Langmuir 1996, 12, 4125-4133
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Electrophoretic Mobility Study of Dodecyltrimethylammonium Bromide in Aqueous Solution and Adsorption on Microspheres1 Renliang Xu* and Guillermo Smart Scientific Instruments, Coulter Corporation, P.O. Box 169015, Miami, Florida 33116-9015 Received March 7, 1996. In Final Form: June 6, 1996X The adsorption of the cationic surfactant dodecyltrimethylammonium bromide (DTAB) on uniform microspheres (polystyrene latex (PSL) particles) of various sizes has been studied using electrophoretic light scattering, dynamic light scattering, viscosity, and conductivity measurements. The measurements were performed on PSL particles of different diameters at different surfactant concentrations in an aqueous solution of 0.001 M NaBr. Initially, the uncoated surfactant-free latexes are negatively charged. After adsorbing a trace amount of the positive DTAB ions, the electrophoretic mobility of the latexes changes from negative to positive. The electrophoretic mobilities of the DTAB-adsorbed latexes increase with increasing DTAB concentration until reaching a maximum and then flatten out. The different magnitudes and patterns for the electrophoretic mobilities of the PSL particles of different sizes indicate that there are different adsorption mechanisms for the adsorbed surfactant on the surfaces of different curvatures. This observation is similar to the previous investigation of the adsorption of block copolymer micelles on PSL particles, where a trend was found in which the adsorbed layer thickness is inversely proportional to the diameters of the PSL particles. Dynamic light scattering experiments have provided useful information on the adsorption only at very low DTAB concentrations, since the measured hydrodynamic radii are biased at high DTAB concentrations due to the effects from the change in the solution ionic strength and viscosity. On the basis of this observation, two adsorption models are proposed which account for the adsorption of the surfactant on large PSL particles and on small PSL particles, respectively.
Introduction Adsorption of charged molecules, such as cationic and anionic surfactants, and neutral molecules, such as nonionic surfactants and polymers, on different types of substrates, mostly silica and polymers, has been the subject of many investigations in the recent decade. In most of these studies, either theoretical predictions and computer simulations based on different models and assumptions or experimental studies utilizing various modern physical chemistry techniques, the substrates employed are flat or nearly flat. Even for experimental studies using small colloidal particles as the substrates, the issue of surface curvature was often not brought up. In addition to its academic interests, adsorption of amphiphiles on curved surfaces, especially on colloidal particles, is of great practical importance and has broad industrial applications. For example, adsorption of polymer chains or surfactants on surfaces of colloids can modify the suspension rheology that can enhance oil recovery, change paint properties, and improve waste water treatment efficiency. Adsorption can also sterically stabilize ink and pigment vesicles and modify the surface properties of many colloidal systems. In biological applications, adsorption of proteins on liposomes is used for adjusting the functionality of liposomes in drug-delivery systems. Antibody or antigen adsorption on colloids is significant to many clinical applications. However, there are only a few theoretical works2,3 and experimental studies4-9 related to adsorption of polymers on curved surfaces where particular attention was paid to the curvature effect in the adsorption mechanism. In a series of previous X
Abstract published in Advance ACS Abstracts, August 1, 1996.
(1) This work was presented at the 69th Colloid & Surface Science Symposium of the American Chemical Society at Salt Lake City, UT, June, 1995. (2) Johner, A.; Joanny, J. F. Macromolecules 1990, 23, 5299. (3) Kislenko, V. N.; Berlin, Ad. A.; Moldovanov, M. A. Kolloidn. Zh. 1993, 55 (1), 83. (4) Garvey, M. J.; Tadros, Th. F.; Vincent, B. J. Colloid Interface Sci. 1974, 41, 57; 1976, 44, 440.
S0743-7463(96)00206-5 CCC: $12.00
publications,10-13 the adsorption of polystyrene-poly(ethylene oxide) (PS-PEO) block copolymer micelles in aqueous solution on polystyrene latex (PSL) particles of different sizes has been reported. The results show that for the block copolymer micelle adsorption there exists a three-step adsorption mechanism: (1) two-body collision adsorption, (2) surface mobile motion for the adsorbed micelles, and (3) adsorbed micelle deformation. In the above dynamic process, the surface curvature difference in the substrate affects the rate of each step, resulting in the difference in the adsorbed layer thickness. This difference, confirmed by both electrophoretic mobility measurements and hydrodynamic radius measurements, exists in that the smaller the particle is the thicker the adsorbed layer will be. In the block copolymer micelle adsorption, the sizes of the adsorbent (copolymer micelles with diameters of 2050 nm) and of the substrate (PSL particles with diameters of 70-200 nm) are the same order of magnitude. Thus, a distinguished particle size dependence on adsorption may be expected. If the size difference between the adsorbent and the substrate is big, e.g., small molecules adsorbed on big particles, the particle surface should be (5) Ahmed, M. S.; El-Aasser, M. S.; Vanderhoff, J. W. In Polymer Adsorption and Dispersion Stability; Goddard, E. D., Vincent, B., Eds.; ACS Symposium Series 240; American Chemical Society: Washington, DC, 1984; p 77. (6) Baker, J. A.; Pearson, R. A.; Berg, J. C. Langmuir 1989, 5, 339. (7) Lee, J.; Martic, P. A.; Tan, J. S. J. Colloid Interface Sci. 1989, 131, 252. (8) Tan, J. S.; Martic, P. A. J. Colloid Interface Sci. 1990, 136, 415. (9) Cosgrave, T.; Griffiths, P. C.; Lloyd, P. M. Langmuir 1995, 11, 1457. (10) Xu, R.; Winnik, M. A.; Riess, G.; Chu, B.; Croucher, M. D. Macromolecules 1992, 25, 644. (11) Xu, R.; d’Oliveira, J. M. R.; Winnik, M. A.; Riess, G.; Croucher, M. D. J. Appl. Polym. Sci.: Appl. Polym. Symp. 1992, 51, 135. (12) d’Oliveira, J. M. R.; Xu, R.; Jensma, T.; Winnik, M. A.; Hruska, Z.; Hartrez, G.; Riess, G.; Martinho, J. M. G.; Croucher, M. D. Langmuir 1993, 9, 1092. (13) Xu, R.; D’Unger, G.; Winnik, M. A.; Martinho, J. M. G.; d’Oliveira, J. M. R. Langmuir 1994, 10, 2977.
