Anal. Chem. 2004, 76, 930-938
Modifying the Adsorption Behavior of Polyamidoamine Dendrimers at Silica Surfaces Investigated by Total Internal Reflection Fluorescence Correlation Spectroscopy Karla S. McCain, Peter Schluesche, and Joel M. Harris*
Department of Chemistry, University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112-0850
Polyamidoamine (PAMAM) dendrimers were modified and tested for use as solution-phase diffusion probes in silica nanostructures. In order for the successful application of dendrimers as solution-phase probes, their interactions with silica surfaces must be understood and controlled, so that the motion of the probe is not influenced by adsorption. Adsorption/desorption kinetics of PAMAM dendrimers and their diffusion in solution near silica surfaces were investigated with total internal reflection fluorescence correlation spectroscopy (TIR-FCS). Dendrimers of generations 3, 5, and 7 were dye-labeled with carboxyrhodamine 6G. Because PAMAM dendrimers are positively charged in solution (having primary amines as end groups), significant adsorption of these molecules to the negatively charged silica surface was observed. Adsorption/desorption rates and the equilibrium constant for adsorption were determined by fitting the autocorrelation functions to a kinetic model. The desorption rate decreases and the absorption equilibrium constant increases with higher dendrimer generation. To reduce the adsorption of these probes to silica surfaces, the labeled dendrimers were reacted with succinic anhydride, converting the primary amine end groups to negatively charged carboxylic acid groups. These carboxylated dendrimers did not detectably adsorb to silica from aqueous solution. TIR-FCS was used to determine their freesolution diffusion constants near silica surfaces, and the corresponding hydrodynamic radii compare favorably with values reported from forced Rayleigh scattering measurements. Dendrimers are regularly branched, highly monodisperse polymers with a well-defined molecular architecture consisting of a core, regularly branching repeat units, and terminal groups.1 Polyamidoamine (PAMAM) dendrimers are synthesized from an ethylenediamine core with branching units containing tertiary amine and amide functionality (Figure 1). Full generation (G1, * To whom correspondence should be addressed. E-mail: harrisj@ chemistry.chem.utah.edu. (1) Tomalia, D. A.; Baker, H.; Dewald, J.; Hall, M.; Kallos, G.; Martin, S.; Roeck, J.; Smith, P. Macromolecules 1986, 19, 2466-2468.
930 Analytical Chemistry, Vol. 76, No. 4, February 15, 2004
G2, etc.) PAMAM dendrimers are terminated with primary amine groups, which are convenient because they allow for standard dyelabeling procedures.2 Because of their unusual structure, dendrimers have been employed in a wide variety of applications including magnetic resonance imaging enhancement reagents,3 drug delivery,4 sensor materials,5 and catalysis.6 Dendrimers have also been used as calibration standards for size exclusion chromatography because of their spherical shape and monodispersity.7 Because dendrimers are highly monodisperse and available in sizes ranging from ∼3 to ∼20 nm, they have great potential for use as diffusion probes for nanoscale porous structures. For example, measuring the dendrimer diffusion coefficient as a function of its size can give insight as to how tortuosity of a porous material is influenced by the size of the diffusion probe. Determining the largest size dendrimer that could penetrate a structure could define the maximum pore size. In order for dendrimers to be developed as diffusion probes for porous structures, their adsorption properties must be well characterized and controlled. Any time that a dendrimer probe spends adsorbed to a surface instead of diffusing in solution complicates the interpretation of the results. This issue is especially important because of the high surface area-to-volume ratio of nanostructured materials. The adsorption of PAMAM dendrimers to silica and alumina has been previously studied and shown to depend predictably on solution pH, ionic strength, and dendrimer generation.8 However, these measurements were performed ex situ by allowing the system to come to equilibrium and then quantifying the residual amount of dendrimer remaining in the supernatant. There have been fewer (2) Hermansen, G. T. Bioconjugate Techniques; Academic Press: San Francisco, 1996. (3) Wiener, E. C.; Brechbiel, M. W.; Brothers, H.; Magin, R. L.; Gansow, O. A.; Tomalia, D. A.; Lauterbur, P. C. Magn. Reson. Med. 1994, 31, 1-8. (4) (a) Liu, M.; Frechet, J. M. J. Pharm. Sci. Technol. Today 1999, 2, 393-401. (b) Sideratou, Z.; Tsiourvas, D.; Paleos, C. M. Langmuir 2000, 16, 17661769. (5) Albrecht, M.; Gossage, R. A.; Spek, A. L.; vanKoten, G. Chem. Commun. 1998, 1003-1004. (6) Niu, Y.; Yeung, L. K.; Crooks, R. M. J. Am. Chem. Soc. 2001, 123, 68404846. (7) Dubin, P. L.; Edwards, S. L.; Kaplan, J. I.; Mehta, M. S.; Tomalia, D.; Xia, J. Anal. Chem. 1992, 64, 2344-2347. (8) Ottaviani, M. F.; Turro, N. J.; Jockusch, S.; Tomalia, D. A. J. Phys. Chem. B 2003, 107, 2046-2053. 10.1021/ac035100c CCC: $27.50
© 2004 American Chemical Society Published on Web 01/13/2004
Figure 1. Chemical structure of generation 1 PAMAM dendrimer. Propagation to generation 2 is shown on one of the end groups. The number of end groups increases geometrically with generation with a G3 dendrimer containing 32, G4 containing 128, and G7 containing 512.
