Anal. Chem. 1995, 67, 1766-1771
Anomalous Diffusion. Surface Plasmon Resonance Measurements as Probes of Nanometer-Scale Film-Swelling Dynamics for CH30H in Poly(methy1 methacrylate) Phillip A. Drake and Paul W. Bohn* Department of Chemistty, University of Illinois at Urban-Champaign,
Surface plasmon (SP) resonance position measurements were used to study CH30H permeant-induced interfacial swelling processes in ultrathin (d 5 35 nm) poly(methy1 methaaylate) (PMMA) films,which are the key molecular events in the anomalous case I1 diffusion process. An instrumental system was developed for precision control of sample thermal history with a feedback temperature regulation system based on a digital velocity proportional integral controller control algorithm to address the extreme temperature sensitivity of diffusion processes in glassy polymers. Excellent agreement between measured and calculated SP reflectivity curves was obtained after inclusion of a small interfacial Ag/dielectric roughness layer, the properties of which were calculated from Maxwell-Garnett theory. Experimentswith bare Ag films demonstrated that the change in optical response of the Ag-PMMA composite structure was dominated by the change in the optical properties of the PMMA upon CH3OH uptake. Thus, changes in the resonance position of SP curves were used to measure the film swelling, AV, and changes in the average optical frequency dielectric constant of the swollen film, E, from which the permeant volume fraction, 4, was calculated. These curves were based on Fresnel reflectivity relationships for four- and fie-layer systems exhibiting one-dimensional swelling. Changes in film thicknesses were observable with this method with a resolution of less than 1 A. Permeant volume fractions corresponding to resonance shifts were also calculated and found to be identical for films in the 100-300-A-thickness regime.
600 South Mathews Avenue, Urbana, Illinois 61801
polymer films.'+ With a little more effort, composition information as a function of film dimension can be acquired through the use of common spectroscopic and depth-profiling techniques.+25 In none of these methods, however, does the signal provide information on the length scale on which polymer/permeant interactions operate.26 Consequently, current transport models, which have heretofore necessarily been based on macroscopic measurements, have a predominantly continuum character. Molecular aspects of diffusion are, in general, poorly understood. A case in point is s d e d case I1 anomalous diffusion,in which transport is controlled by the creep deformation rate of a glassy polymer in response to the presence of a small concentration of permeant molecules; Le., the critical rate-controlling transport phenomena are thought to involve the relaxation of a small interfacial region of polymer that bears the osmotic stress built up between a glassy core polymer (unpenetrated) and a fully relaxed (completely penetrated) rubbery region. It differs from Fickian diffusion in that, after an initial induction period, a sharp
Interest in transport phenomena through polymer thin films and membranes has increased steadily over the past several decades due to their importance to analyte-selective sensor membranes, pervaporative separators, dialysis membranes, and films used in solvent and mineral extraction or recycling. Other systems of substantial industrial value based on diffusive transport of materials to and from polymer films include photoresists and controlled chemical delivery systems (such as drug patches and implants). Understanding transport and diffusion mechanisms is obviously essential for optimizing current applications and designing new systems. Phenomenological observation of polymer/ permeant system behavior at macroscopic-length scales is straightforward. Traditionally studies have targeted concentration changes in feed or permeate fluids or weight (and dimension) changes in
