Acoustic Wave Sensors: Theory, Design

Chapter 1 Why Acoustic Sensors? Precise measurement tools are necessary parts of most successful scientific and engine...

Author: D. S. Ballantine Jr. | Robert M. White | S. J. Martin | Antonio J. Ricco | E. T. Zellers | G. C. Frye | H. Wohltjen | Moises Levy | Richard Stern

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Chapter 1

Why Acoustic Sensors?

Precise measurement tools are necessary parts of most successful scientific and engineering enterprises. The sensing devices that we consider in this volume are such tools, capable of measuring physical, chemical, and biological quantifies. What they have in common is that they all employ acoustic waves in their operation. The purpose of this introductory chapter is to provide an overview of these devices, and to answer the question: why use acoustic sensors?

1.1

What Is a Sensor?

The sensors we consider here produce an output signal in response to some input quantity, as indicated schematically in Figure 1.1(top). The output signal is usually electrical m an analog voltage or current, a stream of digital voltage pulses, or possibly an oscillatory voltage whose frequency represents the value of the input quantity. The range of input quantities covered in this book is large, including physical quantities such as the mechanical properties of thin films, and chemical and biological quantities such as the concentrations and identities of unknownspecies in air or liquid media. Inside the typical sensor of Figure 1.1(top), a process of transduction takes place, converting the input event into an electrical signal. The sensor may also contain circuitry that converts the often feeble electrical signal from the transduction process into a more robust form suitable for use outside the sensor itself. The output signal may be stored in a computer memory for later examination. Possible applications would have the signal activating an alarm to warn of the 1 ACOUSTIC WAVE SENSORS

Copyright 9 1997 by Academic Press All rights of reproduction in any form reserved. ISBN 0-12-077460-7

2

1.

Why Acousac Sensors? SENSOR i

i lll

i

i

i

i

I'! ,, ,r/2, the upper film surface is 180 ~ out of phase (Figure 3.15c) and frequency is higher than for the uncoated device. In addition, the system is highly damped in the vicinity of resonance, making sensor operation more difficult. Although it is difficult to directly observe the dynamic behavior of the film, which varies across the film thickness, its influence on the TSM resonator elec-

68

3. Acoustic Wave Sensors and Responses

b

a ,

I

c

|,

ii

p/ I I I I

I I I

/

I

I l l l I I l,

Figure 3.15 The dynamic film response generated by the oscillating resonator surface varies with the acoustic phase shift tk across the film [40]: (a) for ck < < ~'/2, synchronous motion occurs; (b) for tk ~ r overshoot of the upper film surface in-phase with the resonator surface occurs (film resonance occurs when ck = Ir/2); (c) for tk > ~'/2, the upper film surface is 180~ out-of-phase. The film is the thin region at the top; the crystal is below. (Reprinted with permission. See Ref. [40]. 9 1991 IEEE.)

trical characteristics can be more readily determined. By considering the mechanical coupling between the resonator and a film overlay, an equivalent circuit model can be derived that relates the near-resonant electrical characteristics to the film properties. This model allows prediction of how film properties influence the resonant frequency and damping. In addition, in the regime where the film is deformed, measurement of the electrical characteristics of a film-coated resonator can be interpreted to obtain the film's shear storage and loss moduli [40].

3.1.9

ELECTRICAL CHARACTERISTICS OF A TSM RESONATOR COATED WITH A VISCOELASTIC FILM

Chemically sorbent films are commonly coated on TSM resonators to construct gas or vapor sensors. The absorption of species by these films leads to a change in the areal mass density as well as plasticization or softening of the film. Corn-

3.1 Thickness-Shear Mode Resonator

69

monly, however, polymer films are either sufficiently soft to begin with, or become softened by temperature or vapor absorption, that the criterion for considering the film as an ideal mass layer, namely that tk "~ ~r/2, is not satisfied. Then, a more detailed model for the resonator-film interaction must be considered. The equivalent circuit model of Figure 3.7 can be used to describe the nearresonant electrical characteristics of the quartz resonator coated by a viscoelastic film. The surface film causes an increase in the motional impedance, denoted by the complex element Ze. From Equation 3.19, this element is proportional to the ratio of the surface mechanical impedance Zs contributed by the film to the characteristic shear wave impedance Zq of the quartz. The oscillating resonator surface may be considered as a source for shear waves that are radiated into the contacting film. The upper film surface reflects these radiated shear waves downward, so that the mechanical impedance seen at the quartz surface is dependent upon the phase shift and attenuation undergone by the wave in propagating across the film. When the film is rubbery, significant phase shift across the film occurs. Consequently, the coupling of acoustic energy into the film depends upon thin-film interference. The finite thickness of a film on the resonator surface makes the calculation of the mechanical impedance at the surface analogous to that of an appropriately terminated transmission line [41 ]. Noting the correspondence between stress and voltage and between particle velocity and current, the stress-free upper film surface is analogous to a short-circuited electrical transmission line. From this analogy, the input impedance seen at the resonator/film interface is [40]

Zs = Txy [

= Zo tanh ('yhf),

(3.36)

Vx [y=hq where Zo = (Gpf)112 and 3' = Jto(pf/G)ll2; G and pf are film shear modules and density; hq is quartz thickness. Equations 3.19 and 3.36 can be combined to find the change in (electrical) motional impedance that arises from a viscoelastic film on a thickness-shear mode resonator [40]:

Nzr

(Gpf)l/2

. . . . . Id, . qpq Ze . . 4K2tosCo

tanh (Thf).

(3.37)

For lossless films, G" = 0 and Ze is imaginary; in this case, Ze represents energy stored in the film, becoming infinite at film resonance when th = mTr12 (m odd). For lossy films, G" > 0, and Ze becomes complex, with the real part (R2) representing power dissipation in the film and the imaginary part (L2) representing energy storage. The dependence of Ze in Equation 3.37 on ~/hfmakes it difficult to resolve Ze into real elements R2 and L2, except in a few limiting cases.

70


A condition of film resonance occurs when the acoustic phase shift ~ across the film reaches an odd multiple of 7r/2. This enhances the coupling of acoustic energy into the film, resulting in a greater extraction of electrical energy from the source. Consequently, dramatic changes in the motional impedance occur at film resonance (these arise from the complex Ze contribution (Equation 3.37)). These changes lead to changes in the resonant frequency, Af, and damping, R2, for the coated resonator that can be determined from Ze using Equations 3.21 and 3.23. Figure 3.16 shows the changes in resonant frequency, Af, and damping, R2, as a function of film phase shift tk and loss tangent (G"/G') calculated from Equations 3.21, 3.23, and 3.36. The behavior of Af and R2 with ~ is distinct in each of the regimes of dynamic film response outlined previously: (a) For ~b ,~ 7r/2, Af decreases linearly with ~b and damping is nearly fixed at the uncoated resonator value. (b) For ~b ~ zr/2, Af decreases more rapidly with ~b, while R2 increases from the uncoated resonator value. In this regime, dynamic calculations indicate overshoot of the upper film surface, leading to significant deformation in the film. (c) For ~b ~ 7r/2 (film resonance), Af increases rapidly, while R2 is maximum. The discontinuity that occurs in resonant frequency can be attributed to the abrupt change in mode shapes shown in Figure 3.15 (b and c). Energy dissipation in the film diminishes away from resonance. 3.2

Surface Acoustic Wave (SAW) Devices

The stress-free boundary imposed by the surface of a crystal gives rise to a unique acoustic mode whose propagation is confined to the surface and is therefore known as a sulface acoustic wave (SAW). In 1887 Lord Rayleigh discovered this mode of propagation in which acoustic energy is confined very near the surface of an isotropic solid [5]. This mode, now known as the Rayleigh wave [5], is of interest to seismologists because it is excited by earthquakes. The utility of Rayleigh waves in sensor applications is also due to the surface confinement of energy, allowing them to be excited by surface electrodes [42] in piezoelectric materials and also making the wave extremely sensitive to surface perturbations. In order to satisfy the stress-free boundary condition, coupled compressional and shear waves propagate together in a SAW such that surface traction forces are zero (i.e., T..~ = 0, where .~ is normal to the device surface). The generalized surface acoustic wave, propagating in the z-direction, has a displacement profile u(y) that varies with depth y into the crystal as u(x,y,z,t) = (ux(y)eJ4"l,~ + Uy(y)eJ4~2~+ Uz(y)eJ4J3~)eJ~t-Tz,

(3.38)

3.2 Surface Acoustic Wave (SAW) Devices

71

3500

3000 2500

C

A

A

2000

B

1500 1000 500 0 C

A

-20

N 3: _v

B -40

A -60

-80

-100

I . . . . . . . . . .

0

,

. . . . . . . .

'r

,

rJ2

,,

'3~4

~rdn) Figure 3.16 Variation in resonant frequency (Af) and damping (R2) vs the film phase shift ~b for various values of the film loss tangent (G"/G'): (A) 0.1; (B) 0.25; (C) 1.0. (Reprinted with permission. See Ref. [40]. 9 1991 IEEE.)

where to is the angular frequency (2,n'f); 3' is the complex propagation factor; Ux, Uy, and Uz represent displacement components in the x-, y-, and z-directions, re-

72


spectively, and ~ the phases of the components with respect to Uz. The component Uy is perpendicular to the surface, Uz is in the direction of propagation, and Ux is transverse to the yz plane (i.e., the sagittal plane). The displacement components ui(y) vary approximately as e -2'ry/x, where )t is the SAW wavelength along the surface and y is distance into the substrate; amplitude thus decays rapidly with distance into the bulk of the crystal. A crosssectional view of the strain field generated by a surface wave propagating along the surface of a crystal is shown in Figure 3.17. The strain energy density, also shown in the figure, indicates that the majority of wave energy is contained well within one wavelength of the surface, which thus acts as a waveguide. At higher frequencies (i.e., shorter wavelengths), acoustic energy is confined more closely to the surface and wave sensitivity to surface perturbations increases. The sensitivity of SAW devices to surface perturbations is dependent upon the wave amplitude at the surface. The wave amplitude can be represented by the surface particle velocities Vxo, Vyo, and Vzo in the x-, y-, and z-directions, respectively. These are listed in Table 3.1 (page 74) for several different substrate materials. For propagation in an isotropic medium or along a pure-mode direction of a crystal (e.g., a plane of symmetry), Equation 3.38 reduces to a Rayleigh wave, characterized by having no transverse component: Ux = 0. Since Uy and Uz are 90 ~ out of phase, the particles move in an elliptical orbit in the sagittal plane; the surface motion resembles that of the ocean under the influence of a passing wave. The presence of the surface-normal displacement component makes the SAW poorly suited for liquid sensing applications. When the SAW medium is contacted by a liquid, this component generates compressional waves in the liquid; the power thus dissipated leads to excessive attenuation of the SAW. 3.2.1

S A W E X C I T A T I O N AND DETECTION

The discovery by R. M. White of the University of California at Berkeley that surface acoustic waves could be excited and detected by lithographically pattemed interdigital electrodes on the surface of piezoelectric crystals [42] has led to widespread use of SAW devices in a number of signal-processing applications. These include frequency filters, resonators, delay lines, convolvers, and correlators [43,44]. A surface acoustic wave (SAW) is most conveniently excited on a piezoelectric crystal using an interdigitated electrode pattern, or interdigital transducer (IDT), as shown in Figure 3.18 (page 75). Application of a voltage between alternately connected electrodes causes a periodic electric field to be imposed on the crystal. When an altemating voltage is applied, a periodic strain field is gen-

3.2 Surface Acoustic Wave (SAW) Devices Probed Film

I~,

"~

73

.._1

STRAIN ENERGY

== 13

Figure 3.17 Deformation field due to a SAW propagating to the right along a solid surface (top) and the associated distribution of potential energy (bottom).

74

3. Acoustic Wave Sensors and Responses Properties of Several SAW Substrate Materials

Table 3.1 9

,

,

,

,,

,

,

,

,,

,

,

,,

i

,,

,

==

,

,

,

,,

,,,

,

,

Substrate Cut

Propagation Direction Quartz ST X Lithium Niobate -y Z Gallium Arsenide Z X + 22.5 ~ ii

i ill

V~o

Vyo

V~o

Propagation Velocity

coP

coP

coP

4~

4Jz

3.158

0.13

1.34

0.88

90

90

0

3.488

0

0.83

0.56

--

90

0

2.763

0.16

1.22

0.91

0

90

0

( x l 0 s cmls)

( x l O-6 cml/Z gt/Z)

(degrees)

ill

erated in the piezoelectric crystal that produces a standing surface acoustic wave. This standing wave gives rise to propagating waves that are launched in both directions away from the transducer; the wavefronts are parallel to the transducer fingers. The transducer operates most efficiently when the SAW wavelength, A, matches the transducer periodicity, d. This occurs when the transducer is excited at the synchronous frequency, defined by fo = vo/d, where Vo is the SAW propagation velocity. As discussed in Section 2.2.1, propagation of a mechanical wave in a piezoelectric medium is accompanied by an associated wave potential, ~b. When the wave is incident on a receiving transducer, this potential induces a current flow in each transducer electrode; these currents combine to produce a current flow in the external detection circuit. The addition of current contributions in the receiving transducer is also optimized when the transducer periodicity matches the acoustic wavelength. Thus, a reciprocity relation holds, as it must for a passive linear device, between the wave and external signals.

3.2.2

INTERDIGITAL TRANSDUCER FREQUENCY RESPONSE

Each transducer finger may be considered to be a discrete source for the generation of surface waves in a piezoelectric medium because the piezoelectrically generated stress varies with position near each transducer finger. A simple trans-


75

fer function relates the continuous wave (CW) voltage V1 applied to a finger and the electrical potential associated with the waves radiated in each direction [43]"

d~+-

I,*sV],

=

(3.39)

where/Xs is a substrate-dependent constant, (h+ is associated with the rightward propagating SAW, while ~b- is a leftward propagating SAW. The parameter/Xs may be considered frequency independent: the frequency response of the transducer arises mainly from interference between finger contributions, and is relatively insensitive to the frequency response of the individual elements. This

r (a) . ,.. V" 9

--!

(b)

' i. x......

o

i

i

i

. . . .

V1

2

II

"3

ii

Transmitter

(c)

i

'

Receiver

,T,TTT

t-

T~~T,

Piezoelectric Substrate .

.

.

.

.

.

.

.

.

.

.

Ill

.

.

.

.

.

.

-!

Figure 3.18 Interdigital transducer, formed by patterning electrodes on the surface of a piezoelectric crystal, for exciting surface acoustic waves: (a) SAW electrical potential, (b) plan view, (c) side view.

76


approximation is typically made in analyzing wave scattering from an array of elements: the "element factor" is typically considered frequency-independent compared with the "array factor." When an array of fingers is excited, as occurs with an interdigital transducer (IDT), the wave potential for a rightward propagating wave ~+ evaluated at position z is a vector sum of the contributions from each finger: Nf-I

dP+(z)=l~s E

VneJkCz-zn)'

(3.40)

n=O

where zn is the position of the nth finger excited with voltage Vn; Nf is the total number of fingers. Equation 3.40 has the form of a discrete Fourier transform [45] of the sequence Vn. Consequently, the frequency response of the device is proportional to the Fourier transform of the sequence of transducer finger contributions. Schemes have been devised to vary the individual finger contributions in order to achieve a desired frequency response. The interested reader is referred to excellent books on SAW filter design by Datta [43], Morgan [44], and Ristic [46]. If Nf identical fingers are spaced periodically with period d and excited with alternating voltages Vn = (-1)n Vo, Equation 3.40 becomes Nf-I

~b+(0) = IxsVo ~

( - 1)ne-jnkd/2.

(3.41)

n=O

The sum in Equation 3.41 is a geometric series whose elements become unity, and add constructively, when kd/2 = mTr, where m is an odd integer. This condition defines the relationship between SAW wavelength, A, and transducer periodicity, d, for coherent addition, as shown in Figure 3.19. The IDT excites odd harmonics at odd multiples of the synchronous frequency: fm= mfl. Moving away from the synchronous frequency, the addition of components from individual fingers becomes incoherent, giving rise to the frequency response [~+(f)[=

sin (X) X

(3.42)

in which X=

Np~(f - fo)

fo

0.43)

where fo is the transducer's synchronous frequency and Np is the number of IDT periods: Np = Nf/2. The wave potential as a function of the detuning parameter

3.2 Surface Acoustic Wave (SAW) Devices 4-

I-

--

4-

'i,,i i

,ii

--

I ........I I, , ""I, .i

i.~ +x

I

I

I

I

I

I

I

I

I

I

~lJ

I

\lJ

I I I Figure 3.19

+

I

I

77

"-

I

I I

I I

I I

I I

Relationship between transducer periodicity and coherently excited waves.

X, described by Equation 3.23, is shown in Figure 3.20 (page 78). Note that when X is a multiple of 11",th+ is zero ~ a result of complete cancellation between finger contributions. Consequently, the frequency interval B between the first nulls on either side of the synchronous frequency is B -

2

Np

.

(3.44)

Thus, the transducer bandwidth B is inversely proportional to the number of IDT fingers. As will be described in Chapter 4, a narrow bandwidth is desirable for oscillator applications in order to avoid spurious oscillations and to improve stability. The frequency response measured between a pair of transducers having Ao = 32/xm and Np = 50 finger pairs is shown in Figure 3.21 (page 79). The amplitude, shown on a log (decibel) scale, shows the characteristic sin(X)/X behavior. The delay line phase shift q0 is

2 ~rfL q~(f) = k L -

Vo

,

(3.45)

78


10

X s

m,/I,

i

__._

X-Ir

f,i

--..

Figure 3.20

... L

X

v

The calculated transducer response, sin(X)/X, vs the "detuning parameter,"

X. (Reprinted with permission. See Ref. [46a].)

where L is the path length (center-to-center distance) between transducers. Differentiation of Equation 3.45 shows that the phase slope dq~/dfis proportional to L/A, the transducer separation in wavelengths.

