Langmuir 2001, 17, 2889-2892
A Novel Method To Determine Effective Charge of Polystyrene Latex Particles in Aqueous Dispersion Yong-Kuan Gong and Kenichi Nakashima* Department of Chemistry, Faculty of Science and Engineering, Saga University, 1 Honjo-machi, Saga 840-8502, Japan Renliang Xu Particle Characterization, Beckman Coulter, Inc., PO Box 169015, Miami, Florida 33116-9015 Received October 23, 2000. In Final Form: February 9, 2001
Introduction Aqueous dispersions of colloidal particles are widely used in various fields of chemistry and chemical engineering. Almost all colloidal particles carry charges on their surfaces. The effect of electrostatic interactions between the colloidal particles themselves and other particles and small ions is a fundamental and important subject for colloidal dispersions. The distribution of small ions in a dispersion is highly influenced by polycharged particles (polyions) which at times results in a high concentration of counterions in the vicinity of these colloidal particles. This phenomenon is termed counterion association and is an important feature of colloid systems.1 Counterion association, which accounts for screening of the intrinsic particle charge, causes a particle to have an effective or apparent charge (Zeff) which is less than the intrinsic charge (Z, the total number of ionizable groups bound on a particle surface) and affects the colligative, transport, and spectroscopic properties of the dispersion.1-9 The electrostatic stability of colloidal dispersions, which is a major factor in avoiding aggregation, is often described in terms of the Dejarguin-Landau-Verwey-Overbeek (DLVO) theory.10-15 When the DLVO theory is applied, * To whom any correspondence should be addressed. Fax: +81-952-28-8548. Phone: +81-952-28-8850. E-mail: nakashik@ cc.saga-u.ac.jp. (1) Rymde´n, R. J. Colloid Interface Sci. 1988, 124, 396. (2) Roberts, J. M.; O’Dea, J. J.; Osteryoung, J. G. Anal. Chem. 1998, 70, 3667. (3) Lindman, B. In NMR of Newly Accessible Nuclei; Laszlo, P., Ed.; Academic Press: New York, 1983; Vol. 1. (4) Chitanu, G. C.; Rinaudo, M.; Desbrie`res, J.; Milas, M.; Carpov, A. Langmuir 1999, 15, 4150. (5) Roberts, J. M.; Linse, P.; Osteryoung, J. G. Langmuir 1998, 14, 204. (6) Behrens, S. H.; Semmler, M.; Borkovec, M. Prog. Colloid Polym. Sci. 1998, 110, 66. (7) Larsen, A. E.; Grier, D. G. Nature 1997, 385, 230. (8) Ito, K.; Ise, N.; Okubo, T. J. Chem. Phys. 1985, 82, 5732. (9) Moroi, Y. Micelles: Theoretical and Applied Aspects; Plenum Press: New York, 1992. (10) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: San Diego, CA, 1992. (11) Prost, J.; Rondelez, F. Nature 1991, 350 (Suppl.), 11. (12) Schmits, K. S. Langmuir 1997, 13, 5849. (13) Russel, W. B.; Saville, D. A.; Schcowalter, W. R. Colloidal Dispersions; Cambridge University Press: Cambridge, 1989. (14) Evans, D. F.; Wennersto¨m, H. The Colloidal Domain; VCH Publishers: New York, 1994. (15) Ross, S.; Morrisson, I. D. Colloidal Systems and Interfaces; John Wiley & Sons: New York, 1988.