Thomas, N. L.: Windle, A. H. Polymer 1977,18, 1195. Thomas, N. L.: Windle, A. H. J, Membr. Sci. 1978,3, 337. Thomas, Pi. L.; Windle, A. H. Polymer 1980,21, 613 Thomas, N. L.; Windle, A. H. Polymer 1981,22, 627. Thomas, N. L.: Windle, A H. Polymer 1982,23, 529. Michaels, A S.; Bixler, H. J.; Hopfenberg, H. B. J. Appl. Polym. Sci. 1968, 12, 991. 870. Cohn, D.; Marom, G. Polym. Eng. Sci. 1982,22, Okamoto, K:Tanihara, N.; Watanabe, H.; Tanaka, K,: Kita, H.; Nakamura, A.; Kusuki, Y.; Nakagawa, IC J Polym. Sci., Polym. Phys. Ed. 1992,30, 1223. Weisenberger, L. A.; Koenig, J. L. Appl. Spectrosc. 1989,43, 1117. Weisenberger, L. A.: Koenig, J. L. J. Polym. Sci., Polym. Lett. Ed. 1989, 27, 55. Grinsted, R. A.: Koenig, J. L. Macromolecules 1992,25, 1229. Grinsted, R A.: Clark, L.; Koenig, J. L. Macromolecules 1992,25, 1235. Hui. C . Y.; Wu. K C.; Lasky, R. C.; Kramer, E. J.J. Appl. Phys. 1987,61, 5129. Hui. C . Y.; Wu. K C.; Lasky. R. C.: Kramer, E. J. J. Appl. Phys. 1987,61, 5137. Mills. P. J.; Green, P. F.; Palmstrom, C. J.; Mayer, J. W.; Kramer, E. J. J. Polym. Sci., Polym. Phys. Ed. 1986,24, 1. Papanu, J. S.; Hess, D. W.: Bell, A T.: Soane, D. S. J Electrochem. Soc. 1989,136, 1195. Lasky, R. C.; Kramer, E. J.: Hui, C. Y. Polymer 1988,29, 673. Lasky, R. C.: Kramer, E. J.: Hui. C. Y. Polymer, 1988,29, 1131. Mills, P. J.; Kramer, E. J. J. Mater. Sci. 1989,24, 439. Gall, T. P.; Lasky, R. C.; Kramer, E. J. Polymer 1990,31, 1491. Nicolais, L.; Drioli, E.; Hopfenberg, H. B.; Tidone, D. Polymer 1977,18, 1137. Schlotter, N. E. J. Phys. Chem. 1990,94, 1692. Fell, N. F. Jr.: Bohn, P. W. Appl. Spectrosc. 1991,45, 1085. Umezawa, K; Gibson, W. M.: Welch, J.T.;Araki, K; Barros, G.; Frisch, H. L. J Appl. Phys. 1992,71, 681. More, A. P.: Donald, A M.; Henderson, A Polymer 1992,33, 3759. Drake, P. A.: Bohn, P. W. A n d . Chem. 1994,66, 79.
1766 Analytical Chemistiy, Vol. 67, No. 7 7 , June 7, 7995
0003-270019510367-1766$9.00/0 0 1995 American Chemical Society
concentrationfront moves at a constant velocity. In addition, case I1 theory1-5J3-15J7-20*27-38 predicts a sharp permeant concentration front separating the polymer into glassy (zero permeant concentration) and rubbery (essentially constant permeant concentration) regions. An induction period prior to front formation is observed, in which the polymer at the permeant interface is thought to become plasticized. Obviously since the glassy and rubbery bulk regions involve either zero or large and constant permeant concentrations,respectively, the crux of the physical phenomena that determine case I1 behavior must be at the interface between the two regions. In order to understand better the anomalous diffusion process at a molecular level we ask questions like, What is the characteristic time scale, ZR,for polymer chain relaxation at the interface? What is the physical extent of the interfacial region? At what composition does the solvent front gain its macroscopically measured velocity, vf? How does the microstructure of the polymer itself affect the dynamics? Clearly, in order to address these questions we require experimental probes that target the pertinent length and time scales, implying that analytical techniques used to study the critical plasticization phenomena must be capable of monitoring events at the nanometer-length scale, as well as probing sample changes in situ and in real time. In addition, the probe should be independent of the particular chemical and physical properties of the polymer/penneant system. In the work reported here, we demonstrate that careful measurements of shifts in the resonance positions of surface plasmons exhibit all the above attributes, by using surface plasmon resonance measurements to study the dynamic properties of 10nm-thick films of poly(methy1 methacrylate) (PMMA) in response to CH30H vapor exposure, a classic case I1 diffusion system. These films are sufkiently thin that they do not display the classical phenomena typically associated with case I1 behavior, Thus, they can be used as models for interfacial behavior, since their response should mimic that at the glassy/rubbery interface. Indeed, films of these dimensions should display dynamics determined entirely by the same kinds of molecular-level plasticization phenomena, i.e., chain solvation and molecular rearrangement, which govern the interfacial response in macroscopic (d 2 1pm) case I1 systems. METHODOLOGY
