Total Internal Reflection Fluorescence-Correlation Spectroscopy

Anal. Chem. 2003, 75, 3616-3624

Total Internal Reflection Fluorescence-Correlation Spectroscopy Study of Molecular Transport in Thin Sol-Gel Films Karla S. McCain and Joel M. Harris*

Department of Chemistry, University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112-0850

Total internal reflection fluorescence correlation spectroscopy is used to measure mass transport rates through thin sol-gel films. Fluctuations in the fluorescence signal derive from molecular statistics due to the small number (∼1000) of rhodamine 6G dye molecules in the observation region. Autocorrelation of the fluctuating signal is fit to a model describing diffusion in the evanescent wave excitation. Silica sol-gel films were prepared by dipcoating 27-nm porous silica particles, which were synthesized by a base-catalyzed sol-gel method, onto microscope slides. The measured diffusivities ranged from 1 to 2 orders of magnitude slower than free diffusion and decreased with increasing number of dips used to prepare the film. Scanning electron microscopy (SEM) was used to examine the film structure and showed that increasing the number of dips produced more uniform and wellordered films. To determine what role the dip-coating process plays in inducing order, deposited films were further dipped into ethanol containing no particles. These films were annealed by this process and become more ordered, as determined by SEM, and show a corresponding reduction in the molecular diffusivity. Sol-gels are a group of materials that are produced from the hydrolysis of metal alkoxides.1,2 Sol-gels prepared from silicon alkoxides to produce porous silica structures are an important class of materials that have applications in chromatography,3,4 in fuel cells,5 and as sensor supports.6-8 A knowledge of molecular transport within sol-gel materials is important for successful implementation in all of these areas. For example, the time response of a sensor is related to how quickly analyte molecules can diffuse into the sol-gel to encounter dopant reagent molecules that produce the sensor response. The cycle time of such a sensor depends on how quickly those molecules can diffuse in to and * Corresponding author. E-mail: [email protected]. (1) Brinker, C. J.; Scherer, G. W. Sol-Gel Science: The Physics and Chemistry of Sol-Gel Processing; Academic Press: Boston, 1990. (2) Iler, R. K. The Chemistry of Silica; John Wiley and Sons: New York, 1979. (3) Hayes, J. D.; Malik, A. Anal. Chem. 2000, 72, 4090-4099. (4) Nakanishi, K.; Shikata, H.; Ishizuka, N.; Koheiya, N.; Soga, N. J. High Resolut. Chromatogr. 2000, 23, 106-110. (5) Anderson, M. L.; Stroud, R. M.; Rolison, D. R. Nano Lett. 2002, 2, 235240. (6) Han, L.; Niemczyk, T. M.; Lu, Y.; Lopez, G. P. Appl. Spectrosc. 1998, 52, 119-122. (7) Wang, C.; Li, C.; Lin, Y.; Chau, L. Appl. Spectrosc. 2000, 54, 15-19. (8) Makote, R.; Collinson, M. M. Anal. Chim. Acta 1999, 394, 195-200.

3616 Analytical Chemistry, Vol. 75, No. 14, July 15, 2003

out of the structure. Diffusion of molecules within sol-gel materials is not simple because these materials are heterogeneous and can contain a size range of porosities.1 Measurements of diffusion in sol-gel materials have most often relied on leaching experiments carried out on bulk samples.9 Diffusivities are measured on the time scale of hours as a result of the slow, tortuous diffusion over macroscopic distances through which the transport is measured. More recently, electrochemistry has been used to study changes in the diffusivity of molecules in sol-gels as the monoliths experienced gelation.10 Due to the slow transport rate through sol-gel structures, thin films of these materials have been used as coatings on optical fibers11 and on infrared internal reflection elements12 for sensor applications. Silica sol-gel films of base-catalyzed silica particles have also been used as a substrate to study the kinetics of silane binding reactions using attenuated total reflectance Fourier transform infrared (ATR-FT-IR) spectroscopy.13 In these experiments, it was found that the reaction kinetics were complicated by slow transport of the silane reagent through the film. To understand the influence of molecular transport on the observed reaction kinetics, concentration jump experiments were also performed. The accumulation of a probe solute molecule into the film after a concentration jump was characterized by a fast (less than 1 s) initial rise that was too fast to be monitored in the ATRFT-IR experiment, followed by a slow exponential increase in solute concentration in the film. The slow exponential increase was shown not to vary with film thickness and was ascribed to diffusion through the intraparticle pores within individual particles. It was hypothesized that the fast step arose from diffusion in the interparticle pore space created by the packing of the colloid particles, where changes in particle packing would be expected to affect the rate of this fast interparticle transport. In this work, we have sought to investigate the more rapid molecular transport process in silica sol-gel films using total internal reflection-fluorescence correlation spectroscopy (TIRFCS). TIR-FCS was first used to examine binding kinetics of immunoglobulin G at protein-coated silica/water interfaces14-16 (9) Watson, J.; Zerda, T. W. Appl. Spectrosc. 1991, 45, 1360-1365. (10) Howells, A. R.; Zambrano, P. J.; Collinson, M. M. Anal. Chem. 2000, 72, 5265-5271. (11) Kao, H. P.; Yang, N.; Schoeniger, J. S.. J. Opt. Soc. Am. A 1998, 5, 21632171. (12) Han, L.; Niemczyk, T. M.; Lu, Y.; Lopez, G. P. Appl. Spectrosc. 1998, 52, 119-122. (13) Rivera, D.; Harris, J. M. Anal. Chem. 2001, 73, 411-423. (14) Thompson, N. L. Ph.D. Thesis, University of Michigan, Ann Arbor, MI, 1982. 10.1021/ac0207731 CCC: $25.00