© 1996 American Chemical Society
4126 Langmuir, Vol. 12, No. 17, 1996
like a flat surface when viewed by a small molecule. Thus, the relative particle curvature change should have less effect on adsorption. Although seemingly obvious, an experimental study is needed to prove or disprove this assumption. However, in the case of small molecular adsorption on large particles, the size measurement of the particles may no longer be a sensitive mean, since the relative size change of the particles is so small that it often falls within the experimental error limits. Those methods used for adsorption on flat surfaces, such as ellipsometry, evanescence wave analysis, or atomic force microscopy, are also not feasible because the suspended particles are undergoing thermal motion. On the other hand, the adsorption may significantly change the surface charge condition of the particle, especially if the adsorbent is of opposite charge to that of the surface. Thus, ζ potential measurements may provide a sensitive way to monitor even trace amounts of adsorption on the surface. In the present study, the adsorption of the cationic surfactant dodecyltrimethylammonium bromide (DTAB) on the negatively charged, surfactant-free PSL particles of different sizes is studied as a function of surfactant concentration at a fixed amount of PSL particles in 0.001 M NaBr aqueous solution using electrophoretic light scattering, dynamic light scattering, viscosity, and conductivity measurements. The objectives are to characterize the electrophoretic behavior of DTAB in aqueous solution and to study the adsorption mechanism when a small surfactant carrying an opposite charge adsorbs onto a particle hundreds of times larger, where the driving forces are hydrophobic interaction and affinity effect in addition to Coulombic attraction. Although DTAB is a common cationic surfactant that has been used as a model compound in adsorption studies,14-17 studies on the curvature effect of the substrate for DTAB adsorption have not been reported. Both electrophoretic light scattering (ELS) and dynamic light scattering (DLS) are versatile techniques in studying colloidal particles, e.g., their dimensions, shape, and surface conditions. Dynamic light scattering, also termed photon correlation spectroscopy (PCS) or quasi-elastic light scattering (QELS), has been widely used in the research of macromolecules and colloids for decades. Although the pioneering work in ELS was carried out over two decades ago, the applications of this technology have only started recently due to the current availability of commercial instrumentation.18 In an ELS measurement, both the oriented motion (electrophoretic movement) of the particles under an applied electric field and the random Brownian motion are detected from the Doppler frequency shift of their scattered light when these particles are illuminated by a coherent light beam. Since the electrophoretic motion of a particle is closely related to its surface charge density and surface molecular conformation, the high sensitivity of ELS measurements allows for the detection of minor changes on the particle’s surface, especially when such changes lead to little or no variations in the particle’s dimensions. In the present study, since dodecyltrimethylammonium bromide (DTAB) molecules (or micelles) are very small (a few nanometers in length) when compared with the PSL particles, ELS is possibly the best noninvasive method to monitor and detect the (14) Kayes, J. B. J. Colloid Interface Sci. 1976, 56, 246. (15) Tanaka, A.; Ikeda, S. Colloids Surf. 1991, 56, 217. (16) Rodenas, E.; Dolcet, C.; Valiente, M.; Valeron, E. C. Langmuir 1994, 10, 2088. (17) Zhao, J.; Brown, W. Langmuir 1995, 11, 2944. (18) Ware, B.; Haas, D. D. In Fast in Physical Biochemistry and Cell Biology; Sha’afi, R. I., Fernandez, S. M., Eds.; Elsevier: Amsterdam, 1983; Chapter 8.
Xu and Smart Table 1. Physical Properties of Polystyrene Latex Microspheres in Suspension IDC batch number dry diameter dEMa (nm) hydrodynamic diameter, dDLSb (nm) polydispersity index, PIc area per charge group (nm2/SO4-1) electrophoretic mobility, µ ((µm‚cm)/(V‚s)) concentration, CPSL (M) charge group per particle (SO4-1) total particle surface area (cm2/mL)
L91
L249
L707
10-158-45 91 ( 8.6% 93.2
10-262-28 249 ( 3.5% 244.2
10-198-53 707 ( 1.6% 720.1
0.02 21.16
0.04 7.72
0.08 2.26
-3.19
-4.50
-3.65
2.8 × 1.3 × 103
3.4 × 2.4 × 104
3.9 × 10-14 7.2 × 105
44
4.0
0.37
10-10
10-12
a Determined from transmission electron microscopy of 500 randomly selected particles. b Determined from DLS measurement in a 0.001 M NaBr suspension. c See ref 21 for the definition.
adsorption of DTAB due to significant surface charge changes of the PSL particles that occur during adsorption. In the present study, the characteristics of DTAB in aqueous solution, namely the critical micelle concentration (cmc), the electrophoretic mobility of DTAB micelles, and the dissociation degrees of the DTAB unimers and DTAB micelles, are determined from ELS, conductivity, and viscosity measurements. Two adsorption models, the brush model for the DTAB adsorption on a curved surface and the pancake-to-cauliflower model for the DTAB adsorption on a flat surface, are proposed and elucidated from the experimental results. Experimental Section Materials. The surfactant DTAB (>99%) and sodium bromide (>99.99%) from Sigma Chemicals were used without further purification. The purity of DTAB was confirmed by the good agreement between the cmc value obtained from both conductivity and viscosity measurements in the present study and the literature values. The water used was treated in sequence with a 1 µm prefilter, a carbon black tank, a cation resin bed, an anion resin bed, and a 0.2 µm filter. The water was then distilled in a device with all Teflon tubing. The residue conductivity of the water was less than 1 µS/cm. Certified latex particles were obtained from Interfacial Dynamics Corp. These PSLs are ultraclean, surfactant-free uniform microspheres with sulfate and hydroxyl surface groups. The particles were extensively dialyzed by the manufacturer to remove impurities. These surfactant-free particles are stabilized by the sulfate surface groups and are stable up to about 0.25 M univalent electrolyte concentrations. They will undergo aggregation in the presence of even low concentrations of divalent cations. The physical properties of the PSL used in the present study are listed in Table 1. Sample Preparation. A stock solution of 0.08 M DTAB in 0.001 M NaBr was prepared. DTAB solutions of different concentrations from 0 to 0.08 M were made by adding different amounts of the stock solutions to the desired amounts of 0.001 M NaBr solution. The samples were then prepared by adding a certain amount of the vendor-supplied PSL suspension to the DTAB solution so that the scattering intensity of the sample fell within the range suitable for both DLS and ELS measurements. The final PSL concentrations in the sample solutions are listed in Table 1. The solutions used for the DTAB mobility measurements were prepared by dissolving the desired amount of DTAB in distilled water or 0.001 M NaBr. The solutions were then filtered through a 0.2 µm Millipore membrane filter before being transferred into the sample chamber. All measurements were performed at 25.0 ( 0.1 °C. Viscosity Measurements. The viscosity measurements were performed using a Cannon-Ubbelohde semi-microviscometer. The viscometer was calibrated with a NIST traceable standard from Cannon. Electrophoretic Light Scattering. The electrophoretic mobility values µ ((µm‚cm)/(V‚s)) were obtained using the Coulter
Electrophoretic Mobility Study of DTAB
