Anal. Chem. 1893, 65, 3382-3388
3382
Mass Transport Phenomena in Thin Films of Poly(2-vinylpyridine) Studied via Optical Guided Wave Techniques Nicholas F. Fell, Jr., and Paul W. Bohn’ Department of Chemistry and Beckman Institute, University of Illinois at Urbana-Champaign, 600 South Mathews Street, Urbana, Illinois 61801
The unique ability of optical waveguide techniques to determine simultaneously film thicknesses and mass transport behavior in swollen polymer films is utilized in these experiments to make accurate determinations of diffusion coefficients of fluorescein into HzO-swollen poly(2-vinylpyridine) films from aqueous solution. The diffusion behavior is determined from fitting the fluorescencetime curvesto an intensity expression derived from Fick’s second law and the appropriate boundary conditions to obtain the diffusion coefficient of the fluorophore in the film. Two techniques for characterizingthe fluorescencebehavior spatially and temporally are critically compared. Fiber optic-based detection schemes suffer from inaccuracies relative to the use of an imaging camera based on a charge-coupleddevice (CCD) array.The diffusion coefficients obtained show no significant dependence on the bulk solution concentration in the range 1 nM I[fluorescein] I10 pM of the fluorophore. The value of the diffusion coefficient was found to be in the range 1 X cm2/s ID I3 X lo-” cmz/s and was found to vary widely with small changes in sample preparation conditions.
INTRODUCTION Thin polymer films are ubiquitous in modern technology,’ so development of techniques for the in situ characterization of their properties is crucial. For example, in many chemically modified electrode systems, solvent-swollen polymer films are used either to provide protection for the device or to enhance selectivity.2 The determination of the diffusion coefficientis critical to the quantitative use of these electrodes, since diffusive processes are responsible both for loading the electroactive material into the polymer film and for the delivery of solution species to the outer layers of the polymer, where electrical communication with a redox shuttle is established. A serious difficulty in the determination of diffusion coefficients in polymer films is the necessity to determine the film thickness under the same conditions used in the e ~ p e r i m e n t .Many ~ polymers are significantly plasticized in common solvents, so the films swell, which makes the determination of the film thickness difficult, since the swollen film thickness must be determined. The determi-
* Author to whom correspondence should be addressed.
nation of the swollen film thickness presents a significant challenge for most of the “standard”methods for determining film thickness; however, it is a simple process when optical waveguide techniques are used. Optical waveguide techniques, however, allow the determination of the film thickness in situ by measuring the eigenmode distribution in the solution environment: which, since it can be done both before and after the film is exposed to a permeant solution, can yield both unswollen and swollen film thicknesses. Raman scattering or fluorescence from the permeant in the film, excited by one or more simultaneously propagating eigenmodes, can then be monitored as a function of time and the resulting signals used to characterize the mass transport behavior of the permeant in the film. In the case of simultaneous multimode excitation, permeant spectroscopic signals can be used to report on mass uptake, since the combination of eigenmodeslaunched in these experimenta results in a roughly homogeneous intensity distribution in the ~ a v e g u i d e .Thus, ~ both thickness and transport information can be obtained within the same experimental modality. Optical waveguide techniques provide a unique combination of advantages for the characterization of diffusion processes. They allow the in situ, nondestructive, realtime examination of thin films while providing molecularly specific information through the collection of Raman scattering or fluorescence from the film, solvents, and permeant. Waveguide techniques are well-suited to the examination of films in the 0.2-10-rm-thickness regime, a size regime in which many technologically important films lie. In addition, by resolving the fluorescence both spatially and temporally, it is possible not only to extract a mass transport coefficient but also to determine whether the mechanism of the diffusion is Fickian or case I1 from the functional form of the response. Previous work which demonstrated the utility of optical guided wave techniques for the characterization of case I1 diffusion in polystyrene films6 is extended in the present experiments by examiningthe Fickian transport of fluorescein into poly(2-vinylpyridine) (PPVP), a representative waterswellable film. The choice of fluorescein was made on the basis of its well-characterized fluorescence and water solubility. The selection of a considerably weaker fluorophore could have been made, since strong signals were obtained with 1200 r W of guided laser radiation, even at very small loadings. In this paper we develop the appropriate mathematical formalism for analysis of optical waveguide fluorescence (or for that matter any linear spectroscopic signal) data to extract information about mass transport behavior. A careful comparison is made of two data collection schemes, one based on fiber optic image delivery to a remote spectrometer, and the other based on direct imaging onto a CCD,