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the effective charge of particles needs to be known. Unlike the intrinsic charge, the effective charge is not a thermodynamic quantity and is difficult to measure directly.2 Methods developed to obtain the theoretical values of electrokinetic characteristics16-18 are not applicable to deionized latex dispersions.19 For a deionized and protonated latex dispersion, although the pH measurement can indicate the activity of hydrogen ions, it is difficult to relate the activity of hydrogen ions to the concentration of hydrogen ions since the definition of mean activity coefficient is not welldefined.20 In addition, when a conventional pH meter is used, charged solid particles in suspension may also influence the potential of the indicator electrode.21 The total number of ionizable groups bound on a particle surface is usually determined by conductometric titration.20,22,23 Several experimental methods have been used to infer values of the effective charge: conductivity or conductance,8,19,24 shear modulus,25 light scattering,26 microelectrode voltammetry,2,5,27 torsional resonance,28 and electrophoresis.28 Among these methods, conductivity measurement is the simplest one. In one such method,19,24 an experimental conductometric coefficient, fexp, is defined as the ratio of the measured conductivity value to the ideal one which is calculated as the product of the total counterion concentration and its molar conductivity. fexp is used to estimate the “effective” dissociated groups (effective charge and free counterion concentration). This treatment, however, neglects the contribution of polyions to the conductance. Although the conductivity of the polyion could be very small compared with that of small ions,8 theoretically, it should be considered. To explore an experimental link between the nature of colloidal particles and the property of the dispersion, we intend to present what we believe is a more precise method for determining the fraction of the free counterion concentration (f) and, thus, the effective charge. In addition to f and fexp, the effective charge is also discussed using another approach by determining a value for f *, which is based on the measurement of molar conductivity of the sulfuric acid group (-SO4H) attached to polystyrene latex (PSL) particles. In this work, PSL particles having different radii and numbers of sulfate groups on the surface were used as model particles to study counterion association in colloid systems. (16) O’Brien, R. W.; White, L. R. J. Chem. Soc., Faraday Trans. 2 1978, 74, 1607. (17) Ohshima, H.; Healy, T. W.; White, L. R. J. Chem. Soc., Faraday Trans. 2 1983, 79, 1613. (18) Zukosky, C. F., IV; Saville, D. A. J. Colloid Interface Sci. 1986, 114, 32, 45. (19) Sumaru, K.; Yamaoka, H.; Ito, K. Ber. Bunsen-Ges. Phys. Chem. 1996, 100, 1176. (20) James, R. O.; Davis, J. A.; Leckie, J. O. J. Colloid Interface Sci. 1978, 65, 331. (21) Oman, S. Electrochim. Acta 1991, 36, 943. (22) Labib, M. E.; Robertson, A. A. J. Colloid Interface Sci. 1980, 77, 151. (23) Bangs, L. B. Uniform Latex Particles; Seragen: Indianapolis, IN, 1984. (24) Yamanaka, J.; Matsuoka, H.; Kitano, H.; Ise, N. J. Colloid Interface Sci. 1990, 134, 92. (25) Palberg, T.; Kottal, J.; Bitzer, F.; Simon, R.; Wu¨rth, M.; Leiderer, P. J. Colloid Interface Sci. 1995, 169, 85. (26) Versmold, H.; Wittig, U.; Ha¨rtl, W. J. Phys. Chem. 1991, 95, 9937. (27) Aoki, K.; Lei, T. Electrochem. Commun. 1999, 1, 101. (28) Palberg, T.; Ha¨rtl, W.; Wittig, U.; Versmold, H.; Wu¨rth, M.; Simnacher, E. J. Phys. Chem. 1992, 96, 8180.
10.1021/la001483n CCC: $20.00 © 2001 American Chemical Society Published on Web 03/30/2001
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Notes
Theoretical Consideration For a thermodynamically ideal polyelectrolyte solution, the conductance would consist of the contributions from polyions, counterions, and any other ions. If all other ions are removed and the counterions are completely converted to H+, the conductivity (Gi) can then be expressed as
Gi ) λH+[H+]i + λP- [P-]
(1)
where [H+]i and [P-] are the concentrations of free H+ and the dissociated polyion (P-), before titration, respectively. Although the polyion carries many negative charges, for simplicity and convenience in the discussion below we denote it as P- and express its concentration as the molarity of equivalent monovalent groups. λH+ and λP- are the molar conductivities of H+ and P-, respectively. Several studies have confirmed that the addition of NaOH exchanges H+ with Na+ in deionized and protonated PSL dispersions. During this process the degree of dissociation is not changed. There are no detectable differences in the interaction between particles surrounded by a double layer of H+ from that of Na+.25,26 It has been reported that Na+ does not show specific