3.2.3

SAW PERTURBATION MECHANISMS

When SAW devices are used for sensors or thin-film characterization, the measured responses arise from perturbations in wave propagation characteristics, specifically wave velocity and attenuation, resulting from interactions between the SAW and a surface layer. Because a SAW propagating in a piezoelectric medium generates both mechanical deformation and an electrical potential, both mechanical and electrical coupling between the SAW and surface film are possible. Consequently, a number of interactions between surface waves and a surface film have been found that give rise to velocity and attenuation responses. SAW-film interactions that arise from mechanical coupling between the wave and film include mass loading caused by the translation of surface mass by the SAW surface displacement, and elastic and viscoelastic effects caused by SAWinduced deformation of a surface film. SAW-film interactions that arise from electrical coupling between the wave and film include acoustoelectricinterac-

50i

--"

-r

"

"'

'~

.......~ . . . . . .

Calculated

' ............ " ........

Insertion

Measured

Insertion

~ ........

Loss

Loss ....... ; .........." ' ' | . . . . . .

80 ~

................

"

t

70

0 8O 0

B~

-r,=r .4..)

(D

r

90

0

,A

100bD--

1

II

,I

t I

4.'1

I

"l

m.

|

r%

gO

"- ,,,,"

110 90

95

100

105

Frequency (MHz) Figure 3.21 See Ref. [46a].)

The frequency response measured between a pair of interdigital transducers. (Reprintedwith

,~---"

#B m.

80


tions between electric fields generated by the SAW and charge carders in a conductive film. This section examines the velocity and attenuation changes caused by several interactions between SAWs and surface layers. This survey is by no means exhaustive---new interactions are being discovered all the time. 3.2.4

SAW MASS LOADING

The simplest interaction, and the one most utilized for SAW sensor applications, is the response due to changes in the areal/mass density (mass/area) on the device surface. The harmonic motion of the crystal surface caused by the passing surface wave causes particles bound to the surface to be translated in an elliptical orbit in synchronism with the SAW surface displacement. The effect on wave velocity and attenuation of this interaction may be derived from energy considerations. Movement by the wave of a surface layer that is sufficiently thin or rigid that it moves synchronously with the wave causes an increase in the kinetic energy density, U,, of the wave without dissipating any wave energy. From the discussion in Section 2.3, this is expected to change the wave propagation velocity without affecting attenuation. The change in average kinetic energy per area of surface is AUk =

p,.V2

+ V2 yo +

V2zo),

(3.46)

where Vxo, Vyo, and Vzo are the SAW particle velocities at the surface and Ps is the surface mass density. Particle velocities are related to particle displacement u by vi = jtoui. This increase in kinetic energy density results in a decrease in wave velocity, according to Equation 2.48. Combining Equations 2.47, 2.48, and 3.46 yields an expression for the change in wave velocity arising from surface mass loading: ~_~V ~.

Vo

tO

ps

V xo +

v yo +

v zo

tOP

toP

toP

.

(3.47)

Due to the greater confinement of wave energy near the surface that occurs as operating frequency increases, surface particle velocities increase in proportion to (pto)l/2. Thus, the quantities in parentheses (Vio2/toP), being independent of wave amplitude and depending only on the substrate material, remain constant. Slobodnik et al. have tabulated these normalized surface particle velocities for a large number of substrates [47]; parameters for the most commonly used SAW substrates are listed in Table 3.1. Note that for propagation along a crystalline axis of lithium niobate (LiNbO3), two components of par-


81

ticle velocity are generated (in the y- and z-directions). X propagation in the ST cut of quartz (a rotated cut chosen for its desirable temperature characteristics), however, results in three components of particle velocity because of the lack of crystal symmetry. Grouping all the substrate-dependent constants together results in the expression for the mass-induced change in SAW propagation velocity" Av =

Vo

-Cmfop,,

(a.4a)

where the mass sensitivity factor Cm is

Cm=T

2 + .1)2o ~rrVo Vxo . . . . + .V. zo .. toe top toe

(3.49)

Note from Equation 3.48 the frequency dependence of the SAW mass sensitivity: the fractional velocity change Av/vo varies with operating frequency fo. Because the mass layer is assumed (in this case) to be lossless, Equation 2.55 implies that attenuation is unchanged by mass loading. Example 3.5: (a) Calculate the mass sensitivity factor CmfOr a IO0-MHz SAW device on ST-cut quartz. (b) If a SAW device is incorporated in an oscillator loop, so that fractional frequency changes track fractional velocity changes (i.e., Aflfo = Av/vo), calculate the sensitivity S = dfldps. (c) Calculate the limit of mass resolution for a typical SAW oscillator stability of 1 Hz.

(a) Using Equation 3.49 with normalized surface particle velocities (V2xo/oJP, etc.) obtained from Table 3.1, Cm = 1.29 • 10-6 cm2-s/g. (b) The sensitivity calculated for the 100-MHz SAW device is S = dAf/dps = -Cmf2o = - 13 Hz-cm2/ng. (c) The limit of mass resolution is Rm = 3AflS = 3 Hz/(13 Hz-cm2]ng) = 0.23 ng/cm2.

Solution:

The previous example illustrates the superior mass sensitivity of the SAW device in comparison with the TSM resonator: sensitivity is some 200 times larger for the 100-MHz SAW device than for the 5-MHz TSM resonator. Part (b) of the Solution also reveals that mass sensitivity, when expressed in the form df/dps, increases with f2. The velocity and attenuation changes resulting from depositing a mass layer on a 97-MHz SAW device using an ST-cut quartz substrate are shown in Figure 3.22 (page 82). Velocity decreases linearly in this thickness regime, yielding cm = 1.32 • 10 -6 cm2-s[g, in good agreement with the mass sensitivity factor calculated above for a 100-MHz SAW. As predicted from the model, the relative attenuation change (Aa[k, where a is the attenuation and k = 2~r/A is the wavenumber) due to mass loading is negligible in comparison with Av/vo (shown on the same scale).

100

.

.

.

.

=

'

=

.....

= '

i

"=

. . . . . .

~

800.

. . . . .

0

~

>0 "~

Cl) Slow (v < cD

Immersible?

Fast Fast

Yes

Low

Med

Discrete

R

No

Med-High

High

Discrete or

D or R D D or R

Frequency

of Operation

Mechanical Strength

Discrete or Multiple Fabrication

Fast

Yes

Med-High

Med

Multiple Discrete

Slow

Yes

Low

Low-Med b

Multiple

,

i

i

i

Delay-line or R_esonator

i

aST-quartz is a highly temperature stable single-crystal SAW cut. SAWs made with piezoelectric films deposited on silicon or other substrates typically have lower temperature stability. bFPW devices utilize thin membranes that are mechanically rugged if their transverse dimensions are not too large.

References

145

mass that these sensors can detect. Other important factors that are dealt with in later chapters are the instabilities (noise) of the device in its operating condition - - bare, coated with a sorptive layer, in contact with a liquid - - and the noise contributed by the associated electronic measurement equipment.

3.5.3

Q U A L I T A T I V E C O M P A R I S O N OF A C O U S T I C S E N S O R S

Table 3.5.2 summarizes qualitatively the characteristics of the four sensor families discussed. The reasons for many of the entries should be apparent from the preceding discussion. Additional points to note are: (1) The thermal stability of any of the devices made from temperaturestable crystal cuts is degraded considerably when the device is coated with a polymeric film used for vapor sorption. Contact with a liquid may also introduce temperature variations that affect the short-term noise of the entire system. (2) The devices whose particle motions are transverse only, or whose phase velocities are lower than the speed of sound in the liquid, can be immersed in a liquid without suffering excessive radiative loss. (3) A high frequency of operation may lead to a high gravimetric sensitivity, but at the expense of more costly electronics. In viscosity sensing, the higher the operating frequency the lower the maximUm viscosity that can be sensed. (4) Discrete devices can, of course, be connected in arrays to obtain better selectivity or higher accuracy. Devices fabricated concurrently may have more similar characteristics than discrete devices made at different times, and so be better suited for use in arrays.

References 1. 2. 3. 4.

Sauerbrey, G. Z. Phys. 155, 206-222 (1959). Numura, T. and Minemura, A. Nippon Kagaku Kaishi, 1621 (1980). Konash, P. L. and Bastiaans, G. J. Anal. Chem. 52, 1929-1931 (1980). Tiersten, H. In Linear Piezoelectric Plate Vibrations; Plenum: New York, Chap. 10 (1969). 5. Rayleigh, Lord Proc. London Math. Soc. 17, 4-11 (1885). 6. Benes, E. J. Appl. Phys. 56, 608 (1984). 7. Granstaff, V. E. and Martin, S. J. J. Appl. Phys. 75, 1319-1329 (1994).

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8. Rosenbaum, J. F. Bulk Acoustic Wave Theory and Devices; Artech: Boston, Sect. 10.5 (1988). 9. Martin, S. J.; Granstaff, V. E.; and Frye, G. C. Anal. Chem. 63, 2272-2281 (1991). 10. Reed, C. E.; Kanazawa, K. K.; and Kaufman, J. H. J. Appl. Phys. 68, 1993-2001 (1990). 11. Mecea, V. and Bucur, R. V. Thin Film Solids, 60, 73-84 (1979). 12. Granstaff, V. E. and Martin, S. J. J. Appl. Phys. 75, 1319-1329 (1994). 13. Cady, W. G. Piezoelectricity; McGraw-Hill: New York, 1946. 14. Martin, S. J.; Frye, G. C.; Ricco, A. J.; Senturia, S. D. Anal. Chem. 65, 2910-2922 (1993). 15. White, F. M. Viscous Fluid Flow; McGraw-Hill: New York (1974). 16. Glassford, A. P. M.; J. Vac. Sci. Technol. 15, 1836-1843 (1978). 17. Martin, S. J.; Frye, G. C.; and Wessendorf, K. O. Sensors and Actuators A44 209-218 (1994). 18. Kanazawa, K. K. and Gordon II, J. G. Anal. Chem. 57, 1770-1771 (1985). 19. Muramatsu, H.; Tamiya, E.; Karube, I. Anal. Chem. 60, 2142-2146 (1988). 20. Beck, R.; Pittermann, U.; Weil, K. G. Ber. Bunsenges. Phys. Chem. 92, 1363-1368 (1988). 21. Yang, M.; Thompson, M. Anal. Chem. 65, 1158-1168 (1993). 22. Tiean, Z.; Liehua, N.; Shouzhou, Y. J. Electroanal. Chem. Intelfacial Electrochem. 293, 1-18 (1990). 23. Ballato, A. IEEE Trans. Sonics UItrason. SU-25, 185-191 (1978). 24. Bruckenstein, S.; Shay, M. Electrochimica Acta 30, 1295-1300 (1985). 25. Schumacher, R. Angew. Chem. Int. Ed. Engl. 29, 329-343 (1990). 26. Beck, R.; Pitterman, U.; Weil, K. G. J. Electrochem. Soc. 139, 453--461 (1992). 27. Beck, R.; Pittermann, U.; Weil, K. G. Ber. Bunsenges. Phys. Chem. 92, 1363-1368 (1988). 28. Martin, S. J.; Frye, G. C.; Ricco, A. J.; Senturia, S. D. Anal. Chem, 65, 2910--2922 (1993). 29. Schlichting, H. Boundary-Layer Theory; McGraw-Hill: New York, 1979; Ch. 11. 30. Rajakovic, L. V.; Cavic-Vlasak, B. A.; Ghaemmaghami, V; Kallury, M. R. K.; Kipling, A. L.; Thompson, M. Anal. Chem. 63, 615-621 (1991 ). 31. Kipling, A. L.; Thompson, M. Anal. Chem. 62, 1514-1519 (1990). 32. Rajakovic, L. V.; Cavic-Vlasak, B. A.; Ghaemmaghami, V; Kallury, M. R. K.; Kipling, A. L.; Thompson, M. Anal. Chem. 63, 615-621 (1991). 33. Thompson, M.; Arthur, C. L.; Dhaliwal, G. K. Anal. Chem. 58, 1206-1209 (1986). 34. Thompson, M.; Dhaliwal, G. K.; Arthur, C. L.; Calabrese, G. S. IEEE Trans. Ultrason. Ferroelec. Freq. Contr. UFFC-34, 127 (1987). 35. Mecea, V. M. Sensors and Actuators A, 41-42, 630-637 (1994). 36. Mecea, V. M. Sensors and Actuators A, 40, 1-27 (1994). 37. Haardt, H. Dissertation, Universit~it Kiel (1971).

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Chapter 4

Materials Characterization

The field of materials science has grown dramatically in the past decade, with new materials being synthesized and/or developed for applications such as lubrication, corrosion protection, electronics, paints and coatings, and chemical separations. Many of these materials have complex properties quite different from those associated with simple "ideal" substances. Since the chemical and physical properties of a material determine its ability to meet the often stringent specifications required for a given application, characterizing the properties of materials plays a vital role in materials science. Thin film technology is an excellent example. Thin film materials are currently used in a wide variety of industrial applications. For example, thin films are used as protective or passivating layers [1-3], as conductive or photoactive (i.e., photoresist) layers [1], as dry lubricants [3], as catalysts [4], as gas separation membranes [5], and as optical layers [6]. Thin films can be formed by a variety of processes [ 1-8], including spraying, spin-coating, dip-coating, chemical vapor deposition (CVD), evaporation, and sputtering. To effectively optimize thin film properties, techniques to directly characterize thin film materials are critical. These techniques can be utilized as research and development tools to characterize new materials or, at the other extreme, as on-line probes of film properties during production. A major challenge in developing techniques for characterizing film materials is the limited amount of material present. For example, in a one-micrometer-thick film, there is only 10 -4 cm 3 of material for each cm 2 of film area. Thus, a 10cm 2 film has a volume of only one microliter and a mass on the order of one milligram. Many material characterization instruments do not have sufficient sensitivity to analyze these small volumes or masses [9]. In addition, those tech150 ACOUSTIC WAVE SENSORS

Copyright 9 1997 by Academic Press All righls of reproduction in any form reserved. ISBN 0-12-077460-7

4.1 Overview of Applications

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niques with the required sensitivity (e.g., reflectance spectrometry, X-ray fluorimetry) have other disadvantages such as excessive cost, extensive sample preparation, long analysis times (no real-time monitoring), and restrictive sample environments (i.e., vacuum) [6,9]. Acoustic wave (AW) devices are ideally suited to thin film characterization due to their extreme sensitivity to thin film properties [10]. The sensitivity of AW devices to a variety of film properties (see Chapter 3), such as mass density, viscoelasticity and conductivity, makes them versatile characterization tools. The ability to rapidly monitor changes in device responses resulting from changes in thin film properties permits their use for monitoring dynamic processes such as film deposition, chemical modification (e.g., photo-polymerization, corrosion), and diffusion of species into and out of films. In this chapter, we explore the current and potential future applications of AW devices for materials characterization and process monitoring. Because of the limited mass of material that can be applied to the AW device surface, the majority of these applications deal with the chemical and physical characterization of thin-film properties. This thin film focus should not be thought of as a limitation of AW devices, but rather as a useful capability - - the direct measurement of properties of materials in thin-film form. Since material properties can depend on the physical form (e.g., film, bulk) of the material (see Section 4.3.1.3), AW devices are uniquely suited to directly characterize thin-film materials. These considerations also indicate that even though it is possible to use AW thin-film data to predict bulk material properties, such extrapolations should be performed with care.

4.1 4.1.1

O v e r v i e w of Applications C H A R A C T E R I Z A T I O N OF T H I N F I L M M A T E R I A L S

The development of AW thin-film characterization techniques has occurred largely because of the interest by various research groups in developing chemical sensors based on coated AW devices (see Chapter 5). Thus, many of the film characterization techniques described here were developed in an effort to characterize sensor coatings or to interpret the observed responses from AW chemical sensors in operation. As described in Chapter 3, mass detection limits for AW devices are typically at or below one ng/cm 2. These low detection limits translate into hundredths of a monolayer of atoms and film thicknesses of hundredths of nanometers. This

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4. Materials Characterization

sensitivity permits quantitative detection of submonolayer mass changes in thin films formed on AW devices. This extreme mass sensitivity can be used to advantage in the characterization of film properties such as film thickness (Section 4.4.1) and surface area and pore size distribution (Section 4.3.1.2). In addition, it is useful for real-time monitoring of processes such as film deposition (Section 4.4.1), materials modification (Sections 4.4.2 and 4.4.5), corrosion (Section 4.4.3), and diffusion (Section 4.2.2). It can also be used to monitor adsorption at surfaces from both gases and liquids (Section 4.3). Using AW devices to monitor dynamic processes such as diffusion and corrosion can dramatically reduce the time required to quantify these processes. For example, as discussed in Section 4.2.2, diffusion equilibration times typically increase with the square of the diffusional length. For a thin film, this length scale, the film thickness (h), is very small. This enables the quantification of diffusion coefficients as low as 10-15 cm2/sec in less than one day, whereas months would be required using many conventional techniques that use thick films or bulk samples. For corrosion monitoring, the dramatic decrease in mass detection limits obtainable using coated AW devices, as compared with conventional balances and sample coupons, allows detectable mass changes to be achieved in minutes or hours rather than days or months (Section 4.4.3). AW device sensitivity to viscoelastic parameters and electrical properties can be used to advantage in some film characterization techniques. In these situations, a comparison of the AW device response to a model of the AW/thin film interaction is often crucial to the effective evaluation of thin film parameters. These additional interaction mechanisms typically involve changes in both the wave velocity and the wave attenuation for SAW, APM and FPW devices, and changes in both resonant frequency and admittance magnitude in TSM devices. In contrast, mass loading does not contribute to wave attenuation or decreases in admittance since moving mass involves no power dissipation (see Chapter 3). Having detectable changes in two sensor responses allows the amount of information that can be extracted regarding film properties to be increased, since agreement between both responses and predictions from the model aids in the discriminating power of the characterization technique. A demonstration of this can be found in the ability to determine viscoelastic parameters based on monitoring both sensor responses during a temperature cycle for a polymer-coated device (Section 4.2.1.2). These responses are also useful in elucidating the changes occurring during such processes as polymer cross-linking (Section 4.4.2), or the absorption of species in polymers (Section 4.2.1.3).