(1)Swalen,J.D.;AUara,D.L.;Andrade,J.D.;Chandross,E.A.;Garoff, (4) Bohn, P. W. Anal. Chem. 1986,57,1203. S.;Israelachvili, J.; McCarthy, T. J.; Murray, R.; Pease, R. F.; Rabolt, J. (5)(a)Schlotter, N.E. J.Phys. Chem. 1990,94,1692. (b) Miller, D. F.; Wynne, K. J.; Yu, H. Langmuir 1987,3,932-950. R. Ph.D. Thesis, University of Illinois, 1987. (2)Faulkner, L. R. Chem. Eng. News 1984,(Feb 27), 28. (6)Fell, N. F., Jr.; Bohn, P. W. Appl. Spectrosc. 1991,45,1085. (3)Taylor, M. E.Ph.D. Thesis, University of Illinois, 1991. 0003-2700/93/0385-3382$04.00/0
0 1993 American Chernlcal Soclety
ANALYTICAL CHEMISTRY, VOL. 85, NO. 23, DECEMBER 1, 1993
n4 Superstrate
t
I
Y Zero O Y dr: A
8883
{ni,ti}. This method has been demonstrated with one-layer films by Ulrich and Torge' and by Swalen and co-workere? In these experiments it is important to pay carefulattention to the manner in which coherent radiation is coupled into the
polymer waveguide structures. There are several techniques for efficientlycoupling light into a waveguide structure. Prism coupling is the most easily implemented form of coupling n2UnswdlsnFilm into thin polymer films. However, it suffers from several disadvantages. The coupling efficiencyis dependent on the n, Substrate size of the coupling gap, so the pressure used to hold the prism to the guide surface is a vital, and hard to control, fador. Also,the coupling gap must contain the same material as the guided region superstrate in order to minimize intermode scattering,'6 and the prism edge can damage the n5 "Backside" f i and thus stronglyattenuate the guided radiation. Grating coupling is generally less efficient than prism coupling, but F W 1. Sample structure. A thin polymer film with lower layer once the gratings have been fabricated, it is much easier to refractive 1xn2 and thickness t2 and upper layer refractive index tbandthiduw#lst.~is-on a fusedquartz stbstratewflhrefrecthre implement, especially when the superstrate is a liquid. index nl. The environment around the sample is described by the Therefore, grating coupling has been used in these experisuperstrate refractive krdex, n4,and the backside refractive index, n5. ments. For example, DeGrandpre and co-workers recently CY is the incident (observed)angle for the ii@tt,O1 is the angle inside demonstrated the use of grating coupling in liquid environthe substrate. and Oh is the guiding angle for mode n u m k m In layer i. a12and~54rePr(WBnfthepheseshlttsatthesubslrate-tihrlnterface ments for absorbance measurements," and Bolton and Scherer have used the eigenmode analysis technique to and the fllm-supcnstrate interfaces, respectively. The +larder diffraction of thepting is coupled into the film, while the O-wder beam examine the effect of varying levels of humidity on bovine passc#lthrwghtheRkn. In ordarforguldingtooccu, n2 1 tb > nl serum albumin f i i refractive index and thickness on the 1 n4,ns. The coordhrete system is a8 depicted. several micrometer thickness scale.18 The coupling equation for translating the observed angles into the internal angles with special reference to the artifacts and experimental is simply a combinationof Snell's law and the gratingequation: uncertainties associated with both. Finally, the CCD system n, sin a = n, sin O1 = n2 sin O, - ( v X / L ) is used to characterize the concentration dependence of mass (1) transport for fluorescein diffusion into HzO-swollen poly(2where n, is the refractive index of the material below the vinylpyridine)films and to delineate some of the fadors which substrate, a is the observed coupling angle, 81 is the angle affect sample-to-sample variability. inside the substrate, ez, is the guiding angle inside the polymer, Y is the grating order (typically +1 for the films THEORY studied here), X is the wavelength of the light used, and L is the grating period. WaveguideTheory. Optical waveguidephenomena have While it is necessary to attain single-mode operation to been known for many years to occur in structures such as obtain the f i i thickness,it is undesirablein the determination that shown in Figure 1, where the film refractive index is of 111888transport properties. This is due to the fact that the greater than both the substrate and superstrate refractive electric field distributions in the film are mode dependent. indexes. The relationship between the optical properties of The observed spectroscopic intensity is proportional to the the f i i structure, {nipti};i = 1-4 (the set of refractive indexes product of the square of the electric field amplitude and the of the various components and their thicknesses), and the probe number density in the f i i integrated over the thickness propagation constantsfor guided radiation has been discussed of the f i i . ' J 9 The entire film thickness is monitored as well by a number of authors for both the single thin f i i (threeas a length of guide propagation, so the function must be layer) and double thin f i i (four-layer) It is clear integrated over the film thickness, w,and the length of the from these previous studies that the distribution of mode imaged propagation region, A, according to, angles, {Oil; i = O...m, changes with changes in the refractive index and thickness of the f i i ; Le., the angular region, AO, in which they are observed becomes narrower as the f i i index approaches the value of either the superstrate or where substrate refractive indexes, and the mode distribution changes. Also,the number of modes increaseswith increasing fiithickness. In short, the measured propagation constants and may be wed in conjunction with the appropriate form of the eigenvalueequation to yield refractiveindexes and thicknesses (3b) for the thin f i i ( s ) in the structure, i.e., {nz,tz, n3, t 3 ) , (cf. Figure 1). The use of this strategy also allows the prediction and I ( t ) is the fluorescence intensity as a function of time; of the propagation constants, K i = ni sin Oi, for a given set of F(z,t)isthe fluorophoreconcentration in the film as a function of both position and time; F ( t ) is the total fluorophore (7) Ulrich, R.; Torge, R. Appl. Opt. 1973, 12, 2901. concentration in the film aa a function of time; I&) ie the (8) Swalen,J.D.; Tacke, M.; Santo, R.; Fiecher, J. Opt. Commun. 