Figure 1. Apparent electrophoretic mobility values obtained at different cell positions in the ELS measurement. The parabolic profile is caused by electroosmotic flow of the liquid due to the surface charge of the interior surfaces of the cell. The squares are from the Coulter mobility control, which has a mobility value of -4.20 (µm‚cm)/(V‚s). The triangles are from a mixture of L91 and 0.007 M DTAB in a 0.001 M solution of NaBr. The symmetric shape of the profiles indicates that the upper cell surface and the lower cell surface have the same surface conditions. Two arrows indicate the two stationary layers where the electroosmotic flow is null and the true electrophoretic mobility can be obtained. Delsa 440SX. The Coulter Delsa 440SX instrument performs a simultaneous four-angle electrophoretic light scattering measurement using a rectangular capillary cell. The cell has two gold-plated silver electrodes with the feature of electric field focusing that reduces possible electrode surface electrolysis and heat generation at high ionic strength and ensures an undisturbed and homogeneous electric field at the scattering cross section. A detailed description of the instrument can be found elsewhere.19 All electrophoretic mobility measurements for the PSL/DTAB mixtures were performed using an electric field of 7-8 V/cm with a duration time of 1 min (using a 2 s on and 1 s off sequence alternating the electric field polarity) at both the upper and lower stationary layers of the cell. Measurements were performed this way in order to avoid electroosmosis and possible errors caused by shifting of the stationary layers due to changes in the cell surface conditions.20 Figure 1 shows two electroosmotic flow profiles of the cell obtained by using the Coulter mobility control, which is a well characterized PSL in suspension having a stable electrophoretic mobility of µ ) -4.20 ( 0.40 (µm‚cm)/(V‚s), and by using one of the sample solutions. This figure verifies that both the upper and lower stationary layers produce the same results and that the profiles have a parabolic shape. Because the Delsa 440SX performs measurements at four different scattering angles simultaneously, any difference in the mobility distributions obtained from different angles is an indication of either measurement artifacts or sample heterogeneity. In the present study, since the PSL particles are uniform spheres with very small polydispersity index (PI), as shown in Table 1, and are expected to be uniform even after adsorption, the scattering from DTAB unimers or micelles will be completely masked by the scattering of the PSL particles. Thus, the Doppler spectrum obtained should be unimodal with the peak value indicating the mobility value. In this instance, the deconvolution of the Brownian motion from the Doppler spectra is not necessary19 and the mobility obtained from the four angles should be the same. Thus, the concordant mobility distributions obtained from the simultaneous multiangle measurement can be used to verify the validity of the data (to exclude experimental artifacts) and check the sample homogeneity (to detect aggregations). Dynamic Light Scattering. The effective hydrodynamic diameters of the PSL particles in suspension were obtained from their translation diffusion coefficients using the Stokes-Einstein equation.10 The measurement of the translational diffusion coefficients of the PSL particles was accomplished using the Coulter N4 Plus instrument. The Coulter N4 Plus is a multiangle dynamic light scattering instrument equipped with a 10 mW He-Ne gas laser as the light source. The scattered light from the sample solution in a square cuvette is collected by fiber optics (19) Xu, R. Langmuir 1993, 9, 2955. (20) Pelton, R.; Miller, P.; McPhee, W.; Rajaram, S. Colloids Surf., A 1993, 80, 181.
Langmuir, Vol. 12, No. 17, 1996 4127 at six scattering angles from ca. 11° to 90° and detected by a photomultiplier tube. The instrument is controlled by Microsoft Windows-based software utilizing an ODBC compliant database, so that all information obtained from the experiment is readily available for communication with many types of commercially available software. In the present study, because all samples are nearly monodisperse, each sample was measured only at one scattering angle for a duration of 15 min. Occasionally, additional measurements were made at other angles to verify and confirm the results. The 90° scattering angle was used to perform the measurements of the sample solutions of L91 and L249, and the 60° angle was used for the sample solutions of L707. The secondorder cumulants method was used to fit the intensity-intensity autocorrelation function in order to obtain the translational diffusion coefficient and the polydispersity indices of the samples.21 The accuracy of the mean particle size obtained is expected to be 2% with repeatability being better than 5%.21 When the PI or the mean size values were unexpectedly large, the particle size distribution analysis utilizing the CONTIN algorithm was used to obtain information about possible aggregation.22 Conductivity Measurements. The conductivity measurements were performed at the same time the ELS measurements were performed using the Coulter Delsa 440SX. The calibration was carried out using a NIST traceable conductivity standard from Fisher Scientific.
Results and Discussion DTAB in Aqueous Solution. DTAB is a common cationic surfactant and has broad applications. DTAB forms polydisperse spherical or cylindrical micelles with or without the addition of electrolyte at high concentrations. When DTAB micelles are formed, their physical properties, such as surface tension, conductivity, and viscosity, will change. The critical micelle concentration (cmc) of the DTAB solution is a function of the solution temperature and the type and concentration of the electrolyte.17,23 The micelle aggregation number is a function of the DTAB concentration, the solution temperature, and the type and concentration of the electrolyte in the solution. Although there are a few reports on the micelle aggregation number,16,23-27 there is little information on the electrophoretic mobility of DTAB micelles. In the present study we use ELS to measure the electrophoretic mobility of DTAB micelles as a function of the DTAB concentration and the applied electric field. In the ELS measurement, when the DTAB concentration is higher than, but close to, the cmc, two mobility peaks were observed. A typical electrophoretogram is shown in Figure 2. The lower mobility peak agrees with the literature value for the ion mobility of a DTA+ ion ()2.34 (µm‚cm)/(V‚s)),28 and the value for the peak at higher mobility corresponds to the mobility of DTAB micelles. Both mobility values show no dependence on the applied electric field from 5 to 35 V/cm, as shown in Figure 3. For DTAB solutions at concentrations much higher than the cmc, there is only one peak observed in the electrophoretogram. However, this peak shows a strong dependence on the DTAB concentration, both in deionized water (DI) water and in 0.001 M NaBr aqueous solution. Figure 4 shows the electrophoretic mobility (µ) of DTAB micelles in water and in 0.001 M NaBr solution at different DTAB (21) International Standard ISO/DIS 13321, International Organization for Standardization, Geneva, 1995. (22) Provencher, S. Comput. Phys. Commun. 1982, 27, 213, 229. (23) Ikeda, S.; Saso, Y. Colloids Surf. 1992, 67, 21. (24) For example: Herrington, K. L.; Kaler, E. W.; Miller, D. D.; Zasadzinski, J. A.; Chiruvolu, S. J. Phys. Chem. 1993, 97, 13792. (25) Caponetti, E.; Causi, S.; DeLisi, R.; Floriano, M. A.; Millioto, S.; Triolo, R. J. Phys. Chem. 1992, 96, 4950. (26) Lusvardi, K. M.; Full, A. P.; Kaler, E. W. Langmuir 1995, 11, 487. (27) Phillips, J. N. Trans. Faraday Soc. 1955, 51, 561. (28) Handbook of Chemistry and Physics, 73rd ed.; CRC Press: New York, 1993.
