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J. Phys. Chem. B 2008, 112, 10890–10897
Single Ion Diffusive Transport within a Poly(styrene sulfonate) Polymer Brush Matrix Probed by Fluorescence Correlation Spectroscopy Carmen Reznik, Qusai Darugar, Andrea Wheat, Tim Fulghum, Rigoberto C. Advincula, and Christy F. Landes* Department of Chemistry, UniVersity of Houston, Houston, Texas 77204-5003 ReceiVed: April 28, 2008
Diffusive transport within complex environments is a critical piece of the chemistry occurring in such diverse membrane systems as proton exchange and bilayer lipid membranes. In the present study, fluorescence correlation spectroscopy was used to evaluate diffusive charge transport within a strong polyelectrolyte polymer brush. The fluorescent cation rhodamine-6G was used as a counterion probe molecule, and the strong polyelectrolyte poly(styrene sulfonate) was the polymer brush. Such strong polyelectrolyte brushes show promise for charge storage applications, and thus it is important to understand and tune their transport efficiencies. The polymer brush demonstrated preferential solvation of the probe counterion as compared to solvation by the aqueous solvent phase. Additionally, diffusion within the polymer brush was strongly inhibited, as evidenced by a decrease in diffusion constant of 4 orders of magnitude. It also proved possible to tune the transport characteristics by controlling the solvent pH, and thus the ionic strength of the solvent. The diffusion characteristics within the charged brush system depend on the brush density as well as the effective interaction potential between the probe ions and the brush. In response to changes in ionic strength of the solution, it was found that these two properties act in opposition to each other within this strong polyelectrolyte polymer brush environment. A stochastic random walk model was developed to simulate interaction of a diffusing charged particle with a periodic potential, to show the response of characteristic diffusion times to electrostatic field strengths. The combined results of the experiments and simulations demonstrate that responsive diffusion characteristics in this brush system are dominated by changes in Coulombic interactions rather than changes in brush density. More generally, these results support the use of FCS to evaluate local charge transport properties within polyelectrolyte brush systems, and demonstrate that the technique shows promise in the development of novel polyelectrolyte films for charge storage/transport materials. I. Introduction Advances in the measurement and theoretical description of ion/polyelectrolyte interactions1–4 have contributed to a growing understanding of the dynamics of polyelectrolyte thin films. Ultimately, a detailed characterization of ion transport properties and solvation response within these thin films will advance applied technologies that utilize associated switchable surfaces,5,6 and charge storage and transport properties of the films.7 Arenas in which these kinds of properties will play a role include biosensing6 and fuel cell technologies.8,9 Already, the charge transport behavior of polyelectrolyte thin-films has led to the successful commercial adoption of the fluorinated synthetic polymer, NaFion (Dupont), as a fuel cell proton exchange membrane (PEM).10 Both polyelectrolyte nanostructure and local solvation dynamics affect ion transport efficiencies,11 and several recent studies suggest that modifications to thin film nanostructures could lead to potential PEM design improvements.12,13 Specifically, poly(styrene sulfonate) (PSS) membranes that exhibit favorable transport properties have been observed to degrade over time. Improvements to membrane lifetimes have been achieved by the inclusion of cross-linked resins within the PSS PEM matrix.8 Additionally, it is possible to increase charge transfer capacities by over an order of magnitude by using a polymer brush architecture, which has higher internal order * Corresponding author. E-mail:
[email protected].
Figure 1. Polymer thin films: (a) isotropic film, and (b) polymer brush thin film. The arrows show the orientation of the polymer chains with respect to the surface.
