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Modification of Electrostatic Interaction by Rhodamine 6G Adsorption on Polystyrene Latex as Assessed by Frequency Domain Photon Migration Yingqing Huang, Virany Yuwono, and Eva M. Sevick-Muraca* The Photon Migration Laboratories, Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843-3122 Received May 2, 2002. In Final Form: September 7, 2002 To demonstrate assessment of electrostatic interactions using first principles models, the isotropic scattering coefficients of negatively charged polystyrene latex were measured with frequency domain photon migration (FDPM) as the effective surface charge was changed by adsorbing positively charged surfactant, Rhodamine 6G (R6G). Measurements were conducted on dense suspensions (volume fraction ) 0.186) at an ionic strength of 5 mM NaCl equivalent with varying amounts of positively charged R6G adsorbed on the particle surface. The FDPM measurements of isotropic scattering were then fitted to a model prediction obtained by solving the Ornstein-Zernike integral equation using the hard sphere Yukawa interaction model with mean spherical approximation as closure. The results show that the parameter estimate of surface charge decreased with adsorbed R6G showing the ability to use multiply scattered light to characterize electrostatic interaction in dense suspensions.
1. Introduction The ability to mediate colloidal particle interactions could be critical for controlling stabilities, rheology, as well as self-assembly processes. Yet, the measurement of parameters that govern interactions within dense colloidal suspensions remains elusive. For the case of electrostatic interaction, the intrinsic surface charge (also called structural surface charge) is governed by the functional groups on the particle surface and is measured by titration. Nonetheless, titration is inconvenient for dynamically evaluating the electrostatic interaction in dense suspensions.1-3 In addition, the ionization equilibrium of surface groups and the ion condensation of the counterions impact electrostatic interactions. The effective surface charge, which discounts the ion condensation and charge regulation, is typically used to describe electrostatic interactions. Currently, there is no direct method for measuring either surface charge or electrostatic potential at the particle surface. The zeta potential, ζ, which is defined as the electrostatic potential at the particle shear plane, is used to characterize the particle electrostatics. From electrophoretic measurements in diluted suspensions, the zeta potential, ζ, can be used to determine the effective surface charge, zeff, through the analytical solution of Poisson-Boltzmann equation with suitable approximations.4 The Smoluchowski approximation is applied when the thickness of electrical double layer κ-1 is thin in comparison to the particle radius R (κR > 100); and the Deybe-Hu¨ckel approximation assumes low surface potential and low ionic strength (κR < 0.1). Generally, most * To whom correspondence should be addressed. Phone: (979) 458-3206. Fax: (979) 845-6446. E-mail:
[email protected]. (1) Belloni, L. Ionic condensation and charge renormalization in colloidal suspensions. Colloids Surf. A. 1998, 140, 227. (2) Hunter, R. J. Zeta Potential in Colloid Science; Academic Press: New York, 1981; Chapter 3. (3) Gong, Y. K.; Nakashima, K.; Xu, R. A novel method to determine effective charge of polystyrene latex particles in aqueous dispersion. Langmuir 2001, 17, 2889. (4) Hiemenz, P. C.; Rajagopalan, R. Principles of Colloid and Surface Chemistry, 3rd ed.; Marcel Dekker: New York, 1997; Chapter 11.