studies examining the adsorption/desorption kinetics of dendrimers. Nagaoka and Imae used surface plasmon resonance to follow the adsorption kinetics of PAMAM dendrimers onto a gold surface with a self-assembled monolayer of 3-mercaptopropionic acid and observed very slow uptake kinetics (∼100 s).9 van Duijvenbode et al. examined the adsorption kinetics of poly(propyleneimine) dendrimers on glass by light reflectivity measurements.10 However, their data were dominated by contributions from slow transport to the surface and were not sensitive to adsorption kinetics. In this work, total internal reflection-fluorescence correlation spectroscopy (TIR-FCS) was used to determine the adsorption equilibrium constant, adsorption/desorption kinetics, and diffusion coefficients of dye-labeled PAMAM dendrimers at a fused-silica/ solution interface. TIR-FCS is an equilibrium measurement where fluctuations in the fluorescence signal as a function of time are measured. These fluctuations are the result of individual fluors entering and leaving an observation volume defined by the evanescent wave. These fluctuations contain information about both the average number of fluors in the observation volume and the rates that govern their residence time in the observation volume. Autocorrelation of the fluctuating signal allows the determination of kinetic parameters without the need for a concentration jump. TIR-FCS was developed by Thompson and Axelrod to measure the binding kinetics of immunoglobulin G to a protein-coated silica/water interface.11 More recently, TIR-FCS has been used to examine the adsorption/desorption kinetics of rhodamine 6G at a C-18 modified silica/solution interface12 and the diffusion of (9) Nagaoka, H.; Imae, T. Int. J. Nonlinear Sci. Num. Sim. 2002, 3, 223227. (10) van Duijvenbode, R. C.; Rietveld, I. B.; Koper, G. J. M. Langmuir 2000, 7720-7725. (11) Thompson, M. L.; Axelrod, T. P. Biophys. J. 1981, 33, 435-454. (12) Hansen, R. L.; Harris, J. M. Anal. Chem. 1998, 70, 4247-4256.
rhodamine 6G in sol-gel films.13 In addition to this kinetic information, from the magnitude of the fluctuations, it is possible to determine the average number of fluors in the observation region, which can be used to quantify the number of molecules at the surface and thus determine an adsorption equilibrium constant.14 TIR-FCS is employed here to measure the adsorption/ desorption kinetics and equilibrium constants for G3, G5, and G7 amine-terminated PAMAM dendrimers at a fused-silica/solution interface. The preparation of nonadsorbing carboxylated G3, G5, and G7 is also described. Free-solution diffusion coefficients of these carboxylated structures near a silica surface interface were also determined by TIR-FCS. THEORY In fluorescence correlation spectroscopy, excess noise in the fluorescence signal arises from fluctuations in the number of fluors in a small probe volume.15 In TIR-FCS, this volume in an interfacial region bounded by the area of the laser beam and the depth of penetration of the evanescent wave. When the laser spot size is much larger than the evanescent wave depth of penetration so that lateral diffusion can be neglected, these fluctuations can be attributed to diffusion through the evanescent wave, adsorption and desorption of molecules to and from the surface, photobleaching, and chemical reactions. The relative magnitude of fluctuations compared to the average fluorescence signal contains information about the number of molecules in the probe volume, while the frequency of fluctuations contains information about the rates of processes from which the fluctuations arise. To extract this information, the autocorrelation,15 G(τ), of the (13) McCain, K. S.; Harris, J. M. Anal. Chem. 2003, 75, 3616-3624. (14) Hansen, R. L.; Harris, J. M. Anal. Chem. 1998, 70, 2565-2575. (15) Thompson, N. L. In Topics in Fluorescence Spectroscopy, Volume 1: Techniques; Lakowicz, J. R., Ed.; Plenum Press: New York, 1991.