compared to an isotropic thin film architecture.7 The increased order within a polymer brush is achieved from end-grafting polymer chains to a surface as depicted in Figure 1. At a high grafting density the polymer chains tend to extend in the direction normal to the surface.14 In the case of strong polyelectrolytes such as NaFion and PSS, additional interchain Coulombic repulsion due to the presence of fixed charges along the polymer chain gives rise to further extension of the chain.15 The increase in charge transfer seen in an oriented polymer brush system is attributed to transport of charges along the length of the oriented polymer chains rather than via chain hopping through the disordered arrangement present in an isotropic membrane.7 In summary, polymer brush membranes provide an intriguing polyelectrolyte system for transport study: first, because of the
10.1021/jp803718p CCC: $40.75 2008 American Chemical Society Published on Web 07/16/2008
Diffusive Transport within PSS Polymer Brushes response of charge transport performance within this type of oriented system to tunable brush internal nanostructures; and second, because of the degree of control over bulk morphology that is possible by tuning the environmental (solvation) conditions. Numerous theoretical treatments of the characteristics of polymer brushes in response to solvation conditions have been reported for both neutral14 and charged15 brush systems. Recently several groups have begun to address the dynamics of polymer brush systems. For example, Fytas et al. have used evanescent-wave dynamic light scattering to probe polymer chain dynamics,16 Choi et al. have used cyclic voltammetry to measure rates of electron transfer in a polyelectrolyte brush,11 and Limpoco et al. have used friction force measurements to characterize shear forces in various solvent subphases for polystyrene brushes.17 Additionally, several studies using fluorescence correlation spectroscopy (FCS) to look at diffusion of various mobile polymer macromolecules in association with polymer brush systems have been reported.18,19 In this work, we contribute a detailed description of the competing processes that drive internal transport characteristics of a strong polyelectrolyte brush system by using FCS to characterize ion mobility within a PSS polymer brush membrane. We report on the diffusion of rhodamine-6G (R6G), a positively charged fluorescent ion, as it interacts with a negatively charged polyelectrolyte brush, and we resolve the response of diffusion characteristics to changes in the polymer brush ionic environment as controlled via solvent pH. Lastly, we present a simple 2D random walk model for the motion of a charged particle experiencing a periodic potential field. Through our experimental results and this model we show that responsive diffusion characteristics are dominated by electrostatic interactions between the probe molecule and the strongly charged polymer brush. II. Materials and Methods A. Materials. R6G (max abs/em: 530/566 nm) (Figure 2a) was purchased from Invitrogen and diluted to a concentration of approximately 60 pM in water in order to achieve single molecule conditions. Orange fluorescent 40 nm carboxylatemodified FluoSpheres beads (max abs/em: 540/560 nm) were also purchased from Invitrogen and used to calibrate the FCS focal volume. The bead solution was diluted 1:10 000 in water before using. Sodium styrene sulfonate was purchased from Sigma Aldrich. Extra dry toluene over molecular sieves was purchased from Fisher Scientific. Triethyl-amine was purchased from Sigma Aldrich. The azo-initiator was synthesized as described previously.17 Spectroscopic grade sulfuric acid (J.T. Baker) was used to acidify solutions. MB-grade water (Hyclone, VWR) was used for all dilutions. Number 1 borosilicate 22 × 22 mm coverslips (VWR) were washed in MB-grade water, dried, and plasma cleaned for 2 min with oxygen. Silcon wafers (Silicon Quest International) were cleaned in the same manner. Red pliable silicon purchased from Scientific Instrument Services (Ringoes, NJ) was used to construct sample chambers. The silicon was cut into squares of less than 22 × 22 mm, with an 8 mm diameter hole punched in the center. These squares were cleaned with detergent and water and, after drying, placed atop cleaned or PSS-treated coverslips. The silicon was made to adhere to the surface by firmly pressing the silicon onto the glass. Sample solution containing the fluorescent probe was placed within the central cavity, and, to prevent evaporation of the solution during readings, a second clean coverslip was placed over the filled chamber. B. Preparation of Polymer Brush Matrix. Surfaces modified with PSS polymer brush (Figure 2.b), were prepared from
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Figure 2. Chemical composition of (a) R6G, and (b) PSS brush.
