest gradient shown for the Kolomenskii data is expected to provide the highest measurement sensitivity. Both Snopok et. al’s [228] and Peterlinz and Georgiandis’ [24] data are considered inappropriate because of the deflections that occur for T > 70°C. The remaining five R-T correlations collapse into a nearly single curve, despite the noticeable discrepancies in their measured dielectric constants. The dielectric constant of a thin metal film is given by Drude model [320,321] as:

ε ≡ ( n R + in I ) 2 = 1 −

ω p2 ω (ω + iω c )

(5.18)

where ω is the angular frequency of the incident light and ωp and ωc are the plasmon and collision frequencies, respectively. It is shown that the temperature dependence of ωp is negligibly small compared to that of ωc [258]. The collision frequency ωc consists of the phonon-electron scattering frequency ω cp and the electron-electron scattering frequency ω ce [224] as follows:

ω c = ω cp + ω ce ω cp (T ) = ω 0 [(

2 T + 4( )5 5 TD

TD / T

∫ 0

z4 dz e −1

(5.19)

z

ΓΔ 1 hω 2 [( k B T ) 2 + ( ) ] ω ce (T ) = π 4 6 4π 2 hE F

All of the constants and coefficients are listed in Table 5.4. Using n = nR + inI = 0.1718 + i3.637 for the 47.5 nm Au thin film at λ = 632.8 nm, the above equations are solved to determine ωp = 3.7826ω, and ωc = 0.08802ω where the specified ω = 2πc/λ = 2.9788 X 1012 rad/s. Substituting these results into Eq. (5.19) gives ω0 = 1.171 X 1014 rad/s and provides completion of the temperature dependence of the dielectric constant ε of the Au film.

116


The resulting correlation of SPR reflectance R with T can be calculated by incorporating the T-dependence of the dielectric constant of Au as well as the dielectric constant of the test medium (water, at present) into Eq. (5.14). Figure 5.21-a shows the resulting R-T correlation in the case of using a BK7 prism associated with a 47.5-nm Au layer with water as the dielectric medium, with and without accounting for the temperature effect on the dielectric constant of gold. In order to ensure measurement accuracy, inclusion of the T-effect on the dielectric constant of the metal layer is strongly recommended. Using the R-T correlation, the evolvement of near-wall temperature profiles are nonintrusively mapped when a hot water droplet at 80°C reaches the Au film surface at 20°C and spreads, either in an air environment (Fig. 5.21-b) or a water environment (Fig. 5.21-c) [230,322]. The most favored R-T correlation, based on Kolomanskii’s dielectric constant, is then used to convert the recorded SPR image intensity distributions into corresponding temperature fields. The gradual heat and energy transport in the air environment allows the contact surface shape to remain circular and spread concentrically. In the water environment, however, the more aggressive diffusion of hot water into cold water deforms the contact surface shape and spread, and the contact surface temperature approaches the environmental level more rapidly. Table 5.4 Parametric values used to calculate (Eq. (5.19)) the temperature-dependent dielectric constants and refractive index values for the case of a thin Au layer. Symbols

Description

Values

TD

Debye temperature

170 K

EF

Fermi energy

5.53 eV

kB

Boltzmann’s constant

1.3807 × 10-23 J/K

Γ

Scattering probability

0.55

Δ

Fractional scattering

0.77

h

Plank constant

1.0546 X 10-34 J⋅ s


117

0.6 W/ Temp. effect of metal W/O Temp. effect of metal

R e fe lc ta n c e R

0.5 0.4 0.3 0.2 0.1 0.0 20

(a)

30

40

50

60

70

Temperature (Celsius)

80

90

(a) 80° C

4.3 mm

16 s 0.63 s

0.15 s

(b) 0.03 s

0.2 s

1s

5.17 mm

(c) Fig. 5.21 (a) The correlation of the SPR reflectance R with water temperature T, either with or without accounting for the temperature dependence of the RI for the 47.5-nm thick gold layer. Full-field mapping of transient temperature fields are determined when a hot water droplet (80°C) falls on the cold Au surface (20°C) in an (b) air environment and (c) water environment, respectively [322].