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Figure 2. Electrophoretogram of 0.025 M DTAB in DI water measured at a 17.5° scattering angle using an electric field of 17.2 V/cm.
Xu and Smart
the critical chain length, and ao the optimal surface area). When Pa < 1/3, the micelle will be spherical, and when 1/3 < Pa < 1/2, the micelle will be spheroidal or cylindrical with spherical heads. For long saturated hydrocarbon chains, V/lc = 21 Å2.31 The optimal surface area ao, normally between 45 and 65 Å2, depends on the hydrophilic head structure of the surfactant. ao values ranging from 49 to 62 Å2 for DTAB have been reported.15,32,33 Thus, a Pa value of 0.43-0.34 indicates that the DTAB micelles would be spheroidal in shape. Micelles grow with increasing aggregation number, but the surface charge density, incurred from the hydrophilic head, will remain approximately constant if the counterion dissociation degree is unchanged. Thus, the ζ potential of the micelle will remain approximately unchanged. However, because of the size (or shape) differences in micelles of different aggregation numbers, the measured electrophoretic mobility will be different according to the following analysis. In a spherical micelle of 32 DTAB unimers with each unimer having a hydrocarbon volume of 350 Å3,33 the core radius (r) can be estimated to be 14 Å. The micelle core radius increases to 20 Å for a micelle consisting of 89 DTAB unimers. At constant ζ potential the mobility varies with the κr value, where κ is the Debye-Hu¨ckel parameter characterizing the particle surface electric double layer.
x
Figure 3. Electrophoretic mobilities of DTAB micelles and DTA+ ions at different electric fields using a 0.025 M DTAB aqueous solution. The error bars represent the estimated experimental error limits. The solid line indicates the literature value for DTA+ ions.
Figure 4. Electrophoretic mobility (µ) and aggregation number (N) of DTAB micelles. The hollow symbols are the µ values (the left ordinate): squares are DTAB in distilled water; diamonds are DTAB in 0.001 M NaBr solution. The filled symbols are the N values of DTAB in water from the literature (the right ordinate): diamonds, ref 16; inverted triangle, ref 26; triangle, ref 23; circle, ref 24; square, ref 25.
concentrations where the contribution to the ionic strength of the solution from sodium bromide is negligible when compared with the contribution from the ions dissociated from the DTAB molecules. The µ values are inversely proportional to the aggregation number (N) while both µ and N change with DTAB concentration. The decrease in mobility when the aggregation number increases can be explained from a geometric consideration. The commonly accepted shape for a DTAB micelle at low salt concentration is spherical. A rod shape has been observed at high salt concentrations.29 According to the packing model,30 the geometrical shape of a surfactant micelle can be predicted by a critical packing parameter Pa (≡V/aolc, where V is the hydrocarbon chain volume, lc (29) Zielinski, R.; Ikeda, S.; Nomura, H.; Kato, S. J. Colloid Interface Sci. 1988, 125, 497.
The κ value ()3.288 12∑ciz2i nm-1 with ci and zi being the concentration (M) and valence of ion i, respectively) can be estimated from the DTAB concentration, the counterion dissociation degrees of DTAB unimers (Ru) and micelles (Rm), and the micelle aggregation number N. Using the N values from ref 16 and the Ru and Rm values from the present study (see below), we estimated the κ values of DTAB micelles at different DTAB concentrations. Combining the κ values with the micelle radii, we found the parameter κr to vary from 0.52 to 8 when the DTAB concentration increases from 0.02 to 0.16 M. According to the theoretical model for the relation between electrophoretic mobility and ζ potential of a sphere,34 such a change in the κr value would cause a ca. 10% change in the mobility, at a constant ζ potential, which agrees with the present observation. On the other hand, a randomly oriented rod would have a much smaller mobility change (ca. 1-2%) for the same variation in κr at a constant ζ potential.35 Thus, the change in mobility at different DTAB concentrations indicates that the DTAB micelles more closely resemble spheres. The cmc value for DTAB in aqueous solution (reported as ranging from 0.0142 to 0.0165 M) has been determined using techniques such as electrochemistry,36 ultrasound velocity,29 surface tension,15 photochemistry,37 and, mostly, conductivity.24 The cmc decreases when the added salt concentration increases. In the present study, we determined the cmc for DTAB in 0.001 M NaBr aqueous solution using both conductivity measurements and viscosity measurements. Figure 5 shows the plot of ηsp/CDTAB versus CDTAB, where the specific viscosity ηsp is calculated from ηsp ) (η/ηwater) - 1. The slope change in the plot indicates the formation of micelles from which the cmc value of 0.0146 M is (30) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J. Chem. Soc., Faraday Trans. 1 1976, 72, 1525; Biochim. Biophys. Acta 1977, 470, 185. (31) Tanford, C. J. Phys. Chem. 1972, 76, 3020. (32) McGrath, K. M. Langmuir 1995, 11, 1835. (33) Brady, J. E.; Evans, D. F.; Warr, G. G.; Grieser, F.; Ninham, B. W. J. Phys. Chem. 1986, 90, 1853. (34) Wiersema, P. H.; Loeb, A. L.; Overbeek, J. Th. G. J. Colloid Interface Sci. 1966, 22, 78. (35) Stigter, D. J. Phys. Chem. 1978, 82, 1417. (36) Zana, R. J. Colloid Interface Sci. 1980, 78, 330. (37) Lee, K. H.; Mayo, P. D. Photochem. Photobiol. 1980, 31, 311.