colloidal suspensions can be described by physics that lie between these two approximations. Within industrial processes involving dense dispersions and emulsions, electrophoretic measurement is not directly applicable because dilution alters original solvent conditions impacting counterion condensation and ionization equilibrium. Consequently, techniques have recently been developed to characterize electrostatic interactions in dense suspensions. For example, electroacoustic techniques have been applied to measure zeta potential as well as particle size distribution of concentrated suspensions.5,6 Values of zeta potentials obtained from electroacoustic sonic amplitude (ESA) or colloidal vibration potential (CVP) measurements differ from those obtained from standard electrophoresis.4,7,8 Furthermore, these perturbative techniques require an oscillatory electric force or sonic field, which may disturb the equilibria between particles and resultantly, the structure of the dispersion. In our laboratory, we have been developing, a static, timedependent light scattering based method, frequency domain photon migration (FDPM) as a nonperturbative measurement of electrostatic interactions in dense colloidal suspensions. FDPM involves launching sinusoidally modulated light into a multiply scattering medium. As the “photon density wave” propagates, its amplitude is reduced, and it experiences a phase lag because of the scattering and absorption properties of the medium. The absorption coefficient, µa, is defined as the reciprocal mean free path that photon travels before being adsorbed. The absorption coefficient is linearly dependent upon the concentration (5) O’Brien, R. W.; Cannon, D. W.; Rowlands, W. N. Electroacoustic determination of particle size and zeta potential. J. Colloid Interface Sci. 1995, 173, 406. (6) Carasso, M. L.; Rowlands, W. R.; Kennedy, R. A. Electroacoustic determination of droplet size and zeta potential in concentrated intravenous fat emulsions. J. Colloid Interface Sci. 1995, 174, 405. (7) Babchin, A. J.; Chow, R. S.; Sawatzky, R. P. Electrokinetic measurements by electroacoustic methods. Adv. Colloid Interface Sci. 1989, 30, 111. (8) Goetz, R. J.; El-Aasser, M. S. Effects of dispersion concentration on the electroacoustic potentials of O/W miniemulsions. J. Colloid Interface Sci. 1992, 150 (2), 436.
10.1021/la025901v CCC: $22.00 © 2002 American Chemical Society Published on Web 10/30/2002
Rhodamine 6G Adsorption on Polystyrene Latex
of chromophores in the medium and can be calculated using µa ) ∑iiCi where Ci is the concentration of chromophore i with the absorption cross section, i, per concentration unit. The isotropic scattering coefficient, µs′, is defined as the isotropic mean free path that a photon travels before being scattered into a new random direction; and it is directly related to the concentration and spatial arrangement of scatters in the medium. In concentrated suspensions where multiple light scattering occurs, the transport of light can be accurately approximated by the diffusion approximation of the radiative transfer equation.9,10 Upon detecting the amplitude attenuation and phase-delay of the intensity modulated wave at a known distance away from the incident light source, one can extract the isotropic scattering coefficient and the absorption coefficient of the medium.9,10 Because of the high precision and accuracy associated with FDPM measurements,10 recovery of particle size information is possible from the FDPM measurements of isotropic scattering coefficients of dense monodisperse, polydisperse, and bidisperse hard sphere suspensions.11-14 FDPM is also as an effective technique to assess structure in turbid, dense suspensions.15,16 More recently, we have obtained parameter estimate of the effective surface charge of dense polystyrene latex suspensions as a function of ionic strength (1-120 mM NaCl equiv) by fitting the FDPM measured isotropic scattering coefficients to solutions of the Orstein-Zernike (O-Z) integral equation using the hard sphere Yukawa (HSY) potential model with mean spherical approximation (MSA) as the closure relation.17 In this study, we sought to demonstrate change in the parameter estimate of effective surface charge with the change in the surface charge caused by Rhodamine 6G (R6G) adsorption. Although the parameter of effective surface charge is strictly dependent upon the assumption of the HSY model and may not adequately predict titratable surface charge, its variation with amount of absorbed cationic surfactant should nonetheless reflect changing electrostatic interactions. Prior to presenting the methods and results, the background of scattering and electrostatic interaction is briefly reviewed in the following section. (9) Sevick, E. M.; Chance, B.; Leigh, J.; Nioka, S.; Maris, M. Quantition of time- and frequency resolved optical spectra for the determination of tissue oxygenation. Anal. Biochem. 