Chapter 6

Reflection Interference Contrast Microscopy (RICM)

When an incident light is reflected from multiple surfaces of semi-transparent dielectric materials, interfering fringes appear; some popular examples include the colorful contours that appear on a soap bubble and the concentric color rings of a compact disk surface. Since the fringe patterns are associated with thin dielectric films, mathematical analyses of these patterns should allow for the determination of the thin film thicknesses, or the corresponding gap thicknesses. The first microscopic application of this method was introduced by Curtis [323], who used socalled interference reflection microscopy (IRM) to observe the adhesion sites of embryonic chicken heart fibroblasts. As a variation of IRM, RICM stands for “reflection interference contrast microscopy,” which has been primarily applied to cell physiology [324-328]. The basics of the interference of plane waves are summarized in Section 6.1, and the principles and practical issues of OSSM are presented in Section 6.2. Selected applications of RICM for near-field fluidic characterizations are presented in Section 6.3.

6.1 Interference of Plane Waves Light propagation is described as mutually orthogonal electro-magnetic (EM) radiation, which is governed by the Maxwell equations. The interference of two or more EM waves comprises the basic principle of RICM [329]. When the light waves are sufficiently distanced r from the source, the far-field light waves are well represented by one-dimensional plane waves and their polarization is defined as the orientation of the electric field oscillation. The electric field vector solutions of the hyperbolic Maxwell equations describe two plane waves at arbitrarily different polarizations but with an identical frequency ω [5]: r r E1 (r , t ) = Eo1 cos(k1 ⋅ r − ωt + ε 1 ) (6.1) r r E 2 (r , t ) = E o 2 cos(k 2 ⋅ r − ωt + ε 2 ) where the wave parameter or propagation number k = 2π/λ and ε denotes the initial phase of each wave.

120

6 Reflection Interference Contrast Microscopy (RICM)

When the two waves are superimposed, the average light intensity I is determined by the ensemble average of the square of the resulting electric field E = E1 + E 2 ; i.e.:

(

)(

r r r v v I = E 2 = E1 + E 2 ⋅ E1 + E 2

)=

r r r r r r r r E2 E2 E12 + E 22 + 2 E1 ⋅ E 2 = o1 + o 2 + 2 E1 ⋅ E 2 = I 1 + I 2 + 2 E1 ⋅ E 2 2 2

(6.2) A mathematical manipulation using the trigonometric identity gives: r r 1 r r 1 r r E1 ⋅ E 2 = E o1 ⋅ E o 2 cos (k1 ⋅ r + ε 1 − k 2 ⋅ r − ε 2 ) = E o1 ⋅ E o 2 cos δ 2 2

(6.3) where δ represents the optical phase differential of the two plane waves. Therefore, if two plane waves are perpendicularly polarized ( Eo1 ⊥ Eo 2 ), r r E1 ⋅ E2 = 0

and the resulting light intensity is an arithmetic sum of the two individ-

ual intensities; I = I 1 + I 2 , or I = I 1 + I 2 = 2 I o for two perpendicular waves of an identical intensity I o . If the two waves are in parallel oscillations, however, the interfered light intensity is given by: r r I = I 1 + I 2 + E o1 ⋅ E o 2 cos δ = I 1 + I 2 + 2 I 1 I 2 cos δ

(6.4)

Or, for two identical waves ( I 1 = I 2 = I o ): I = 2 I o (1 + cos δ ) = 4 I o cos 2

δ

(6.5)

2

The resulting interference modulates, depending upon δ. Thus, the constructive interference occurs at: I max = 4 I o at δ = 0, ± 2π , ± 4π , … [OPD = 0, ± λ , ± 2λ , …]

(6.6)

and the destructive interference occurs at:

1 3 I min = 0 at δ = ± π , ± 3π , … [OPD = 0, ± λ , ± λ , …] 2 2

(6.7)

The optical path length differential (OPD) is given by OPD ≡ δ ⋅ λ . Note that the 2π OPD must be smaller than the optical coherence length of the light source

6.2 Principles and Practical Issues of RICM

121

Table 6.1 Coherence lengths of several light sources [5].

Source Mean wave length (nm) Coherence length _______________________________________________________________________ IR

10,000

25,000 nm

Mercury arc

546.1

< 0.03 cm

White light (Sun)

550

900 nm

Kr86 discharge lamp

605.6

0.3 m

Stabilized He-Ne laser

632.8

~ 400 m

Special He-Ne laser

1153

15 x 106 m

(Table 6.1) in order to physically form the predicted interference patterns. If the OPD exceeds the coherence length, no fringes, or fringes with extreme noises, will result.