Electrophoretic Mobility Study of DTAB
Langmuir, Vol. 12, No. 17, 1996 4129
0.88 from the slope of the line at low DTAB concentrations in Figure 6. When the DTAB concentration is above the cmc, the conductivity can be calculated by
G ) 9.6485[CNaBr(µNa+ + µBr-) + cmc‚RDTAB(µDTA+ + µBr-) + (C - cmc)RDTAB,M(µBr- + µDTAB,M)] ) 1.433 - 1.822RDTAB,M + 123.9RDTAB,MCDTAB 46.80RDTAB,MC2DTAB (2)
Figure 5. Specific viscosity of DTAB in 0.001 M NaBr solution. ηsp ) (η/ηwater) - 1, where ηwater ) 0.890 cP (cmc ) 0.0146 M, as determined by the cross point of the two lines obtained from a linear fitting of the data points).
Figure 6. Conductivity of DTAB in a 0.001 M NaBr solution. The lines are from a linear fitting of the data points below C ) 0.0145 M (G ) 0.130 + 88.7CDTAB) and a second-order polynomial fitting of the data points above C ) 0.0145 M (G ) 1.031 + 27.6CDTAB - 3.88C2DTAB). The cross point indicates the cmc value ()0.0147 M).
determined. The extrapolated intercept of the line below the cmc value is the intrinsic viscosity [η] of DTAB unimers, from which the effective hydrodynamic volume (Ve) of a hydrated DTAB unimer can be estimated by using the Einstein equation ([η] ) 5Ve/2M), assuming a spherical shape. A Ve value of 670 Å3 is obtained from such an estimation, which is almost twice the volume of a dry C12 chain without taking into account its head volume. From the conductivity measurement of DTAB in 0.001 M NaBr solution at different DTAB concentrations, we obtained the cmc value as well as the counterion dissociation degrees of DTAB unimers and DTAB micelles. Figure 6 shows the conductivity of DTAB in 0.001 M NaBr solution as a function of DTAB concentration. From the turning point where the slope of the concentration dependence of the DTAB solution conductivity changes, a cmc value of 0.0147 M is determined, which agrees well with the value determined from the viscosity measurement. The increasing conductivity is due to the dissociated ions from the salt and the DTAB molecules in the solution. Below the cmc, the conductivity of the solution is given by
G ) 9.6485[CNaBr(µNa+ + µBr-) + CDTABRDTAB(µDTA+ + µBr-)] ) 128.2CNaBr + 100.7CDTABRDTAB
(1)
In eq 1, µi is the ion mobility of ion i, whose value can be found from the literature,28 and RDTAB is the dissociation degree of the DTAB unimers. Thus, from the intercept of the linear fitting of the data points below the cmc value, one can verify the measurement uncertainty or the error limit, and from the slope of the line, the dissociation degree of the DTAB unimers can be found. We found RDTAB )
where RDTAB,M and µDTAB,M are the dissociation degree and mobility of the DTAB micelles, respectively. If we assume that RDTAB,M does not change with the DTAB concentration and take µDTAB,M from the mobility measurement results (in Figure 4, a linear fitting to the mobility values yields µDTAB,M ) 4.72-4.85C((µm‚cm)/(V‚s))), we have the second equality in eq 2. A RDTAB,M value of 0.22 is obtained from both the intercept and the slope of the fitted line at concentrations higher than the cmc. The second-order coefficient, which is from the concentration dependence on the micelle mobility, is too small to retrieve a reliable RDTAB,M value from the measurement due to experimental errors and fitting uncertainty. The dissociation degree (RDTAB,M ) 0.22) of the DTAB micelles agrees with the literature value.33,36 DTAB Adsorption on PSL. For the purpose of closely monitoring how the adsorption of the DTAB surfactant onto the surfactant-free PSL is taking place, a series of samples with fixed amounts of PSL, but at various concentrations of DTAB, were prepared. The increment of the DTAB concentration was arranged logarithmically from 5 × 10-6 to 8 × 10-2 M. The DLS and ELS measurements were performed using equilibrated mixtures of DTAB and PSL in 0.001 M NaBr solution. In both DLS and ELS measurements, since the mass of a latex particle is several orders of magnitude larger than that of DTAB unimers and micelles, the scattering from DTAB is completely masked by the scattering from PSL. In a DLS experiment, the hydrodynamic diameter (d) of a hard sphere is obtained by applying the StokesEinstein equation to the measured translational diffusion coefficient (DT) of the sphere based on the frictional thermal motions of solvent molecules and the sphere:
d)
kBT 3πη0DT
(3)
where kB is the Boltzmann’s constant, T the absolute temperature, and η0 the solvent viscosity. In eq 3, one assumes spheres in dilute solution with the solvent being a continuum. However, for PSL in a surfactant solution, there are a few effects that affect the determination of the PSL diameter using eq 3. It has long been noticed that the d values of latexes of various materials in DI water determined by DLS are always larger than those determined by electron microscopy (EM), which is a measurement of the dry diameters. The difference in the sizes determined by these two techniques can be as large as 10%. The difference decreases with the increase of the solution ionic strength. At high solution conductivity, e.g. G > 1 mS/cm, the d values determined by DLS often agree with the EM results. There are several explanations for this phenomenon, such as the conformation change of the surface hairy layer,38,39 the change in the surface hydrophobicity,40 or the compressing of the swell or hydrated surface layer.41 The change in the d value when the (38) Goossens, J. W. S.; Zembrod, A. Colloid Polym. Sci. 1979, 257, 437. (39) Brouwer, W. M.; Zsom, L. J. Colloids Surf. 1987, 24, 195.