© 2003 American Chemical Society Published on Web 06/04/2003

and more recently to study small-molecule adsorption/desorption kinetics at a C-18 modified silica interface.17 In this experiment, fluorescence is measured as a function of time, and fluctuations are observed due to the diffusion of individual molecules at equilibrium in to and out of the interfacial volume defined by the evanescent wave excitation. The frequency content of these fluctuations contains information about the kinetics of mass transport. By autocorrelating the fluorescence signal, this kinetic information can be extracted. TIR-FCS requires high sensitivity detection because the relative amplitude of the fluctuations is inversely proportional to the square root of the number of molecules in the excitation region, generally 100 molecules or less to achieve ∼10% fluctuations.18 TIR-FCS allows for the examination of mass transport in the interfacial region defined by the evanescent wave, a distance less than the wavelength of light. When the film thickness is greater than the evanescent wave depth, the fluorescence fluctuations should probe only the molecular motion within the film. With moderate excitation intensity, TIR-FCS allows fluorescence fluctuations to be recorded at 10-100-µs intervals.17 Finally, because TIR-FCS is an equilibrium experiment, there is no need for a concentration jump to follow kinetics, so that fast transport processes can be examined without the limitations of a slow change in interfacial solution concentration. THEORY An evanescent wave is created when light is reflected at the interface between a material with a higher index of refraction, n1, and a material with a lower index of refraction, n2, at an incident angle, θ, greater than the critical angle,14

θcrit ) sin-1(n2/n1)

(1)

The intensity of this evanescent wave decays exponentially into the material of lower refractive index with a distance dependence,14

I(z) ) I0e-z/dew

(2)

G(τ) )

〈F(t)F(t + τ)〉 - 〈F(t)〉2

(4)

〈F(t)〉2

where

〈F(t)F(t + τ)〉 ) lim

1

∫

T/2

Tf∞T - T/2

F(t)F(t + τ) dt

(5)

The decay of these fluctuations is determined by kinetic factors related to how long the fluor remains in the excitation volume and include diffusion, adsorption, and photobleaching. By analyzing the time dependence of these fluctuations, it is then possible to extract the rates associated with these processes. Because the radius of the laser beam (∼100 µm) is much larger than the depth of penetration of the evanescent wave (∼100 nm), fluctuations arising from diffusion through the evanescent wave occur on a much faster time scale than diffusion across the large laser spot. Data are taken at such a rate as to sample these faster fluctuations; thus, this experiment only measures diffusion occurring perpendicular to the interface. The autocorrelation function for free diffusion in an evanescent wave is described by the following function.19

G(τ) )

{

( ) }

kτ 1 (1 - 2kτ)ω[i(kτ)1/2] + 2 2NA π

1/2

(6)

where

ω[i(kτ)1/2] ) ekτ erfc((kτ)1/2)

(7)

The amplitude of this function is inversely proportional to the number of molecules in the observation volume, NA, and decays monotonically with a rate, k, describing the rate of diffusion of molecules leaving and entering the evanescent wave. This transport rate, k, is defined as

k ) D/dew2

where the depth of penetration, dew, is given by14

dew ) (λ0/4π)(n12 sin2 θ - n22)-1/2

according to14

(8)

(3) where D is the diffusion constant and dew is the evanescent wave depth.