cleaned coverslips via surface-initiated polymerization.20,21 AIBN initiator17 was dissolved in 30 mL of dry toluene, 150 µL of triethylamine was added as hydrocholoric acid scavenger, and coverslips were submersed for 1 h in the solution to covalently bind the initiator to the surface. After treating the coverslips with the initiator, they were rinsed with water and submerged in a solution of sodium styrene sulfonate monomer (0.32 M). Polymerization was initiated at 60 °C in a constant temperature bath after dissolved gases were removed from solution via a series of three freeze/pump/thaw cycles. The polymerization reaction was allowed to proceed for 6 h. After polymerization, the coverslips were removed and continuously rinsed with water for 12 h in a Soxhlet extractor to clean the brush matrix of free polymer. All FCS analysis was confined to a single synthesis batch. C. FCS Set-Up. Figure 3 shows a schematic of the FCS instrumentation. A 532 nm solid state laser (VERDI, Coherent) was used for sample excitation. The light was circularly polarized, attenuated, and expanded to overfill the back aperture of the FLUAR 100× 1.3 NA oil immersion microscope objective (Carl Zeiss, GmBH).22 This resulted in a 1/e2 beam radius and 1/2 heights of ∼230 nm and ∼1 µm, respectively. The power at the sample was maintained at ∼800 W/cm2 for R6G studies. Fluorescence was collected and refocused by the same objective,23 and separated from excitation light via a dichroic mirror (z532rdc, Chroma Technology) and a notch filter (NHPF-532.0, Kaiser). The signal was refocused and passed through a polarizing beam splitting cube (PBSH-450-1300-050, CVI Laser) to two detectors (SPCM-AQR-15, Perkin-Elmer). A closed-loop xyz piezo stage (P-517.3CL, Physik Instrumente) with 100 µm × 100 µm × 20 µm travel dimensions and 1 nm specificity was used to position the sample using a surface probe controller (SPM 1000, RHK Technology). TTL output from the detectors was augmented and split via a fan-
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Figure 3. Homebuilt FCS/polarization microscope.
out buffer (PRL-414B, Pulse Instruments) to two separate computer boards, one for single photon counting trajectories (PMS-400-A, Boston Electronics Corporation), and the other for 2D imaging (RHK Technology). For all FCS calculations, output from only one of the detectors was used, after verifying equivalent performance on the two channels. D. FCS Theory. Simple translational diffusion of a solute in solution is characterized by a diffusion coefficient given by the Stokes-Einstein relationship:
D)
k·T 6π · η · Rh
(1)
This diffusion coefficient is inversely proportional to the effective solvent viscosity, η, and solute hydrodynamic radius, Rh. The ability to determine this diffusion coefficient, therefore, yields information describing the characteristics of the solute and/or solvent. Specifically, solute-solvent interactions and responses to environmental change are reflected in the effective diffusion coefficients measured under changing conditions. Elson and Madge demonstrated24 that it is possible to extract a diffusion coefficient for fluorophores diffusing through a laser spot from the autocorrelation (AC) analysis of the temporal fluorescence fluctuations. The AC function, eq 2, represents the self-similarity of a signal, F(t), over a set of lag times (τ) that range from τ0 to τmax:
〈δF(t) × δF(t + τ)〉 G(τ) ) 〈F(t)〉2
Figure 4. (a) Cartoon of FCS focal volume and diffusing fluorophores. (b) AC functions obtained from several fluorescent probe molecules diffusing in water. Inset is a representative signal trajectory. Curves are averages of 2 runs.