4.1 Overview of Applications 4.1.2

153

CHARACTERIZATION OF FLUID PROPERTIES

Another area of materials characterization involves characterizing the properties of a contacting fluid. Since the fundamentals of acoustic wave/liquid interactions are covered in detail in Chapter 3, this topic will not be repeated here. However, it seems relevant to provide a brief summary of some of the fluid properties that can be measured. Since SAW devices are excessively damped with liquids, these characterization techniques generally involve only APM, FPW, and TSM devices. Once again, the utility of using two sensor responses can be important. Two key properties that can be probed are viscosity (7/) and density (p). As discussed in Sections 3.1.5 (TSM), 3.3.3 (APM), and 3.4.2.4 (FPW), the responses are often proportional to the square root of the product (pr/); data showing trends vs (pr/) 1/2 have been reported using TSM (see Figure 3.10) [11-15], APM (see Figure 3.35) [16], FPW (see Figure 3.48) [17-19], and Love wave devices [20]. In some cases, one property is held constant to probe the other, for example probing viscosity at constant density [18,21 ]. In many cases, simple trends are shown such as the maximum in viscosity at intermediate concentrations of water/ethanol mixtures [15,22,23], or increasing response with increasing sugar content [22]. It has been observed with TSM devices that rough surface features result in liquid trapping and a term proportional to/9 and an ability to separate out p and 7) (see Section 3.1.6 and Figure 3.11) [24,25]. Similarly, since FPW devices have a velocity dependence proportional to density (see Section 3.4.2.2) and velocity and loss terms proportional to (pr/) 1/2 (see Section 3.4.2.4), it may be possible to use FPW device responses to characterize both p and r/simultaneously. Wave velocity in a fluid, which is a strong function of density, has been probed using longitudinal-mode resonators for analyzing gases (e.g., pressure or changes in composition) [26-28]. SAW devices have also been used with thin liquid layers and a reflector plate for probing liquid properties (e.g., changes in density due to changes in salt concentration) [29,30]. Both of these devices rely on probing the reflected compressional wave, and depend on the separation of the AW device and the reflector. Acoustoelectric interactions enable solution electrical properties to be probed with AW devices. It should be noted that these acoustoelectric interactions can be "shorted out" using a conductive (e.g., metal) layer between the substrate and the solution for APM and FPW devices. Similarly, for TSM devices, if the grounded electrode is placed in contact with the solution, no acoustoelectric effect should be present. The key parameter that has been monitored is solution conductivity. For example, measurements of AW responses vs conductivity have been reported using TSMs [ 11,15,31,32] and APMs (see Figure 3.36) [ 16,33-35].

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The APM interaction is described in Section 3.3.4 while the TSM interaction is probably due to parasitic conduction through the solution. In one APM study, porous thin films were found to have an effect on conductivity trends, proposed in the study to be due to changes in solution conductivity in the porous regions [35]. Another explanation could be changes in the dielectric constant in the region of the film, since the dielectric constant has an effect on conductivity responses for APM devices (see Section 3.3.4) [16,34]. In another study, a TSM was used with a conductivity electrode to make a sensitive probe of conductivity that had little dependence on solution viscosity and density [36]. In addition, the parasitic contribution to the static capacitance in TSM devices has been correlated with solution dielectric constant [11,12]. Some sensors for extrinsic properties have also been demonstrated. For example, sensors for mass-flow rate using SAW [37,38] and APM [38] devices combined with either on-chip resistors [38] or acoustic absorbers [37] for device heating have been demonstrated. These devices use the temperature sensitivity of the devices to probe temperature changes induced by convective cooling by the flowing gas. Another investigation showed that the magnitude and direction (relative to the wave velocity) of an imposed shear stress could be monitored with a SAW device. This was proposed to be useful in developing a sensor for local and global turbulence [39]. Finally, a capacitance-dependent TSM sensor system has been demonstrated for measuring liquid volumes in the 0-1 ml range [40]. The demonstrations cited above illustrate how AW devices can be used to probe intrinsic and extrinsic fluid properties. This capability can be useful for providing in-situ probes of critical solution properties such as viscosity, density, and conductivity. This capability should prove useful in the monitoring of process streams or critical fluids (e.g., automotive oil condition monitoring [41 ]).

4.2

Characterization of P o l y m e r s

A polymer can be defined as a compound consisting of a large number of repeating units, called monomers. These monomers are joined together by covalent bonds to form a long chain. The degree of polymerization is defined as the number of repeating units in the chain. The properties of the polymer depend on the overall size of the polymer chain (i.e., average molecular weight) and on the inter- and intra-molecular forces that hold the polymer together [42--44]. The intramolecular forces consist of the covalent bonds that join the repeat units into chains, and any covalent bonds that may join adjacent chains together (crosslinkages). In addition, the polymer chains are held together by a variety of in-

4.2 Characterization of Polymers

155

termolecular forces, including hydrogen bonding, dipole-dipole interactions, and London dispersion forces resulting from the synchronization of electron motion in the interacting atoms (see Chapter 5 for a discussion of chemical interactions). The physical and chemical properties of the polymer depend on the types and relative strengths of these inter- and intra-molecular interactions. The sheer volume of polymeric material produced has increased dramatically in the last decade and, insofar as the chemical and physical properties of these materials can be modified, the number of applications for polymers has expanded [ 1,2,5]. In general, the polymer properties of interest can be categorized as diffusion/permeation properties or as mechanical (e.g., viscoelastic) properties. The measurement of diffusion/permeation properties is straightforward when diffusion of a species into a polymer film produces a simple mass-loading effect. Experimental determination of these properties using AW devices will be discussed in Section 4.2.2. In addition to the mass-loading effect, the presence of dispersed molecules in a polymer has a plasticizing effect, inducing changes in viscoelastic properties, as described in Section 4.2.1.3. Measurement of these viscoelastic properties is more complex. There are a number of texts that provide an excellent discussion of the viscoelastic behavior of polymers, including theoretical models to explain such behavior [42-44]. While an in-depth discussion of these models and their ramifications is beyond the scope of this work, a brief summary of viscoelastic behavior is supplied below.

4.2.1

VISCOELASTIC PROPERTIES

The viscoelastic properties of a polymer can be described in terms of how the polymer deforms in response to an applied stress. Elasticity refers to the ability of a material to return to its original shape after it has been stressed. Elastic behavior implies a linear relationship between stress, T, and strain, S, (T oc S). Viscosity is a measure of the flow resistance of the polymer or polymer solution. Viscous behavior implies a linear relationship between shear stress and the rate of strain (T oc OS/Ot). Rigid materials tend to display elastic behavior, whereas fluid or soft materials display viscous behavior. In many polymers, a combination of elastic and viscous responses arises as a direct consequence of the chain structure, hence the term "viscoelastic" properties. The concepts of stress, strain and displacement have already been introduced in Chapter 2 in describing the propagation of acoustic waves in an elastic medium, and in Chapter 3 in describing the various sensing mechanisms. The two deformation modes of interest are elongation and shear deformation. Elongation refers to the change in length

156


(in a given direction) of a polymer sample upon application of a longitudinal unit stress (i.e., stretching or compressing). Shear deformation refers to the deformation behavior of the sample under the application of a lateral force on one surface. How a polymer behaves under the force of an applied stress depends on a number of variables, including temperature, pressure, and the time frame (i.e., frequency) and nature (i.e., shear vs elongation) of the stress. As described in more detail in Section 3.1.8, the viscoelasticity of a polymer can be described by a complex modulus. The modulus is defined as the stress associated with a unit strain, and has units of force/unit area (dynes/cm2). It can be thought of as the stiffness or rigidity of the polymer, and is related to the inter- and intra-molecular forces at work within the polymer. In general, polymer film/acoustic wave interactions are dominated by the shear component of displacement (see Chapter 3). Thus, it is the shear modulus which can be effectively probed with AW devices. This shear modulus can be represented by G = G' + jG" where G', the storage modulus, is associated with energy storage and release during the periodic deformation associated with the oscillating stress, and G", the loss modulus, is associated with the dissipation of energy, usually as heat. The modulus depends on the molecular structure of the polymer, the average molecular weight, the temperature, and, in general, the rate (frequency) of applied shear stress. The interchangeability between temperature and strain rate in determining the modulus was first described by Williams, Landel and Ferry [45] and became the basis of the so-called "time-temperature superposition principle." This dependence can be explained in terms of the molecular motions in the polymer chain by examining the mechanism by which a polymer reacts to an applied stress. When the polymer is deformed on a time scale, Ts, that does not allow significant thermal motion of polymer chains with respect to each other (i.e., rotational freedom of the polymer chains is limited), the polymer behaves as a rigid or "glassy" material. The glassy state is characterized by large shear moduli, on the order of 101~dynes/cm 2. As temperature increases, thermal energy in the system becomes sufficient to overcome the molecular forces, permitting free rotation around the bonds of the polymer chain. This additional rotational freedom is manifested as a softening or "relaxation" of the polymer, and the polymer is described as an "elastomer." Modulus values of elastomers are on the order of 107 dynes/cm 2. The temperature at which the transition from the glassy to the elastomeric state occurs is called the glass transition temperature Tg. Another way to look at this is to consider that the polymer exhibits a characteristic relaxation time, ~'. If the stress is applied for a time period Ts that is much


157

shorter than the relaxation time (Ts < < ~'), polymer chains do not have time to move with respect to each other and the polymer behaves as an elastic solid characterized by a stiffness/x. As temperature increases, z decreases until Ts > > ~', at which point thermal motion allows (uncrosslinked) chains to move with respect to each other and the polymer behaves as a viscous liquid characterized by a viscosity r/. Tg can be defined as the temperature where Ts ~ I", at which point the polymer deforms both elastically and viscously, giving rise to viscoelastic behavior. It should be noted that Tg for an amorphous, glassy polymer is not the same as the melting temperature Tm for a semi-crystalline polymer. Both glassy and semi-crystalline materials are characterized by high modulus values, yet the two transition temperatures are associated with distinctly different phenomena. The former (Tg) is a relaxation, or second-order transition, and exhibits the time (frequency) dependence discussed above. In addition, this Tg transition generally occurs over a significant temperature range (i.e., is not abrupt) due to heterogeneities in the polymer and the fact that chain motion is an activated process. The latter (Tin) arises because of a chemical phase change, or first-order transition, and is independent of frequency. Melting transitions typically occur only in polymers having chains sufficiently linear to allow "packing" in a regular crystalline-like manner. Just like other melting transitions (e.g., ice to water), the temperature at which the transition occurs can depend on whether the temperature is being raised or lowered to induce the transition. This is due to the fact that nucleation of the crystalline phase during cooling does not occur until a lower temperature (i.e., supercooling) as a result of the high curvature of a newly nucleated phase [46]. In polymers, these melting transitions may not always occur at a single temperature. Instead, the presence of different molecular chain structures can result in multiple transitions, often denoted by Greek letters [45]. Even though these transitions are different in many ways, as demonstrated below, the way in which acoustic energy interacts with polymeric materials permits us to use AW devices to probe changes in polymer film viscoelastic properties associated with these transitions. It should be emphasized up front, however, that evaluating the viscoelastic properties (e.g., modulus values) requires an ability to effectively model the film displacement profiles in the viscoelastic layer. As described in Section 3.1.8, the film displacement effects are dictated by the phase shift, ~b, across the film. Since ~b depends on film thickness, perturbations in acoustic wave properties due to changes in viscoelastic properties (e.g., during polymer transitions) do not typically depend simply on the intrinsic polymer properties. This can lead to erroneous predictions if the film

158


dynamics are not taken into account. However, if these dynamics are effectively modeled, the AW device response can be used to quantitatively evaluate the shear modulus values (see Section 4.2.1.2).

4.2.1.1

Determination of Transition Temperatures

The attenuation and velocity of acoustic energy in polymers are very different from those in other materials due to their unique viscoelastic properties. The use of ultrasonic techniques, such as acoustic spectroscopy, for the characterization of polymers has been demonstrated [47,48]. For AW devices, the propagation of an acoustic wave in a substrate causes an oscillating displacement of particles on the substrate surface. For a medium in intimate contact with the substrate, the horizontal component of this motion produces a shearing force. In such cases, there can be sufficient interaction between the acoustic wave and the adjacent medium to perturb the properties of the wave. For polymeric materials, attenuation and velocity of the acoustic wave will be affected by changes in the viscoelastic behavior of the polymer. Because of the oscillatory nature of the acoustic wave, probing of polymer viscoelastic properties using AW devices is analogous to the high rate/short time scale probing of polymers mentioned previously. The wave period, which is the inverse of the AW frequency, determines the time scale of the applied strain. Wave attenuation and velocity, or resonant amplitude and frequency, can be monitored at a relatively fixed frequency (rate) while scanning the temperature. The use of SAW devices to identify Ts and Tm for a variety of polymers has been reported. Both attenuation (output amplitude) [49,50] and velocity (frequency) [51,52] changes have been monitored. In two of these studies, relatively thick sample films were tested [50,51 ], and the results were consistent with Ts and Tm values from other experimental methods, such as differential scanning calorimetry (DSC). (It should be noted that the slow processes (large Ts) used in techniques such as DSC result in these techniques probing the static or low-frequency Tg values.) An example of this type of trend is shown in Figure 4.1 for a film being pressed onto the surface of a SAW device using a clamping system. No increase in T8 was observed, indicating that the measured attenuation/velocity changes were the result of changes in the AW/polymer coupling due to increased adhesion of the polymer to the AW device surface. This transition from a poorly coupled film, which has a correspondingly low perturbation in wave amplitude, to a film coupled to the acoustic wave, resulting in significant atten-


159

1.0

>

O O

E

V

uJ Q

0.8

l" ..J 11. ram=

'< ,.J

0.6

O

.< Z

0 m

U)

0.4

::) n_ I::)

0

Tg=75* 0.2

O 0.0

!~_ 30

I 60

C~o6itie~J 90

, I ...... 120

130

TEMPERATURE (oc) Figure 4.1 Glass transition detection using a polyethylene terephthalate film clamped o n t o the surface of a SAW device. (Reprinted with permission. See Ref. [50]. Copyright 9 1979 American Chemical Society.)

uation of the wave, occured when the polymer became softer as the temperature is raised above the static (low-frequency) Tg. Another technique for evaluating the static Tg uses an indirect approach that probes relatively slow processes. King [53] described how changes in diffusion rates (as indicated by the time to sorb 90% of the final sorption value) and solubility values could be used to probe the change from a glassy (slow diffusion) to a rubbery (diffusion several orders of magnitude faster) state. Using polystyrene on TSM devices, King showed that Tg values in agreement with those

160


obtained by other techniques could be determined, as well as showing that the transition occurred over a temperature range of about 20~ (interpreted as being due to the sample having a distribution of molecular weights). TSM-determined partition and diffusion coefficients vs temperature have also been used to probe transition temperatures in synthetic lipid multibilayer films [54]. Other studies have demonstrated the utility of FPW devices to identify both the static and dynamic Ts of polymer films simultaneously [55-57]. As shown in Figure 4.2, the static (low-frequency) Tg Was observed as a change in the slope of the acoustic velocity vs temperature curve; the change in slope was interpreted as a change in the rate of polymer expansion at the polymer static (low-frequency) Tg. The dynamic (or frequency-dependent) Ts was identified as a minimum in a plot of the acoustic wave amplitude vs temperature (indicative of a maximum in the loss modulus G"). These basic trends are consistent with results using bulk transducers to generate longitudinal waves at 2.5 MHz in polymer disks combined with a technique for measuring the thickness of the polymer disk with temperature [47]. For the one polymer (poly(vinylacetate)) where both the static and dynamic transitions were observed, the static transition was found to be about

4780

%

4760 A

N "I"

>.

4740

tO Z uJ =)

o

uJ

4720

u..

4700

4680

........ 0

1 10

I 20

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..

TEMPERATURE

I 40

.....

I .. 50

I 60

.

.

.

.

.

.

(~

Figure 4.2 Frequency vs temperature for a poly(t-butyl acrylate)-coated FPW device

showing a slope change at the static (low-frequency) Ts. 9 1992 American Chemical Society.)

(Reprinted with permission. See Ref. [56].


161

60~ lower than the dynamic transition probed by the 5 MHz FPW device. Previous SAW studies have also reported detecting the dynamic Tg using thin films sprayed or cast on the SAW device surface. The observed Tg values (indicated by trends in the frequency response) were reported to be increased by ~50~ compared to DSC or other low-frequency techniques [50,52]. These results, indicating Tg values at AW frequencies significantly higher than the static Tg values, are consistent with the time-temperature superposition principle. To enable probing of the frequency dependence, one SAW study used a multi-frequency SAW device (i.e., a single ST-quartz substrate bearing five different SAW delay lines) to probe the temperature-dependent behavior of polymer films [58]. Multifrequency probing of viscoelastic properties has also been performed using TSM devices probed over many harmonics using a network analyzer [59,60]. The minimum amplitude (maximum attenuation) reported in the FPW study has also been observed during temperature ramps of polymer-coated SAW devices [61--65]. Examples of data for both velocity and attenuation are shown in Figure 4.3. In this study, it was determined that the observed trends were due to film resonance conditions (see Sections 3.1.8 and 3.2.7). This was strongly indicated by the fact that the temperature of the maximum attenuation decreased with increasing film thickness h; in fact, a more-than-60~ in the temperature of the maximum attenuation is demonstrated for only a three-fold increase in film thickness (0.44 to 1.37/zm). These results highlight the importance of considering film dynamics when investigating viscoelastic properties and transitions using AW devices [61,63,64]. Regarding the FPW work described above, it is important to consider whether this amplitude minimum is due to film resonance or if the films were thin enough (h about 0.5 to 1 /zm) that the phase shift ~b is much less than Ir/2 at the frequency of the FPW device (5 MHz). This latter condition would indicate that the observed amplitude minimum would represent the maximum in G" that occurs at the glass transition. FPW devices have the advantage for this application of high sensitivity at lower frequencies (smaller th values and an ability to stay in the acoustically thin realm). Thus, it appears that the film was acoustically thin for these FPW tests and that the responses are tracking changes in the film properties (i.e., h, G', and G"). This same question regarding film resonance is even more relevant for the earlier higher frequency SAW work [50,52], since film resonance results in frequency trends similar to those reported as being due to the glass transition. If film resonance effects are occurring in these studies, the reported Tg values would still be close to the actual Tg since it is the dramatic change in modulus values during the glass transition that would result in significant changes in the phase shift and the onset of film resonance. However, the

162

4. Materials Characterization 3.5

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Temperature (C) Figure 4.3 Attenuationand frequency vs temperature for 97-MHz SAW devices with various film thickness of polysobutylene (PIB). The maximum in attenuation and the sigmoidal frequency excursion are due to the onset of film resonance as the polymer softens with temperature. The temperature at which these AW trends occur depends on the thickness of the coating (thicker coatings yield lower temperatures). (Reprintedwith permission. See Ref. [61]. 9 1994 American Chemical Society.)