The theoretical basis for TIR-FCS was developed by Thompson et al., who described how transport and binding kinetics influence the observed correlation signal.14-16 TIR-FCS is based on observing a small population of molecules at equilibrium in the volume defined by the area of the laser beam and the depth of the evanescent wave. If the number of molecules in this excitation region is small, spontaneous fluctuations in their numbers appear as low-frequency noise in the fluorescent transient. The time dependence of these fluctuations can be extracted by calculating the autocorrelation, G(τ), of the fluorescence transient, F(t), (15) Thompson, N. L.; Burghardt, T. P.; Axelrod, D. Biophys J. 1981, 33, 435454. (16) Thompson, N. L.; Axelrod, D. Biophys J. 1983, 43, 103-114. (17) Hansen, R. L.; Harris, J. M. Anal. Chem. 1998, 70, 4247-4256. (18) Thompson, N. L. In Topics in Fluorescence Spectroscopy, Volume 1: Techniques; Lakowicz, J. R., Ed.; Plenum Press: New York, 1991.

EXPERIMENTAL SECTION Silica Particle and Film Preparation. Silica particles were prepared by a modified Sto¨ber synthesis.20 About 7.5 mL of tetraethoxysilane (Aldrich) was added to 150 mL of absolute ethanol (Omnisolve) followed by the addition of 7 mL of a 25% ammonia solution in water. This mixture was stirred for 36 h and then allowed to stand for at least 2 weeks to ensure that all ethoxy groups had hydrolyzed. Then 50-mL aliquots of this sol were diluted to 200 mL with absolute ethanol, which resulted in a particle concentration of 0.3% (w/w). Fused-silica microscope slides (Esco Products) were dip-coated with this silica sol using a motorized stage to control the withdrawal rate at 1.0 cm/s. The (19) Starr, T. E.; Thompson, N. L. Biophys. J. 2001, 80, 1575-1584. (20) Coenen, S.; DeKruif, C. G. J. Colloid Interface Sci. 1988, 124, 104-110.

Analytical Chemistry, Vol. 75, No. 14, July 15, 2003

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Figure 1. Instrumental layout used for TIR-FCS experiments. L1 is a best form lens with a focal length of 3 in. to focus the beam at the surface, and L2 is a 1:1 relay lens with a focal length of 2 in. to focus the emitted light onto the PMT. A is an aperture, and F1 is a long-pass cutoff filter. See text for details.

number of dips was varied to control the film thickness. In films that were prepared on clean, hydrophilic fused silica, a uniform interference color could be observed visually to the edges of the slide, indicating very uniform, flat films. As the number of dips increased above 25, however, the interference color was diminished. The effects of annealing were tested by dipping films in absolute ethanol immediately after the silica layers were dip-coated onto the slide. Films were used within 24 h of preparation. Particle and Film Characterization. Scanning electron microscopy (SEM) images of the sol-gel films were acquired using an Hitachi model S3000N SEM. Silica films were dip-coated onto clean glass microscope slides and then overcoated with 10 nm of gold by thermal evaporation. Transmission electron microscopy (TEM) images of individual sol particles were acquired using an Hitachi model H7100 TEM. Samples were prepared by evaporating 10 µL of an aqueous sol onto a TEM grid. Nitrogen adsorption analysis was performed by Particle Technology Labs on an aggregated precipitate of the silica sol. An aliquot of sol was allowed to evaporate, producing a clear, glassy material that was crushed slightly to ∼1-mm particle size before the analysis. The sample was degassed for 15.25 h at 200 °C prior to analysis. A type IV isotherm was observed. The nitrogen adsorption isotherm was acquired over 40 points, and Barrett, Joyner, and Helenda (BJH) analysis was used to determine the pore size distribution. The BJH method21 was used to extract pore volume information from nitrogen adsorption iso(21) Barrett, E. P.; Joyner, L. S.; Halenda, P. P. J. Am. Chem. Soc. 1951, 73, 373-380.