which the AC curves were calculated, is shown in the inset. Note that this displayed signal is binned up from the 10 µs acquisition time to 10 ms. Elson and Madge specifically derived the AC function for a system with a focal volume defined by a Gaussian profile and free diffusion in x and y, but with boundaries along the optical axis, which are of the same order as the focal volume parameters in z. This expression describes two-dimensional diffusion within a laser focal volume and is given by
G(τ) )
1
( ) 1+
(3)
τ τd
where τD is the characteristic diffusion time, which is related to the diffusion coefficient by
τD )
(2)
Here, 〈F(t)〉 is the time average of the fluorescence signal, and δF(t) ) F(t) - 〈F〉. The maximum lag time, τmax, is selected based on the expected decay profile of the AC function, which is dependent on characteristic diffusion times and must be selected to include the range of times over which the decay occurs. Figure 4a shows a representation of fluorescent solute diffusing within a laser focal volume defined by a Gaussian intensity profile that extends to a 1/e2 intensity boundary in x and y, and by a Lorentzian profile for the intensity boundary along the optical axis, z. Typical normalized AC decay curves for R6G and 40 and 100 nm polystyrene beads diffusing in water are shown in Figure 4b. A representative signal trajectory, from
1 · Veff〈C〉
r02 4D
(4)
Building on this work, Aragon and Pecora derived the following expression for the three-dimensional AC function of a fluorescence signal, assuming a detected Gaussian intensity profile for x, y, and z: 24,25
G(τ) )
1 · Veff〈C〉
1
1 r0 2 τ 1+ z0 τd
( ) ( ( ) ( )) τ 1+ τd
·
1⁄2
(5)
where r0 is the beam waist radius, and z0 is 1/2 the 1/e2 intensity distance along the optical axis as seen in Figure 4a. By fitting the experimentally obtained AC curve with the derived AC expression, τD, and the diffusion coefficient can be obtained. The AC expressions for two- and three-dimensional
Diffusive Transport within PSS Polymer Brushes diffusion were derived for a low concentration regime, as depicted in Figure 4a, in which several fluorescent molecules are present in the focal volume simultaneously. The advent of highly sensitive detectors allowed extension of this technique to a single molecule regime.26 In this work, the concentration of R6G was kept very low (∼60 pM) so that, on average, a single R6G molecule entered the laser focal volume at a time. By keeping the concentration of R6G very low, the fluorescence measurements from each of the single R6G molecules as they pass through the focal volume serve to report on the local diffusion environment, without affecting the native bulk Na+/ H+ counterion distribution within the polymer brush. E. Data Acquisition and Analysis. Acquisition Parameters. All AC functions were calculated directly from signal trajectories as seen in the inset in Figure 4, using programs written in Matlab (R2006a). All AC curves shown in this paper are normalized. Data were acquired with a bin time of 10 µs. To optimize computing performance, the data were further binned during analysis to 1 ms for all data with long diffusion times. The maximum lag time, τmax, was set at 12 s for all standards diffusing in water, and at 300 s for all diffusion processes occurring in the presence of polymer brush, so as to cover the appropriate lag-time range. All data were averaged over an acquisition period of 5 min, either directly within the AC calculation in the case of samples analyzed with a 300 s τmax, or via post AC function averaging in the case of standards diffusing in water with a τmax of 12 s. Focal volume parameters were fit using AC curves for 40 nm beads diffusing in water and eq 5. This allowed us to retrieve diffusion constants with an error less than 8%. Agreement between the fitted and experimental AC curves is good, with a root-mean-square error of below 0.02% for our setup. Application to the Thin Film System. The application of FCS to a thin film system requires consideration of the placement of the sample with respect to the focal volume. Figure 5a represents the physical system we investigated, and our positioning of the polymer brush sample within the focal volume. The focal volume z0 distance was fit at 1 µm,27 giving a total focal volume height of 2 µm. The thickness of free radical polymer brush thin films can range from tens to hundreds of nanometers depending on synthesis conditions and solvent quality.17,28,29 After setting the focus at the coverslip, we used the piezo-stage controller to position the coverslip 500 nm below this point, so that the entire 1/e2 focal volume rested just at the coverslip surface, as is depicted in Figure 5a. Within the focal volume, then, this geometry encompasses polymer thin film and the water solvent. It should be noted that polymer brush thin film characteristics such as density and chain dynamics vary in z, along our optical axis.28 Our FCS measurements provide an average diffusion response over the z axis. To ensure that our measured AC function was not dependent on relative placement of the sample chamber over the focal volume due to factors other than the geometry of the thin-film sample itself, the AC functions for 40 nm beads diffusing in water (constituting a homogeneous environment) were measured with the sample at various positions with respect to the focal volume. The diffusion constants obtained at different positions of the coverslip below the beam waist are shown in Figure 5b. For a homogeneous sample within a range of positions applicable to our experimental conditions, the data show that our instrumental setup does not impart a bias to the AC function as a function of sample positioning in the z direction.