Surface Plasma Resonances. Surface plasmons are electromagnetic waves associated with the collective oscillations of conduction electrons at a metal/dielectric interface. Figure 1 shows a schematic diagram of the optical components used to excite surface plasmon resonances in the Kretschmann configuration. When the component of the wavevector of incident radiation parallel to the interface, k,, matches that of the surface Alfrey, T., Jr.; Gumee, E. F.; Lloyd, W. G. J. Polym. Sci., C 1966, (12), 249. Korsmeyer, R W.; Von Meerwall, E.; Peppas, N. A. J. Polym. Sci., Polym. Phys. Ed. 1986,24,409. Wang, T.T.; Kwei, T. K. Macromolecules 1973, 6, 919. Korsmeyer, R W.; Peppas, N. A. Polym. News 1984, 9,359. Petropoulos, J. H.J. Polym. Sci., Polym. Phys. Ed. 1984.22, 183. Yilmaz, L.; Tosun, I. J. Polym. Sci., Polym. Lett. Ed. 1982,20,569. Cole, J. V.; Lee, H. H. J. Electrochem. SOC.1989, 136, 3872. Sarti, G. C. Polymer 1979,20,827. Sarti, G. C.; Apicella, A Polymer 1 9 8 0 , 2 1 , 1031. Hayes, C. IC; Cohen, D. S. J. Polym. Sci., Polym. Phys. Ed. 1992,30,145. Fu, T. 2.; Duming, C. J. AIChE J. 1993.39, 1030. Kawagoe, M.; Nunomoto, S. Polymer 1991,32,3130.
sample layer
/
superstrate Ag film
sapphire p r i s m y /
\/ k, = k,np sin 0,
Figure 1. Schematic diagram of the surface plasmon excitation geometry in the Kretschmann configuration.
plasmon at the frequency of excitation, k,,(co), excitation of the surface plasmon occurs, and energy is transferred from the bulk electromagneticmode into the surface plasmon excitation. Varying the angle of incidence of the incoming radiation provides a simple way to vary k,, since k, = Ron, sin e, where ko is the magnitude of the incident wavevector, np is the refractive index of the coupling prism, and 8, is the angle of incidence. A plot of reflected intensity vs angle of incidence will, thus, exhibit a sharp minimum at the resonance position. Shifts in the position of the resonance reflect changes in film thickness and composition, because the momentum, ti&,, of the surface plasmon is a sensitive function of the optical properties of both the metal and any dielectric film or other material immediately adjacent to the metal. Thus, surface plasmons are interface-specific and are especially well-poised to study such interfacial phenomena as fluid condensation, metal and semiconductor behavior, and the properties of selfassembled and Langmuir-Blodgett monolayers and multilayers. Several excellent monographs and reviews are available on the theory and applications of surface pla~mons.3~-~~ In the present experiments, changes in film thickness and dielectric function were monitored in real time as PMMA samples responded to the introduction of permeant vapor. Shifts in surface plasmon (SP) angular resonance positions were used to track the polymer response to CH30H exposure. Swelling Model. Previous investigations of substrate-sup ported micrometer-thick polymer films indicated that swelling is initially constrained to a single dimension and that relaxation to three-dimensional swelling occurs only after the permeant front has passed completely through the film and reached the sub ~trate.~3 In the model that follows we assume that, for very thin (d 5 100nm) polymer films, swelling occurs only in the direction normal to the plane of the film. This assumption is supported by the fact that no swelling and then shrinking behavior is observed in our experimental data; i.e., in contrast to macroscopic films, film thickness increases monotonically from the dry to the completely swollen polymer film. Equation 1gives the geometric
dependence of the instantaneous volume fraction of permeant, 4, Electromagnetic Surface Modes; Boardman, A. D., Ed.; Wiley: New York, 1982; pp 143-200. Surface Polaritons; Agranovich, V. M., Mills, D. L., Eds.; North Holland: Amsterdam, 1982. Raether, H. Surface Plasmons on Smooth and Rough Surfaces and on Gratings; Springer-Verlag: New York, 1988; Vol. 111, pp 4-37. Sambles, J. R J. Phys. Chem. Solids 1988,50, 1. Welfor, K. Opt. Quant. Electron. 1991.23, 1.