6.2 Principles and Practical Issues of RICM Considering the fluid filling the gap between two glass plates (Fig. 6.1), two primary reflections occur: at the top and bottom inner surfaces. The top reflection is internal, as the reflection occurs in the internal medium of a higher refractive index (RI), and thus the bottom reflection is external. The two reflected waves inherently differ by an OPD of half wavelength, as long as their polarization is not altered after the reflections [5]. Therefore, the total OPD is equal to the summation of the OPD associated with the finite fluid gap and the inherent OPD of λo / 2 ; i.e., OPDTotal = 2nd +

λo

(6.8)

2

The constructive interferences, or brightest fringes, occur when: OPD Total = 2nd +

λo 2

= mλo

( m = 0, ± 1, ± 2, ...)

(6.9-a),

and the destructive interferences, or darkest fringes, occur when: OPDTotal = 2nd +

λo 2

1⎞ ⎛ = ⎜ m + ⎟ λo 2⎠ ⎝

( m = 0, ± 1, ± 2, ...)

(6.9-b)

122


Therefore, the darkest fringe intensities are located at d = 0, λ/2, λ, 3λ/2, … and the brightest fringe intensities are located at d = λ/4, 3λ/4, 5λ/4, … (this also explains the “optically flat” surface if the surface flatness is within λ/4, creating no visible fringes). The resulting repeated bright and dark patterns are called “Fizeau” fringes, or more commonly “natural” fringes [330]. While the monochromatic RICM fringes provide the thin film thickness differentials, they lack information on the slope of the film (Fig. 6.1-a). When a white light source is used, multispectral fringes are formed on the order of increasing or decreasing wavelengths, depending on an ascending or descending slope of the thin film, respectively. In other words, for a progressively thickening film, the spectral order will be B, G, R, B, G, R …, while for a progressively thinning film, the order will be R, G, B, R, G, B, … (Fig. 6.1-b). Thus, the multispectral RICM fringes provide comprehensive mapping of the thin film thickness and slope distributions.

Index matching fluid (n ~ ng)

ng> nf nf Fluid gap: d

Fig. 6.1 A schematic illustration of the formation of natural, or Fizeau, fringes for the thin liquid film held between two glass plates: (a) monochromatic fringes, and (b) multi-spectral (R-G-B) white light fringes [334].

The setup for RICM can use a simple standard microscope system, with no need of any specific accessory, and its alignment is relatively straightforward. Nevertheless, one should consider three practical issues with regards to RICM setup [331]:

6.3 Near-Field Applications of RICM

123

(1) The use of an objective lens with a high numerical aperture (NA): The relatively shallow depth-of-field associated with a high NA makes the high-order fringes that occur outside the near-field disappear and provides more clearly defined fringes for the near-field region. (2) The use of a powerful light source: Since the intensity of reflected light is usually below 1% that of incident light, a sufficiently powerful light source is necessary to get good images. However, this may create unwanted “heating” of the test section, unless an effective IR filter is used. (3) The reduction of stray lights: Stray lights, which come from outside of the test region, blur the fringes and make them difficult to analyze. The use of indexmatching oil can suppress the interference associated with stray light reflections, to a degree. Stray lights may also be generated inside the objective, and these may be reduced by using an “antiflex” device, which uses polarizers and analyzers to minimize the internal stray lights [332,333].

6.3 Near-Field Applications of RICM 6.3.1 Thin-Film Thickness Measurements Pentane film on a clean glass surface is visualized by monochromatic fringes (λo= 520 nm) in Fig. 6.2-a and by multispectral “rainbow” fringes of white light in Fig. 6.2-b, while the corresponding slope thickness distribution is presented in Fig. 6.2c. Note that the pentane film is formed between the glass surface and the above air interface, both reflections are external, and no inherent λo/2 addition is necessary in Eq. (6.8); i.e., the constructive, or bright, fringes occur when OPDTotal = 2nd = mλo . The deformed fringes formed around the impurity particles very clearly identify impurities in the film [334].

6.3.2 Electrohydrodynamic (EHD) Control of Thin Liquid Film Thin liquid film conforms to the basis of heat and mass transport of two-phase heat exchanging devices such as heat pipes and thermosyphons. The evaporative heat and mass transports can be substantially increased if the thin film can be actively controlled and expanded. Electrohydrodynamic (EHD) phoresis has the potential to actively control the aforementioned thin liquid film. The total EHD force that arises from the action of the electric field applied through the thin liquid area is given by [335]: 1 1 ∂ε Fe = qe E − E 2∇ε + ∇E 2 ρ 2 2 ∂ρ

(6.10)

where qe is the electric field space charge density, E is the applied electric field strength, and ε is the dielectric constant of the liquid. The first term in Eq. (6.10)

124


(a)

(b)

(c) Fig. 6.2 RICM images of both pure- and particle-contaminated pentane thin films, created on a clean glass surface by using the following: (a) a monochromatic light source (λo = 520 nm), (b) a white light source (350 nm < λo < 650 nm), and (c) calculated thickness contours from the multispectral RICM fringes for the pure pentane thin film in (b) [334].