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Figure 5. Placement of thin film sample within focal volume. (a) Representation of the physical system. (b) Independence of the AC function on depth for a homogeneous environment. Shown are diffusion constants for 40 nm beads diffusing in water at different positions of the coverslip/sample relative to the focal volume. The inset is a cartoon image of two possible positions of the coverslip with respect to the focal volume. The standard deviation of the diffusion constant over these measurements was z0. In our case, fitting of data obtained in the presence of the polymer thin film with both the 2D and 3D equations yielded less than 2% difference in both the diffusion constant, D, and the normalized root-mean-square error for the fits. This difference is well within our experimental standard deviation, therefore, all data reported herein was fit with eq 5. III. Results The Surface. Shown in Figure 6 are 1 × 1 µm2 atomic force microscopy (AFM) images of a clean coverslip substrate, and the dry PSS-modified coverslip surface. The average surface roughness is approximately 4 nm, with a maximum valley-topeak variance of ∼12 nm. In comparison, AFM of the blank coverslip shows an average surface roughness of approximately 3 Å, and a valley-to-peak variance of 10 Å for the same size region. The AFM surface scans showed complete coverage with
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Figure 8. AC curves for modeled signal trajectories showing a fast and slow diffuser with an order of magnitude difference in diffusion constants, along with two curves generated from a mix of the slow and fast signals at different modeled relative concentrations of: 1:1 (black) and 20:1 (green) (slow:fast).
Figure 6. AFM images of (a) a clean coverslip, and (b) a PSS polymer brush modified surface.
Figure 7. AC functions shown for R6G diffusing in water over a clean coverslip with a characteristic diffusion time (shown in axes) and an associated diffusion constant of 4.0 ( 0.3 × 10-10 m2/s, and also in water over a coverslip modified with PSS brush, with D ) 7 ( 2 × 10-14 m2/s. The PSS diffusion curve is an average over three runs. Inset shows extension of the AC function to the time resolution necessary to pick up diffusion events with decay times on the order of R6G in water.
polymer brush, with a qualitatively uniform coverage profile across multiple regions. The dry thickness of the brush under our experimental conditions is approximately 50 nm, as obtained by ellipsometry measurements performed on a silicon wafer prepared under identical conditions. This agrees well with values obtained from the literature of between 10 and 100 nm for surface-initiated free radical polymerization.17,28,29 Dependence of charge transport behaviors as a function of thickness and surface coverage density of strong polyelectrolyte brush systems represents a future extension of this FCS diffusion study. Interaction of the Fluorescent Probe and the Brush. The first experimental results demonstrate that R6G diffusion within the PSS polymer brush can be distinguished from diffusion in water. Figure 7 shows that the presence of the PSS polymer brush in the FCS focal volume markedly slowed the diffusion of the fluorescent probe. Calculated diffusion times increased by 4 orders of magnitude, from an average τD of 5.7 ( 0.5 ×
10-5 seconds in water to a τD of 0.30 ( 0.09 s in the brush, with associated diffusion constants of 4.0 ( 0.3 × 10-10 m2/s and 7 ( 2 × 10-14 m2/s, respectively. Additionally, our FCS studies demonstrate preferential interaction between the R6G counterion and the brush, as opposed to R6G and the solvent. This preference is evident when comparing the experimental AC curves at short times (Figure 7, inset) with the AC curves of a simulated system that has both fast and slow diffusers (Figure 8). Signal trajectories for the simulated system were generated with contribution from two Gaussian signals with an order of magnitude difference in diffusion times. The simulated curves demonstrate the convolution of diffusion decay times evident in the AC function when there are both slow and fast diffusers contributing to a signal trajectory. Note that these convolution features remain clear for diffusion constants differing by up to 4 orders of magnitude in this model (data not shown). As seen in the inset of Figure 7, our experimental data do not show evidence of significant water-like fast diffusers, despite that fact that the FCS focal volume encompasses both brush and a significant volume of the water environment. Recall that we estimate a 2 µm dimension of the focal volume in z, and a brush height of rlim