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fluorescent transient, F(t), is calculated where
G(τ) )
〈F(t)F(t + τ)〉 - 〈F(t)〉2 〈F(t)〉2
(1)
of molecules as are adsorbed on the surface. Rt is the rate at which a molecule diffuses this distance into solution. The third characteristic rate is Re, the rate of transport through the evanescent wave, which is defined as
Re ) D/dp2
(7)
and where,
〈F(t)F(t + τ)〉 ) lim
Tf∞
1 T
∫
T/2
-T/2
F(t)F(t + τ) dt
(2)
The decay of the autocorrelation function, G(τ), is related to the rates of the interfacial kinetic processes that are responsible for changes in the molecular populations. The theory that predicts the shape of the autocorrelation function for TIR-FCS is based on a model where a fluorescent molecule, A, diffuses to a surface adsorption site, B, to become an adsorbed molecule, C.16
A+BhC
(3)
where A is the concentration of fluor in solution while B, the concentration of surface adsorption sites, and C, the surface concentration of adsorbed species, are defined in units of molecules per area. An adsorption equilibrium constant is defined as follows, both in terms of equilibrium concentrations and rates:
Keq ) kads/kdes ) [C]/[A][B]
(4)
where D is the free solution diffusion coefficient of A and dp ) λo/4π (n12 sin2θ - n22)1/2 is the depth of penetration of the evanescent wave intensity15 where λo is the vacuum wavelength, θ is the angle of incidence, and n1 and n2 are the refractive indices of the denser (substrate) and rarer (solution) media, respectively. Re describes fluctuations that arise from molecules diffusing in free solution in the evanescent intensity distribution given by I(z) ) Io exp(-z/dp), where z is the distance from the interface where the evanescent wave is launched. The relative values of the three characteristic rates determine the shape and time decay of the autocorrelation function. In the case that Rr , Re, which is true for most observed systems of interest, the full autocorrelation function can be approximated by a weighted sum of the autocorrelation functions of two extremes: the limit of only surface binding (no molecules in solution) and the limit of no surface binding (no molecules on the surface):16
G(τ) )
{
1/2 R1/2 1 - R2
{
(1 - 2Re)w[i(Reτ)1/2] + 2
M-1),
where Keq is the equilibrium constant (in kads is the adsorption rate constant (in M-1 s-1), and kdes is the desorption rate constant (in s-1). The autocorrelation function for this system depends on three characteristic rates, which relate to the physical processes that change the population of moleclues at the interface.11,16 This model also assumes that the radius of laser spot size is much larger than the evanescent wave depth so that diffusion across the laser spot can be neglected. The first rate is Rr, the reaction rate or the relaxation rate for adsorption and desorption at the surface, defined as
Rr ) kads[A] + kdes
(5)
This rate is the sum of the adsorption and desorption rates and reflects fluctuations that result from molecules binding and debinding at the surface. The second characteristic rate is Rt, the bulk normal diffusion transport rate, which is defined as
Rt ) D([A]/β[C])2
(6)
where D is the free solution diffusion coefficient of A and β is the fraction of unoccupied surface binding sites. Rt is the rate at which a change of concentration on the surface is relaxed by a change in concentration in solution. The ratio [A]/[C] has units of length and is the distance into solution that contains the same number (16) Starr, T. E.; Thompson, N. L. Biophys. J. 2001, 80, 1575-1584.