Analytical Chemistry, Vol. 67, No. 11, June 1, 1995
1767
32
36
34
36
40
42
0 00
44deg
Incident Angle (deg)
Figure 2. SP resonance curve calculated from the exact Fresnel equations for a four-layer system at A = 514.5 nm with the following ~ -1 1.O jO.365, dAg = 54.2 nm, optical parameters: ep = 3.1 3, C A = €film = 2.24, &m = 10.6 nm, and ealr = 1.001,
+
on the dimensions of the film, where x, y, and z are film dimensions, with the plane of the film containing the x and y coordinates. Film volume is represented by V, and the subscript 0 indicates an initial (unswollen) state. Equation 1 reduces to a simple relationship between the instantaneous film thickness, the initial thickness, and the penetrant volume fraction,
If it is further assumed that the dielectric function of the polymer film changes in a homogeneous manner; Le., the relationship between 4 and the dielectric constant of the permeant, ~ p (in , condensed form) and that of the polymer, epoly,can be approximated, 6
= E P 4 + Epoly(l
- 4)
(3)
These assumptions are valid, if (1) the film is sufficiently thin that no case I1 boundary is formed; i.e., the dielectric constant of the polymer is actually constant at any one instant in time throughout the entire thickness of the film,or (2) shifts in plasmon resonance positions behave in similar fashions for homogeneous films and two-layer (swollen and unswollen) films with identical average dielectric properties over the thickness of the film. Model calculations for l h m - t h i c k PMMA films and CH30H permeant have been performed, which indicate that the above approximation is valid. Implicit in eq 3 is the assumption that the volume of the swollen film is approximately the sum of the volume of the dry polymer and liquid volume of the imbibed penetrant; Le., the volume of mixing is small. Figure 2 shows a calculated SP resonance curve for a film thickness and dielectric constant profile similar to that used in the present experiments. Families of these curves were generated by varying C$ from 0 to 0.25 and submitting polymer film thickness and refractive index values calculated from eqs 2 and 3 to Fresnel reflectivity equations for a four-layer system. Figure 3 shows a resulting plot of expected resonance position vs C$ for a 1@nm PMMA film exposed to CH30H vapor. Third- and fourth-order polynomial fits to data sets such as this were produced for films of starting thicknesses equivalent to those used in permeation runs. Empirical functions created from fitting coefficients were then used to convert experimentally measured resonance positions to C$ and film thickness values. 1768 Analytical Chemistry, Vol. 67, No. 17, June 7 , 7995
0 05
0 10 0 15 Permeant Volume Fraction ($)
0 20
0 25
Figure 3. Relationship between permeant volume fraction and SP resonance position calculated from families of cuwes similar to Figure 2.