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therms. BJH analysis uses a cylindrical pore model and relates the volume of nitrogen desorbed from the core of pore at a given pressure to its radius, correcting for additional surface desorption. Atomic force microscopy was used to measure the dip-coated silica film thickness. A step edge was created in a 20-dip film by masking off a portion of the slide with a piece of transparent tape (3M) before dip-coating. This step edge was then exposed and imaged with a TopoMetrix atomic force microscope in contact mode in order to determine the thickness of the film. TIR-FCS Experiments. Sol-gel coated slides were placed in a flow cell secured to the stage of an inverted microscope (Nikon, TE 200); see Figure 1. The 514.5-nm line from an argon ion laser (30 mW) was directed at 76° from normal through a 72° fusedsilica dove prism, a thin layer of glycerol, and the coated slide. The evanescent wave decayed exponentially at the interface with a characteristic depth 156 nm (see below). Rhodamine 6G (Exciton) was used as a diffusion probe in these experiments, dissolved at a concentration of 20 pM in a 90/10 methanol/water solution containing 50 mM sodium chloride. These conditions were found to prevent adsorption of the dye to silica surfaces. Retention of rhodamine 6G (R6G) on a bare silica column was characterized using nitrate ion as a dead volume marker. R6G actually eluted slightly before nitrate, implying a negative capacity factor, k′ = -0.05. This elution order indicates that R6G experiences a smaller void volume probably due to its larger size and is negligibly retained under these conditions. Fluorescence from the excitation region defined by the evanescent wave was collected by a 60×, 0.7 NA microscope objective, filtered by a high-pass

cutoff filter, and focused onto a photomultiplier tube (PMT; Hamamatsu R928). Current pulses from the PMT were amplified 10 times (Phillips, model 9604) and counted in 100-µs time bins with a multichannel scalar (EG&G, MCS-pci). Files of 16 384 time bins (1.6384-s observation time) were collected and autocorrelated off-line. For each experimental condition, 100 files were gathered, autocorrelated, and averaged. Autocorrelation functions were calculated by a program written in FORTRAN running on a 800-MHz PC. Data were Fourier transformed, multiplied by their complex conjugate, and then inverse Fourier transformed to produce the autocorrelation. Each transient file was processed separately and then combined by averaging the calculated autocorrelations. The first point (τ ) 0) in the autocorrelation was removed before fitting because it is dominated by photon shot noise.22 The bandwidth of the photomultiplier tube is greater than 100 MHz so that the correlation due to photon shot noise decays within a few hundred nanoseconds. The decay of the experimentally obtained autocorrelation functions was fit to theory describing diffusion in an evanescent wave. The data were fitted in a FORTRAN program by calculating a theoretical curve for an array of rates, performing a linear least-squares step to determine the best fit amplitude and offset,23 and calculating the residuals. The best fit rate was taken to be that which minimized the sum of the square of the residuals. Uncertainties were calculated from triplicate data sets. The uncertainty associated with fitting, estimated from the χ2 surface, was smaller than the error associated with run-to-run reproduciblity by a factor of ∼2. RESULTS AND DISCUSSION Particle and Film Characterization. The silica sol particles were found to be spherical and have a mean diameter of 27 ( 4 nm by TEM, which is reasonable for the reaction conditions under which they were prepared.20 Particles produced by this method have been previously shown to have considerable internal porosity1,24 based on the density of the particles compared to fused silica and comparison of the BET surface area measured by nitrogen adsorption versus the expected surface are of solid particles. The BET surface area of the particles used in this study was determined to be 398 m2/g. Solid fused-silica particles with a diameter of 27 nm would have a surface area of 106 m2/g. The extra surface area measured by nitrogen adsorption for these particles is strong evidence that they contain internal pores. As a result, the films that result from the dip-coating of these particles can have two different types of porosity, an intraparticle porosity due to pores contained within individual particles and an interparticle porosity created by the packing of the particles in the film. The diameter of the smallest possible interparticle pore is ∼15% of the diameter of the particles from which the film is made.25 For a close-packed array of 27-nm spheres, the interparticle pore diameter is 4 nm. This gives us a lower limit on the pore size that can exist between particles. BJH analysis indicated that 15% of the pore volume was from pores smaller than 4 nm, and this pore volume can be attributed to intraparticle pore (22) Hansen, R. L.; Harris, J. M. Anal. Chem. 1998, 70, 2565-2575. (23) Wong, A. L.; Harris, J. M. Anal. Chem. 1989, 61, 2310-2315. (24) LeCloux, A. J.; Bronckart, J.; Noville, F.; Dodet, C.; Marchot, P.; Pirard, J. P. Colloid. Surf. 1986, 19, 359-374. (25) Wirth, M.; Xiao, D.; Anthony, S.Nanometer Layers of Living Polymers for Chemical Separations. Pittsburgh Conference, March 18, 2002.