where ξ is an interaction constant that includes charge on the diffusing particle, solute dielectric constant, and a temperature term; Z is the variable field strength; and rlim is a cutoff radius limiting the electrostatic field due to point charges far away from the regions through which the counterion diffuses. Note that we have neglected excluded volume effects in this simulation. Further details on the simulation conditions are provided in the Supporting Information. The strength of field (b) in Figure 11 results from an order of magnitude change in the variable Z from that of field (a). This corresponds to a 10 times stronger field in (b). As we can see, stronger electrostatic interactions shift the AC decay to longer times, and contribute to slower characteristic decay times. The random walk model shows this effect across several orders of magnitude (data not shown). Future expansions to the model include extension to three dimensions, and inclusion of a field gradient that will address spatial asymmetry in the field. V. Conclusions We have used FCS to evaluate the diffusive transport behaviors of a positively charged counterion (the fluorescent probe) in the presence of a strong polyelectrolyte brush. We have shown that FCS is able to clearly resolve charge transport characteristics within the strongly charged polymer brush thin film. We plan to conduct further experiments in which this technique is used to classify and optimize polyelectrolyte brush systems to maximize charge transport/storage characteristics and minimize degradation. We have shown that two competing mechanisms contribute to diffusional dynamics within the strong polyelectrolyte brush,
Diffusive Transport within PSS Polymer Brushes and undoubtedly to the macroscale charge transfer efficacy. In considering charge transport performance of a PEM, it is necessary to consider the effects of an interaction potential on the AC function as predicted by the model, as well as the effects of the corresponding brush density. Because our fluorescent probe, R6G, functions as a counterion in this system, and because we can use FCS to measure the ion transport directly in the brush, it should be possible to use this technique to optimize macroscale charge transport properties toward the goal of obtaining better polyelectrolyte membranes. Acknowledgment. We thank the following individuals: Alexei Tcherniak (Rice University, Dr. Stephan Link) for many discussions contributing to FCS application and analysis; Dr. Bittner and Dr. Lubchenko (University of Houston), for helpful discussion regarding the random walk model; and to Nicel Estilore, Jin Young Park, and Guoqian Jiang (University of Houston, Dr. Advincula) for polymer brush characterization. Additionally, we thank both the Texas Center for Super Conductivity, and the University of Houston for generous funding of this work. Supporting Information Available: Data showing reproducibility of the ACs for the 40 nm beads used as our calibration standard, and details regarding the random walk simulation. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Biesheuvel, P. M. J. Colloid Interface Sci. 2004, 275, 97–106. (2) Kumar, N. A.; Seidel, C. Macromolecules 2005, 38, 9341–9350. (3) Ahrens, H.; Forster, S.; Helm, C. A. Phys. ReV. Lett. 1998, 81, 4172–4175. (4) Pristinski, D.; Kozlovskaya, V.; Sukhishvili, S. A. J. Chem. Phys. 2005, 122, 014907/1–014907/9. (5) Zhou, F.; Huck, W. T. S. Phys. Chem. Chem. Phys. 2006, 8, 3815– 3823. (6) Zhou, F.; Zheng, Z.; Yu, B.; Liu, W.; Huck, W. T. S. J. Am. Chem. Soc. 2006, 128, 16253–16258. (7) Whiting, G. L.; Snaith, H. J.; Khodabakhsh, S.; Andreasen, J. W.; Breiby, D. W.; Nielsen, M. M.; Greenham, N. C.; Friend, R. H.; Huck, W. T. S. Nano Lett. 2006, 6, 573–578. (8) Chen, S.; Krishnan, L.; S., S.; Benziger, J.; Bocarsly, A. B. J. Membr. Sci. 2004, 243, 327–333.
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