1991, 195 (2), 330. (10) Sun, Z.; Huang, Y.; Sevick-Muraca, E. M. Precise analysis of frequency domain photon migration measurement for characterization of concentrated colloidal suspensions. Rev. Sci. Instrum. 2002, 73 (2), 383. (11) Sun, Z.; Tomlin, C. D.; Sevick-Muraca, E. M. Recovery of particle size distributions from frequency-domain photon migration measurement of opaque colloidal suspensions. AIChE J. 2002, 47, 1487. (12) Sun, Z.; Tomlin, C. D.; Sevick-Muraca, E. M. Investigation of particle interactions in concentrated colloidal suspensions using frequency-domain photon migration: monodisperse systems. J. Colloid Interface Sci. 2002, 245, 281. (13) Sun, Z.; Tomlin, C. D.; Sevick-Muraca, E. M. Approach for particle sizing in dense polydisperse colloidal suspension using multiple scattered light. Langmuir 2001, 17 (20), 6142. (14) Sun, Z.; Sevick-Muraca, E. M. Investigation of particle interactions in dense colloidal suspensions using frequency domain photon migration: bidisperse systems. Langmuir 2002, 18, 1091. (15) Banerjee, S.; Shinde, R.; Sevick-Muraca, E. M. Assessment of S(0,φ) from multiple scattered light. J. Chem. Phys. 1999, 111 (20), 9133. (16) Huang, Y.; Sevick-Muraca, E. M. Assessment of small angle and angle-averaged structure factor for monitoring electrostatic colloidal interactions using multiple scattered light. J. Colloid Interface Sci. 2002, 251, 434. (17) Huang, Y.; Sun, Z.; Sevick-Muraca, E. M. Assessment of electrostatic interactions in dense colloidal suspensions using multiply scattered light. Langmuir 2002, 18 (6), 2048.
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2. Theoretical Background 2.1. Scattering from Monodisperse Concentrated Suspensions. Upon application of liquid state theory,18-20 µs′ can be predicted from the following relationship:21
µs′(λ) )
∫0π F(σ,λ,θ) S(σ,λ,θ,φ) ×
6φ (2πm/λ)2σ3
sin θ(1 - cos θ) dθ (1) where F(σ,λ,θ) is the form factor, addressing the amplitude of scattered light at incident wavelength λ, by a particle of diameter σ at scattering angle θ; φ is the volume fraction of colloidal particles in a suspension; and m is the refractive index of solvent in the suspension. The static structure factor, S(σ,λ,θ,φ), accounts for the interference of scattered light from neighboring particles and contains the information regarding the correlated particle position which is governed by interparticle interactions. Upon using a model of interaction and an approximated closure relation, the structure factor can be predicted from the solution of the O-Z equation.19,20,22 2.2. Electrostatic Interaction among Colloidal Particles. The most popular models used to describe electrostatic interactions are the hard sphere Yuakawa (HSY) model and primary model (PM). The HSY model expresses the interaction potential within a charged monodisperse suspension in terms of volume exclusion with a repulsive Yukawa tail:
u(r) )
{
∞ r σ
(2)
where e is electron charge; 0 is the electric permittivity of vacuum; is dielectric constant of the suspending medium; zeff is the effective particle surface charge; and κ is the inverse Debye screening length. HSY model assumes that (1) particle interactions are effectively two body interactions with moderate overlapping of electric double layer, (2) the microions in the solution are described by pointlike charges, (3) the surface potential is small and the ionic strength is low, and (4) van der Waals’s attractive force among particles is negligible. The HSY potential model does not conserve charge neutrality of the suspension, and charged particles interact with each other through overlapping electric double layers. The primary model describes particle interactions in terms of volume exclusion with direct Coulombic interaction:
uij(r) )
{
r e σij ) (σi + σj)/2 ∞ 2 e zeff,izeff,j/(4π0r) r > σij
(3)
where electroneutrality is conserved by requiring: ∑i Fizeff,i ) 0. Here, Fi is the number density of the component i in the colloidal mixture. Unlike the HSY interaction model, the electroneutrality of the dispersion is maintained, and (18) Vrij, A.; Nieuwenhuis, E. A.; Fijnaut, H. M.; Agaterof, W. G. M. Application of modern concepts in liquid state theory to concentrated particle dispersions. Discuss. Faraday Soc. 1978, 65, 101. (19) Hansen, J. P.; McDonald, J. R. Theory of Simple Liquids. Academic Press: New York, 1986. (20) Vrij, A. Light scattering of a concentrated multicomponent system of hard spheres in the Percus-Yevick approximation. J. Chem. Phys. 1978, 69 (4), 1742. (21) Banerjee, S.; Shinde, R.; Sevick-Muraca, E. M. Probing static structure of colloid-polymer suspensions with multiply scattered light. J. Colloid Interface Sci. 1999, 209, 142. (22) Salgi, P.; Rajagopolan, R. Polydispersity in colloids: implications to static structure and scattering. Adv. Colloidal Interface Sci. 1993, 43, 169.