volume. However, it is possible that some of the pore volume corresponding to pore diameters larger than 4 nm is from an intraparticle pore population. For these films then, there is not a large difference in pore diameter between intraparticle and the smallest interparticle pores. It is expected, therefore, that molecules could sample both regions on similar time scales but that diffusive behavior due to interparticle diffusion would respond to changes in the film structure or particle packing (see below). The thickness of a 20-dip film was determined to be 450 ( 120 nm by imaging a step edge with an AFM. Because the mass of the films has been shown to vary linearly with the number of dips,26 it is assumed that the thickness also varies linearly with the number of dips. The films used in this study, therefore, vary from 140 nm for a 6-dip film to 580 nm for a 25-dip film. The deposition of the material from solution onto a surface by substrate withdrawal can be quantitatively predicted27 by controlling the thickness of the solution layer that adheres to the substrate. For a wetted surface, the thickness of the solution layer, l, remaining on the surface is given by28

l ) 0.944(ηU)2/3/(Fg)1/2γ1/6

(9)

where, η is the solution viscosity, U is the withdrawal rate, F is the solution density, g is rate of acceleration due to gravity, and γ is the surface tension of the solution. For the conditions used to prepare the dip-coated sol-gel films, the thickness of the layer of solution left behind is 10 µm, corresponding to 2.4 µg/cm2 silica deposited per dip. Using this value and the film thickness measured for a 20-dip film, the density of the films is estimated to be 1.1 g/cm3. This density corresponds to a film that is 50% solid fused silica and contains 50% free space. This result is consistent, within 10%, with the total pore volume measured by nitrogen adsorption analysis of 0.5 cm3/g. Although nitrogen adsorption analysis was performed on an evaporated sample of the sol, which likely has somewhat different particle packing from the dip-coated films, the density determined from the film thickness and dipping parameters are in close agreement. Evanescent Wave Characterization. Because of the complex porosity of sol-gel materials, determining their refractive index when filled with a solvent is difficult. Ellipsometry can be used to measure the refractive index of thin films at an air interface; however, this measurement is complicated by adsorbed water that may fill appreciable volumes in small pores and contribute to the measured refractive index. The Clausius-Mosotti equation describes the relationship between the refractive index (n), the number density (N), and the molecular polarizibility (R) for a dense material.29

n2 - 1 )

NR 1 - NR/3

(10)

Because the mixing of the silica and methanol in the sol-gel film occurs on distances less than the wavelength of light, the volume (26) Rivera, D.; Poston, P. E.; Uibel, R. H.; Harris, J. M. Anal. Chem. 2000, 72, 1543-1554. (27) Lacy, W. B.; Olson, L. G.; Harris, J. M. Anal. Chem. 1999, 71, 2564-2570. Hanley, D. C.; Harris, J. M. Anal. Chem. 2001, 73, 5030-5037. (28) Landau, L.; Levich, B. Acta Physiochim. U.R.S.S. 1942, 17, 42-54. (29) Rossiter, V. J. Electromagnetism; Aabspec: New York, 1998.


3619

fractions of silica and methanol (which wets the silica surface and should fill the free space) were used to correctly weight the NR term. The refractive index of the film was determined to be 1.393, which was slightly less than a simple average combination of the refractive indices of fused silica and methanol. This film refractive index corresponds to a critical angle of 72° and an evanescent wave depth of 156 nm for 76° incident light at a fused-silica substrate/sol-gel film interface. It should be noted that the thickness of the films used in this study varied from 140 to 580 nm, so that in all but the thinnest films, the evanescent wave is contained entirely within the film. While this is not strictly true for 6-dip films, it should be noted that because the evanescent wave decays exponentially, only 10% of the intensity penetrates to distances farther than 140 nm away from the sol-gel film/ microscope slide interface. Thus, the signal is dominated by fluorescence collected from within the sol-gel film. To corroborate that the evanescent wave in these experiments was being launched from the fused-silica microscope slide/solgel interface (instead of the sol-gel film/solution interface), a control experiment was done with a fluorescent molecule that was too large to penetrate the film. A generation 7 poly(amidoamine) dendrimer was dye-labeled with carboxyrhodamine 6G, and the terminal amine groups were carboxylated by reaction with succinic anhydride to avoid adsorption to the silica surface. This fluorescent probe should not penetrate the film because of its 19-nm diameter,30 which is greater than the largest pores found in the nitrogen adsorption BJH analysis. TIR-FCS measurement of this probe through a 15-dip film produced no detectable increase in the signal over that of the background, and no diffusion decay was present in the autocorrelation transient. These results confirm that the evanescent wave is launched at the fused-silica substrate/ sol-gel film interface. Transport of Rhodamine 6G in Silica Sol-Gel Films. Figure 2 shows representative autocorrelation plots and their fits to eq 6 for a series of sol-gel films made from increasing numbers of dips. The data were collected for rhodamine 6G in 90/10 methanol/water solution containing 50 mM sodium chloride. As discussed above, a largely organic solvent with high ionic strength was chosen in order to avoid adsorption of the cationic dye to the silica surface and thus ensure that fluctuations were the result of diffusion within the sol-gel film rather than adsorption/desorption kinetics. High-performance liquid chromatography measurements of the retention of this dye on a bare silica column indicated that, under these solution conditions, adsorption was negligible (see above). To further examine this issue, fluorescent transients were taken from a flat, bare silica slide with no solgel film. No correlation relaxation was observed using either 10or 100-µs time bins, indicating that there was no measurable adsorption/desorption kinetics on the time scale of this experiment. The correlation relaxation due to free-solution diffusion in the evanescent wave is very fast and should only be observed in the first one or two points for 100- and 10-µs time bins, respectively. The rate of molecular diffusion in the sol-gel films was found to decrease with increasing number of dips used to prepare the film (Table 1). This decrease is most pronounced between the thinnest films, leveling off for the thickest films (Figure 3). To (30) McCain, K. S.; Schluesche, P.; Harris, J. M., presented at FACSS 2002, Providence, October 15, 2002; manuscript in preparation for Anal. Chem.