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} )}
1/2 1/2 1/2 1/2 R1/2 ] - R1/2 ] 1 w[- i(R2 τ) 2 w[- i(R1 τ)
(
Reτ π
GCC(0) +
1/2
GAA(0) (8)
where
w(ξ) ) e-ξ erfc(- iξ) 2
and
R1/2 1,2
(
Rr2 ) - 1/2 ( - Rr 4Rt 2R Rr t
(9)
)
1/2
(10)
The GCC-dependent term is the autocorrelation function in the limit of no molecules in solution, which describes the relaxation of fluctuations due to adsorption/desorption events and is only a function of Rr and Rt. The GAA-dependent term is the autocorrelation function in the limit of no surface binding, which describes fluorescence fluctuations due to diffusion within the z-dependent intensity profile of the evanescent wave and depends only on Re. GAA(0) and GCC(0) are the weighting factors for these two components of the autocorrelation function, and their relative values describe how much of the decay of the autocorrelation function is derived from adsorption/desorption versus diffusion through the evanescent wave. In the case where Rr is much smaller than Rt, it is possible to simplify this equation further. When Rr , Rt, R1,21/2 can be estimated by (iRr1/2. Then by applying the identity for w-functions,17
w(z) + w(- z) ) 2 exp(z2)
(11)
Equation 8 reduces to
or diffusing in solution. To calculate Keq, it is necessary to differentiate between these two populations of molecules. If N is the total number of molecules within the probe volume, then
G(τ) ) exp(- Rrτ)GCC(0) + {(1 - 2Reτ)w[i(Reτ)1/2] + 2(Reτ/π)1/2}GAA(0) (12) where Rr, Re, GAA(0), and GCC(0) are as defined previously. This reduces the number of characteristic rates describing the process to only two and results in a simple exponential dependence on Rr. In addition to this kinetic information, it is also possible to determine the average number of molecules in the evanescent wave by considering the amplitude of the autocorrelation.14 The statistical approach used here relies on the propagation of errors from a Poisson distribution, which describes the sampling of molecules in a small probe volume surrounded by a large solution volume. The fluorescence signal, F, is proportional to the number of molecules in the probe volume:
〈F〉 ) k〈N〉
(13)
where k is the proportionality constant describing the average number of photons collected per molecule per unit time. The molecule-to-molecule fluctuations in k (due to different trajectories through the evanescent wave, for example) are averaged over a sample of N molecules14 so that the fluorescence variance is dominated by the much greater contribution from the fluctuations in the number of molecules, governed by Poisson statistics:
σF2 ) k2〈N〉
(14)
so that the number of molecules can be estimated by taking the ratio the fluorescence squared to its variance. Thus, the average number of molecules in the observation volume is
〈N〉 ) 〈F〉2/σF2
(15)
and 〈F〉2 and σF2 can be calculated from the autocorrelation function. The autocorrelation at zero offset (τ ) 0) is equal to the mean-squared fluorescence intensity, 〈F2〉 and decays at long times (τ ) ∞) to the squared mean fluorescence intensity, 〈F〉2. So, 〈F〉 can be calculated by taking the square root of the autocorrelation function at long times. The variance in fluorescence signal can be calculated by the difference between the mean-squared and squared-mean intensity values.
σF2 ) 〈F2〉 - 〈F〉2
(16)
Therefore, by measuring the autocorrelation at zero offset and long times, it is possible to determine the average number of molecules in the probe volume based on molecular statistics. It is important to note that this method does not require calibration in order to quantify the number of molecules within the probe volume. This method counts all of the molecules within the evanescent wave, whether they are adsorbed to the surface (17) Abramowitz, M.; Stegun, I. A. Handbook of Mathematical Functions; Dover Publications: New York, 1974.
New ) Vew[A]
(17)
Nsurf ) N - New
(18)
and
where New is the number of molecules in solution in the evanescent wave, Nsurf is the number of molecules adsorbed to the surface, and Vew is the probe volume defined by the depth of penetration of the evanescent wave and the spot size of the laser at the interface.
EXPERIMENTAL SECTION Modification and Characterization of Dendrimers. Generations 3, 5, and 7 PAMAM dendrimers (Aldrich), provided as stock solutions in methanol, were dye-labeled with 5- and 6-carboxyrhodamine 6G succinimidyl ester (Molecular Probes) by the following procedure.2 A small aliquot of the dendrimer was placed in a vial with a stir bar with a small amount, ∼0.5 mg, of 1-methylmorpholine, which acted as a catalyst. The reactive dye label was dissolved in N,N-dimethylformamide (DMF), added dropwise to the stirring dendrimer solution, and allowed to react for 1 h at room temperature (Figure 2). The total reaction volume for each generation was 1 mL, and the amount of dye per dendrimer end group was less than 10% for all generations. Because of the wide variety of molecular weights between dendrimer generations, the concentration of dendrimers was decreased at higher concentrations in order to keep the concentration of end groups relatively constant. G5 and G7 dendrimers had end group concentrations of 0.035 M, and G3 had an end group concentration of 0.018 M. The concentration of dye label was kept nearly constant at ∼1.8 µM and resulted in theoretical maximum labeling ratios of 5% for G5 and G7 and 10% for G3. Labeled dendrimers could be further modified by reaction with succinic anhydride to produce carboxylic acid end groups.2 For this reaction, a stoichiometric amount of succinic anhydride was dissolved in a few drops of DMF AND then added to the reaction mixture after 1 h. A precipitate was formed almost immediately which could be redissolved with the addition of several drops of dilute acetic acid. Dye-labeled dendrimers were separated by dialysis. The reaction mixture was placed in a Float-a-lyzer dialysis tube (Spectrum), with a 1-mL volume and a 3500 MW cutoff, and dialyzed against 1 L of pure water. The dialysis bath was changed three times. The yield of the reactions and the quality of the dialysis separation were quantified by high-performance liquid chromatography (HPLC) with fluorescence detection. The dendrimers were found to be react almost stoichiometrically with the reactive dye labeling resulting in 8.5, 5.4, and 5.4% of end groups labeled for G3, G5, and G7, respectively. This resulted in 2.8 labels/dendrimer for G3, 6.9 labels/dendrimer for G5, and 28 Analytical Chemistry, Vol. 76, No. 4, February 15, 2004
933
Figure 2. (a) Reaction scheme for dye-labeling dendrimers. Dendrimers were allowed to react at 1 h at room temperature in DMF. (b) Reaction scheme for modifying dendrimer end-groups from primary amines to carboxylic acids by reaction with succinic anhydride.