1976, 1R. .%7. intensity of the guided radiation as a function of position in (9) Tien, P.K.Appl. Opt. 1971, IO, 2395. the thickness direction; b is a combination of constants, such (10) Kogelnik,H.;Weber, H.P. J. Opt. Soc. Am. 1974,64, 174. (11) Tien, P.K. Rev. Mod.Phys. 1977, 49 (2). 361. (16) Saavedra, 5. S.;Reichert, W. M. Appl. Spectrwc. 1990,44,1210. (12) Kernten, R.T.Opt. Acta-l976,22, 515. (17) DeGrandpre, M. D.;Burgese, L. W.; White, P. L.; Goldman, D. (13) Kersten, R. T. Opt. Acta 1976,22, 503. 5. Anal. Chem. 1990,62, 2012. (14) Kogelnik,H. In Topics in Applied Physics; Tamir, T., Ed.; (18) Bolton, B. A.; Scherer, J. R. J. Phys. Chem. 1989,93, 7635. Springer-Verleg: New York, 1986; Vol. 7, Chapter 2. (19) (a) Stephens, D. A.; Bohn, P. W . Appl. Opt. 1986,25,2866. (b) (15) Tamir, T. In Topics in Applied Physics; Tamir, T., Ed.; Miller, D. R.; Han,0. H.;Bohn, P.W . Appl. Spectrwc. 1987,41, 249. Springer-Verleg: New York, 1986; Vol. 7, Chapter 3. n3Swdla Film
--.
/
O L + Order l
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ANALYTICAL CHEMISTRY, VOL. 65, NO. 23, DECEMBER 1, 1993
as the incoupling efficiency, the optical collection efficiency, and the quantum efficiency of the fluorophore; E is the molar absorptivity of the fluorophore; and the coordinate axes are as shown in Figure 1.
in time. We begin with Fick's second law,
In order to understand the interaction of the guided radiation with a diffusing chemical species, it is necessary to examine the electric field distribution in the film. Kogelnik and Weber,'o among others, have detailed the development of the electric field expressions. The electric field for a TE mode in a one-layer film, and only type of guided mode used in these experiments, is described in eqs 4-9:
where F is the fluorophore concentration in the film, D is the mass transport coefficient, t is time, and z is the film thickness coordinate. D is called the mass transport coefficient, since in this case it combines both partitioning across the filmsolution boundary and fluorophore motion in the film. The next step is to define an appropriate set of boundary conditions. In the case under consideration, z = 0 is the filmsubstrate interface and z = w is the film-solution interface, so two boundary conditions are,
E? = Aed2 E4.= A
COS(KZ)
E, = (A COS(KW)
substrate
+ B sin(rtz)
+ B sin(Kw))eY(Z+")
(4) film
superstrate (6)
where 6 = (ni sin' Om
+ niki)'iz
and A and B are constants, w is the film thickness, and all the other variables are as previously defined. These equations make it clear that the electric field decays exponentially into both the superstrate and substrate and that it varies sinusoidallyin the film as a function of z. Therefore, the excitation intensity, which is proportional to Ei2(z)in eq 3, varies as a function of mode number, m, and position, z. Of course, in these expressions the time dependence has been suppressed. Also, in any real waveguide, the field intensity decays exponentially as a function of x, the propagation direction. Thus, the electric field can be described as E,(z,x) = SE,(z)e-P"
F=Fo,
(5)
(10)
where E,(z) is described by eqs 4-9, S is a proportionality constant, and p is the loss coefficient, which is a sum of three terms: the surface scattering loss, the volume scattering loss, and the absorption loss.1ga Ideally, it is necessary to include the mode-dependent electric field dependence, E&), in eqs 2 and 3; however, in the experiments performed in this work, typically several modes were excited simultaneously. Since non-phase-matched multimode excitation results in addition of intensities, not amplitudes, the amplitude profile resulting from simultaneous excitation of several high-order eigenmodes is roughly uniform across the film,5 thus allowing us to approximate E,2(z) IO. The validity of this assumption will be demonstrated below. It is important to note that, in the waveguide, it is the electric field intensities which sum, not amplitudes, because the eigenmodes are orthogonal solutions to the wave equation, and no effort is made to phasematch different modes. Diffusion Theory. It is evident from eqs 2 and 3 that an appropriate expression for the fluorophore concentration in the film is required. Examination of the data obtained in these experiments indicates that only Fickian diffusion is observed, so the followingdiscussion will be limited to Fickian diffusion.20 In order to understand the transport properties of the permeant in the plasticized film from the fluorescent response, it is necessary to develop a mathematical expression for the fluorophore concentration in the film at a given point
-
(20) Crank, J. The Mathematics of Diffusion; Oxford University Press: New York, 1956; Chapter 1.
z=w,
tLO
(12)
F=0, O