Figure 2. Experimental autocorrelations and resulting fits to eq 6 for 20 pM R6G+ in 90/10 methanol/water solutions with 50 mM NaCl in sol-gel films of varying depth. Films were prepared from the following number of dips from top to bottom: 6, 10,15, 20, and 25 dips. For clarity, only one of every 25 points has been plotted.

Table 1. Film Thickness Dependent Transport Rate of R6G+ in Silica Sol-Gel Films no. of dips/ no. of annealing dips

ka (s-1)

Db (cm2/s)

6 10 15 20 25

1300 ( 300 540 ( 60 480( 60 230 ( 50 210 ( 30

(3.1 ( 0.7) × 10-7 (1.3 ( 0.1) × 10-7 (1.2 ( 0.1) × 10-7 (6 ( 1) × 10-8 (5.1 ( 0.7) × 10-8

a Measured diffusion rate. b Diffusion constant calculated from eq 6 using 156-nm evanescent wave depth.

the film. The slowing of diffusion rate with number of dips could arise either from the reduction of contributions from fast free solution diffusion that are sampled when the film is not much thicker than the evanescent wave depth or from changes in the structure of the film as the number of dips is increased. To determine whether this measurement was sensitive to concentration fluctuations in the free solution beyond the solgel film, numerical modeling of the diffusion within the thin film in contact with solution was performed. Fick’s second law, in one dimension, describes change in concentration with time

∂C(x,t) ∂ 2C )D 2 ∂t ∂x

(12)

where C is the concentration as a function of time and distance, t is time, D is the diffusion coefficient, and x is position.33 For a system of constant diffusivity, the solution to this differential equation for a ∂ function change in concentration at x ) 0 in a semi-infinite medium is given by33

C ) M/(πDt)1/2 exp(- x2/4Dt)

Figure 3. Diffusion rates (k) and the corresponding diffusion constant (D) plotted as a function of the number of dips in the film. Error bars are ( one standard deviation from an average of three measurements.

Figure 4. Tortuosity plotted as a function of the number of dips in the film. Error bars are ( one standard deviation from an average of three measurements.

compare these values to the free solution diffusion coefficient, the tortuosity factor for transport in the films is calculated:31

T ) Dsoln/Dsol-gel

(11)

where Dsoln is the free solution diffusion coefficient for R6G and Dsol-gel is the measured diffusion coefficient in the sol-gel film. The previously measured value of Dsoln ) 4.5 × 10-6 cm2/s for R6G32 was used for this calculation. As shown in Figure 4, tortuosity increased linearly for increasing number of dips from a value of ∼15 for a 6-dip film to a value of ∼90 for a 25-dip film. This indicates that diffusion in these films was 15-90 times slower than free diffusion in solution and that the tortuosity experienced by the molecules increased with the number of dips comprising (31) Latour, L. L.; Kleinberg, R. L.; Mitra, P. P.; Sotak, C. H. J. Magn. Reson., A 1995, 112, 83-91. (32) Hansen, R. L.; Zhu, X. R.; Harris, J. M. Anal. Chem. 1998, 70, 1281-1287.