125

represents the Coulomb force for ionized fluid molecules. In highly dielectric fluids with a low permittivity, such as pentane, the EHD current discharge is low, and the first term is negligibly small. The second and third terms in Eq. (6.10) represent forces resulting from nonuniformity in the dielectric permittivity and electric field, respectively. If there is no significant spatial variation in the dielectric constant, we assume ∇ ε = 0 and neglect the second term. Then, the EHD force Fe is dominated by the nonuniformity in the electric field of the third term. Since Fe is proportional to the gradient of the scalar magnitude of E2, the fluid molecules always move toward the electrode of the dense electric field near the electrode, as shown in Fig. 6.3. Note that the white circular blurred images represent the tip of a sharply serrated electrode placed on the outer surface of the glass plate while the RICM is focused on the thin film region on the inner surface of the glass plate. The movement of thin film always directs toward the electrode that creates the denser electric field, regardless of the polarity of the electrode. This phenomenon is called dielectrophoresis [336].

Fig. 6.3 The progressive movement of the pentane thin film toward the denser electric field, near the electrode (the blurred white spot images), with increasing charging voltage Vcharge [photo by K.D.K].

The test cell (Fig. 6.4-a) is comprised of two 105-mm square, 1-mm thick flat glass plates spaced 8 mm apart [337]. The saw tooth-shaped electrode is located above the meniscus, so that the thin film can be attracted by and extended toward the highly stressed and nonuniform electric field formed near the electrode tips. The quantitative results (Fig. 6.4-b) given by the fringe analysis of the multispectral

126


RICM images clearly show the progressive dielectrophoresis of the pentane thin film to the saw tooth electrode with increasing Vcharge, thereby increasing the local electric field strength. The microscale dielectrophoretic control of thin liquid film formation has thus successfully been characterized by the RICM imaging technique. 8 mm

x

(a)

h (μm)

x (μm)

(b) Fig. 6.4 (a) The test cell consists of two (top and bottom) glass plates with the electrodes placed on the outer surface of the top glass plate. The test cell is laid at 5-degrees inclination from the horizon and the RICM images the thin pentane film along the inner surface of the top glass plate, and (b) the RICM image analysis results show the progressive electrophoretic movements of the pentane thin film toward the electrode with increasing applied voltage [337].


127

6.3.3 Dynamic Fingerprinting of Live-Cell Focal Contacts The history of cell-substrate imaging with RICM is quite long. The first pioneer, A.S.G. Curtis, suggested that RICM can be applied to measuring the cell-substrate gap in 1964 [323]. An effort to improve this method by using an objective lens with a high NA was implemented by Izzard and Lochner [338], while Gingell and Todd [339,340] attempted to establish a theoretical basis for the quantification of cell substrate separation distances. A more recent biofluidic application of RICM is exampled by the continuous monitoring of the cell-gap morphology of live porcine pulmonary artery endothelial cells (PPAECs) under different externally stimulating conditions, such as a cytotoxic environment and then recovery through a fresh medium [341]. The cell-gap morphology in the near-field, such as focal adhesions1 and close contacts, play an important role in cellular motility, cellular adhesion, and signal transduction. The differential interference contrast microscopy (DICM) dorsal-view images (Fig. 6.5-a) show two live PPAECs’ continuous shrinkage under Cytochalasin D, an agent notorious for disrupting the actin-filament, before showing their recovery, following replacement of Cytochalasin D with a new, fresh medium. The corresponding RICM ventral-view images (Fig. 6.5-b) complete the dynamic fingerprinting of the near-field morphology. The focal contacts [342-344], representing the locations of the closest cell-substrate proximities, appear as dark fringes. However, close contacts, or areas slightly farther from the substrate, appear as broad and gray fringes. The remaining areas represent larger cell-to-substrate distances and are brighter than both the focal and the close contacts.2 Upon administration of Cytochalasin D, the close contacts as well as the remaining brighter areas noticeably diminish in size, in response to the cellular shrinkage and retraction caused by the toxic agent. Finally, following replacement with the new medium, both the close contacts and the brighter areas gradually recover, reaching their original distribution after approximately 5 hours. Both the pseudo-color overlaid images (Fig. 6.5-c) and the pixel gray level (PGL) contour maps (Fig. 6.5-d) allow for a comprehensive observation of the ventral morphology changes. The contours are false-colored to blue for the darker fringes and to red for the brighter fringes by a 1000-PGL binning. The contours of PGLs below 6500 are separated in order to identify for focal contacts (Fig. 6.5-e). Note that the focal contacts along the edges of the cell remain largely unchanged, despite the cytotoxic conditions.