labels/dendrimer for G7. Carbon 13 nuclear magnetic resonance (NMR) spectroscopy confirmed that the carboxylation reaction had taken place and was complete. 13C NMR spectra were acquired on a Varian Inova 500-MHZ spectrometer and were collected with a 5-mm Varian switchable broadband probe. For NMR studies, the dendrimers were not dye-labeled, were dissolved in dimethyl sulfoxide at a concentration of 30 mg/mL, were placed in a Shigemi tube. 13C NMR spectra of the dendrimers were consistent with their structures and literature assignments.18 The spectrum of the carboxy-terminated dendrimer included several additional peaks, due to the derivitazation, including one at 174 ppm, corresponding to the carboxylic acid carbon. The spectrum of the carboxy-terminated dendrimer showed the disappearance of the peak at 42 ppm due to the carbon next to the terminal amine group that was observed in the spectrum of the amine-terminated dendrimer. TIR-FCS Measurements. The TIR-FCS instrument used in this work has been described in detail elsewhere.13 Briefly, the 514.5-nm line from an argon ion laser was passed at 76° from normal through a 72° dove prism and totally internally reflected, producing an evanescent wave with a 164-nm depth of penetration at a fused-silica/solution interface. The internal reflection spot was produced in a flow cell that was attached to the top of a inverted microscope (Nikon). Solutions with ∼20 pM dendrimer were made in 50/50 water/methanol with no added electrolyte and found to have a pH 5.5, implying that the amine-terminated dendrimers and carboxy-terminated dendrimers should be positively and negatively charged, respectively. Fluorescence excited by the evanescent wave was collected by a 60×, 0.7 NA microscope objective, passed through a high-pass filter, and a 2-mm aperture, and imaged onto a photomultiplier tube (Hamamatsu, (18) Peterson, J.; Allikmaa, V.; Subbi, J.; Pehk, T.; Lopp, M. Euro. Polym. J. 2003, 39, 33-42.
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R928). Current pulses from the PMT were ×10 amplified (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 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 very first point (τ ) 0) in the autocorrelation was removed before fitting because it is dominated by photon shot noise.14 The bandwidth of the photomultiplier tube is greater than 100 MHz so that the correlation due to photon shot noise decays entirely in less than 100 ns. Fitting the Autocorrelation Function. The general procedure for fitting the data was written in a FORTRAN program that calculated a theoretical curve for an array of rates, performed a linear least-squares step to determine the best-fit amplitude and offset, and calculated the residuals.19 The best-fit rate was taken to be that which minimized the sum of the square of the residuals. Reported uncertainties were determined from triplicate data sets. The uncertainty associated with fitting, estimated from the χ2 surface, was smaller than the error associated with run-to-run reproducibility by a factor of ∼2. Autocorrelation functions of carboxy-terminated dendrimers did not show any detectable influence from adsorption to the surface (see below) and were thus fit to the second half of eq 8, which describes diffusion through the evanescent wave in the absence of adsorption. Diffusion coefficients were calculated from (19) Wong, A. L.; Harris, J. M. Anal. Chem. 1989, 61, 2310-2315.