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solution conductivity changes introduces a barrier in detecting the DTAB adsorption from DLS measurements. Because the solution conductivity increases with the addition of DTAB, the apparent size reduction when the solution conductivity changes will certainly offset any size increment of the latex particles due to the adsorption of DTAB. If the adsorption layer thickness is less than the apparent size reduction caused by the conductivity effect, the apparent PSL diameter from DLS measurements may not increase but reduce when adding DTAB to the suspension. The second effect is that with the addition of DTAB the solution viscosity changes. Since the PSL particles are undergoing Brownian motion in an environment of DTAB solution, i.e., not only water molecules, one cannot use the viscosity of water in eq 3 to compute the d value. The viscosity may increase up to a few percent when the DTAB concentration is higher than tens of millimolars while DTAB adsorption onto PSL at these concentrations may cause the maximum PSL size change to be only a few percent or less. Equation 3 applies to a simple liquid where there is only one characteristic length scale from the solvent or solvent mixture. When there is more that one characteristic length scale in the fluid, even the use of the macroscopic solution viscosity will not fully correct the deviation from the Stokes-Einstein behavior in the particle’s translational diffusion because the effect of different length scales on the Brownian motion of a sphere cannot be attributed to a single solution viscosity.42 In a micelle solution there are three characteristic length scales, one each for water molecules, unimers, and micelles. However, for DTAB solutions at concentrations below or slightly above the cmc, because the individual unimer volume is much closer to that of a water molecule than to that of a large suspended latex particle, one may treat the fluid as a continuum as the first-order approximation to the Stokes-Einstein behavior if the solution viscosity instead of the water viscosity is used when applying eq 3. From the DLS measurement all particles after adsorption are still mostly monodisperse in size with the PI values only slightly increased from those of the uncoated PSL particles for L90 and L249 samples. But for L707, it not only experiences an aggregation in the DTAB concentration range between 4 × 10-5 and 1 × 10-4 M but the PI value almost doubles (originally 0.08 to ∼0.15) at other DTAB concentrations, even though particle size distribution analyses show that the PSLs are still unimodal. Figure 7 plots the PI values for the three samples at different DTAB concentrations. For all three PSL samples, we found a decrease in the PSL diameters when increasing the DTAB concentration after an initial diameter increase at very low DTAB concentrations. For L90, the diameter gradually increases from 93 to 98 nm after adding trace amounts of DTAB (CDTAB ) 1 × 10-4 M). The diameter then decreases continuously to about 93 nm when further increasing the DTAB concentration. For L249, the trend is the same, but the initial increase in the diameter is only about 4 nm and the decrease makes the PSL diameter smaller than that of the uncoated ones. For L707, except for the aggregation that occurs between 4 × 10-5 and 1 × 10-4 M DTAB concentration, the diameter at all concentrations is less than that of the uncoated one. The decrease in diameter can be as large as 25 nm. Figure 8 shows the diameters of PSL in different DTAB concentrations as measured by DLS using the solution viscosity in (40) Duke, S.; Brown, R.; Layendecker, E. Part. Sci. Technol. 1989, 7, 223. (41) Johnson, P. Langmuir 1993, 9, 2318. (42) Phillies, G. D. J.; Hunt, R. H.; Strang, K.; Sushkin, N. Langmuir 1995, 11, 3408.
Xu and Smart
Figure 7. Polydispersity index values of samples L91 (crosses), L249 (circles), and L707 (diamonds) at different DTAB concentrations. The two numbers at the top indicate the PI values for L707.
Figure 8. Hydrodynamic diameters of the three PSL samples at different DTAB concentrations. The values were obtained using the second-order cumulants fitting algorithm. For the data of L91 at DTAB concentrations below 4 × 10-5 M, where small amounts of aggregates were found, the diameters of the nonaggregated particles from the size distribution are used. The error bars indicate an estimated (3% measurement error. The crosses and circles are for L91 and L249, respectively, using the left ordinate, and the diamonds are for L707, using the right ordinate. The two numbers at the top indicate the sizes of the aggregates of L707. The three lines indicate the dDLS values for the three uncoated PSL samples.
Figure 9. Relative diameter changes as measured by DLS for the DTAB-coated PSL particles at different DTAB concentrations. a is the maximum size change observed for the PSL particles. a ) 5.5 nm for L91, a ) 4 nm for L249, and a ) 0 nm for L707. d0 is the diameter of the uncoated PSL.
eq 3 as compared with those of the uncoated PSL (the solid lines in Figure 8). As seen in Figure 9, where the reduction of the measured diameters is plotted as a function of the DTAB concentration, the three PSL samples experienced the same trend of size reduction that approaches a minimum when the DTAB concentration is at about 0.02 M. The diameters then increase slightly at higher concentrations. The decrease in the measured diameters at increasing DTAB concentrations below the cmc is mainly due to the effect of the solution ionic strength on the diffusion coefficient
Electrophoretic Mobility Study of DTAB
measurement, as was discussed earlier. Above the cmc, in addition to possible micelle adsorption, which will cause a bigger size increment than unimer adsorption, the d value will be affected by deviation from Stokes-Einstein behavior due to the fluid characteristic length scale change. These two effects may explain the minimum and the consequent increase of the measured d value. The phenomenon that adsorbent-covered particles display smaller sizes than that of the uncoated ones using the DLS measurements has been reported in several adsorption studies.13,17,38 In a single-layer adsorption, the maximum adsorption layer thickness would approach a fully stretched DTAB chain that has an estimated length of 1.9 nm. This maximum layer thickness would be only 0.5% of the diameter for an L707 particle and 4% for an L91 particle. In a careful DLS measurement, the achievable experimental uncertainty in determining the translational diffusion coefficient could be less than 2%. Thus, for L707 if only considering single-layer adsorption, i.e., without considering the viscosity and conductivity effects discussed earlier, one does not expect to observe any changes in the diffusion coefficient from the DLS measurement. In the adsorption of DTAB on a PSL particle, there are two types of driving forces: (1) hydrophobic interaction between the hydrocarbon portion of the PSL surface and the hydrocarbon chain of the DTAB molecules and (2) electrostatic attraction between the cationic head groups of the DTAB and the negatively charged sulfate groups on the PSL surface. Because these two interactions are coexistent, there are several ways for single DTAB unimers to be adsorbed on the surface: (A) it can be tail-down for the hydrocarbon chains adsorbed on the hydrophobic portions of the particle surface, or (B) it can be head-down for the opposite charge attraction taking place between the positive heads of the surfactant and the sulfate groups of the particles. In the latter case, (C) a second layer adsorption is possible from the tail-down adsorption of the subsequent unimers to the tails of the first adsorption layer through hydrophobic interaction. If one only considers fully stretched DTAB unimers adsorbed on the surface, then scenarios A and B should have similar maximum adsorption layer thicknesses which are smaller than that of scenario C. At a DTAB concentration higher than the cmc, micelle adsorption may take place. The micelle adsorption (scenario D) should have a similar effect as that of scenario C with respect to the size and mobility changes of the PSL. The electrophoretic mobility of the coated particles for these adsorption mechanisms would be µb < µa < µc ∼ µd. Of course, these scenarios may be coexistent. We have observed different behaviors on their size changes when adding trace amounts of DTAB to L91 and L249 samples where both the viscosity and conductivity effects are negligible. At very low DTAB concentrations (CDTAB < 7 × 10-5 M), the diameter increase of L91 gradually increases to twice that of a fully stretched DTAB chain. With further increase of the DTAB concentration (CDTAB ) 1 × 10-4 M) the maximum size increment of L91 is more than twice but less than three times that of a fully stretched DTAB chain. This may represent a brush model in which all adsorbed chains are standing up following scenario A or scenario B at very low DTAB concentrations. Scenario C may take place at CDTAB ) 1 × 10-4 M, where there may be a partial second-layer adsorption of tail-down-oriented DTAB unimers onto the tails of the head-down unimers of the first layer, as proposed by Kandori.43 For L249, the maximum diameter increment is smaller and about twice a fully stretched DTAB chain. This clearly indicates that at low concentrations L249 has a single-layer adsorption. It can be
Langmuir, Vol. 12, No. 17, 1996 4131
Figure 10. Mobility of the DTAB-coated PSL microspheres at different DTAB concentrations: triangles, L91; circles, L249; diamonds, L707. The connections between the data points serve as guidelines only.