163

specific Tg value, and the interpretation that the AW trends are directly indicating changes in G' and G", would not be accurate if film resonance is causing the observed trends. This is clearly shown by the results in Figure 4.3.

4.2.1.2

Extraction of Storage and Loss Moduli

In this section we will describe how a proper accounting for film dynamics, based on a model of the thin-film/acoustic-wave interactions, can be used to quantitatively evaluate the shear modulus values as a function of temperature. As described in Section 3.1, an equivalent-circuit model can be used to relate the measured TSM electrical characteristics to the elastic properties, density, and thickness of a polymer film coating the device. Consequently, measurements made with polymer-coated TSM devices can be used to extract the shear elastic properties of the film. In order to separate properties of the film from those of the crystal, admittance-vs-frequency (Y-vs-f) measurements are made on the TSM resonator before and after deposition of a film. Fitting the equivalent-circuit model to measurements made on the uncoated device is crucial, allowing extraction of all of the circuit elements except Ze ~ the impedance element arising from the film (Figure 3.7). Once the uncoated resonator has been characterized, the impedance element Ze arising from a film coating. If measurements at only a single harmonic are used, film thickness and density must be known to extract G' and G". Admittance-vs-frequency measurements made at several temperatures on a polyisobutylene-coated TSM resonator were fit to the equivalent-circuit model of Sections 3.1.3 and 3.1.9 to determine values of G' and G" for the film [66]. These extracted values are shown in Figure 4.4, along with 5-MHz values obtained from the literature for polyisobutylene having an average molecular weight of 1.56 • 106 [44]. We note excellent agreement between the extracted and literature values of G' from - 2 0 ~ to 60~ and in G" from - 2 0 ~ to 10~ Above 10~ the extracted G" values are approximately 30% higher than the literature values. These results illustrate how AW devices can be used to quantitatively evaluate the viscoelastic properties of polymer films. Similar models for other AW devices, such as the model for SAW devices coated with viscoelastic layers (Section 3.2.7 and [61 ]), can enable these other devices also to be used to determine modulus values. However, the pure shear motion of the TSM does simplify the model, and the evaluation of the modulus values as compared with the more complex displacements of other AW devices such as the SAW device (a comparison of the models of Section 3.1.9 for the TSM and Section 3.2.7 for the SAW demonstrates this point).

164


10.0 04

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9.5

c

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"0 =

t3

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01 0

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--

8.5

-

'~

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-- ~ --

G

kk

t!

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0

20

40

60

80

Temperature (~ Figure 4.4 Components of the shear elastic modulus extracted from admittance vs frequency measurements using a 15.6 /xm-thick polyisobutylene-coated TSM resonator. Lines are literature values for the polyisobutylene modulus [44] at 5 MHz. (Reprinted with permission. See Ref. [66] @ 1991 IEEE.)

4.2.1.3

Absorption P h e n o m e n a and Plasticization

Absorption of a solute liquid or vapor into a polymer film can profoundly affect the viscoelastic behavior of the polymer. The magnitude of this effect depends on the nature of the solute/polymer interactions and on the amount of solute absorbed. The solute/polymer interactions can range from simple dispersion to hydrogen-bonding and other specific interactions. The extent of absorption can be described by the partition coefficient, K, which quantifies the thermodynamic distribution of the solute between two phases (K = concentration in polymer divided by the concentration in the liquid or vapor phase in contact with the polymer). It has long been known that acoustic wave devices can be used to probe solubility and partition coefficients [53,67]. Due to the relevance of these topics to chemical sensors, more comprehensive discussions of these interaction mechanisms and the significance of the partition coefficient are included in Chapter 5. The major effects of solute absorption by a polymer are swelling (change in


165

volume) and plasticization. Both effects are a direct consequence of the solute/polymer interactions. As a solute absorbs into the polymer, it interrupts the intermolecular forces at work between the individual polymer chains, and the polymer swells. For polymers in which these forces are strong, due to a high degree of cross-linking or crystallinity, the swelling will be minimal. Lightly crosslinked or linear polymers can experience significant swelling. A theoretical analysis of the effect of compressive tensions resulting from this swelling is presented by Bartley and Dominguez [68]. The effect of vapor uptake on adhesion of polyimide films, possibly due in part to swelling effects, has been described [69,70]. Grate and coworkers [57,71 ] first proposed and documented, using predicted uptakes from gas chromatograph (GC) retention volumes, how these swelling effects can enhance the sensitivity of SAW chemical sensors over the predicted mass-loading values. This increased sensitivity has been confirmed by separate researchers [72]. Concurrent with the swelling phenomenon, the polymer may undergo significant changes in its viscoelastic properties. The presence of absorbed solute molecules in the regions between the polymer chains can act as a lubricant. Due to the interruption of the polymer intermolecular forces, the individual chains may move more freely and the polymer softens. The net results are a decrease in the Tg of the polymer that is dependent on the concentration of absorbed solute [73,74], and a broadening of the elastomeric region. This effect is called plasticization and has been observed using AW devices [51,61-65]. Mass changes associated with solute absorption will produce a change in the AW velocity without significant attenuation of the wave. Modulus changes associated with the glass transition will produce both velocity and attenuation changes. Examples of experimental results for solvent plasticization are shown in Figure 4.5. This plot is a parametric representation of data similar to that shown in Figure 4.3 for a temperature ramp, except the parameter being changed to move along a given curve is the concentration of the absorbing species in the vapor phase contacting the device [ 10,62,75]. As expected, significant velocity and attenuation changes are observed. In addition, the trends with different chemical species can be used to understand the plasticizing action. Since attenuation does not depend on the mass loading, a position on the curve at a given attenuation (e.g., the point of maximum attenuation) can be used as an indicator of the viscoelastic transition. If the velocity shift at the point of peak attenuation is plotted against the liquid density of the absorbing species, a linear relationship is observed [62]. Extrapolating the line to a density of zero should give the value of velocity shift due to changes in the viscoelastic properties. This is verified by the agreement of this extrapolated velocity shift with the value obtained in an ex-

166


1.5 PENTANE

1.0

: iN

0.5

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I

m

0.0

1.5 V VV

METHYLENE CHLORIDE

1.0 A

0.5

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0 >r

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0.0

1.5 1.0

0.5 TRIC HL OROETHYLEN E

0.0

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A V/Vo

0.0

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( x 10 "3)

Figure 4.5 Normalized attenuation-vs-velocity changes for a polymer-coated SAW device as vapor partial pressures are varied from 0% (at dashed line) to 80% of saturation. The polymer, Kraton D1102, is an ABA triblock copolymer, where A is polystyrene (approximately 28% by weight) and B is polybutadiene. (Reprinted with permission. See Ref. [62].)


167

periment where temperature changes were used to induce the viscoelastic transition. These trends are observed even though the maximum attenuations are not due directly to a maximum in the loss modulus (as stated in the original article [62]), but rather to film resonance effects that depend on the changes in the polymer modulus. The correlation with density is consistent with the plasticizing action depending only on the volume of chemical absorbed. This type of plasticizing action would be expected if no specific chemical interactions occurred between the absorbing species and the polymer. In contrast, results with a polyimide film and water, methanol, and ethanol vapors yielded trends which depended on the molecular weight of the absorbing species [76]. These trends indicate that the plasticizing action depends on the number absorbed, possibly indicating that the plasticizing is mainly due to the single hydroxyl group found for each species. Again, extrapolation to a molecular weight of zero can be used to extract the responses due to changes in the polymer properties. These results show that changes in viscoelastic properties with chemical uptake can result in significant AW responses, making these property changes important in developing and optimizing chemical sensors using polymer films (see Chapter 5) [57,61-64,71,72,76-79]. For example, the unique curves generated in a plot of attenuation vs velocity for different chemical species (see Figure 4.5) can be used to discriminate between chemical species, increasing the information provided by an AW chemical sensor [63,64,76,80,81]. These results, combined with those comparing SAW responses to predicted uptakes based on GC retention volumes, also indicate that the common practice of converting frequency shifts to amount absorbed assuming that the response is only due to mass loading can lead to erroneous results when working with viscoelastic polymers. Finally, they show that dual-response (attenuation and velocity) AW devices are particularly well suited for probing viscoelastic property changes. 4.2.2

4.2.2.1

DIFFUSION AND P E R M E A T I O N

Real-Time Monitoring

The wide variability of absorption and diffusional properties of chemical species in organic polymer films makes them useful as selective or complete permeation barriers (e.g., gas separation membranes and passivating layers [1,5,82]) and selective chemical sensor coatings [83]. For these applications, a method for rapidly and directly evaluating the solubility and diffusional properties in thin films is useful. Diffusional properties can be evaluated by monitoring the transient up-

168


take of a chemical species as it diffuses into a polymer sample. AW devices have sufficient sensitivity to monitor this transient uptake in real time in thin polymer films [84-86]. The use of AW-determined diffusion rates vs temperature for probing polymer transition temperatures is discussed in Section 4.2.1.1. A schematic of the device used in this AW technique is shown in Figure 4.6. A thin film of constant thickness h is formed on the impermeable substrate of the AW device. The film, initially in equilibrium with a partial pressure Pl of a gas-phase species, experiences an absorption transient as species diffuse into the film following an increase in the partial pressure to P2. Experimentally, this change in concentration is typically achieved using a gas test system with valves that can be activated to switch from one stream at Pl (typically Pl = 0) to another stream at P2. This absorption transient results in a transient AW frequency response that can be used to characterize the diffusional properties.

4.2.2.2

Fickian Diffusion

Even though diffusion in polymers is generally a complex process, it is possible to find systems that exhibit relatively simple Fickian diffusional behavior. For example, concentration-independent Fickian diffusion has been observed in many polymers when the temperature is far below the polymer's glass transition tem-

Figure 4.6 Schematic representation of a thin polymer film formed on an impermeable AW device substrate. The SAW device probes the concentration profile C(x,t) integrated over the film thickness. (Reprinted with permission. See Ref. [86].)

4.2 C h a r a c t e r i z a t i o n of P o l y m e r s

169

perature and/or diffusant activity is low [87,88]. In these situations, the concentration profile in the film can be determined from Fick's Second Law for a onedimensional system. For a constant diffusion coefficient D, the relevant equation is [89,90]

OC 02C = D~ Ot Ox2 '

(4.1)

where C(x,t) is the concentration of the absorbing species in the polymer, x is the distance from the polymer/substrate interface, and t is time measured from the onset of the change in the partial pressure of the absorbing species. The relevant boundary and initial conditions for this system are: (1) OC/Ox = 0 at x = 0 and all t, (2) C(h,t) = Co(P2) for t -> 0, and (3) C(x,t) = C0(Pl) for t < 0 and 0 -< x -< h, where Co(p) is the concentration in the polymer in equilibrium with a partial pressure p of the absorbing species. Equation 4.1 can be solved under these conditions to yield the following analytical expression [89]" oo

C(x,t) - Co(P2)

--

2AC0 ~

sin(~x/h)e-q'2~

,

(4.2)

n=l

where ~ = "rr(n- 1/2) and ACo = Co(P2)- Co(p1). Equation 4.2 can be integrated over the film thickness to give the following expression for the total moles, M(t), absorbed as a function of time:

M(t) = Mm~ 1 - 2 ~ e-~O~/h2 n=l 1~2 '

(4.3)

where Mmax is the incremental amount of species absorbed in the film after equilibrium is attained (Mmax - hAACo, where A is the area of the film). Equation 4.3 predicts an accumulation of species proportional to N/t until M(t) is approximately 60% of saturation (Mmax); thereafter, the inability of species m penetrate the substratr decreases the net flux into the film. A common technique for evaluating D is to use a gravimetric method to monitor M(t) [87,90] and then extract D and C0(p) by fitting the data to an equation similar to Equation 4.3 (the exact form of this relationship depends on sample geometry). Since equilibration times for Fickian diffusion are proportional to h2/D, the ability to monitor absorption transients in thin films (small h values) directly using AW devices enables a dramatic decrease in the equilibration time as compared to the use of bulk samples with conventional gravimetric techniques. In addition, since diffusional properties of thin films may differ significantly from bulk samples prepared from the same material [91 ], direct evaluation of thin-film properties can be advantageous.

170


Fickian diffusion was observed using a polyimide-coated SAW device for a wide variety of chemical species [86]. SAW frequency transients obtained for N20 and methanol are shown in Figure 4.7 (pages 172-173); p increased from zero to the indicated values. The expected behavior is observed: an increase in the response upon increasing p that saturates at a new level, indicating that the film has approached equilibrium with the new gas-phase concentration. The expected linear region of the data when plotted vs X/t is observed. These SAW frequency transients were used to determine diffusion coefficients using an alternative "frequency version" of Equation 4.3 where M(t) is replaced with Af(t)/fo and Mmax is replaced by Afmax/fo. The curve through the points represents a nonlinear least-squares fit of the data to this equation. The variable parameters in this fitting routine were: (1) D, (2) Afmax, and (3) to, the starting time for the change in partial pressure. The value of to was allowed to vary in order to account for the time lag between switching the valves and the arrival of the flow to the device. Excellent fits to the data were obtained with an rms error in both cases of less than 1% of Afmax. The D values obtained were 2.3 • 10-ll cm2/sec for methanol and 8.0 • 10-lo cm2/sec for N20. It should be noted that studies with this film at various methanol concentrations indicated that the diffusion coefficient is not constant, but rather increases with increasing concentration [86]. The use of Equation 4.3 is still justified, however, since the concentration steps shown in Figure 4.7 are small enough that the diffusion coefficient does not change significantly. This concentration dependence can be important for chemical sensors, since it requires challenging the sensor at the low concentrations expected in practice in order to evaluate the speed of the sensor response (see Section 5.3.6). Fickian diffusional behavior in polyimide has also been observed by Denton et al. [82] using a capacitive technique and, for the desorption branch only, by Bartley and Dominguez [68] using a SAW device. The absorption transient in the Bartley and Dominguez study exhibited a non-Fickian linearity with time. As described in detail below, non-Fickian behavior was also observed by Brace et al. [92] in their SAW study. This disagreement is not surprising considering that the various polyimide films differ significantly because of the use of different starting solutions and thermal treatments. These differences in the polymer films also show up in differences in the sign of the frequency response. The polyimide used to generate the data in Figure 4.7 exhibits a positive frequency response when challenged with relatively low concentrations ( P/Po < 0.1, where P0 is the saturation vapor pressure) of the various species tested. The other two SAW studies, however, report negative frequency responses to the vapor challenges. The positive response shown in Figure 4.7


171

must be due to a combination of a negative mass response and an additional positive response that is large enough to overwhelm the mass-induced response. This additional response is probably due to viscoelastic property changes caused by the plasticizing action of the absorbing species (see Section 4.2.1.3). These viscoelastic effects probably occurred in the other studies but to a smaller extent compared to the mass-loading effect. As described in Section 4.2.1.3, this makes the evaluation of concentrations in the films based on the frequency response questionable for all of these studies. When mass loading is not the dominant sensing mechanism, sensor response may not be linear with concentration in the film. This departure from linearity has been observed with polymer films [61,64,86]. An investigation into the possible effect of this nonlinearity on the evaluation of D values from SAW frequency transients indicated that errors in D values (factor of two error) could be obtained if the nonlinearity of the response is large [86]. However, using small steps in partial pressure, this nonlinearity in the response can be minimized, allowing the effective evaluation of diffusion coefficients based on AW frequency transients. It has been noted by other researchers that the molecular size of the absorbate has a dramatic effect on the diffusion coefficient [93,94]. An exponential relationship is observed between D and the size (represented by the b parameter in the van der Waals equation of state) of the absorbate [94,95]. As shown in Figure 4.8 (page 174), an exponential dependence on the molar volume of the absorbing species was observed with an almost four-order-of-magnitude decrease in D for only a 2.3-times increase in molar volume. The potential for using this variability in D values to advantage in the development of chemical sensors has been discussed [86,96,97]. The basic concept is to use the evaluation of D to determine the chemical species that is providing the sensor response and the magnitude of the response (e.g., Afmax) to evaluate concentration. The results presented above illustrate the utility of using AW frequency transients to evaluate diffusional processes in thin polymer films. The ability to use thin films allows the rapid evaluation of D values from 10 -9 to 10 -15 cm2/sec [86]. The upper limit on D is set by the requirement for multiple data points during the transient response, while the lower limit results from the long times required to approach equilibrium. Thus, thinner films (hundreds of nanometers) are better for probing slower diffusion, while thicker film (micrometers) are better for faster diffusion. An electronics scheme capable of rapid data acquisition [98] would enable larger D values to be quantified based on following the rapid transients. Another way to probe faster diffusion times is to use very thick films. As men-

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v~" (seconds) 1 / 2 Figure 4.7 Frequency shift as a function of V~ during diffusion of (a) methanol, and (b) N20 into a 1.8-pm polyimide film. The lines through the points are fits of Equation 4.3 to the data, giving D values of 2.3 • 10-11 and 8.0 • 10- lo cm2/sec for methanol

and N20, respectively.

(Reprinted with permission. See Ref. [86].)

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tioned in Chapter 3, FPW devices can operate when coated with a thick gel having a solids concentration belc, w about 5%. The device behaves as if it were simply in contact with the liquid solvent for the gel, and no significant change in FPW device velocity or attenuation occurs as the gel sets because dilute gels have very low shear moduli [99]. The semi-logarithmic plot of Figure 4.9 illustrates the use of the FPW device to follow diffusion in a gel. Here, a 500-/xmthick, 2% wt./vol, agar gel was made on a FPW device, with deionized water as solvent. After the gel had set, it was exposed to a 0.1 M NaCI solution; the ions diffused into the gel and finally reached the mass-sensitive region within the evanescent decay length of the membrane, a distance of 16/zm in this case. From the observed mass loading, one can determine the diffusion constant of ions in the gel to be 9.8 • 10 - 6 cm2/s, two orders of magnitude higher than could be probed with thinner films on SAW devices [99]. A similar test was made with whole human blood; in this case, the gel acted as a filter that allowed only the smallest molecules to diffuse toward the membrane and be detected, while holding back blood cells and other large molecules.