these fitted Re values were using eq 7. The Stokes-Einstein equation20 was then be applied to estimate molecular radii in solution:
D ) kT/6πηa
(19)
where D is the diffusion coefficient, k is Boltzman’s constant, T is the temperature, η is the solvent viscosity, and a is the hydrodynamic radius of the molecule. The analysis for amine-terminated dendrimers is more complex because of their adsorption to the silica surface. Due to the uncertainty that arises from fitting two rates simultaneously, it was necessary to estimate and fix Re while floating Rr. Re was estimated using the diffusion coefficients for the amine-terminated dendrimers predicted by the Stokes-Einstein equation above. This proved a reasonable approximation, because of the small influence of Re on Rr. Varying Re by an order of magnitude only changed the fitted Rr value by 10%. In order for adsorption and desorption rates to be calculated from Rr, Keq must be known. For small molecules, the equilibrium constant for adsorption can be measured independently by HPLC.14 However, because of the size of the dendrimer molecules, HPLC analysis is ambiguous because of the size exclusion of the dendrimer from small pores in the silica packing material. In fact, amine-terminated dendrimers eluted before free dye in solution, despite the fact that their multiple positive charges cause them to be strongly adsorbed to the surface. Therefore, to determine Keq, the magnitudes of the fluorescence fluctuations from TIR-FCS measurements were used to count the number of molecules in the observation volume. In the case of these strongly adsorbing molecules, this number was dominated by molecules adsorbed to the silica surface. To calculate Keq from this number and the concentration of dendrimer in solution, it is necessary to have an estimate for [B], the density of adsorption sites on the surface. This site density was estimated from the concentration of dendrimers that would result when they are close packed on the surface, using the measured hydrodynamic radii for the carboxy-terminated dendrimers. With this information, Keq was calculated using eq 4. In this case, where [A] is very small, Rr ) kads[A] + kdes ≈ kdes and eq 4 can be used to estimate kads. RESULTS AND DISCUSSION Adsorption/Desorption Equilibria of Amine-Terminated Dendrimers. Figure 3 shows the autocorrelation functions for amine-terminated dendrimers and their fits to eq 12. To interpret the kinetic parameters, it is first necessary to determine Keq by counting the molecules at the surface. For the 20 pM solution used in this study, New ) 157 molecules should be found in solution in the probe volume defined by the evanescent wave and the aperture, calculated by eq 17. The total number of molecules, N in the probe volume, determined from eqs 15 and 16, range from 9000 to 20 000. Within the observation area, this number of dendrimers corresponds to less than 10-3 of a monolayer, so that the adsorption isotherm should be linear and there should be no impact by the probe molecules on the local optical properties of the interface. Note also that, for these strongly adsorbing den(20) Berg, H. C. Random Walks in Biology; Princeton University Press: Princeton, NJ, 1983.
Figure 3. Experimental autocorrelations and resulting fits to eq 12 for 20 pM G3, G5, and G7 amine-terminated dendrimers in 50/50 methanol/water solutions against a fused-silica substrate. For clarity, only one of every 25 points has been plotted. Table 1. Dependence of Dendrimer Generation on Adsorption Equilibrium generation
Keq (M-1)a
∆Gads (kJ/mol)b
∆Gads per end group (kJ/mol)
3 5 7
5 ( 1 × 104 (1.8 ( 0.2) × 105 (1.7 ( 0.1) × 106
-26.6 ( 0.5 -29.9 ( 0.3 -35.5 ( 0.1
15.0 ( 0.3 5.5 ( 0.06 3.95 ( 0.02
a Equilibrium constant calculated from eq 4 by counting molecules in the probe volume. bFree energy of adsorption calculated from eq 20. c Free energy per the number of end groups within 0.5 nm of the surface calculated based on eq 21.
drimers, New is negligible compared to N and N ≈ Nsurf. Table 1 lists the adsorption equilibrium constants calculated from the number of molecules adsorbed to the surface. Keq increases exponentially with increasing dendrimer generation. The free energy for the adsorption of the dendrimers is defined as,
∆Gads ) -RT ln(Keq)
(20)
where R is the gas constant and T is temperature. A plot of ∆Gads versus dendrimer generation shows that the free energy change decreases monotonically with dendrimer generation (see Figure 4a). This can be explained by examining how the number of end groups a dendrimer has near the surface changes with generation. Analytical Chemistry, Vol. 76, No. 4, February 15, 2004
935
Table 2. Dependence of Dendrimer Generation on Adsorption/Desorption Kinetics generation
kdes (s-1)a
kads (M-1 s-1)b
3 5 7
70 ( 20 6.3 ( 0.6 6(2
(3.36 ( 0.5) × 106 (1.11 ( 0.3) × 106 (9.84 ( 0.1) × 106
a Desorption rate constant calculated from eq 5 and the fit of the autocorrelation function to eq 12. b Kads calculated from eq 4.
Figure 4. (a) Free energy of adsorption (∆Gads) as a function of dendrimer generation for G3, G5, and G7 amine-terminated dendrimers measured in 50/50 methanol/water solutions against a fusedsilica substrate. Line is to guide the eye. (b) The number of dendrimer end groups within 0.5 nm of the surface for G3, G5, and G7 amineterminated dendrimers, assuming a spherical model for the dendrimer with no deformation. Line is to guide the eye.