Figure 11. Mobility of the DTAB-coated PSL microspheres at different DTAB concentrations in a unit of the total numbers of DTAB molecules in the solution per PSL surface charge. The symbols are the same as the ones in Figure 10.
predicted that if L91 and L249 do follow the adsorption as described, their mobility change with adsorption should behave differently; i.e., L91 should have a larger mobility change than that of L249 due to differences in the charge incurred and the charged layer location during adsorption. The electrophoretic mobilities (µ) of the PSL samples increase with the addition of DTAB surfactant. At low DTAB concentrations, the µ values change rapidly from the originally negative values for the uncoated PSL to positive values when the DTAB concentration is increased. With further increases in the DTAB concentration above ca. 1 × 10-3 M, the µ values increase very slowly. For L707, the µ value even decreases slightly at CDTAB higher than 0.001 M. However, the patterns of the µ values are different for the three PSL samples. As shown in Figure 10, the µ values at high DTAB concentrations (CDTAB > 0.01 M) are different for the three samples. L707 has the highest value; L91 has the lowest value; and the value for L249 is in the middle. The mobility changes of the coated PSL samples at low DTAB concentrations show even bigger differences for the three samples. For the purpose of revealing the mobility change in a span of five decades of the DTAB concentration, we plot the PSL mobilities as a function of the DTAB concentration logarithmically scaled to the PSL surface charge (Figure 11) and to the PSL surface area (Figure 12) to examine the curvature effect on adsorption. In Figures 11 and 12, the differences of the mobility values among the three PSL samples are distinguishable and significant. For L91, even at the lowest DTAB concentration (5 × 10-6 M), which corresponds to only one DTAB per square nanometer of the surface area, even if they are all adsorbed, the µ has already changed to positive. On the other hand, for L707, at the same lowest concentration, which corresponds to 80 DTAB chains per square nanometer of the surface area and 180 (43) Kandori, K.; Ishiguro, H.; Kon-no, K.; Kitahara, A. Langmuir 1989, 5, 1258.
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Figure 12. Mobility of the DTAB-coated PSL microspheres at different DTAB concentrations in a unit of the total numbers of DTAB molecules in the solution per unit PSL surface area. The symbols are the same as the ones in Figure 10.
DTAB chains per surface charge (SO4-1) if they are all adsorbed, the µ is still negative. This finding tells us that, at surfaces of different curvatures, not only may the adsorption conformation be different but also the degree of DTAB dissociation may be different. From these two zoomed plots, we notice that L707 has the steepest increase in the µ value when the DTAB concentration increases before it reaches a maximum and is the only sample in the present study for which the crossing of zero mobility is encountered. At zero mobility, the PSL formed aggregates (as observed in the DLS measurements) because of the lack of the electric repulsive force to prevent aggregation from the attractive force. Although at low DTAB concentrations L91 has higher µ values than those of L249 and L707, the µ value of L91 increases to a nonflat plateau that is lower than those of the other two samples. L249 has an almost flat plateau region. Although both scenario A and scenario B as described earlier may coexist, there are several discussions as to which is the preferred mechanism in the cationic surfactant adsorption onto negatively charged surfaces. In a study of the adsorption of cationic surfactants of different chain lengths onto the same negatively charged particles, Kayes found that the concentrations Cµ)0 at which the coated PSL has zero mobility are in an increasing order as the chain length decreases; i.e., Cµ)0,C10TAB > Cµ)0,C12TAB > Cµ)0,C14TAB . Each increment of two carbons in the hydrocarbon chain leads to almost a one order of magnitude smaller Cµ)0 value. The mobility plateau values are in the order µplateau,C10TAB < µplateau,C12TAB < µplateau,C14TAB.14 This finding strongly suggests that scenario A is more preferable. The reason for such a preference may be due to the fact that when two species approach each other in a random collision, either DTAB head-down to the charged sites on the surface or DTAB tail-down to the noncharged areas on the surface will cause adsorption to take place. The probability for the former to take place will be much smaller, since the charged surface groups only occupy a small portion of the surface. Furthermore, once the neighboring area of a charged site has been occupied by the tail-down chains, even a head-down chain cannot approach that site because of the repulsion from the screen formed by the heads of those adsorbed chains. The zero mobility crossing concentration and the plateau mobility will be related to the chain length only when the adsorbed chains are tail-down. This is because the longer the chain length, the further the separation of the positive charges from the negative surface charges and thus the less influence of the surface charges on the effective potential at the shear layer. Taking into account the above analysis, in the present study where the same surfactant chains adsorbed on the surfaces of different curvatures, we can propose two adsorption models corresponding to adsorption on the surfaces having a large curvature (small
Xu and Smart
Figure 13. Two adsorption models for DTAB adsorbed on a curved surface (A) and on a flat surface (B) at low concentration.