4.2 Characterization of Polymers 10000 -

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500

600

TIME (seconds) Figure 4.9 Response of 5.6-MHz FPW device coated with 500-/zm-thick agar gel upon immersion in 0.1 M NaCI, showing gravimetric detection of ions that diffuse to within an evanescent decay length of the sensor membrane. (Data provided by Amy Wang and Ben Costello, U.C. Berkeley and Berkeley Microlnstruments, Inc., respectively.)

4.2.2.3

Non-Fickian Diffusion

The Fickian diffusion described above is relatively easy to analyze, and demonstrates the capabilities of AW devices for monitoring transient uptakes. However, Fickian diffusion in polymers is the exception rather than the rule. A wide variety of transient responses have been observed, often due to the long time constants required for relaxation of the polymer chains upon absorption of species into the film [93,95]. A detailed discussion of these trends is beyond the scope of this book, and the reader is referred to the polymer literature for these details [93,95]. Brace et al. [92] investigated polymer/water interactions using SAW devices coated with either polyimide or cellulose acetate butyrate (CAB). In this study thermodynamic parameters were evaluated from the absorption isotherms, and transient responses to step changes in concentration were monitored. The transient responses observed were not consistent with Fickian diffusion, but could be described using a generalized relaxation equation containing two additive terms. Results under various conditions indicated that relaxation in the polymer system is much slower than diffusion of water.

176


Laatikainen and Lindstr/Sm [ 100] used TSM devices to investigate absorption in cellulose acetate and poly-(hexamethylene adipamide). In addition to measuring absorption isotherms and partition coefficients, they reported on transient responses to changes in methanol concentration for a cellulose-acetate-coated TSM device (Figure 4.10). At low concentrations, the linear response with X/t is consistent with Fickian behavior, and diffusion coefficients can be evaluated (D = 4.8 X 10 -l~ and 1.6 x 10 -9 cm2/sec for steps 1 and 2, respectively). It is seen that the initial diffusion rate increases with concentration in the polymer (based on the initial slope of the curves), until, at higher concentrations, a two-stage absorption transient occurs. This behavior, which is typical of glassy polymers, is due to the fact that diffusion begins to become faster than the polymer relaxations [95]. Recent work investigating gas sensor applications using TSM devices coated with the conductive polymer poly(pyrrole) revealed in some interesting diffusional properties. In one study on absorption of various alcohols [ 101 ], methanol was found to show Fickian behavior (D = 2.2 • 10 -12 cm2/s), while larger alcohols were found to have slower diffusion rates (D = 1.3 • 10 -12, 6.4 X 10 -13, and 2.4 • 10 -13 cm2/s for ethanol, n-propanol, and n-butanol, respectively) and trends indicative of non-Fickian diffusion. In another study that used a TSM device combined with measurements of film conductivity [102], the trends were consistent with Fickian diffusion except for the TSM frequency response, which demonstrated non-Fickian trends for methanol. These observations were interpreted as indicating that the conductivity changes to methanol were due solely to one stage of the two-stage sorption observed with the TSM. This may be due to the conductivity only probing the swelling of the polymer and not any subsequent sorption. In this study, the TSM measurements helped in determining the mechanism of conductivity changes in poly(pyrrole)films. In a final study investigating dichloromethane absorption from aqueous solutions [103] into poly(N-methylpyrrole) and poly(N-methylpyrrole/polystyrenesulfonate), the sorption rate was found to be independent of film thickness. This was interpreted as being due to rapid diffusion through pores in the polymer, followed by slow diffusion into the bulk of the polymer. The effect of oxidation state on sorption rates was also investigated. The preceding results show that the ability of AW devices to follow the transient uptake of a species into a thin film allows these devices to be used to probe a wide variety of diffusional processes. As described for Fickian diffusion, a significant advantage of the AW technique is the ability to use thin films, which results in the rapid evaluation Of the diffusional properties even in polymers that exhibit very slow transient uptake.


9

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177

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1 modes; sensitivity is one-half as great for n = 0 mode (see Chapter 3 and ref. 15). gFor unresolved modes. Value is experimental only, as calculation is not possible for mixed modes (see ref. 25). N/A = not applicable. aS m

228

5. Chemical and Biological Sensors

rigid coatings that are strongly bound to the surface, mass accumulation in or on the coating yields a proportional frequency decrease as in Equation 5.1. Most physical and chemical interactions between analytes and sensor coatings lead to changes of mass. Thus, this sensing mechanism offers the greatest latitude in the selection of sorptive or reactive coating materials, including a wide variety of organic polymers [42]. In addition, the performance of a given coating can sometimes be predicted a priori through knowledge of chemical reactions or by reference to solubility theory and/or appropriate models, as described in Section 5.4. The key challenge to implementing this detection mechanism in a useful sensor is imparting selectivity. Strategies for accomplishing this are discussed in later sections.

5.2.2

MECHANICAL PROPERTIES

Interactions with an analyte can cause changes in the mechanical properties of the coating. An increase in mass loading alone produces a decrease in frequency without affecting attenuation. In contrast, changes in mechanical properties of the coating can produce changes in both the frequency and the attenuation of the AW, as described in Chapters 3 and 4. Furthermore, these changes can either increase or decrease either or both of the two AW propagation parameters, depending on the details of the relationship between film thickness, acoustic wavelength, and the complex modulus of the film at the frequency and temperature of operation. The mechanical properties of a thin film can be generally classified as either elastic or viscous in nature. In many cases, these two properties are so interdependent that treating one without the other is neither practical nor realistic, so they are considered together as viscoelastic properties. The case of purely viscous interactions was treated in Chapter 3 for the contact of liquids with AW devices. A few liquid absorbent films and liquid-like, low molecular weight polymer films (which might be adequately treated as liquids in terms of their physical interactions with acoustic waves), have been examined [43-47]. Similarly, there are some cases where mechanical effects are (almost) purely elastic; this case is discussed next. In general, however, many thin-film materials, including most polymers, must be treated as viscoelastic materials to fully account for their interactions with acoustic waves. Investigation of viscoelastic effects on acoustic wave sensor response represents a particularly active area of research.

5.2 Detection Mechanisms

229

In the instance that mechanical effects can be adequately treated as purely elastic, the frequency of a SAW device is perturbed by modulus changes according to A f e = S ef 2oA - 7

A + 21a,

'

(5.2)

where S e is a constant that depends on the substrate material, h is the coating film thickness, v is the surface-wave velocity, and/x and A are the shear modulus and Lam6 constant (bulk modulus) of the coating, respectively. Note that the presence of the "A" outside the term in parentheses indicates that the change in the entire term is utilized to compute the elastic perturbation. This form is convenient because it applies to either the deposition of an elastic material (in which case h changes from zero to the thickness of the deposited film), or changes in the elastic moduli and/or thickness of a film already present on the device surface. Organic polymers comprise the most common type of coating used with AW sensors due to their capability to reversibly sorb vapors and liquids. For those polymers whose interactions with AWs can be treated as perfectly elastic, the fact that h is invariably larger than/z means that the value of the term (A + /z)/(A + 2/x) is constrained between 0.67 and 1; thus, this ratio can be approximated using a value of 0.84. The magnitude of a purely elastic perturbation is then proportional to the product of shear modulus and thickness, with no more than a 16% error. In much of the work published on the use of polymer coatings for SAW vapor sensing, the polymer's elastic modulus has been considered small enough for modulus effects to be neglected; most of these studies did not, however, consider viscoelastic effects at all. Furthermore, the modulus values assumed in such cases have been based on static or low-frequency determinations. This is a likely source of additional error, because the effective modulus of a polymer increases with the frequency of applied stress. In fact, for (nonacoustic) measurements performed in the range of 1-30 MHz (the highest frequencies reported), shear moduli in the range of 108-109 N/m E are found for many organic polymers that have low-frequency/z values of 106-107 N/m 2 [48-51 ]. Shear-modulus values in this range are sufficiently large so that they must be accounted for if the effect of adding a polymer film to an AW device surface is to be properly modeled. The frequency shift obtained upon deposition of such a coating is smaller ( ~ 10%) than that predicted from mass effects alone, because the sign of the righthand side of Equation 5.2 is opposite to that of Equation 5.1.

230


Just as in the case of film deposition, exposure of a polymer to an analyte must generally be considered in the context of viscoelastic changes in the film. Again, there are some cases in which the perturbation is largely elastic. In such instances, absorption of the analyte more commonly causes a modulus decrease, thereby enhancing the magnitude of the negative frequency shift attributable to mass loading. Recent reports suggesting a greater role for changes in the stiffness or viscosity of the coating film are preliminary and, in some cases, contradictory. Bartley and Dominguez suggested that internal stress created during vapor sorption in polymers might lead to an increase in frequency [52]. They derived an expression for the sensor response that included terms for mass loading and elastic stiffness changes (as in Equations 5.1 and 5.2), as well as a third term to account for the increase in frequency expected if compressive stresses were created within the coating upon vapor sorption. For typical polymers, however, this term is expected to be about an order of magnitude less than the mass-loading term. Interfacial stress was implicated by Thompson et al. to explain transient frequency increases in liquid-phase bioassays using TSM sensors with immobilized coatings [53,54]. Zellers et al. reported on the relative responses of polymercoated FPW and SAW sensors to changes of mass, density, and elastic stiffness [ 18] using a computer model developed previously. Results using high-frequency modulus values for different devices operating at the same acoustic wavelengths indicated that the fractional change of velocity resulting from changes of elastic stiffness were small relative to thickness- and density-induced changes. In contrast, a follow-up of earlier work [55] by Grate et al. compared partition coefficients, K, determined by gas chromatography to those determined using the same stationary phases as coatings on a SAW device [56]. They found that the SAW-derived values were four to six times greater than chromatographically determined values, with the latter reflecting only mass uptake. Typical comparisons are presented in Figure 5.1 for various polymers. Although differences between the chromatographic support material and the planar SAW device surface might account for part of the disagreement, the discrepancies were largely attributed to changes in the modulus of the coating upon vapor sorption and the effect of such changes on SAW frequency. Several factors hinder a complete analysis of these results, including uncertainties in modulus values at high frequency, as well as the effects of absorbed vapors on the moduli as a function of vapor concentration. The conclusion derived from this work was that responses of polymer-coated SAW vapor sensors might be dominated by modulus effects rather than mass-loading effects.

5 A

L.

0 C

I

4

W m nxm DI23

3 E

I

e

rn x

x rn x

2 io

0 ..J

taalb O

1

2

3 Log K (from G LC)

4

5

Figure 5.1 Comparison of K values (partition coefficient) calculated from SAW response data with K values from GLC retention. The K values are for fluoropolyol (FPOL - 1 ) , poly(epichlorohydrin) (PECH - F]), and polyisbutylene ( P I B - x) exposed to a variety of organic vapors. The solid line is the line of perfect correlation. (Adaptedwith permission. See Ref. [56]. 9 1992 American Chemical Society.)

t~ IT i.mo

I',O

232


Other studies have reported frequency increases for polymer-coated SAW devices upon exposure to water vapor at elevated temperatures ( 0), the exponential term usually dominates the temperature dependence. Unlike many cases of adsorption, desorption has a significant activation energy barrier (the molar desorption energy, Ed), which is always greater than or equal to the analyte-substrate interaction energy. Desorption depends on a desorption rate constant (kd) and on the number of occupied sites, so that a general expression for the desorption rate can be written as

( d-~tt)des = --kdO'- --Ofae -ed/Rr

(5.15)

268


in whichfa is an attempt frequency 9, typically in the range of 1012-1014/sec. The Arrhenius temperature dependence of desorption is determined by the exponential activation energy term. In terms of adsorption-based sensors, the net effect of desorption being more temperature-dependent than adsorption is two-fold. First, the equilibrium concentration of adsorbed analyte depends significantly upon temperature, with higher temperatures resulting in lower adsorbed analyte concentration. Second, the rate at which a sensor "recovers" when the ambient concentration of analyte diminishes to zero is very temperature dependent. The above expressions for adsorption and desorption rates were derived assuming that the two processes occur independent of one another. In reality, however, the two processes are not entirely independent. When adsorption raises the surface concentration of an adsorbate to an appreciable level, desorption begins to compete. Also, in many "real-world" situations, nonzero concentrations of ambient-phase analyte are present during desorption as well as adsorption. The relationship between thermodynamics and kinetics for the process of adsorption can be examined. Equilibrium is achieved not when adsorption ceases, but when the rates of adsorption and desorption precisely balance one another. This is why equilibrium is sometimes referred to as dynamic: to stress its nonstatic nature. When this is the case, surface occupancy is no longer changing with time, i.e., dO/dt = 0. Setting Equations 5.13 and 5.15 equal to one another and rearranging reveals k~ kd

=

0 p ( l - 0)

.

(5.16)

The righthand side of Equation 5.16 is the same as that given in Equation 5.7 above for the Langmuir adsorption model, with K,, = ka/kd. The experimental significance of Equation 5.16 is that measuring any two factors (adsorption rate, desorption rate, or equilibrium constant) uniquely determines the third. The expressions given above for/ca and kd lead to

ka Ka =

SoNo f x/2 Mer

s.17)

This rather cumbersome expression for the equilibrium constant is useful for the insight it gives into dependencies on a range of parameters. For example, one 9Attempt frequency is roughly correlated with the vibrational frequencies associated with the adsorbate-surface bond. Thus, the lower end of the range for f,, (1012/sec) is typical of the weaker bonding associated with physisorption, while the upper end of this range (lOm4/sec) is characteristic of stronger chemisorptive bonds.

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

269

can tell at a glance how changes in the molecular weight of the adsorbate, the number of sites on the surface, or the activation energy of desorption will perturb a given equilibrium between ambient-phase and adsorbed analyte. Such information is useful in designing or selecting adsorbent materials for sensing applications. In addition, it demonstrates the temperature dependence of Ka: increasing temperatures translate into a decrease in the equilibrium adsorption coefficient. In some cases, adsorption of analyte can be followed by a chemical reaction. The Langmuir-Hinshelwood (LH) and power-law models have been used successfully in describing the kinetics of a broad range of gas-solid reaction systems [105,106]. The LH model, developed to describe interactions between dissimilar adsorbates in the context of heterogeneous catalysis [107], assumes that gas adsorption follows a Langmuir isotherm and that the adsorbates are sufficiently mobile so that they equilibrate with one another on the surface on a time scale that is rapid compared to desorption. The power-law model assumes a Freundlich adsorption isotherm. Both models assume that the surface reaction is first-order with respect to the reactant gas, and that surface coverage asymptotically approaches a monolayer with increasing gas concentration. The LH model assumes that the adsorption process is at equilibrium and that the chemical reaction at the surface is the rate-limiting step. The LH expression for the rate, r, of an irreversible gas/solid reaction is r =

kK~p l +Kop

,

(5.18)

where k is the reaction rate constant, Ka is the equilibrium adsorption constant for the gaseous reactant, and p is the partial pressure. The equilibrium constant, Ka, would be expected to exhibit a temperature dependence as discussed above, i.e., Ka decreases wtih increasing temperature. The reaction rate constant k, however, would be expected to increase with temperature, so that the overall dependence of the reaction rate on temperature cannot be determined a priori. Rearranging Equation 5.18 into the following form allows comparison of sensor data with the model using linear-regression analysis: p= r

1 kKa

p k

.

(5.19)

Since p is proportional to the gas concentration and r is proportional to the rate of change of the sensor response, plotting [gas concentration/rate of response] vs concentration yields a straight line.

270


The power-law kinetic expression for a reaction that is first-order in the adsorbed gaseous reactant is [ 106] r = Fp line,

(5.20)

where F is a combined reaction-rate/adsorption constant and nr is a constant > 1. Adherence to this model is indicated if there is a linear relationship between the logarithm of the rate of the chemical reaction and the logarithm of adsorbate concentration. Application of the LH and power-law models to responses from reagent-coated SAW sensors has been described by Zellers et al. [108].

5.4.3.2

Transport Through Films

To this point, it has been assumed that only the outermost layer of the coating, be it perfectly smooth or highly porous, is involved in the adsorption process. When this is not the case, the simple surface adsorption-based models discussed above are inadequate. For physisorption on/in porous solids, transport into mesopores and micropores often limits the rate of adsorption. Two-stage equilibria are frequently observed: the more accessible outer surfaces equilibrate rapidly and remain in equilibrium with the ambient phase, acting as a source for slower transport of the adsorbate into the interior of the solid. Establishment of complete equilibrium can be a slow process. Hindered diffusion, the primary transport mechanism in porous solids, can be qualitatively described as a series of "hops" by the analyte, via gas-phase diffusion, from one surface site to the next. Thus, hindered diffusion is composed of two main components: a pure diffusion-related term, often Fickian in nature, associated with movement of the analyte in the gas phase; and a term describing the noninstantaneous equilibration between gas-phase analyte and the solid surface at each point where the analyte "touches down" (adsorbs). In extended porous solids (e.g., a chromatographic column tightly packed with porous beads), transport is often more complex, requiring the consideration of such factors as eddy diffusion and Knudsen effusion. This is important if there is a significant pressure drop along the path of the analyte [109]. Finally, the presence of any external fields (thermal, electric, etc.) must be considered as well. Differences in mass transport rates provide a potential means for discriminating between different gases and vapors, it is known, for example, that transport through molecular sieves can be a sensitive function of molecular size and shape [ 110]. For gases and vapors that have only weak physical interactions with a porous adsorbent layer, however, transport rates are often too high to allow


271

collection of enough data during the initial phases of adsorption to allow such discrimination [ 111 ]. For many chemisorptive interactions, particularly those involving chemical bond formation, reaction may proceed beyond the surface and into the bulk of the coating layer, providing far greater dynamic range but complicating kinetic analysis considerably. Bulk reaction between analyte and coating can alter the coating surface area; furthermore, as surface reaction sites saturate, the analyte must diffuse below the surface to reach unreacted sites. While a simple, exposure-dependent linear correction might be devised to account for surface-area changes, treatment of transport into the bulk is more difficult. The mass-transfer resistance associated with diffusion into a viscous liquid or solid reagent layer often slows the overall rate of reaction. When a nonvolatile product is formed during the reaction, analyte molecules must diffuse through a progressively thicker product layer. The Fickian model for diffusion is often appropriate, with the caveat that the thickness of the film through which diffusion occurs must be continuously adjusted according to integrated analyte exposure. Under these conditions, the so-called unreacted-core model described by Levenspiel [ 112] may be appropriate for describing the chemical reaction. This model depicts the gas-solid reaction as proceeding from the outer surface of the solid inward, with production of a progressively thicker product shell around a shrinking core of unreacted starting material, as illustrated in Figure 5.10. The use of this model to predict kinetic behavior is complicated by the need to specify the

Figure 5.10 Representation of the unreacted-core gas/solid reaction model for a particle of unchanging size. As reaction time progresses from left to right in the figure, the reaction surface recedes into the particle, the unreacted core shrinks, and the "ash layer" (containing the reaction product) increases in thickness.