(13)

where M is the total amount of solute in the perturbation. To account for a change in diffusivity between the sol-gel film and free solution, eq 12 was solved numerically using the CrankNicolson implicit method33 for a geometry having two regions with different diffusion coefficients and a reflecting wall at x ) 0. The first region having the smaller diffusion coefficient extends from x ) 0 to x ) b, where b is the film thickness or distance away from the reflective wall. The second region then starts at the film/ solution boundary at x ) b to a long distance (x2 . 4Dtmax) away from the interface. The initial concentration profile was again a ∂ function at x ) 0. Although in an FCS experiment there is no net concentration flux, this is a good approximation of an instantaneous concentration fluctuation at the substrate/film interface (x ) 0). If the evanescent wave is sensitive to fast, free solution diffusion for very thin films, then the time decay of the concentration at x ) 0 would differ significantly from what would be predicted by the simple semi-infinite medium model with a single diffusion coefficient in eq 13. The numerical simulation, however, shows no sensitivity to free solution diffusion beyond the film. When conditions corresponding to the thinnest film used in this study and the observed diffusion coefficient were used in the finite film thickness model, there was negligible difference between the time decay from this modeling and the time decay predicted by the simple semi-infinite medium theory of eq 13. After 2 s, a little more than the entire time data are taken in these experiments; the concentration at x ) 0 differs by only 3% between the models. Even after 20 s, the difference has not increased. This test represents a worst case scenario. For thicker films, or for slower diffusion coefficients, the sampling of free solution diffusion behavior in the concentration at the substrate/film boundary is (33) Crank, J. The Mathematics of Diffusion; Oxford University Press: Oxford, U.K., 1975. (34) Jiang, P.; Bertone, J. F.; Hwang, K. S.; Colvin, V. L. Chem. Mater. 1999, 11, 2132-2140. (35) Dimitrov, A. S.; Nagayama, K. Langmuir 1996, 12, 1303-1311.


3621

Figure 5. SEM images of dip-coated sol-gel films composed of different numbers of dips. Scale bars represent 1 µm.

even less. Thus, the results of this modeling show that contributions from free solution are not the source of the variation in the measured diffusion constants with film thickness and that this variation must arise from changes in the structure of the sol-gel film with an increasing number of dips. Changes in Film Structure. SEM images show a change in film morphology as the number of dips used to prepare the film increases (Figure 5). A 6-dip film is patchy, showing islands of particles surrounded by regions with no particles. The 10-dip film is no longer patchy but is still very rough. The 15-, 20-, and 25dip films are much smoother, indicating a more uniformly packed film. This change in film order explains some of the observed changes in transport properties between different film thicknesses. For the 6- and 10-dip films, there are many defect sites and areas of poor particle packing in the film through which molecules will diffuse faster, contributing to a faster measured rate. Contributions from free solution diffusion in the areas of the 6-dip film that have no particles are too fast to be observed on the time scale (100-µs bins) used in these experiments. Thus, the faster diffusion coefficient observed for the 6-dip film does not arise from an averaging of the diffusion from regions with and without particles, but from a lack of organization within the particle-coated regions. From the SEM data alone, it is not apparent that the structure is changing beyond the 15-dip film; however, the limited spatial 3622


resolution of this technique may not be able to detect more subtle changes in film structure. This observation is, however, consistent with the diffusion rates measured for the 20- and 25-dip films, which are indistinguishable from each other. During each dip into the sol, more particles added to the film, which provide the material needed to fill defects. The film also experiences a capillary force due to the receding meniscus; this capillary force is another mechanism for inducing the structural changes in the films as their thickness increases. To determine whether the addition of more particles to the film is affecting the particle organization, a control experiment was performed in which 6-dip films were further dipped into ethanol containing no sol particles. In Figure 6 are plotted autocorrelations of fluorescence from R6G in films that were annealed by additional dips in ethanol. The diffusion rate does decrease with the increasing number of annealing dips (Table 2), indicating that capillary forces associated with the receding meniscus must change the film structure. The diffusion constant measured for a film annealed with 4 dips in ethanol is indistinguishable from a comparable film with no annealing dips; however, 14 annealing dips do induce a measurable decrease in the diffusion coefficient of ∼50%. SEM was again used to characterize the morphology of these films (Figure 7). A six-deposition/four-annealing dip film still

Table 2. Effect of Annealing by Ethanol Dipping on the Transport Rate no. of dips/ no. of annealing dips

ka (s-1)

Db (cm2/s)

6 6/4 6/14

1300 ( 300 1400 ( 200 700 ( 200

(3.1 ( 0.7) × 10-7 (3.4 ( 0.5) × 10-7 (1.7 ( 0.5) × 10-7

a Measured diffusion rate. b Diffusion constant calculated from eq 6 using 156-nm evanescent wave depth.