Adsorption of these amine-terminated dendrimers to the silica surface should occur through hydrogen bonding of dendrimer terminal amine groups to surface silanol groups and electrostatic interactions between protonated terminal amine groups on the dendrimer and deprotonated silanols on the surface. The number of end groups close enough to the silica surface to interact should influence ∆Gads. The fraction of the dendrimer surface, f, within a distance, a, of the surface onto which the dendrimer is adsorbed can be estimated from the ratio of the surface area of a spherical cap of radius, r, and height, a, relative to the total area of the sphere:
f ) 2πra/4πr2 ) a/2r
(21)
Since the dendrimer chains should have some flexibility that would allow them to rearrange for greater contact with the surface, the fraction of the surface available for interaction is estimated for a value of a ∼ 0.5 nm or about twice the length of a hydrogen bond. Taking the product of the surface fraction from eq 21 and the number of end groups per dendrimer predicts the number of surface-interacting end groups with generation (see Figure 4b). While the surface fraction within a critical distance decreases with increasing dendrimer radius, the total number of end groups increases with a stronger, geometric dependence on generation. The free energy of adsorption per interacting end group was determined by dividing the total free energy change (Figure 4a) by the estimated number of available end groups (Figure 4b), and the results are listed in Table 1. The resulting strengths of the end group interactions with the surface are consistent with the magnitudes of hydrogen bonding or electrostatic attraction to the 936 Analytical Chemistry, Vol. 76, No. 4, February 15, 2004
surface. The adsorption free energy per end group shows a significant decrease with dendrimer generation. This decrease is due to the increasing density of dendrimer end groups on the surface with higher dendrimer generation.6 For a G3 dendrimer, the terminal amine groups have enough flexibility to adopt the best possible conformations with which to interact with surface silanols. However, the G7 dendrimer end groups are much more tightly packed on the dendrimer surface, limiting their ability to change conformation to form the best possible surface bonds. Small-angle X-ray scattering studies of PAMAM dendrimers show a transition from starlike structures at early generations to spherelike structures at later generations.21 G3 dendrimers were determined to have starlike structures, while G5 and G7 dendrimers were determined to have increasingly spherelike structures. This trend is consistent with change in the free energy per interacting end group observed here, where the difference in ∆Gads between G3 and G5 is much larger than the difference between G5 and G7. Adsorption/Desorption Kinetics of Amine-Terminated Dendrimers. The autocorrelation functions and their fits to eq 12 for amine-terminated dendrimers at a fused-silica surface are shown in Figure 3. It was possible to use eq 12 instead of eq 8, because of flow in the system. Solution was flowed at a 1 mL/ min, corresponding to a linear flow velocity in the thin flow cell of 4.4 mm/s. Thus, the solution was completely refreshed over the 33-µm spot in the sample every 7.7 ms. For these highly adsorbed dendrimers, [A]/[B], the distance from the surface containing enough molecules in solution to equal those adsorbed to the surface is quite large, several hundred centimeters, resulting in very slow Rt’s. However, any correlation over those distances is washed out by the rapid flow, essentially removing any contribution of Rt to the autocorrelation. This allows the autocorrelation function to be fit simply to eq 12, which only includes Rew and Rr. Table 2 shows the fitted results of the adsorption/desorption kinetics. The desorption rate constant decreases with increasing dendrimer generation, meaning that larger dendrimers desorb more slowly. As with their equilibrium constants, this is a function of the number of end groups being able to interact with the surface. However, this effect seems to level off between G5 and G7. This could be due to the solvent conditions, 50/50 water/ methanol, pH 5.5, where the total number of end groups close enough to the surface to interact increases with generation, but their charge density does not. At the pH of these solutions, the carboxylate groups would only be partially charged. The pKa of surrounding end groups is influenced by the charge state of its (21) Prosa, T. J.; Bauer, B. J.; Amis, E. J. Macromolecules 2001, 34, 4897-4906.
Table 3. Free Solution Diffusion of Carboxy-Terminated Dendrimers generation
D (cm2/s)a
diameter (nm)b
3 5 7
(5.6 ( 0.8) × 10-7 (3.8 ( 0.4) × 10-7 (1.3 ( 0.2) × 10-7
4.5 ( 0.7 6.6 ( 0.7 19 ( 3
a Diffusion coefficient calculated from eq 7 and the fit of the autocorrelation function to the second half of eq 8. b Diameter calculated from eq 19.