272


amount of available surface area: for solid reagents, the morphology of the asdeposited solid and its evolution with progressive exposure are important. This is also true for viscous liquids that are not deposited as uniform films on the sensor surface. In terms of sensor response, the result of the growth of a product layer upon a reactive coating layer is a gradual reduction in sensitivity, measured as (change in signal)/(integrated exposure) [ 108]. The issue of reagent depletion has received surprisingly little attention considering the number of reagent coatings reported in the literature. The effect of increasing temperature is to increase mass transport rates for all categories of diffusion. The obvious implication of more rapid mass transport for equilibrium-based interactions is more rapid sensor response. In addition, sensors based on the consumption of a reagent layer generally show enhanced sensitivity with increased temperature, because reaction rates and diffusion rates both exhibit a positive Arrhenius temperature dependence.

5.4.4

ADSORPTION-BASED ACOUSTIC WAVE SENSORS

For vapor-phase species, adsorption onto an uncoated (smooth) sensor surface is, in some cases, inadequate for sensitive detection, although measurement of small fractions of a single molecular monolayer have been reported [113,114]; furthermore, nonspecific adsorption (i.e., adsorption that is general to many different species) has been reported as a possible interference on uncoated reference devices [90]. Nonspecific adsorption can be minimized by "deactivation" of the surface, accomplished by replacing polar groups (e.g., OH) with nonpolar functionalities, such as the methyl groups associated with chlorotrimethylsilane, CI(CH3)3Si (see Figure 5.11 for a schematic depiction of this reaction). The result of this so-called "silanization" reaction is a "low-energy" (in the sense of its strength of interaction with potential adsorbates) surface covered with unreactive methyl groups. Surprisingly few volatile compounds or gases interact strongly enough with methyl-covered surfaces to yield appreciable equilibrium surface concentrations. Note, however, that low-volatility species (e.g., oils and many high-molecular-weight organics) condense on any available surface they contact, no matter how chemically inert it may be. For liquid-phase applications, lowenergy surfaces can prevent many cases of nonspecific adsorption as well. With lack of specificity and low sensitivity established as two major drawbacks of uncoated surfaces, it is clear that an important key to the performance of adsorption-based AW chemical sensors is the adsorbent coating material. All


273

Figure 5.11 Generic silanization reaction for immobilization of coating/reagent on sensor surface. In step (1), the silylating reagent react with -Si-OH groups on the (quartz) surface. Subsequent reactions, indicated in step (2), can produce a polymeric coating.

other properties being equal, a film having higher surface area results in a larger number of analyte molecules being adsorbed for a given ambient-phase analyte concentration, the consequences of which are enhanced sensitivity and limit of detection. For reactive and (irreversible) adsorptive coatings, higher surface area translates to higher capacity and thus greater dynamic range. Thus, many of the materials described in the following section are porous, with high internal surface areas. For equal gas-phase concentrations, physical adsorption "favors" the deposition of low vapor-pressure species, in the sense that such molecules have a large heat of vaporization and thus a propensity to remain condensed upon surfaces. This results in some measure of selectivity (although a low concentration of a low-volatility species can give a response identical to a high concentration of a high-volatility species). Additional physical discrimination is obtained by controlling the polarity and hydrogen-bonding capability, with selectivity for analyte(s) determined by the film structure and/or subsequent surface modification. A potentially high degree of discrimination is achieved by the use of sizespecific materials, having a tightly-controlled pore size just larger than the kinetic diameter of the desired analyte. This excludes all larger species from the pores entirely; molecules significantly smaller than the chosen analyte, though able to fit into the pores, have a smaller interaction energy due to the size mismatch.

274


5.4.4.1

Common Materials for Physical Adsorption

Examples of high-surface area solid adsorbents suitable for sensor coatings are granular microporous materials such as activated charcoal, silica gel, alumina gel, porous polymers, and molecular sieves--in particular, zeolites. For most such materials, high adsorption capacity arises from the presence of large numbers of micropores and/or mesopores. The total surface area of a single gram of such materials can exceed 1000 m E [ 115]. Bulk samples of these materials are often used in packed beds for collecting airborne or dissolved species in environmental sampling procedures. Table 5.3 lists several adsorbents along with some of the types of compounds that can be collected with them. The adsorption capacity for different vapors varies widely with the structure and volatility (saturation vapor pressure) of the adsorbate as well as the process used for activation of the adsorbent. When porous adsorbents are used in packed beds, analytes that are efficiently trapped (have significant interaction energies) on these materials must be removed by solvent or thermal desorption [116]. However, if the adsorbent is in thin-film form (vide infra) and the analyte loading is relatively low, adsorption can be spontaneously reversible at room temperature [ 117,118], For AW sensor applications, grains of porous powders must be immobilized by some form of thin-film physical support layer on the device surface. This requirement is nontrivial, as it is a complex problem to create a uniform, wellbound layer of tiny, porous particles that is effectively "glued" to a flat surface without plugging the pores with the "glue" used for attachment. One class of materials that has been studied as a means to immobilize high-surface-area grains

Table 5.3

Adsorbent Materials and Typical Adsorbates

Adsorbent

A dsorbates (vapors)

Activated Charcoal

Most nonpolar and moderately polar organic vapors; alkanes, alkenes, chlorinated aliphatics, ketones, esters, ethers, higher alcohols

Silica and Alumina Gels, Zeolites

Polar vapors: water, alcohols, phenols, chlorophenols, glycols, aliphatic and aromatic amines

Porous Polymers (Tenax, XAD, Chromosorb)

Higher boiling-point organics: acidic and basic organics, multifunctional organics, pesticides, polynuclear aromatic hydrocarbons, etc.


275

in a thin film, and also as high-porosity thin films in their own right, are sol-gels or hydrogels [119]. These materials are synthesized via hydrolysis and condensation of metal alkoxides to form inorganic polymers in solution. Application of a thin layer of the sol-gel solution by dipping or spin-coating, followed by appropriate thermal treatment, produces a porous, rigid, oxide-based thin film. The pore sizes and sorption capacities of sol-gel-derived films are highly dependent on precursor materials and reaction conditions, as well as the final thermal treatment [ 120]. The suitability of an adsorbent for a particular analyte is a function of the presence or absence and strength of each of the physicochemical interactions discussed in Section 5.4.1. The polarity and hydrogen-bonding capabilities associated with M-OH moieties (M = Si, AI) in silica gel and porous alumina render these materials attractive toward polar and hydrogen-bonding analytes. This feature also causes these materials to be highly hygroscopic; in the context of AWsensor coatings, adsorption of water can lead to premature saturation of binding sites, interfering with the detection of all other analytes. The term "molecular sieve" describes a material having pores that closely match the dimensions of a specific molecule. The best-known molecular sieves are composites of microcrystalline zeolites embedded in an inert clay binder. Zeolites are composed of regular clusters of tetrahedral aluminosilicates, with varying percentages of bound cations and water molecules, whose crystal structures incorporate small molecule-sized cavities. Because zeolite pore size is different for each of the numerous different crystal structures in this family, the sizeselective nature can be tailored for specific applications. Studies of the transport of liquid and gaseous organic species in molecular sieves indicate that the diffusion rate and equilibrium concentration of sorbed analyte are sensitive functions of their molecular dimensions, as well as zeolite pore size and shape [ 110]. To broaden the range of chemical species lining the (internal) surfaces of porous oxides and also broaden the application of these materials, chemical surface-modification techniques can be utilized [119]. The most prevalent reagents for this purpose are silane-based coupling and derivatizing agents, which are compatible with many metal and oxide-based surfaces and provide a wide chemical variety of terminal groups [ 121 ]. Figure 5.11 shows the reaction of a "generic" silane with an OH-covered surface. X can be any one of C1, Br, I, OCH3, OC2H5, or OC3H7, with chloro, methoxy, and ethoxy being the most common. R can be one of hundreds of different functional groups, from simple alkyl or aryl groups to organic ligands for transition metals to complicated chelating moieties. When R contains accessible X-like groups, formation of a surface-bound polymer is possible, rather than a discrete surface moieties. Silane-based surface modifica-

276


tion can be carried out in the gas phase, typically using the more volatile CIbased species, in water, or in organic solvents, often with a low concentration of water intentionally added to speed hydrolysis. Many of these reactions proceed readily under mild conditions, reaching completion at room temperature in a few minutes. In addition to silane-based chemistry, virtually any other species that reacts with OH functionalities to produce a strong chemical bond can be used for surface modification of porous oxide-based materials. Examples include highly reactive metal alkyl species such as triethyl aluminum and dimethyl zinc. Most activated charcoal is produced in a low-oxygen environment that creates a largely nonpolar surface [115]. This adsorbent is not greatly affected by atmospheric water below 50% relative humidity (RH). At higher RH levels, however, activated charcoal begins to adsorb water and lose its capacity for other adsorbates. Adsorption on charcoal involves predominantly dispersive interactions whose energies are of the same order as the heat of condensation of many vapors. As a result, less volatile species tend to replace more volatile compounds bound to charcoal adsorption sites. Table 5.4 lists the adsorption capacity of charcoal (in grams of vapor per gram charcoal) for various organic vapors. Treatment of activated charcoal or other carbon-based films with a water/O2-based plasma results in reaction-condition-dependent coverages of OH groups, imparting surface properties intermediate between unmodified charcoal and the more polar oxides discussed above. OH surface functionalities also make it possible to utilize the silane-based reagents described above to chemically modify carbon-based films.

Adsorption Capacities of Organic Vapors on Activated Charcoal

Table 5.4

Adsorbate Vapor Acetone Chloroform Hexane Carbon tetrachloride Ethanol

Capacity at Saturtm'on* (g vaporlg adsorbent) 0.4 1.1 0.4 0.9 0.5

*Based on extrapolations from low-level adsorption assuming a Langmuiradsorption model. See Ref. [122].

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors 5.4.4.2

277

Physisorption-Based Sensors

Physisorption-based acoustic wave sensors have been applied to both gas- and liquid-phase detection. In liquid-phase applications, aqueous metal ions have been detected using TSM devices via deposition on the sensor surface as a result of electrostatic adsorption [81]. This adsorption is sensitive to pH: in the pH range where formation of hydroxide complexes occurs, metal adsorption was not observed. In addition to metal ions, other cationic species were found to adsorb, whereas nonionic or anionic species did not. By adding masking agents such as EDTA (ethylenediaminetetraacetic acid), analyses for specific metals (Ag) were performed [123]. Analysis of halides (Br-, I-) can be performed by adsorption onto a Ag electrode [124-126] (in some cases, the strength of the silver-halide interaction is strong enough to be classified as weak chemisorption rather than physisorption). While some interferences were noted, these were avoided by appropriate sample pretreatment [125]. The analysis of organic analytes has also been performed by taking advantage of reaction of analytes with bromine or iodine; the concentration of halide is then measured by the sensor and analyte concentration calculated indirectly [ 127,128]. As outlined in the previous section, the use of high-surface-area granular adsorbents on piezoelectric devices can provide good sensitivity for the detection of vapor-phase species. King used alumina, silica, and molecular sieves for monitoring humidity [ 1]. Detection of low concentrations of nitrobenzene vapors was reported using a TSM sensor coated with a fine layer of activated charcoal [ 118]. While the charcoal coating exhibited good sensitivity and reproducibility, recovery times upon purging with clean air were on the order of 8-10 min. One of the more unique adsorbent films used for vapor sensing is sputtered polycrystalline zinc oxide, ZnO. Under the appropriate conditions, the crystallites deposit with a common crystallographic orientation (c axis normal to the substrate) on a layer of SiO2 on silicon (ZnO-on-Si); grain boundaries provide adequate surface area for the adsorption of gases and vapors [13,129]. An advantage of this material is that it can simultaneously function as the piezoelectric transduction layer for the construction of thin film-based SAW and FPW devices supported on Si (or virtually any other) substrates [12,17,18]. Some typical adsorption-based acoustic sensor applications are summarized in Table 5.5 on page 278. Suspended in a sol-gel-based thin film as previously described, zeolites have been claimed to provide sensitive response to alcohols (MeOH and PrOH) while excluding other organic vapors (isooctane) solely on the basis of molecular size [ 132]. The excluded molecule is also highly nonpolar, in contrast to the polar alcohols that were detected; the potential role of solute polarity on exclusion has

278

5. Chemical and Biological Sensors Table 5.5

Examples of Adsorption-Based Acoustic Wave Sensors

Analyte

Adsorbent

Device

Detection Limit

Ref.

TSM TSM TSM TSM TSM TSM

0.5/,tM 0.6 ~g/L 0.02/zM -0.5 • 10-12 M 0.2/,tM N

[ 125] [124] [ 127] [ 128] [126] [123] [83]

TSM

0.1 ppm

TSM TSM SAW SAW TSM

100~ since high-temperature, oxide-based semiconductor films have been used in conductivity-based sensors, it is possible that the response mechanism in this case is due to an electronic effect. Edmonds reported using manganese dioxide for the detection of NO2 using a TSM device [142]. The amalgamation of noble metals, specifically gold (Au), by mercury (Hg) has been used for the liquid- and gasphase detection of several species. In water, an Au-coated TSM device was used to detect aqueous concentrations of Hg(II) [143] in the range of 2-30/zM; repeated analysis resulted in a gradual decrease in sensitivity. Au-coated TSM devices have also been used to detect ambient Hg levels in the atmosphere [144], and for the collection of evolved elemental Hg vapor after the reduction of aqueous Hg species [ 145]. The amalgamation reaction has also been used for the detection of atmospheric SO2 [146]. Bubbling an SO2 stream through a solution of mercurous nitrate produces elemental mercury via the reaction: 2SO2 + 2H20 + Hg 2+ ~ Hg(SO3)22- + Hg ~ + 4H + The quantity of evolved elemental Hg, which is proportional to the SO2 concentration, is measured by amalgamation onto an Au TSM device electrode surface. The collected Hg can be thermally stripped from the electrode and the TSM resonator reused for subsequent analyses. Coordination and charge-transfer interactions are commonly used for the detection of electronegative vapor species or species having lone or nonbonding pairs of valence electrons (e.g., NO2, SO2, NH3). For example, semiconducting phthalocyanine (Pc) films have been studied extensively as coatings for (partially) reversible detection of NO2 [67-70,72,147]. The structure of the Pc molecule is illustrated in Figure 5.14; different metals can be complexed in the center of this structure, leading to a range of physical and chemical properties for


283

Figure 5.14 Molecular structure of the metal-phthalocyanine (M-Pc) complex. The central metal atom (M) can be a transition metal (i.e., Cu, Fe, Ni) or a heavy metal (Pb). The metal atom can act as an Lewis acid (electron pair acceptor) and interact with electron donors, whereas the extended aromatic ring structures on the periphery of the complex can interact with electronegative species (electron acceptors).

this class of materials. The delocalized 7r-electron system associated with this highly conjugated molecule can interact with electronegative species (electron acceptors); metal cations in the center of the ring can form complexes with electron donors as well as acceptors. Depending on the choice of AW device substrate, the sensor response arises partly or largely from changes in film conductivity (see Section 5.2.3). As expected, the sensitivity of the Pc film depends in

284


part on the central metal atom, with copper and iron providing the highest sensitivity to NO2 [72], but lead was often reported to give better reversibility. These coatings exhibit excellent selectivity for NO2 over other vapors such as halogen gases, CO2, SO2, H20, and NH3 [147]. In the case of NH3, as well as higher NO2 dose levels, there does appear to be some irreversible interaction resulting in some loss of sensitivity with prolonged exposure. Plasma-polymerized Cu-Pc films have also shown high affinity for planar aromatic compounds (benzoic acid, phenol, etc.) and higher alcohols [66]. While there may be significant charge-transfer interaction with the Pc film in the case of the former compounds, other modes of interaction (e.g., dispersion, H-bonding) are probably operative for the alcohols. Other transition-metal complexes have been used for the selective detection of various compounds. Karmarkar et al. used trans-chlorocarbonyl-bis(triphenylphosphine) iridium(I) [t-IrCl(CO)(PPh3)2] suspended in Nujol (mineral oil) for the selective detection of aromatic hydrocarbons. The iridium complex exhibited less sensitivity to olefinic and aliphatic hydrocarbons [148]. Zellers et al. have performed extensive work with a series of SAW sensor coating reagents of the general formula PtCl2(olefin)(amine) [92a,92c--d,97]. Responses to olefin gases and vapors are based on the mass change accompanying displacement of the initially-complexed olefin. Where ethylene and pyridine are used as the initial ligands, low-ppm sensitivity to several olefin vapors was demonstrated and regeneration of the initial reagent was possible by exposure to ethylene gas in situ. Remarkably high selectivity was possible based on steric factors. For example, 1-butene could be monitored with complete selectivity in the presence of isobutylene; ethyl acrylate could be detected with no interference from methylmethacrylate. Electronic factors were also important, with electron-deficient olefins, such as vinyl chloride, neither reacting with the reagent nor influencing the reaction of several other olefins with the reagent. Replacing ethylene by 1-hexene in the initial reagent permitted detection of butadiene at ppb concentrations; mass amplification resulted from displacement of two hexene molecules for every butadiene that reacted. Low-ppm concentrations of ethylacrylate could be measured with the ethylene complex, but did not react with the 1-hexene complex. A variety of organophosphine transition-metal complexes have been used for the detection of SO2 [149]. Cook et al. used triphenyl- and tribenzyl phosphine compounds as ligands bound to Cu and Mn. Varying the ligand affects the Lewis acid strength of the metal complex, and hence, its ability to bind SO2. One complex (bis(tribenzylphosphine)copper(II) thiophenolateR [Cu(PBz3)2)SPh])exhibited a reversible response to SO2 that was linear in the range of I0-1000 mg/L.