adsorption on polystyrene.21,22 Furthermore, since sulfuric acid is a strong acid,29 we can assume that the replacement of H+ with Na+ does not severely affect the dissociation of -SO4H on the PSL surface. During the titration with NaOH, H+ ions are replaced by Na+ ions due to the formation of water. If we assume that the binding or association ability of the polyion with H+ is the same as that with Na+ and does not change during the titration, one Na+ ion will replace one H+ ion from inside or outside of the electrical double layer. The ions located inside of the double layer are referred to as associated ions, and those located outside the double layer are referred to as free ions (a binary model). The concentration of free Na+ ions at the end point of neutralization [Na+]e should be equal to the concentration of free H+ ions before titration, [H+]i, and [P-] remains constant. If true, the conductivity Ge can be then expressed as
Ge ) λNa+[Na+]e + λP-[P-]
(2)
Ge ) λNa+[H+]i + λP-[P-]
(3)
where λNa+ is the molar conductivity of Na+. The free counterion concentration can be obtained by subtracting eq 3 from eq 1:
[H+]i ) (Gi - Ge)/(λH+ - λNa+)
(4)
The values of λH+ and λNa+ at very low concentrations (10-4 mol/L) are available.30 Gi and Ge can be obtained from the conductometric titration curve. The total concentration of titratable hydrogen ion, [H+]0, which is used to determine the intrinsic charges of latex particles, can also be calculated from the titration curve. This can be calculated by +
[H ]0 ) CNaOHVe,NaOH/V
(5)
where V is the volume of the latex dispersion and CNaOH and Ve,NaOH are the concentration and volume of the (29) Charreyre, M.-T.; Zhang, P.; Winnik, M. A.; Pichot, C.; Graillat, C. J. Colloid Interface Sci. 1995, 170, 374. (30) Handbook of Chemistry and Physics; David, R. L., Ed.; CRC Press: Boca Raton, FL, 1996.
standard NaOH solution used in the titration. Therefore, the fraction of free ion concentration (f) in a deionized PSL dispersion can be determined by the titration curve:
f ) [H+]i/[H+]0
(6)
The effective charge (Zeff) and effective charge density (σeff) of the latex particle can thus be simply calculated if the intrinsic charge (Z) and charge density (σ) are known:
Zeff ) f Z ) Z[H+]i/[H+]0
(7)
σeff ) f σ ) σ[H+]i/[H+]0
(8)
The intrinsic charges and charge density can also be calculated from the same titration curve by using the equations
Z)
4πa3NVe,NaOHCNaOH 3Vφ
(9)
aVe,NaOHCNaOH 3Vφ
(10)
σ)
where a, φ, and N are particle radius, volume fraction of the latex particle, and Avogadro’s number, respectively. σ is expressed in units of mol/m2. The advantage of this method is that both the total concentration of titratable hydrogen ions, [H+]0 (corresponding to Z), and the concentration of free hydrogen ions, [H+]i (corresponding to Zeff), can be determined from the same titration curve. Although the two quantities are obtained from the same titration curve, they are based on different principles. The value of [H+]i is calculated from the measured conductivities before and at the neutralization point of the titration, while the value of [H+]0 is from the acid-base titration only. Experimental Section Materials. Water was purified with a Millipore Milli-Q purification system after having been ion-exchanged and distilled. We employed seven PS latex samples (L711, L714sL718, and CG17). L711 and L718 were synthesized by standard emulsion polymerization in different batches using the same procedure.31 L714sL717 are the partially hydrolyzed products of L718.32-34 CG17 was synthesized according to the recipe for the latex CG17 in Winnik’s work.29 All the latexes were purified by repeated dialysis followed by ion exchange with a mixed-bed resin (BioRad AG 501-X8) until a constant charge density was reached. Prior to use, the resin was washed sequentially with hot deionized water, methanol, and then Milli-Q water to remove residual impurities.35,36 The diameters of the latex particles were determined using an Otsuka ELS-800 dynamic light scattering instrument. Conductometric Titration. The titration was carried out with a conductivity meter (Horiba, model ES-14) at 25 ( 0.2 °C under nitrogen atmosphere. After the Milli-Q water was bubbled with N2 for 20 min, its conductivity was reduced to 0.4 µS/cm. A given volume of concentrated latex was added to the CO2-free (31) Nakashima, K.; Duhamel, J.; Winnik, M. A. J. Phys. Chem. 1993, 97, 10702. (32) Goodwin, J. W.; Hearn, J.; Ho, C. C.; Ottewill, R. H. Br. Polym. J. 1973, 5, 347. (33) Yates, D. E.; Ottewill, R. H.; Goodwin, J. W. J. Colloid Interface Sci. 1977, 67, 356. (34) Goodwin, J. W.; Ottewill, R. H.; Pelton, R. Colloid Polym. Sci. 1979, 257, 61. (35) Kawaguchi, S,; Yekta, A.; Winnik, M. A. J. Colloid Interface Sci. 1995, 176, 362. (36) van den Hul, H. J.; Vanderhoff, J. W. J. Colloid Interface Sci. 1968, 28, 336.