Figure 6. Experimental autocorrelations and resulting fits to eq 6 for 20 pM R6G+ in 90/10 methanol/water solutions with 50 mM NaCl in sol-gel films with 6 deposition dips and varying numbers of annealing dips. From top to bottom, the films were prepared with 0, 4, and 14 annealing dips. For clarity, only one of every 25 points has been plotted.

shows large differences in particle density across the surface and areas where there are no particles to slow the diffusion. This is consistent with its measured diffusion rate, which was indistinguishable from a comparable film with no annealing. A 6-deposition/14-annealing dip film is much more uniform with only small areas with apparently no particles and showed a correspondingly slower diffusion rate. The rate was not as slow however as a 20dip film (no annealing), which suggests that both the addition of particles to fill in defects and the capillary forces due to the receding meniscus help to form more-uniform, well-packed films (Figure 8).

Figure 7. SEM images of six deposition dip sol-gel films that were annealed by dipping in ethanol. The numbers in the left corners refers to the number of annealing dips. Scale bars represent 1 µm.

CONCLUSION TIR-FCS has been found to be an effective tool for investigating molecular transport in thin films. The diffusion of R6G in sol-gel films was found to be highly dependent on the packing of sol particles that comprise the film. Diffusion constants were measured by fluorescence correlation spectroscopy for dip-coated solgel films as a function of the number of sol-gel deposition dips and the number of annealing dips. The diffusion constant was found to decrease by 1-2 orders of magnitude with increasing number of sol-gel dips and increasing numbers of annealing dips. Analytical Chemistry, Vol. 75, No. 14, July 15, 2003

3623

Figure 8. Measured diffusion rates (k) and the corresponding diffusion constants (D) for a 6-dip film plotted as a function of the number of annealing dips. Error bars are ( one standard deviation from an average of three measurements. The horizontal line represents the values for a 20-dip film with no annealing.

Numerical modeling showed that the trend is not a result of sampling free solution diffusion beyond the film but of structural changes in the film. SEM images show better particle packing for increasing numbers of sol-gel dips and annealing dips. The decrease in diffusivity comes from the combination of the addition of more sol particles to the film to fill in defects and the capillary forces associated the receding meniscus. The technique of TIR-FCS could be readily applied to sol-gel films prepared by other procedures, including acid- and basecatalyzed films that are gelled onto a substrate. For films that are dip-coated onto a surface, the annealing technique described in this work might prove to be a fast and convenient method to produce more uniform films, approaching a close-packed arrangement. Currently, very well organized films or colloidal crystals can be prepared by very slow substrate withdrawal or solvent evaporation;34,35 these methods, however, require a long time to produce films. More uniform films should show more uniform


molecular transport, and thus more uniform response rates, when used as sensor materials. For the films in this study, the size ranges of the intraparticle pores (pores within individual sol particles) and the interparticle pores (pores formed by the spaces between particles) overlap. For films made from larger sol particles, these two classes of pores could exhibit two distinct pore size populations. In this case, it might be possible to separate contributions to the diffusivity from diffusion in intraparticle pores and from diffusion in interparticle pores. Future studies with larger particles will attempt to resolve these two contributions and investigate the influence of the size of the diffusion probe molecule on size exclusion effects on transport in sol-gel films. Finally, the diffusivities measured in this paper represent the average diffusion coefficient sampled by the evanescent wave. It is possible that the diffusion coefficient actually varies over the thickness and area of the film. This possibility could be investigated by measuring the diffusion rate as a function of the depth of penetration of the evanescent wave or by imaging smaller regions of the film. ACKNOWLEDGMENT This work was supported in part by the National Science Foundation under Grant CHE-0137569. Fellowship support for K.S.M., provided by the University of Utah Graduate School and Novartis, is gratefully acknowledged. The authors thank Brad Peercy for his assistance with the numerical modeling, Micha Smith for acquiring the SEM images, Bryon Wright for acquiring the AFM images, and Nancy Chandler for acquiring the TEM images. Received for review December 19, 2002. Accepted April 10, 2003. AC0207731

Total Internal Reflection Fluorescence-Correlation Spectroscopy

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