285

The coating exhibited good stability in laboratory air, and retained sensitivity to SO2 even after 2-3 months. Selectivity was also favorable, with little or no interference from 02, CO2, NH3, CO, or NO2. Other transition metal compounds which engage in irreversible redox reactions with SO2 have demonstrated good sensitivity [150]. A wide variety of amines have been employed for sensitive detection of SO2 as well, as reviewed by Guilbault [2] and Alder and McCallum [3]; NO2 appears, however, to act as a significant interference with many of these coatings. Other coordination and/or charge-transfer reagents have been used successfully for the detection of NH3 [ 151], toluene diisocyanate [ 152], phosgene [ 153], and organophosphorous compounds [154]. Due to their importance as model compounds for chemical-warfare agents, much effort has been devoted to the detection of a class of compounds known as organophosphonates. While much of this work has utilized polymer-based coatings (see Section 5.4.6), a number of workers have utilized chemisorptive interactions [155 and references therein]. Using the reported ability of Cu 2+ to act as a catalyst for the hydrolysis of organophosphates as a starting point, Kepley et al. designed a self-assembling monolayer film terminated by coordinatively unsaturated Cu 2+ ions [156]. A SAW device coated with this film responded reversibly to organophosphonates in the gas phase at concentrations from 100 ppb to saturation, with and without relative humidity present. The response of this coated device to organophosphonates was consistent with mass loading in the range of a fraction of one monolayer up to tens of layers. In contrast, the (reversible) response to a wide range of common organic solvents was a positive frequency shift, suggesting a change in film elastic properties and providing a unique form of selectivity. Complexation interactions have also been used for liquid-phase detection of metals. Martin et al. used an immobilized ethylenediamine coating on an SH-APM device to detect aqueous Cu 2+ [ 16]. The ethylenediamine molecule is a bidentate ligand capable of strongly binding transition metals via the amine groups. The sensor readily detected Cu 2+ at a concentration of 2.5 • 10 -4 M. While the metal response was not spontaneously reversible, the bound metal was released upon acidification to give a 10 mM HCI solution. Nomura et al. used oleic acid (deposited as copper oleate) on a TSM device for the analysis of metal ions [ 157]. The coating could be regenerated (bound metals removed) by addition of EDTA to the solution. Interferences from some metals (Cu 2+, AI3+, Fe 3+) were eliminated by the addition of the masking agent acetylacetone. These and other examples of chemisorption-based sensors are listed in Table 5.6, page 286.

Table 5.6

Chemisorption-Based Acoustic Wave Sensors ,,,

Analyte

Coating

Detection Limit

polybutadiene poly(ethylene maleate) polymerized Pc [trans-IrCl ( CO )PPh3 )2] PtCl2(ethylene) (pyridine)

10 ppb/min 200 ppm/min - I)

k; kN; kt

wavenumber; wavenumber corresponding to resonant frequency fN; wavenumber for bulk transverse waves

K

electromechanical coupling coefficient

A; At

wavelength; wavelength of bulk transverse waves

I; I0

400

AppendixA Lists of Symbols by Chapter

inductance; also path length (center-to-center distance) between pair of interdigital transducers /z;/xs

shear modulus; substrate-dependent constant relating electric wave potential to applied transducer voltage (for SAW)

m' ; mso,.ptive; Am; Ammin

added mass per unit area (for FPW); mass per unit area of sorptive layer (for FPW); change in added mass per unit area due to change of fluid density (for FPW); minimum detectable added mass per unit area due to change of fluid density (for FPW)

M

mass per unit area of plate (for FPW)

1)

Poisson's ratio

N; N: Np

integer associated with resonant mode; number of transducer fingers; number of transducer periods perturbation factor

P; Pr; PTl; PT2 Pq; PF; Pq; P~

Ap;/~;

acoustic power; also complex power flow (see definitions p. 27) mass per unit volume (mass density) of quartz; density of fluid (for FPW); change of density of fluid (for FPW); mass per unit volume (mass density) of liquid; mass per unit area of surface layer (areal mass density)

R

resistance; mode resolution parameter (for APM)

Rm

mass resolution of sensor

o'; trc; trl; trs

bulk conductivity; critical sheet conductivity; liquid (solution) conductivity; sheet conductivity of film

S; Si; am

sensor sensitivity to added mass; ith symmetric plate mode; mass sensitivity of sensor (for FPW)

z; Zxy

relaxation time; component of tensile stress in plate

t

time

r; ri: r~

stress tensor; ij th component of stress; x-component of in-plane tension (for FPW)

lax, Uy, Uz

x-, y-, and z-components of displacement

vk; up

kinetic energy density; potential energy density

Chapter 4 ve; VN; Vp; Vs; Vx; VxO; VxO, VyO, VzO; VO

401

speed of sound in fluid; phase velocity of Nth mode (for APM); phase velocity of plate wave; phase velocity of shear wave; x-component of particle velocity in liquid; value of Vx at surface of crystal; three particle velocity components at surface (for SAW); propagation velocity (for SAW)

v; v~; Vo

voltage; excitation voltage of nth transducer finger (for SAW); magnitude of transducer excitation voltage (for SAW)

to; too; ~s

angular frequency (= 2"nf); unperturbed resonant angular frequency; series resonant angular frequency

x; X

rectangular position coordinate; detuning parameter for interdigital transducer, and reference to crystal cut

y; Y

rectangular position coordinate, and distance into substrate (for SAW); reference to crystal cut

Y(~o); Ym.x

admittance; maximum admittance

Z; Z

rectangular position coordinate; reference to crystal cut

Ze; Z~; Zq; Z,; Z0

impedance appearing in equivalent circuit for shear resonator; motional impedance; equivalent shear-wave mechanical impedance for quartz; equivalent shearwave mechanical impedance of surface film; (for Z0 see Equation 3.17 and following)

Chapter 4 /3

defined variable for BET equation (Equation (4.5))

C

concentration of analyte in film

Co C(x,0

equilibrium concentration of analyte in film

D

diffusion coefficient

f;Af

frequency; change in frequency

concentration of analyte in film at depth x at time t

402

Appendix A Lists of Symbols by Chapter

f.

fractional porosity of porous film

G'

storage modulus

G"

loss modulus

rl

viscosity (not kinematic)

hi /(,%)

film thickness

Ao

incident optical wavelength

Ix

modulus (stiffness)

ml

film mass per unit area

M(t)

total mass of sorbed analyte in film at time t

Mmax

incremental change in mass of sorbed analyte

n; nm

number of adsorbed molecules; number of adsorbed molecules in a monolayer

P; Po

partial pressure of vapor; saturated vapor pressure

Pr

partial pressure of vapor at which capillary condensation occurs

spectral density (intensity) of source at wavelength A0

film density Ps

surface mass density of film

psk

skeletal density of porous coating matrix

rc

radius of hemispherical meniscus gas constant

n(~)

rate of change in APM velocity due to film crosslinking at wavelength A0

O"

surface tension polymer relaxation time

T

absolute temperature (Kelvin)

r~

liquid crystal phase transition temperature

r~

polymer glass transition temperature

Tm V~

melting temperature

Y

admittance

molar volume of gas, analyte

Chapter 5 tO

angular frequency

Ze

film impedance element

403

Chapter 5 a; aa

chemical activity of a species in the ambient phase, and adsorbed on a substrate, respectively

a2; a~

solvation parameter for hydrogen bond donor acidity of the solute; complementary solvent coefficient (i.e., solvent H-bond acceptor basicity)

f12; bl

solvation parameter for hydrogen bond acceptor basicity of the solute; complementary solvent coefficient (i.e., solvent H-bond donor acidity).

~t~ , x

activity coefficient of solute i in phase x

r

stiffness (Section 5.2)

Ca

ambient concentration of analyte

Cs

analyte concentration sorbed into film (Section 5.4.2), film surface capacitance (Section 5.2.3)

Cth

threshold concentration for human detection (toxicity limit) Hildebrand solubility parameters for solute i; and for solvent phases x, y permittivity

Ea; Ec, Ed

activation energy of bond formation; chemical bond strength; energy barrier for breaking of a chemical bond

AE; AEv; AEm

energy of solute transfer; energy of vaporization; energy of mixing

fa

attempt frequency for desorption of an adsorbate (Equation 5.15)

fo; Af; AL; Afe; Afs; Afm

initial (unperturbed) frequency; change in frequency change in frequency due to application of a coating; change in frequency shift due to elastic changes;

404

Appendix A Lists of Symbols by Chapter

change in frequency due to sorption of analyte; change in frequency due to mass loading

F

reaction rate/adsorption constant (Equation 5.20)

AGa; AG~

Gibb's free energy change associated with adsorption, and absorption/solvation, respectively

o; o~

fraction of adsorption sites filled by analyte, fraction filled by species i

h

sensor coating/film thickness

AHm; AH~o,,d

enthalpy of adsorption, solution, condensation, mixing, and condensation, respectively

K

geometric factor for fraction of active device area being perturbed (Equation 5.1)

k; ka; ka; ke

reaction rate constant; adsorption rate constant; desorption rate constant; empirical constant for Freundlich adsorption (Equation 5.12)

kl; k2

material constants for piezoelectric substrate (Wohltjen equation)

K

material constant for piezoelectric substrate (Saurbrey equation)

g2


Ka

distribution coefficient for adsorption

KI2; K34

equilibrium constant(s) for stepwise formation of coordination complexes, where the subscript(s) refers to the number of ligands added to the complex in a given step equilibrium partition coefficient

L216; II

solvation parameter, Ostwald's partition coefficient of solute in hexadecane; complementary solvent coefficient (dispersion interactions) film Lam6 constant

/z

film shear modulus

m; Am; Am,,

mass; change in mass; change in mass per unit area

mA; mML

mass of adsorbate/area, adsorbed mass/area at monolayer coverage

Chapter 5

M; M~ ma; mm;

405

molecular weight, or molar mass of species x (analyte, adsorbate) mc; ms

mass of adsorbed analyte; mass of a monolayer of adsorbed analyte; mass of coating; mass of analyte sorbed into coating

NA N; No

Avogadro's number (6.02 x 1023)

ni ; nF

number of moles of species I, empirical constant for Freundlich adsorption (Equation 5.12)

r/

viscosity

p; pi

partial pressure; partial pressure of species i

p; pc

film density or coating density

71"2; S 1

solvation parameter for dipolarity/polarizability interactions; complementary solvent coefficient

R2; r~

solvation parameter for excess molar refractivity; complementary solvent coefficient (i.e., electron pair interactions)

r

rate of reaction

R

Ideal Gas Law constant

or

conductivity

SP

solubility property of interest for LSER application (i.e., K, Vg)

So

"sticking coefficient," indicates probability of collision with an empty site resulting in adsorption (Equation 5.14)

Se; Sm

device specific constants relating frequency shifts to changes in elastic and mass loading effects, respectively

ASa; ASm

entropy of adsorption; entropy of mixing

(for Langmuir adsorption isotherms) number of fill sites/area; total number of sites/area

relaxation time (shear) T

absolute temperature (Kelvin)

Tb"~ Tg'~ T m

boiling point (temperature in Kelvin); (for polymers) glass transition temperature; temperature of melting

406

AppendixA Lists of Symbols by Chapter

Y, Vo

acoustic wave velocity, unperturbed (initial) acoustic wave velocity

m

vi; vc; Vvap; Vx

molar volume of solute i; volume of sorbent coating, volume of vapor phase; volume of condensed phase x specific retention volume of solute (in gas chromatography)

Xi

mole fraction of species i

o.)

angular frequency

Chapter 6 Ol

attenuation

BW

bandwidth

Co

static capacitance

d

periodicity of an interdigital transducer

~s

dielectric permittivity of a substrate

f0; af; fR

IDT center frequency; change in frequency; resonant frequency

~; A,k; 4,.

unperturbed total phase difference; change in phase difference; instrumentally measured phase difference (-~r < tkr < ~')

k

wavenumber

K

acoustic path fraction

K


t,i

insertion loss (expressed in dB)

Lr

tuning inductance wavelength

N

number of finger pairs in an interdigital transducer

n,~

number of acoustic wavelengths

N,~

number of acoustic wavelengths between centers of input and output IDTs

Pa

power dissipated

Chapter 6

407

quality factor (see discussion in Section 6.2.1.1) peak total energy unperturbed acoustic wave velocity; change in acoustic wave velocity angular frequency

Appendix B

absorption (absorb) acoustic aperture

Glossary of Terms

the process of a species present in a contacting gas or liquid phase penetrating into the bulk of a solid material the width of a plane-parallel acoustic wavefront, typically as defined by the overlapping finger length of an interdigital transducer launching the wave

acoustic path fraction

the fraction of the center-to-center distance between input and output transducers of a delay-line-based acoustic wave device that is perturbed by a stimulus and/or covered by a thin film that confers chemical or other sensitivity to the device

acoustic plate mode (APM)

a mode comprised of acoustic waves that are reflected periodically at the planes bounding the surfaces of a thin plate, which thus acts as an acoustic waveguide

acoustically thin

describing a film whose thickness is small compared to the effective acoustic wavelength in that material

active device

a device, such as an amplifier, that requires the input of power, most typically at a voltage of from 5 to 24 volts (DC), to accomplish a desired signal transformation or other function

adsorption (adsorb) AGC

the process of a species present in a contacting gas or liquid phase "adhering" to molecules at the surface of a solid

alcohol

an organic compound having a hydroxyl functional group bonded to a carbon atom, - C - O H

aldehyde

a class of organic chemical compounds characterized by a carbonyl group in one terminal position of a carbon chain, e.g., formaldehyde, HCHO

see

automatic gain control

408

Appendix B Glossary of Terms

409

aliphatic

describing an organic compound in which the carbon atoms are joined in chains, rather than rings (compare aromatic)

alkane

a hydrocarbon compound in which all carbons are joined by single bonds, i.e., - C - C -

alkene

a hydrocarbon compound in which two or more carbons are joined by double bonds, i.e., - C = C -

alkyne

a hydrocarbon compound in which two or more carbons are joined by triple bonds, i.e., - C ~ C -

amalgam amorphous

an alloy of a metal, often gold or silver, with mercury having little or no organized chemical structure (compare crys-

talline) amplifier

a device that produces an output signal whose amplitude is equal to the amplifier gain times the amplitude of the input signal

analyte

a chemical species that is to be analyzed, in terms of its identity and/or concentration

antibody

a protein, usually produced in vivo, that engages in specific chemical interactions with an antigen

antigen

a toxin or other substance that elicits the formation of specific antibodies in vivo

APM

see acoustic plate mode

aromatic

a class of chemical compound characterized by the presence of one or more ring structure in which electronic resonance effects play a major role in bonding (e.g., benzene rings)

AT-cut quartz

quartz crystal that generates shear waves when placed in a timeperiodic electric field; the crystal is cut at a specified angle to the crystallographic axes so that it has a small or vanishing dependence of wave velocity upon temperature at room temperature

attenuator

a device that diminishes the amplitude of a signal by a specified fraction

automatic gain control (AGC)

a feature of an amplifier that automatically adjusts the amplification to maintain a constant output signal level; changes in the gain of such a device are a measure of changes in wave attenuation in an acoustic wave device

balun

a circuit that converts a voltage, such as that applied to an interdigital transducer, from being balanced with respect to ground to being unbalanced with respect to ground, or vice versa (most electrical test equipment has an output that is unbalanced with respect to ground)

410


bandwidth (BW)

for resonant systems, the range of frequencies over which the reflected power is within 3 dB (a factor of two) of its minimum value, attained at fR; for non-resonant systems such as delay lines, the range of frequencies over which the transmitted power is within a factor of two of its maximum value

baseline drift

an often gradual change in the output signal (from a sensor) in the absence of a change of the quantity being measured; for example, baseline drift can be caused by a gradual changes in ambient temperature or gradual changes in the physical properties of a sensor coating material

bidentate

referring to a ligand that can bind to a metal atom or other moiety at two sites in the ligand structure, e.g., ethylene diamine, oxalate anion

bonding p a d

a metal region on a silicon chip, sensor, or other device, provided as a place to make off-chip electrical contact using wire bonding (see)

BT-cut quartz

quartz crystal that generates shear waves when placed in a timeperiodic electric field; the crystal is cut at a specified angle to the crystallographic axes so that it has a small or vanishing dependence of wave velocity upon temperature at room temperature

BW

see

carbonyl

a chemical functionality consisting of an oxygen atom attached to a carbon atom by a double bond, i.e., - C =O

chemisorption (chemisorb)

an adsorption process in which strong interactions, including covalent or ionic bond formation, occur between an adsorbate and a solid surface; such strong interactions often make the adsorption process irreversible

clear-field mask

a lithographic mask that is opaque in the regions where metal is to be retained, and clear elsewhere (the "field")

common-mode

in a two-wire circuit, a signal that appears on both wires; often, a so-called differential amplifier is used to minimize the disturbing effect of common-mode signals

signal

bandwidth

coordination

referring to complex compounds in which ligands (see) are bonded to a central metal atom by a shared pair of electrons supplied by the ligand

crosslinking

the process of forming chemical bonds between polymer chains, resulting in a three-dimensional polymer network that is typically insoluble