Notes
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Table 1. Intrinsic Charge, Effective Charge, and Fraction of Free Counterions of Latex Dispersions Calculated from the Conductometric Titration Data latex
a/nm
φ/%
Ve,NaOH/mL
Gi/µS cm-1
Ge/µS cm-1
Z
Z/a
f
fexp
Zeff
f*
L711 L714 L715 L716 L717 L718 CG17
106 114 114 114 114 114 47
1.58 2.00 2.22 1.67 2.53 1.34 1.90
0.064 0.206 0.312 0.278 0.425 0.306 0.558
5.2 8.0 10.2 6.2 10.0 7.3 13.0
1.5 2.2 3.0 1.5 2.8 2.0 2.9
3280 10380 14080 16780 16940 23020 2210
31 91 123 147 148 202 47
0.62 0.35 0.28 0.21 0.20 0.21 0.23
0.86 0.41 0.35 0.23 0.25 0.25 0.26
2030 3630 3940 3520 3390 4830 508
0.83 0.46
0.40
Figure 1. Conductometric titration curve of latex L714 with a 8.10 × 10-3 M NaOH solution at 25 °C. The volume fraction of L714 is 2%. water to obtain a desired volume fraction. The dispersion was then bubbled again with N2 until the conductivity did not decrease further. The aqueous dispersion (30-35 mL) with 0.5-3% PSL solid content was then titrated while being stirred with a standard solution of NaOH (8.10 × 10-3 M) using a Gilmont micrometer syringe.
Results and Discussion Characterization of Latex Particles. Figure 1 shows a typical conductometric titration curve of PSL having sulfate groups on the surface. The conductivity decreases with the addition of NaOH solution and reaches a minimum when all the protonated sulfate groups are neutralized. The negative slope of 0.115 S cm-1 M-1 is much smaller than the difference (0.299 S cm-1 M-1) between the molar conductivities of H+ and Na+, suggesting the association of H+ and Na+ inside the electric double layer. The sharp change at the end point (as shown in Figure 1 by extrapolation) and large value of the positive slope (0.23-0.25 S cm-1 M-1) shows that there is no evidence for the existence of carboxylic acid moieties on the particle surface. The charge density (σ) of latex particles37 was determined from their conductometric titration curves using eq 10. The intrinsic charge number (Z) was calculated from the conductometric titration curve according to eq 9. The effective charge number (Zeff) was obtained by combining eqs 4-7 and 9. The results are listed in Table 1. The fraction of free counterion concentration (f) in deionized and protonated PS latex dispersions was determined from the titration curves using eq 6. Counterion Association. To compare the f values obtained by the present method with the fexp values obtained by another conductivity method,8,24 fexp was also calculated. As seen in Table 1, all fexp values are higher than the corresponding f values due to the omission of both polyion conductance and incomplete deionization in the fexp determination. In contrast, our method eliminates the error due to omitting the conductance of polyion by (37) Gong, Y.-K.; Nakashima, K.; Xu, R. Langmuir 2000, 16, 8546.