1

2

Focal adhesion, also referred to as “focal contacts” or “adhesion plaques,” are strong adhesive sites used by cells to attach to an underlying substrate; their adhering ability is due to the high local concentrations of binding proteins. It should be noted that focal contacts are associated with the distal end of actin filament bundles and are known to have firm attachment structures to hold the cell in place. In contrast, close contacts have relatively weak and highly dynamic adhesions to the substrate that help sustain rapid movements of cells over the substrate.

128


Fig. 6.5 The cytometric evolution of live porcine pulmonary artery endothelial cells (PPAECs), first after the addition of Cytochalasin D, and then after replacement with a fresh medium: (a) DICM dorsal-view images, (b) the corresponding RICM ventral-view images, (c) false-colored RICM images (green) that are overlaid on DICM images (red), (d) contour maps into bins of 1000 pixel gray levels (PGLs), and (e) contours with PGLs below 6500. The field-of-view size of all images is 80 μm × 80 μm [341].

The correlation of the zero-order natural fringe patterns (Fig. 6.6-a) of RICM and the cell-substrate gap distance d is given by:

⎞ ⎟⎟(I max − I Background ) , ⎠

(6.11)

where δ = 4π nmedium d / λo

(6.12)

⎛ N I Grey = I Background + ⎜⎜ ⎝ N max 2

⎛ 2r ⎞ ⎛δ ⎞ ⎜⎜ ⎟ sin 2 ⎜ ⎟ 2 ⎟ r 1 − ⎝2⎠ ⎠ N= ⎝ 2 ⎛ 2r ⎞ ⎛δ ⎞ ⎟ sin 2 ⎜ ⎟ 1 + ⎜⎜ 2 ⎟ r − 1 ⎝2⎠ ⎝ ⎠

(

)

(

)

6.3 Near-Field Applications of RICM 16000

129

14700

Pixel Grey Level (PGL)

14000 12000 10000 8000

6500

6000 4000 2000

450

0

100

200

300 Depth (nm)

400

500

600

0 0

20

40

60

80

100

Cell-Substrate Gap Distance d (nm)

(a)

Fig. 6.6 RICM image analysis results show (a) the focal contact threshold PGL = 6500 in the zero-order fringes, (b) the number of pixels below 6500 representing focal contacts, (c) the normalized cell-covered area, and (d) the ratio of focal contacts to the cell-covered area as a function of time [341].

130


where I is the PGL, r is the reflectance, and λο is the wavelength in a vacuum. The RIs of glass, the cell-culturing medium, and the cytoplasm membrane are given as 1.515, 1.33, and 1.36, respectively. IBackground is set to 450 PGL, equivalent to the “dark noise” of the CCD, and Imax is set to 14700 PGL, representing the highest intensity among all recorded images. Assuming that the maximum PGL corresponds to the maximum gap detectable by zero order fringes, i.e. dmax = λo/(4*nmedium) = 90 nm, the PGL of 6500 is equivalent to a gap distance of approximately 40 nm. While there is controversy over the range in gap sizes for focal contacts, it is believed that 40 nm is a fairly acceptable estimate for the upper limit [341]. The focal contacts represented by the pixels with PGL < 6500 (Fig. 6.6-b) remain relatively unchanged during the exposure to Cytochalasin D, as well as after replacement with the fresh medium. Note that the decay of focal contact area for the first few minutes is believed to be associated with the initial cell shrinkage in response to the toxic agent; this is made more pronounced by the evolution of the normalized cell-covered area (Fig. 6.6-c). After replacement with the fresh medium, the cell area eventually returns to its initial size. Despite the variation of the cell area, the ratio of focal contacts to the cell-coverage area remains nearly unchanged (Fig. 6.6-d). The sequential and complimentary uses of RICM and DICM therefore allow for a dynamic and comprehensive examination of the cellular morphological changes of live cells under external stimuli.

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