EXPERIMENTAL CONSIDERATIONS Materials. High-purity B&J CH30H (Baxter Healthcare, Muskegon, MI) was used throughout. Sapphire hemicylinders 2.0 cm in length with a radius of curvature of 7.5 mm (Hanick Scientific, Ossining, NY) were cut perpendicular to the major axis of a larger hemicylinder with a diamond saw. Sapphire substrates were cleaned in preparation for sample deposition by agitation for several minutes in a 6 M HN03 bath, followed by rinsing in methanol and mechanical cleaning with methanol-saturated lens paper. Sample Preparation. Silver films were deposited directly onto the sapphire hemicylinder by thermal evaporation at 2-3 A/s at pressures below 5 x Torr. All Ag films were of thickness 540 f 20 unless otherwise noted. Poly(methy1 methacrylate) of low polydispersity (Mp = 333 000; Mw/Mx = 1.06) obtained from Polymer Laboratories (Amherst, MA) was cast from 0.33 to 1.0%(w/w) solutions in chlorobenzene by spincoating in a custom chuck at 3000 rpm for 1 min. Thermal histones of all samples were carefully controlled and followed very similar patterns. Films were first annealed at 125 "C under vacuum for 2 h and subsequently cooled at 0.250 "C/min to within 5 "C of room temperature. All permeation experiments were performed using freshly prepared samples. Film Thickness Verification. Surrogate samples partially masked from Ag deposition and completely coated with a thin polymer film on 1in. x 3 in. fused quartz slides (Quartz Scientific) were prepared under the same conditions and side by side with samples used in permeation experiments. Film thicknesses were verified using physical profilometry of scratches in samples on quartz substrates with a Dektak 3030 Auto 1system Weeco Inst.). Profilometry data were acquired with forces of 8-20 mN applied to a diamond stylus of radius 12.5 pm. Experimental Setup. Figure 4 shows the optical train used for permeation experiments. A spatially filtered (25pm pinhole), expanded beam at 514.5 nm was passed through the sapphire hemicylinder and brought to a focus at the sample surface in the Kretschmann configuration. The reflected beam was then collected and roughly collimated by passing through a final compound lens and detected with a Photometrics Model CH210 CCD camera system. In this setup, with a nonlinear CCD calibration, it was convenient to match the image size to the CCD chip by adjusting the final lens position. This optical system performs the function of mapping a specific k vector onto a given pixel column on the detector array. Integration times of 50 ms were more than adequate to generate a substantial signal with typical power at the sample less than 1 pW. Binned image files
Soleil-Babinet neutral cOmDenSator density filter
aperture
5
m m
i i
polarizer
'201n 100
spatial filter / beam expander
CCD detector
u Figure 4. Optical setup used to acquire complete SP resonance curves simultaneously. The combination of the Soleil-Babinet compensator and the polarizer was used to provide very clean ppolarization at the sample, thus avoiding nonresonant background from s-polarized components. Spatial filtering was accomplished with a 0.12 NA microscope objective and a 25-pm pinhole. sapphire hemicylinder Ag Film (=550A thick) thermocouple junction
Teflon@ wire cladding
Teflon@ cell body
3
0
400
200
600
800
Run Time (min)
Figure 6. Typical sample thermal history produced by temperature program feedback control system. Sample temperature during permeation experiment was 25.0 f 0.1"C.
tency. Power to solenoid valves and the peristaltic pump were regulated through a parallel interface constructed in-house. Temperature control of polymer samples was accomplished by feedback control of a silicone rubberencased resistivetype heating tape (Glascol, Terre Haute, IN) surrounding the aluminum cell support. In addition, the support was drilled and tapped to allow for liquid and gaseous coolant flow for optimum energy transfer to and from the cell. A digital velocity PID controller of the form,
I
fused quartz window Figure 5. Cutaway schematic of sample cell. Polymer samples were cast at the interface of the Ag film (shown inverted in this geometry) and the vapor chamber.