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small counterions are also considered as components in the suspensions. 2.2. Ornstein-Zernike (O-Z) Equation and Mean Spherical Approximation. In a monodisperse colloidal suspension, the total spatial correlation between two particles in an ensemble that are separated from each other by a distance r is represented by total correlation function, h(r). The direct correlation function, c(r), represents the direct spatial correlation between the two particles. O-Z equation relates h(r) and c(r) of a homogeneous and isotropic system:
h(r) ) c(r) + F
∫c(|rb - br ′|)h(r′) drb′
(4)
where b r and b r′ are position vectors. The O-Z equation states that the total correlation between two particles includes the direct correlation between the two particles c(r) and all indirect correlations propagated via an effective third, intermediate particle. The O-Z equation provides a simplistic but effective relation for describing the interactions within an ensemble in terms an effective third particle. O-Z equation is not self-closed, and it needs another approximation relating h(r) and c(r) in order to obtain solution. The mean spherical approximation (MSA) gives the approximated linear relationship in terms of pair distribution function, g(r) ) h(r) - 1 and direct correlation function c(r) by
{
g(r) ) 0 r σ
∫0∞ (g(r) - 1) sin(qr)r dr
4πF q
mated from isotropic scattering data are model dependent. Because the parameter estimate of effective surface extracted from PM model is too small to be physically realistic, we used the HSY model to describe changes in electrostatic interaction from FDPM measurements of isotropic scattering coefficients. 3. Experimental Section
(5)
where β is 1/kBT and g(r) is the pair distribution function which directly contains the information of the colloidal structure. The structure factor, S(q), can then be obtained from the Fourier transform of pair distribution function g(r):
S)1+
Figure 1. Calculated isotropic scattering coefficient using an interaction model and MSA relation (with volume fraction of 0.186, mean size 143 nm, ionic strength of 5 mM NaCl equiv) as a function of zeff [e.c.]. Solid line denotes prediction using the primary model and the dashed line denotes prediction using hard sphere Yukawa model.
(6)
here q ) 4πn/λ sin(θ/2) is the scattering vector. With the MSA, the solution to the O-Z equation has been obtained for primary23,24 and hard sphere Yukawa25 models. 2.4. Effective Surface Charge from Isotropic Scattering Coefficients. With independent knowledge of particle size and ionic strength and with the combination of FDPM measurements of isotropic scattering coefficient and an appropriate model capable of predicting structure factor, one can estimate from eq 1 an effective surface charge, zeff. It is noteworthy that the parameter estimate of effective surface charges is dependent upon the accuracy of the interaction potential model and approximation relation used to predict structure factor, S(σ,λ,θ,φ). Figure 1 represents the isotropic scattering coefficient for a monodisperse suspension (with mean particle diameter of 143 nm at the ionic strength of 5 mM NaCl equivalent) predicted using PM and HSY models as functions of effective surface charge. To obtain comparable scattering coefficients predicted by the HSY model, the PM model requires parameters of effective surface charges to be 2 orders of magnitude less than those used in the HSY model. Clearly, the effective surface charges esti(23) Hiroike, K. Ornstein-Zernike relation for a fluid mixture with direct correlation functions of finite range. J. Phys. Soc. Jpn. 1969, 27 (6), 1415-1421. (24) Hiroike, K. Supplement to Blum’s theory for asymmetric electrolytes. Mol. Phys. 1977, 33(4), 1195-1198. (25) Herrera, J. N.; Cummings, P. T.; Ruiz-Estrada, H. R. Static structure factor for simple liquid metals. Mol. Phys. 1999, 5, 835.