Figure 5. Experimental autocorrelations and resulting fits to the second term of eq 8 for 20 pM G3, G5, and G7 carboxy-terminated dendrimers in 50/50 methanol/water solutions against a fused-silica substrate. For clarity, only one of every 25 points has been plotted.
neighbors,22 so the charge density of the dendrimers might reach a maximum, resulting in a corresponding minimum in kdes that does not change further with higher generation. The adsorption rates, kads, are calculated from kdes and Keq using eq 4. There is no trend in kads with dendrimer generation, and the values for G3 and G5 are within their errors of each other. This lack of a trend indicates that the variation in Keq results from changes in the desorption rate and not the adsorption rate. It is also interesting that the magnitude of kads, 106 M-1 s-1, is much smaller than the predicted diffusion-limited adsorption rate constant,23 kdiff ) kTNav/6000η ∼ 2 × 108 M-1 s-1. These results are consistent with what was observed for the adsorption of rhodamine 6G onto C18 surfaces as a function of solution composition. The adsorption rate constant was found not to change significantly, less than 1 order of magnitude, with solvent composition, while the desorption rate varied by 2 orders of magnitude. The adsorption rates measured for rhodamine 6G onto C18 surfaces were on the order of 104, 2 orders of magnitude slower than was found for these dendrimers. This could be due to differences in the barriers for adsorption at hydrophobic C18 surface versus hydrophilic silica surfaces. Rhodamine 6G adsorbing to a C18 layer was postulated to require changes in solvation (22) van Duijvenbode, R. C.; Rajanayagam, A.; Koper, G. J. M.; Baars, M. W. P. L.; de Waal, B. F. M.; Meijer, E. W.; Borkovec, M. Macromolecules 2000, 33, 46-52. (23) Smoluchowski, M. V. Z. Phys. Chem. 1917, 92, 129-168.
to interact with a hydrophobic, alkyl chain layer, while dendrimer adsorption to the surface should be driven by well-solvated dipolar or electrostatic interactions.14 Diffusion of Carboxy-Terminated Dendrimers. To use dendrimers as probes of solution-phase diffusion in silica materials without complications from adsorption, dendrimers were modified after dye-labeling to produce carboxy end groups. At neutral pH, these dendrimers should be negatively charged (as opposed to positively charged for the amine-terminated dendrimers), which would reduce or eliminate interactions with a negatively charged silica surface. The TIR-FCS autocorrelation functions for the carboxy-terminated dendrimers are shown in Figure 5. Concentration jump experiments monitoring dendrimers diffusing out of a high surface area silica sol-gel film show no evidence of dendrimer adsorption to the silica surface.24 Based on this evidence, the autocorrelation functions were fit to the second term of eq 8, describing diffusion in an evanescent wave. The autocorrelation functions were well fit by this free-solution diffusion model with random residuals, and no improvement in fit was realized by including an adsorption kinetic term in the model. The resulting evanescent wave relaxation rates and diffusion coefficients are listed in Table 3. By using the Stokes-Einstein relationship, eq 19, the hydrodynamic radii of the dendrimers were also estimated and are listed in Table 3. These radii compare very well with literature values measured by forced Rayleigh scattering (FRS).25 The TIR-FCS radii are indistinguishable from those measured by FRS at the 90% confidence level. It is also important to note that these free-solution diffusion coefficients were measured within the evanescent wave depth, 150 nm of the surface, and yet showed no influence of the surface on their rates of diffusion in solution. This is an important result because of the application of these carboxy-terminated dendrimers as probes in nanostructured silica films,24 where they are in frequent contact with silica surfaces in these high surface-area materials. CONCLUSIONS The adsorption/desorption characteristics of PAMAM dendrimers at silica surfaces were evaluated by TIR-FCS in light of the potential use as solution diffusion probes of nanostructured materials, specifically silica sol-gel materials. Amine-terminated dendrimers adsorb quite strongly to the surface, and their free energy of adsorption is well modeled by considering the number of end groups that could interact with the surface. Although fullgeneration, amine-terminated dendrimers are easy to dye-label, (24) McCain, K. M.; Schluesche, P.; Harris, J. M. Anal. Chem. 2004, 76, 939946. (25) Stechemesser, S.; Eimer, W. Macromolecules 1997, 30, 2204-2206.
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their strong adsorption to silica surfaces makes their use as solution diffusion probes in porous silica materials impossible, because of the amount of time they would spend adsorbed to the surface and not moving. By modifying the amine-terminated dendrimers after dye-labeling, however, to produce terminal carboxy groups, it is possible to prevent their adsorption to silica surfaces. This approach however is general. These specific dendrimer probes were developed with the goal of exploring tortuosity in silica sol-gel materials. It would be possible to end group modify these dendrimer probes in a variety of ways to produce functionality that would result in the control of their adsorption to different materials.
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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 Robert Horton for his assistance in acquiring the NMR data.
Received for review September 18, 2003. Accepted December 2, 2003. AC035100C