Figure 14. Two adsorption models for DTAB adsorbed on a curved surface (A) and on a flat surface (B) at high concentration.
particles) and having a small curvature (large particles, we use a flat surface as the analogue), respectively, as shown in Figure 13 for adsorption at low DTAB concentrations and Figure 14 for adsorption at high DTAB concentrations. In Figure 13, the adsorption on a surface with a large curvature takes a brushlike form, where the adsorbed chains stand out from the surface, while the adsorption on a flat surface takes a pancake-like form, where the adsorbed chains lie down on the surface. In the former case because all heads are toward the aqueous environment, such that the Br- ions are dissociated from the chain heads, there is a positively charged outer layer whose charges are separated from the negatively charged surface by the thickness of the adsorption layer. In the latter case, most heads are close to the hydrophobic surface that may prevent the Br- ions from dissociating from the heads. The net change of the particle charge in this case will be small. The surface geometry difference may be the main reason for the above adsorption behavior on a curved surface and on a flat surface.13,44 The space per area above a curved surface is large, allowing more chains to approach the unoccupied or even partially occupied surface. At the same time, on a curved surface, the adsorbed chains have to bend in order to lie down on the surface, but those charged heads increase the difficulty for the chain to lie down because of surface hydrophobicity. On the other hand, the small space above the partially filled areas on a flat surface makes subsequent adsorption difficult and the adsorbed chains can deform to take the maximum affinitive contact between the hydrocarbon chains and the surface because there is little resistance for an adsorbed chain to lie down on a flat surface. At high concentrations, with more and more DTAB chains adsorbed on the surface, the possibility for any head-down adsorption is diminished even if the surface charge groups are still available. The tail-down chains will stick into the brush on a curved surface. Most of them will adsorb on the surface, since the coned space above the surface makes the approach to the partially (44) d’Oliveira, J. M. R.; Martihno, J. M. G.; Xu, R.; Winnik, M. A. Macromolecules 1995, 28, 4750.
Electrophoretic Mobility Study of DTAB
filled area possible or even favorable. Some of the chains may be adsorbed on the tails of the adsorbed head-down chains, which will lead to a locally double-layer adsorption. On a flat surface, because there are chains lying down on the surface the subsequent chains cannot completely lie down. If these chains are tail-down, the preferred landing sites will be those areas without the surface charge groups or without the occupation of the DTAB heads. The adsorbed DTAB surfactant on a flat surface at high concentrations will be cauliflower-like surface aggregates, as depicted in Figure 14B. These cauliflower-like surface aggregates are different from those curved aggregates in the striped patterns for C14TAB adsorbed on a flat uniform hydrophobic surface (graphite)45 because there are charged sites that cause inhomogeneity in the hydrophobicity of the surface. The two adsorption models for surfaces of different curvatures can explain not only the observed particle mobilities at low DTAB concentrations but also their different behavior at high DTAB concentrations. For small particles, once there is no more space for further insertion of DTAB molecules, as the DTAB concentration increases any change in ζ potential will only be from changes in the electrical double layer around the particle, which are much smaller than changes caused by the surface charge increment. However, the µ value of the particle will change due to the solution ionic strength change from the dissociation of the DTAB surfactant. In a simplified notion, the µ value is proportional to the ζ potential by a proportionality function, often called the Henry function f(κr). f(κr) is a monotonically increasing function of κr, ranging from 1 for κr f 0 to 1.5 for κr f ∞. The κr values increase with increasing DTAB concentration. Consequently, the µ value of the particle will increase even without further change in its ζ potential. Considering the head group area of a DTAB molecule, the estimated maximum adsorption for a brushlike geometry would be around a few DTAB per square nanometer of surface area. Thus, for the adsorption curve of L91 in Figure 12, after the third point, the µ value increase may be purely due to the change in the Henry function. For big particles, the cauliflower model predicts a different behavior. With further piling up of the adsorbed DTAB chains the adsorption layer thickness increases. The particles become “softer”. For soft particles that have a loose layer with a hard core, the proportionality between the µ value and the ζ potential is a function of the ratio of the core radius r and the soft layer thickness d, in addition to the Henry function.46 Here we observe a sharp increase in mobility followed by a slow decrease at high DTAB concentration, which are the competitive effects from both the ionic strength change of the solution and the softness change of the particles. In addition, the increasing ionic strength from dissociation of the excess DTAB in the solution may change the dissociation degree of the adsorbed DTAB chains and the compactness of the adsorption layer, leading to the decreasing µ values. The
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origin for this mobility maximum at increasing DTAB concentration is different from that of the similar maximum observed for many bare latex systems, for which the explanation is still inconclusive.47 For the surfactant adsorbed particles, the influence on the particle mobility from the “hairy layer” (if this exists) of the particles, should be minor when compared with the contributions from the oppositely charged absorbent and from co-ion or counterion adsorption. One noticeable phenomenon is that this happens at DTAB concentrations higher than 1000NDTAB/ surface area (nm-2). According to our models, the maximum adsorption in a cauliflower arrangement can only be twice the maximum adsorption in a brush model. From the adsorption curves in Figure 12, we can envisage that, at the same DTAB concentration, there are many more free DTAB unimers or micelles in the case of big particles when there are still available adsorption surfaces than in the case of small particles where the DTAB surfactants would mostly be adsorbed on the particle surface until there are no more unoccupied sites available. Summary From the ELS and DLS measurements, we have demonstrated that the processes for small cationic surfactants of a few nanometers in size adsorbing onto particles that are a few hundred times larger but have different surface curvatures are different. For small particles, the adsorption happens at very low DTAB concentration and then reaches a maximum. For large particles, the adsorption process occurs at higher concentration and expands in two decades of DTAB concentration. The experimental results suggest that the favorable orientation of the adsorbed DTAB chains is the one with the hydrocarbon moiety in contact with the surface and with the head group extending into the aqueous solution, i.e., the tail-down approach. On the basis of the experimental observation, two models are proposed: a brush model for adsorption on surfaces of big curvature and a pancake-cauliflower model for adsorption on flat surfaces. These models explain the mobility behavior of the DTAB-adsorbed PSL particles at different DTAB concentrations. DLS provides information on the dimensional change of the PSL particles upon adsorption of the DTAB surfactants at very low DTAB concentration. At high DTAB concentrations, the hydrodynamic diameters obtained through the Stokes-Einstein equation are biased because of the solution ionic strength and viscosity effects. Attempts to explain the small relative change in PSL diameter due to adsorption using the DLS results at high DTAB concentration may yield erroneous conclusions. Further works on the curvature effect in the adsorption of cationic surfactants of different chain lengths on particles of different sizes will further confirm and clarify the adsorption kinetics. Acknowledgment. The authors wish to thank Coulter Corporation for the support of the present work. LA9602067
(45) Manne, S.; Gaub, H. E. Science 1995, 270, 1480. (46) Ohshima, H. J. Colloid Interface Sci. 1994, 163, 473.
(47) Elimelech, M.; O’Melia, C. R. Colloids Surf. 1990, 44, 165.