containing ATR curves were then collected into RAM memory on a Spear 486 DX computer and compressed into a single multifile using Photometrics CCD9000 software at the end of each run. Cell components included the sapphire hemicylinder, a PTFE cell body, and a quartz window. A cross-sectional schematic of the sample chamber is shown in Figure 5. Components were compressed together in an aluminum support and held in place with a single-threaded retaining ring. PTFE needles were compression fit into the PTFE cell body for superstrate fluid introduction and purge. Thermocouple wire 0-type, 8Gpm diameter, Teflon clad) was also force-fit into the cell body in order to monitor the sample temperature. The wire was oriented such that the thermocouple junction was located in thermal contact with a region of the sample surface away from the Ag film. Experimental Control. In order to control the thermal history of each sample precisely and reproducibly, experimental events were coordinated via a Dell Dimension 486 DX2 desktop computer (Dell Computer Corp., Austin, TX) with in-house software generated with a Labview for Windows graphical programming environment (National Instruments Corp., Austin, TX). This control included shutter activation of the CCD camera, temperature readout, solenoid valve and pump activation for superstrate fluid control, and temperature control. A filtered temperature readout with automatic bandwidth control was generated from the thermocouple using a digital temperature indicator @P41-TC-S2A, Omega Engineering, Inc., Stamford, CT) and polled by the control system at a regular interval via RS232. The thermal history for each permeation experiment was recorded and examined against optical data to ensure run-to-run consis-
where pnis the heater power controller output at the nth sampling period, K, the controller gain, e the error (difference between target and actual temperature), At the sampling interval, TI the reset time, t~ the derivative time, and B the measured value of the controlled variable (temperature in this case), was employed to tie the sample temperature to the programmed set point or sl0pe.4~ Tuning parameters for the controller were calculated with the internal model control method45using measured system parameters K (process or system gain), z (time constant), and e (delay) according to the functions shown in eqs 5-8.
(5)
-- re D-e+2t
z
t --
(7)
6A
- Z(6 +A)
The output from the controller was converted to a duty cycle for the heater administered through the parallel interface. Figure 6 shows a typical thermal history for a sample over the course of a permeation experiment. A typical permeation experiment (44) Seborg, D. E.: Edgar, T.F.: Mellichamp, D. A Process Dyrzamics and Control; Wiley: New York, 1989 p 196. (45) Braatz, R D. The Controls Handbook; CRC Press: Boca Raton, FL, 1995, Internal Model Control chapter, in press.
Analytical Chemistry, Vol. 67, No. 11, June
I, 1995 1769
43.65 {
-
43.60
2
43.50
0
0
cn
"1 \I
n
-Calculated '
;43.45
Experimental
63 43.40
0.2
U
V
0.04 I
I
37
38
I
I
39 40 Angle of incidence
I
I
I
41
42
43deg
Figure 7. ATR data (individual points) and calculated ATR curve = 514.5 nm with the following optical parameters: ep (solid line) at i, = 3.13, €Ag -1 1 .o jl.365, dAg = 54.2 nm, €film = 2.24, driim = 10.6 nm, and tal,= 1.001,
+
consisted of (1) a 9 h thermal pretreatment of the sample as described above, (2) a step change in superstrate concentration from filtered nitrogen to CH30H vapor (saturated at 20.0 f 0.1 "C), (3) a 5 h equilibration period, and (4) a step change in superstrate composition from CH30H vapor to filtered nitrogen. Three identical permeation runs involving all four steps were completed for each sample. Sample temperature and resonance position were monitored throughout the entire experiment. This extreme care was taken to ensure precisely reproducible thermal history and aging pretreatment from run to run. Data Processing. The sampled area of the hemicylindrical prism was aligned with respect to the center of rotation of a system 5 precision rotational stage (Ealing Corp., South Natick, MA) upon which the cell and support were mounted. The aperture shown in Figure 4 was then stopped down to less than 1 mm, and the zero point on the readout of the rotational stage was located by retroreflection. With the aperture still stopped down, the stage was rotated until the narrowed beam passed through the collection lens and onto the detector. At least three images were then collected and corresponding stage positions noted. Functions generated with linear or low-order polynomial curve fits to pixel vs angular stage position data were then later applied to raw data acquired with an unstopped aperture to correlate CCD pixel number with incident k vector, which was tuned by changing the angle of incidence. Because the resonances were typically very sharp, precise resonance positions in individual traces of reflected intensity vs incident angle data were calculated by fitting the data near the minimum in the reflectivity curve to a second-order polynomial, utilizing a simple triangular minimum extrapolation algorithm.