3.1. Samples and Sample Preparation. Polystyrene (PS) latex with the mean size of 143 ( 3 nm (Malvern Zetasizer 3000HS, Worcestershire, U.K.), and a relative deviation of 15% {determined using TEM (Zeiss 10C) associated with Image Pro software (Image Pro 3.0, MediaCybernetics Inc. Silver Spring, MD)} was obtained courtesy of Dow (Midland, MI). To remove ions and the surfactant used to stabilize the suspensions, the polystyrene lattices were first dialyzed (Spectra/Pro: MWCO 6-8,000, Spectrum Laboratories Inc., Rancho Dominguez, CA) in deionized-ultrafilted water until the conductivity of the dialyzing water was less than 6 ppm NaCl equivalents, as measured using a titration controller (Accumet model 150, Fisher). The volume fractions of dialyzed polystyrene lattices were measured by an evaporation method, which involved weighting samples using a 1/10 000 g resolution balance (Denver Instrument M-220D, Fisher) before and after they were dried in an oven (Isotemp, model 280A, Fisher) for 8 hours at 95 °C. The ionic strength was adjusted using a sodium chloride solution (S1240, Spectrum Chemical Mfg. Corp., Gardena, CA). By conductmetric titration,3 the surface charge density was determined to be 6.3 × 10-7 mol/m2, which corresponds to an average 26 000 electron charges per particle. Given the ionic strength (0.1 M NaCl) and particle diameter (143 nm), the Smoluchowski approximation was used to evaluate the effective surface charge of about 1000 electron charge from the zeta potential measurement.4 We note that the estimated effective surface charge computed in this manner represents the charge on the shear plane, rather than the charge on the particle surface. The difference between charges obtained from the conductometric titration and zeta potential measurements suggests that surface counterion condensation or association occurs. 3.2. Rhodamine 6G Adsorption. Rhodamine 6G (R-4127, Sigma, St. Louis, MO) when dissolved in water is a positively charged surfactant. R6G adsorption on negatively charged surfaces occurs via two main mechanisms:26-34 (i) ion condensa(26) Charreyre, M. T.; Zhang, P.; Winnik, M. A.; Pichot, C.; Graillat, C. Adsorption of Rhodamine 6G onto polystyrene latex particles with sulfate groups at the surface. J. Colloid Interface Sci. 1995, 170, 374. (27) Mubarekyan, E.; Santore, M. Characterization of polystyrene latex surfaces by adsorption of Rhodamine 6G. Langmuir 1998, 14, 1497.
Rhodamine 6G Adsorption on Polystyrene Latex tion owing to electrostatic interaction and (ii) condensation owing to the hydrophobicity of R6G. At low R6G surface overages, the electrostatic interaction effect dominates, and at higher R6G surface overages, hydrophobic interactions become significant.26,27 R6G strongly absorbs light at the wavelength of 529 nm and fluoresces at 566 nm with high quantum efficiency. This enables measurement of R6G concentration using fluorescence measurements. R6G does not fluoresce in the red wavelength region. Because time-dependent techniques such as FDPM effectively provides separated optical properties of absorption and scattering, the evaluation of colloid scattering capacity is enabled at 687 and 650 nm without the influence from R6G absorbance or fluorescence. In this study, we adjust the effective surface charge of PS latex by adsorbing positively charged R6G molecules3,26,28,29 and monitor the changes in scattering owing to changes in the electrostatic interaction. To determine the R6G adsorption isotherm, R6G was added to 0.5% (v/v) PS latex suspended in 5 mM NaCl. After equilibration at room temperature for 24 h, the R6G-PS suspensions were centrifuged at 12 000 rpm and 25 000 g (max; Sorvall RC-5B, GMI. Inc., Clearwater, MN) for 45 min, and the