Figure 2. Relationship between conductivity and volume fraction of latex in aqueous dispersions at 25 °C.
considering it in the derivation of the equations and reduces the error due to incomplete deionization by subtracting the conductance of the salt, which is included in Gi and Ge. The difference between f and fexp suggests that although these effects may be small, they are detectable and thus should not be neglected. The linear relationship between conductivity and volume fraction of latex particles as shown in Figure 2a verifies that the sulfuric groups act as strong acids in the latex dispersion although they interact with each other and are connected to the same particle. The molar conductivities of the sulfuric acid groups, λ, which are calculated from the measured conductivity values and the total concentration of surface sulfuric groups, are almost constant over a broad range of particle volume fractions at high concentration. This means that the counterion association constant does not change with the concentration of latex over this range. A similar conclusion was drawn by Yamanaka et al.24 The values of the constant molar conductivities (λc) mentioned above are different among latex samples (Figure 2b). The difference suggests that latex samples have different association abilities with counterions (H+ in this experiment). The high value of λ means a high fraction of free ions. In the deionized and protonated latex dispersion, only the H+ ion and the PSL-SO4- contribute to the conductivity. Since the conductivity of the polyion (PSL-SO4-) is significantly lower than that of hydrogen ion, λc can be simply ascribed to the free H+ in the dispersion. Thus, the fraction of free counterion (H+) concentration can be estimated from the ratio of λc and λH+. We use f * ()λc/λH+) to denote the fraction of free counterion estimated by this molar conductivity method
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as listed in Table 1. These values seem reasonable if we consider the charge densities of the three latex samples. L711 has a very low charge density (0.30 × 10-7 mol/m2), so that its counterion association is low and the f * value is high. L714 and CG17 have relatively high charge densities (1.02 × 10-7 and 1.26 × 10-7 mol/m2). Thus they have strong counterion association resulting in the low f * values. The main principles for determining fexp and f * are the same. In both methods the measured conductance is attributed only to the free H+ and not to the dissociated polyion and possible impurity salts. Therefore, both the fexp and f * values are not as accurate as the f values discussed above. The difference between fexp and f * is that f * is determined from λc, which is obtained by a set of measurements, while fexp is from a single conductance value of only one measurement. The agreement between fexp and f * values suggests that the measured λc is reasonable. The increase of the molar conductivity in the low concentration region of Figure 2b may be caused by the ionization of water. The error that results from neglecting the dissociation equilibrium of water will not influrence the results, as long as the concentration of latex (thus the concentration of acid) is sufficiently high. However, the low concentration of free H+ in the low volume fraction of latex cannot effectively suppress the ionization of water. Thus, the influence of water ionization on the measured conductivity increases as the volume fraction decreases. For example, when the volume fraction of L711 is decreased from 1.5% to 0.2%, the ratio of hydrogen ions ionized from water to that from sulfuric acid increases from 10-4 to 10-2. This relative error is of the same order as that of the measured molar conductivity. Correlation of the Effective Charge with Measurable Parameters. The fraction of effective charge (Zeff/ Z), and thus the fraction of free counterion (f), depends mainly on the charge number and the radius of the particle.2,19 Figure 3 shows the plot of f against Z/a. The fraction of free hydrogen ions in deionized and protonated PSL dispersion decreases exponentially with the increase of Z/a. Published theories do not satisfactorily explain the relationship between f and Z/a in the present study. We have found that the data can be fitted to an empirical equation, f ) 10(Z/a)-0.8. This simple empirical equation could be used to predict the effective charge and counterion association ability of latex dispersion and similar colloidal
Notes
Figure 3. Fraction of free counterion as a function of Z/a: open circle, present study; closed circle, taken from ref 20. The solid line is the empirical curve.
systems. The equation seems also useful in understanding the variation of ion association of latexes having different charge densities.1,2,4,5,8,19,27 Conclusions A method of determining the concentration of free counterion in deionized and protonated PSL dispersion was derived based on the conductometric titration curve. The fraction of free counterion concentration f obtained by this new method is more accurate than those obtained by the conductivity method (fexp and f *). The data can be fitted into an empiric equation, which could be used to predict the fraction of free counterions as well as effective charge of particles from the intrinsic charge and radius of the particle. The molar conductivity of the bound sulfuric acid groups showed a constant value in a broad concentration range, suggesting the existence of a dissociation equilibrium of H+ in the dispersion. This molar conductivity varies from one latex sample to another, depending on the ability of counterion association. This finding can also be employed to estimate the effective charge number and free counterion concentration. Acknowledgment. Y.-K. Gong acknowledges a financial support by the Sasakawa Scientific Research Grant from the Japan Science Society. LA001483N