43.35
-j I 0
I
I
I
5
10
15
I
Exposure Time (min)
Figure 8. Observed shift in resonance position of a 100-A PMMA film in response to exposure to CH30H vapor (saturated at 20 "C). Expanded inset shows initial (t < 1.O min) resonance shift. The solid line through data is a least-squares fit to a double-exponential function and is intended to be a guide to the eye.
RESULTS AND DISCUSSION Figure 7 shows calculated and experimental SP resonance curves for PMMA films of thickness 106 f 6 A. The general shape, width, and position progression with respect to film thickness follows that of calculated curves very well. A small offset in absolute position between the curves was typically observed and attributed to Ag surface roughness features. The magnitude of the shift may be readily accounted for in calculated curves by including a small interfacial roughness layer of intermediate composition, the optical constants of which were calculated with Maxwell-Gamett t h e ~ r y . The ~ ~ ,angular ~~ window represented
in each curve was at least 5". Shifts in resonance positions in each 516 point data set of -0.001" were observable after processing. Reference to Figure 6 shows that this resolution corresponds roughly to a minimum detectable change in permeant volume fraction, A@, of 0.0006. Figure 8 shows the shift in resonance position resulting from exposure of a l06ikthick PMMA film to CH30H vapor. No significant variation in the general form of Os, vs exposure was observed at early exposure times for films of 1@,2@,and 3@nm nominal thicknesses. The overall shift in Osp after permeant introduction can be attributed to two independent effects. First, an offset due simply to the change in dielectric constant of the superstrate occurs as the superstrate composition is changed from nitrogen to CH30H vapor. Cell dead volume calculations and superstrate flow rate control experiments indicate that a complete superstrate composition change requires -3 s in our apparatus. Second, more gradual shifts in Osp occur as the film thickness and dielectric constant profile are modified in response to permeant-induced swelling. Calculations indicate that a superstrate dielectric change from 1.0006 to 1.0011 upon permeant introd~ction~~ should result in a shift of 0.002", while shifts of 20.2" were observed for PMMA films exposed to CH30H vapor. Thus, the large discrepancy between superstrate-onlydielectric changes and the observed shifts in SP resonance position for the PMMA film clearly indicates that the Osp response to CH30H addition is dominated by changes in sample thickness and optical properties. Previous studies of case I1 diffusion in macroscopic samples clearly demonstrate the need for precision control of sample temperature and thermal history. Sample aging and cooling rate through Tg have been shown to affect diffusion characteristics of these systems dramatically. Two critical parameters used in models of case I1 diffusion, polymer viscosity and permeant diffusion coefficient, have both been shown to be exponential functions of temperature as we11.I8 The data in Figure 8 were obtained with a sample temperature of 25.0 f 0.1 "C. Since the measured temperature sensitivity of the SP resonance measurement turned out to be 2.5 x "(ang)/"C, temperature control to *O.l "C resulted in a negligible error. Figure 9 shows plots of film thickness and dielectric constant extracted from processed SP data using eqs 2 and 3. Each plot
(46) Handbook of Chemisty and Physics, 64th ed.: CRC Press: Boca Raton, FL, 1984: p E365.
(47) Aspnes. D. E. In Handbook ofoptical Constants ofsolids; Palik, E. D.. Ed.; Academic Press: Orlando, FL, 1985: pp 104-108.
1770 Analytical Chemistry, Vol. 67, No. 11, June 1, 7995
-
125-
m
120-
-5.