411

crystalline

having highly ordered, long-range structure in which atoms, molecules, or ions are arranged in regularly spaced and repeating patterns

damping

a colloquial term for a decrease of wave amplitude (attenuation) caused by the dissipation of wave energy, as in propagation through a viscous fluid

dark-field mask

a lithographic mask that is clear in the regions where metal is to be retained, and opaque elsewhere (the "field")

dB DC decibel (dB)

see decibel see direct current a logarithmic measure of the ratio of a variable to its reference value: relative power (dB) = 101oglo (P/Pref), where P,'efis the reference power; because of their square-law relationship to power, relative voltage, V, and pressure, p, expressed in dB are given respectively by 201ogl0 (V/Vref) and 201oglo(p/pref), where V,.ef = reference voltage and Prey= reference pressure

delay line

a device for which an electrical signal incident on the input port arrives, after some finite time delay, at the output port; for example, propagation of a Rayleigh wave from one transducer of a SAW delay line to the other typically causes a time delay ranging from a fraction of one to several ~s

device header

a package upon which an electronic device is mounted to permit making electrical connections via a socket and, in some cases, gas or liquid connections via tubing to introduce samples for measurement

diffusion

the process whereby chemical species intermingle, moving from a region of high concentration to a region of low concentration

diffusion coefficient

a parameter that quantifies the rate of diffusion of one species through a gas, liquid, or solid material (the amount of the species diffusing through a unit of cross section per unit time when the volume-concentration gradient is unity)

DIP direct current

see dual in-line package

(DC) direct electromagnetic

feedthrough directional coupler

colloquially, a steady quantity, such as a current or voltage, whose value is independent of time spurious electromagnetic signal coupling between input and output transducers that is independent of the properties of the acoustic path, and therefore not an accurate indication of the value of the intended measurand a device having three or more ports that passes the majority of an input signal straight through to its output port while splitting

412

Appendix B Glossary of Terms off a small, specified fraction of the signal to send to another device or instrument

dosimeter

a sensor or device that provides a measure of the total dose or exposure to a substance over a given period of time

drift

a gradual, often monotonic, change with time in the value of some parameter; often referring to such changes in the sensitivity of, or signal from, a device (compare noise)

dual in-line package (DIP)

a commonly used ceramic or plastic package for physically mounting and making electrical connections to an integrated circuit

elasticity (elastic)

the ability of a material to return to its original shape after it has been stressed; elastic behavior implies a linear relationship between stress and strain

elastomer

a polymeric material that exhibits elastic properties, e.g., rubber

electrochemistry

chemical processes and reactions induced by imposed electrical potentials

ele ctro ne gati vity

the tendency or ability of an atom to attract electrons, especially through a chemical bond

endothermic

designating a chemical reaction or process in which heat is absorbed

enthalpy

a thermodynamic measure of the (thermal) energy content of a chemical system

entropy

a thermodynamic measure of the amount of energy in a chemical system that is not available for work; a measure of the degree of disorder in a system

enzyme

a protein or protein-like substance that acts as a catalyst, speeding up specific chemical reactions

ester

a class of chemical compounds formed by the reaction of an organic acid with an alcohol, e.g., - R - C O O R ' or - R - SO3 - R'

ether

a class of organic compounds characterized by an oxygen atom bonded to two carbon atoms, i.e., - C - O - C -

exothermic

designating a chemical reaction or process in which heat is produced

external phase

the phase shift of a sensor signal that occurs outside the acoustic measurement path, e.g., the phase shift in an electronic amplifier and connecting cables

shift filter

a device that passes signals only within a specified range of frequencies

ftatpack

a metal version of the dual in-line package (see)

Appendix B

Glossary of Terms

413

flexural plate wave (FPW) FPW frequency response

a flexural ultrasonic wave propagating in a thin membrane, formed typically in a silicon chip

frequency counter

an instrument that measures frequency by counting the number of cycles in an accurately known time period

glass transition temperature (Tg)

the temperature at which the relaxation, or second-order transition, from the glassy to the elastomeric state occurs in a polymer; this transition exhibits a time (frequency) dependence

halogens; halides

reactive, non-metallic elements of the VIIb family; compounds containing these elements, e.g., chlorine, C12; hydrogen chloride, HCI

heterocycle

a compound that contains a ring system made up of more than one kind of atom; typical heterocycles consist of carbon plus nitrogen, oxygen, or sulfur

heterogeneous homologous

see flexural plate wave the frequency-dependent characteristics of a device expressed as a function of the excitation frequency, either in terms of insertion loss and phase shift, complex impedance (or admittance), or S parameters

consisting of more than one substance designating a series of chemical compounds whose structural formulas differ in a regular fashion, often by the addition of one or more - C H 2 - groups, e.g., CH3OH, CH3CH2OH, CH3CH2 CH2OH

hydrocarbon

a chemical compound consisting only of carbon and hydrogen atoms, e.g., methane, CH4; benzene, C6H6

hydrophilic hydrophobic hydroxide

having an affinity for water; highly soluble in water

hygroscopic

designating compounds or substances that readily absorb moisture

hysteresis

a dependence of the physical state or response of a substance or system upon its previous history, often manifested as the lagging of an effect behind its cause

IDT immunoassay impedancematching network

having an aversion to water; insoluble in water a chemical compound, usually inorganic, containing the hydroxide ion, OH-, in combination with a cation, e.g., sodium hydroxide, NaOH

see

interdigital transducer

an analytical test for, or derived from, immunological reagents or materials such as antigens or antibodies an interconnected arrangement of components that matches the impedance of a device to that of the instrumentation (or another device) to which it is connected

414


insertion loss

the extent of attenuation of a signal, typically expressed in dB, due to its traversal of a device

interdigital transducer (IDT)

a pair of interpenetrating comb-like structures, typically made from a lithographically patterned thin metal film that has been deposited onto the surface of a piezoelectric substrate; the IDT excites (or detects) acoustic waves when driven (or monitored) at the appropriate frequency

intermolecular

relating to interactions or processes occurring between or among different molecules

intramolecular

relating to interactions or processes occurring between or among the atoms or groups of atoms within a molecule

ionization potential

a measure of the energy required to remove an electron from an atom to infinity, forming an ion

ketone

a class of organic chemical compounds characterized by a carbonyl group in a non-terminal position of a carbon chain, e.g., acetone, C H a - C O - C H 3

kinetics, reaction kinetics

the study of molecular motion; specifically, the factors that determine the rates of chemical reaction, including their dependencies upon chemical concentrations and temperature

Langmuir-B lodgett film

a molecular monolayer film produced by passing a substrate through a water-surface-supported, compressed layer of molecules possessing polar and nonpolar ends (separated by an intervening chain or body of at least a few atoms), conferring a very regular alignment of the molecules; such films are typically produced using a commercial Langmuir-Blodgett trough to control the compression of the molecular layer and dipping of the substrate

lift-off procedure

a lithographic process for patterning thin films in which a layer of photoresist is coated on a substrate, then exposed to light through a mask, and developed prior to deposition of the layer of material to be patterned; following ,thin film deposition, the remaining photoresist is dissolved "out from under" the film in those regions where it is to be removed

ligand

an atom, ion, or molecule that can engage in coordinate bonding with a central (often metal) atom or ion (see coordination)

limit of detection (LOD)

the smallest value of some parameter to which a device responds that can be reliably detected; "reliably" is often taken to mean


415

that the signal measured is no smaller than three times the rootmean-square noise level

linear dynamic range a sensor in which linear proportionality between concentration and response is maintained (LDR) the general class of organic compounds consisting of fats, or lipid having properties similar to fats, e.g., hydrophobicity

lithographic mask

a radiation-transparent (often glass) plate bearing an opaque pattern that is the image (or negative image) of a pattern to be produced using photoresist-based patterning techniques

macropores mask aligner

pores with diameters greater than 50 nm

masking

referring to the action of a chemical reagent that renders an atom, ion, or molecule unreactive toward another chemical reagent

measurand

a quantity to be measured, such as temperature or the chemical concentration of a substance

melting temperature (Tin)

the temperature corresponding to (1) a physical change from the solid to the liquid phase, or, (2) in the case of polymers, a first-order transition from a crystalline to an amorphous state (the melting temperature is independent of frequency)

mesopores micropores microwave modulus

pores with diameters between 3 and 50 nm

molecular permeation

molecular transport of chemical species through a film of material such as a polymer

negative photoresist

photoresist that is rendered insoluble in a chemical developer, typically by photoinduced crosslinking of polymer chains, in

a device that holds a photoresist-coated substrate and lithographic mask in close, uniform proximity, providing uniform, controlled-duration irradiation of the substrate through the mask

pores with diameters less than 2 nm an electromagnetic wave in the 1-100 GHz regime a measure of the stiffness (or elasticity) of a substance, defined as the stress associated with a unit strain and having units of force/unit area (dynes/cm2); for polymers, it is the complex shear modulus that can be effectively probed with AW devices. Shear modulus can be represented by G = G' + jG", where G', the storage modulus, is associated with energy storage and release during the periodic deformation associated with the oscillating stress, and G", the loss modulus, is associated with the dissipation of energy, usually as heat

416

Appendix B Glossary of Terms those regions where it is exposed to (typically ultraviolet) irradiation

network analyzer

an instrument that provides a controlled-amplitude signal to the input of a test device or circuit over a range of frequencies, then records and displays the frequency response (see) of the device/circuit; both transmitted and reflected signals can be measured

noise

in a sensor or other device, irregular, often random variations in output signal resulting from conditions unrelated to the intended measurand, examples being temperature-induced variations of electrical resistance and random particle motions in a solid or fluid

olefin

any of a series of unsaturated, open-chain hydrocarbons containing one carbon-carbon double bond, e.g., propylene, CH3-CH2=CH2

oxidation

a chemical reaction or process that involves the removal of one or more electrons from an atom, ion or molecule (compare

reduction) parallel resonant frequency

for an electrical resonator (particularly one that represents a resonant mechanical system), the frequency at which the magnitude of the electrical admittance is minimum and the phase angle of the admittance is zero; the equivalent circuit model for such a system is characterized by a parallel combination of an inductor and capacitor, the square root of the product of whose values is equal to the reciprocal of the angular resonant frequency

partial pressure

the pressure of one gas or vapor that independently contributes to the total pressure in a gas and/or vapor mixture

partitioning

the process by which a chemical substance distributes between two or more media (phases) based on its affinity for the respective media; at equilibrium, the ratio of the concentrations of a substance in the two phases is equal to the partition coefficient, Kc

passive device

a device that effects some transformation of an input signal without use of any external power source; hence, the output power from a passive device is always less than or equal to its input power

phase shifter

a device that shifts the phase angle of the output signal by a specified (knob- or voltage-selectable) number of degrees relative to its input


417

slope

in an electrical system, the change of phase of a signal per unit change of frequency

phase-locked loop

a circuit in which feedback is used to adjust some parameter so as to maintain the phase difference between two discrete points in the circuit at a constant value

photoresist

photosensitive polymeric film used in photolithographic device fabrication (see lift-offprocedure)

physisorption (physisorb)

an adsorption process characterized by relatively weak interactions, such as those typical of van der Waals forces; because such weak forces occur between all molecules, physisorption is typically reversible and can occur on any surface

piezoelectric

referring to the property exhibited by certain crystals, whereby a polarization charge or voltage is generated upon the application of a mechanical stress; conversely, the tendency to undergo mechanical strain when subjected to an electric field

piezoelectric stiffening pogo pins

the effective increase of elastic modulus of a crystal owing to the presence of piezoelectricity

phase

spring-loaded pins for making electrical contact to a silicon chip, electroded crystal, or other electrical contact

polarizability

the tendency of a molecule's electron cloud to deform under the influence of an external charge or dipole

polynuclear

referring to organic compounds containing more than one aromatic ring, e.g., naphthalene, anthracene

port

an electrical connection to a device or instrument, typically comprised of a ground contact and a signal contact

positive photoresist

photoresist that is made (more) soluble in a chemical developer in those regions where it is exposed to (typically ultraviolet) irradiation

p o w e r meter

an instrument that measures RF power, typically utilizing a sensor that converts incident power to heat and measures the resulting temperature increase

propagating propagation

wave

measurement

see

traveling wave

in a delay-line acoustic sensor, determining the value of the measurand from the measured acoustic wave speed and/or attenuation

protein

one of a class of biologically important, high-molecular-weight compounds consisting of a complex sequence of amino acid units

pyroelectric

relating to the property exhibited by certain crystals, whereby a change of polarization charge (or voltage) results from a change of temperature

418


Q QCM quality factor (Q)

see qualityfactor see quartz crystal microbalance in the context of resonant acoustic devices, Q -fR/BW, where fR is the resonant frequency and BW is the bandwidth; Q can equivalently be defined as toUplPd., where to is the angular frequency, Up is the peak total energy present in the device, and Pd is the power dissipated by the device

quartz crystal microbalance (QCM)

a colloquial term for a thickness-shear mode (see) resonator

radio frequency (RE) receptor

the range of frequencies useful for radio transmission (but below the microwave range); typically in the range 10 kHz-1 GHz

redox

relating to a chemical reaction or process involving the transfer of an electron from one species to another (see oxidation and reduction)

reduction

a chemical reaction or process involving the addition of one or more electrons to an atom, ion, or molecule (compare oxida-

in biochemistry, that portion of a molecule (antibody, enzyme) that engages in specific binding interactions with another molecule (antigen, substrate)

tion) relative humidity (RH)

the partial pressure of water vapor contained in the air compared to that in air, at the same temperature, that is saturated in water vapor

resonance

a condition in which, at a particular frequency, energy in an electrical or mechanical system alternates stably between kinetic and potential energy forms

resonator

in acoustics, a device that supports a standing mechanical wave when excited at the appropriate frequency

RF RF detector

see radiofrequency a device that converts an RF signal into a DC signal, with the DC magnitude being proportional to the RF power

RH

see relative humidity

saturated

in electronics, referring to an amplifier operating at the limit of its output power and therefore unable to produce an increase in output signal amplitude as a result of an increase in input signal amplitude; in chemistry, referring to organic chemical compounds in which there are no double or triple bonds


419

saturation vapor pressure SAW self-assembled monolayer

the partial pressure of the vapor of a liquid that exists in the gas phase in equilibrium with an excess of that liquid

sensitivity

the change in signal of a device (e.g., a chemical sensor) per unit change in the parameter to which the device is sensitive (e.g., the concentration of a chemical species)

series resonant

for an electrical resonator (particularly one that represents a resonaat mechanical system), the frequency at which the magnitude of the electrical admittance is maximum and the phase angle of the admittance is zero; the equivalent-circuit model for such a system is characterized by a series combination of an inductor and capacitor, the square root of the product of whose values is equal to the reciprocal of the angular resonant frequency

frequency

SH.APM shear.horizontal acoustic plate mode (SH-APM) sorption (sorb) ST-cut quartz

see surface acoustic wave an ordered molecular monolayer film produced when a substrate with a crystallographically ordered surface is exposed to a dilute solution or vapor of the coating molecule, which must be capable of two chemical interactions: a strong chemical interaction between the "head group" of the molecule and the surface to orient all molecules similarly, and cumulative Van der Waals interactions between the "backbones" of adjacent molecules that confer regular alignment of the chainlike molecules

see shear-horizontal acoustic plate mode an acoustic plate mode (see) with particle displacement polarized perpendicular to the direction of wave propagation and parallel to the planes defined by the plate's surfaces a term that includes both absorption and adsorption (see) quartz crystal that generates a surface acoustic wave (see) when subjected to a time-periodic electric field typically produced by excitation of an interdigital transducer at the proper frequency; the crystal is cut at a specified angle to the crystallographic axes so that it has a small or vanishing dependence of wave velocity upon temperature at room temperature

stray capacitance

incidental capacitance, usually introduced by connecting wires, that reduces the amplitudes of transducer input or output voltages

substrate

in biochemistry, a substance acted upon by an enzyme and/or consumed in a biochemical reaction; in electronics, a physical platform upon which a device is constructed or fastened

surface acoustic wave (SAW)

a propagating or standing acoustic wave that is confined to the planar surface of a solid plate

420


surface chemical derivatization

the reaction and chemical binding of a chemical species to the surface of a material or device in order to (often permanently) alter the physical and/or chemical characteristics of that surface

synthesized oscillator

an instrument that digitally synthesizes a controlled-amplitude, controlled-frequency signal

thickness-shear mode (TSM)

an acoustic mode propagating in the direction normal to the plane surfaces of a crystalline plate, characterized by particle motion in the crystal that is parallel to the plate surfaces, and displacement maxima at both surfaces; the most familiar example of a TSM-based sensor is the quartz-crystal microbalance (QCM), more properly denoted as a TSM resonator

transmission line triple-transit echoes

an electrical or acoustical wave-guiding structure for delay-line-based devices, traveling acoustic waves that are launched by the input IDT, reflected backwards from the output IDT, reflected back again from the input IDT, and finally received by the output IDT

TSM

see thickness-shear mode

vector voltmeter

an instrument that measures the amplitude (voltage) and relative phase angle of two signals, one of which serves as its reference

viscoelasticity (viscoelastic)

the property of responding with a combination of elastic and viscous responses to a mechanical stimulus; many polymers exhibit viscoelastic behavior as a direct consequence of their chain structure

viscosity (viscous)

a measure of the flow resistance of a substance such as a liquid, polymer, or polymer solution; viscous behavior implies a linear relationship between shear stress and the rate of strain

wave path

the region of an acoustic wave device traversed or occupied, respectively, by a traveling or standing acoustic wave

wire bonding

the process of attaching fine connecting wires between metal bonding pads (see) on a silicon chip (or piezoelectric crystal) and the pins on a sensor device package, such as a device header or DIP (see); some combination of heat, compression, and ultrasonic energy is utilized to form a weld between a soft metal wire (gold or aluminum) and the bonding pad, often formed from a like material

Polymer

Density Solubility (g/cm3) Parameter, 8 (20-25 ~ (cal/cm3)1/2

Monomer Structure

Butyl Rubber (poly(isobutene-coisoprene)) Cellulose polymers: (structure is for unmodified cellulose)

0.925

[-CH2C(CH3)2-]n plus

7"= (*c)

-63

1.5

Re.t: 4:53 5:18

Imle

CH2OH O O

l

cellulose acetate butyrate cellulose triacetate ethyl cellulose Fluoropolyol

O ,,

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