supernatant was collected. The supernatants were then centrifuged again at 56 000 rpm and 33 000g max (Beckman L8-M, Miami, FL) for 45 min. The free R6G concentration in the final supernatant was measured in a 10 mm florescence cell using a spectrofluorometer (Fluorolog-2, Spex Industries Inc., Edison, NJ) at the excitation wavelength of 529 nm, and the emission wavelength of 556 nm. A calibration curve was prepared by plotting the florescent intensity versus known R6G concentration in 5 mM NaCl. The measured fluorescence intensities of final supernatants were then converted to R6G concentration using this calibration curve, and the amount of adsorbed R6G was calculated from mass balance. Figure 2 illustrates the adsorption isotherm of R6G on the dialyzed PS. Gong et al.28 report that across a range of R6G concentrations there are two plateaus in the adsorption isotherm of R6G on polystyrene corresponding to potential electrostatic and hydrophobic condensation mechanisms: the first one starts at approximate supernatant concentrations between 1 and 30 µM; the second one starts at several hundred µM (600-800 µM). The isotherm represented in Figure 2 lies within these two regions, starting at 39 µM and ending at about 700 µM, is roughly the interim region of the two plateaus in Gong et al.’s works. The adsorption isotherm shows that the R6G present in the colloidal suspension is predominantly adsorbed on the polystyrene surface. Consistent with the work of others, we find 99.9% of R6G added to the suspension becomes adsorbed onto the polystyrene surface. The amount of free R6G in the supernatant is negligible in comparison to the amount R6G adsorbed on the PS surface. 3.3. FDPM Measurements. FDPM measurements at 687 nm were conducted on 100 mL of PS latex (of volume fraction, φ ) 0.186 and 5 mM NaCl equiv). To this sample, aliquots of the same PS solutions but containing 4 mM R6G were added.17 (28) Gong, Y. K.; Nakashima, K.; Xu, R. Characterization of polystyrene latex surfaces by conductometric titration, rhodamine 6G adsorption, and electrophoresis measurements. Langmuir 2000, 16, 8546. (29) Estevez, J. H. T.; Lopez Arbeloa, F.; Lopz Arbeloa, T.; Lopez Arbeloa, I.; Schoonheydt, R. A. Spectroscopic study of the adsorption of rhodamine-6G on Laponite-B for low loading. Clay Miner. 1994, 29, 105. (30) Nakashima, K.; Liu, Y. S.; Zhang, P.; Duhamel, J.; Feng, J.; Winnik, M. A. Picosecond fluorescence studies of energy transfer on the surface of poly(butyl methacraylate) latex particles. Langmuir 1993, 9, 2825. (31) Lu, W. L.; Bouyer, F.; Borkovec, M. Polystyrene sulfate latex particles in the presence of poly(vinylamine): absolute aggregation rate constants and charging behavior. J. Colloid Interface Sci. 2001, 241, 392. (32) Tawde, S. R.; Mukesh, D.; Yhhmi, J. V.; Manohar, D. Dye adsorption on self-assembled silane monolayers: optical absorption and modeling. J. Mater. Chem. 1999, 9, 1847. (33) Farinha, J. P. S.; Charreyre, M. T.; Martinho, J. M. G.; Winnik, M. A.; Pichot, C. Picosecond fluorescence studies of the surface morphology of charged polystyrene latex particles. Langmuir 2001, 17, 2617. (34) Feick, J. D.; Velegol, D. Measurement of surface charge nonuniformity on polystyrene latex particle. Langmuir 2008, 18, 3454.
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Figure 2. Average adsorption density of R6G [µmol/m2] on polystyrene surface versus supernatant R6G concentration [µM] in 5 mM NaCl solution.
Aliquot amounts were weighted using a 1/10 000 g resolution balance (Denver Instrument M-220D, Fisher) and added to the solution. After each addition of R6G-PS aliquot sample, the solution was stirred using a sonic stirrer (F60 dismemberator, Fisher Scientific) at low power (