E
- 2.40 - 2.35
t‘6 1 1 5 -
0
-E
- 2.30 - 2.25 - 2.20
thickness
110-
105-
p
b
101
0
I 0
I
I
5
10
I
f2.15
15
0 0
Exposure Time (min)
Figure 9. Poly(methy1 methacylate) film thickness and dielectric constant changes resulting from swelling by CH30H vapor.
features an extremely sharp region at exposure times between 0 and 0.2 min, followed by a monotonically changing region, which levels off at -10 min to a constant value. The qualitative form of the sample swelling curves may be interpreted in terms of a model with discrete time-separated phenomena. First, an initial saturation of the interface occurs. This is accompanied by rapid swelling of the film in order to accommodate solvent molecules, followed by slower relaxation processes in the polymer. In contradistinction to all previous studies of case I1 diffusion, in these experiments, the entire film may be thought of as the “interface”,since the film thickness is smaller than the characteristic extent of the Fickian solvent region ahead of the case I1 front.18,20This interpretation is further substantiated by the lack of an observable induction period for swelling phenomena in these films. Interestingly, the thickness data can allow us to determine the thickness sensitivity of SP resonance measurements for the PMMA/CHr OH system. Changes in permeant volume fraction, Aq5 5 0.01 have been measured. Assuming that the region of data under consideration corresponds to exposure times in which the superstrate composition is constant (>3 s), for films of this thickness, the observed Aq5 corresponds to average film thickness variations within the probed region of P 1A. Figure 10 summarizes changes in film thickness and q5 at equilibrium as a function of the thickness of the unpenetrated sample. Several important observations can be made. First, a linear fit to thickness data extrapolatesto withii 1A of the origin, indicating that the swelling is linear fashion and that the total volume change scales with volume of the glassy polymer used in the experiment. This observation is important, because it is consistentwith observations made on millimeter-lengthscale, i.e., macroscopic, samples. Second, the equilibrium permeant volume fractions are independent of starting volume and are in excellent agreement with PMMA/CH30H equilibrium volume fractions found in the literature for macroscopic samples.38 Because these
I
1
50
100
.
I
I
150 200 Film Thickness at Run Stan
I
I
250
300
tc
0.04 0.02
0.00
Figure 10. Sample thickness change and penetrant volume fraction increase at equilibrium for 106-, 205-, and 326-A (dry thickness) PMMA films.
measurements could be interpreted within the context of an homogeneous swelling model, and because it is known that the macroscopic case I1 behavior is far from homogeneous, these observations unambiguously define the size regime in which these measurements were made as being interfacial,thus validating the original hypothesis that examining ultrathin films can provide a window into important interfacialprocesses in anomalous diffusion. Understanding the basic mechanisms of anomalous diffusion requires that we understand the interface between swollen rubbery polymer and the unswollen glassy core. Almost all previous measurements that had been brought to bear on case I1 systems used experiments that probed length scales much larger than the interface. The present work demonstrates that shifts in position of SP resonances can be a used as an indicator of interfacial swelling and optical constant variation resulting from anomalous diffusion processes in ultrathin polymer films. Excellent temporal resolution of these events may be obtained in situ using direct imaging techniques. Resonance shifts corresponding to thickness changes of less than 1 A are easily resolved, establishingthe SP technique as an important probe for studying anomalous case I1 diffusionin particular and molecular transport at nanometer dimensions in general. ACKNOWLEDGMENT
The authors acknowledge the assistance of Professor Richard Braatz for invaluable aid with the feedback controller and tuning parameters for the feedback temperature control system. This work was supported by the U S . Department of Energy under Grant DOE FG02 88ER13949. Received for review February 27, 1995. Accepted March 27, 1995.@ AC950206W Abstract published in Adoance ACS Abstracts, April 15, 1995.
Analytical Chemistry, Vol. 67, No. 11, June 1, 1 9 9 5
1771
