Dependence of Particle Size on pH, Electrolyte, and Time for

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Langmuir 1997, 13, 1978-1986

Dependence of Particle Size on pH, Electrolyte, and Time for Expandable Copolymer Latexes by Hydrodynamic Fingerprinting† James H. Prescott,‡ Robert L. Rowell,*,§ and David R. Bassett| Advanced Magnetics Inc., Cambridge, Massachusetts 01378, Department of Chemistry, University of Massachusetts, Amherst, Massachusetts 01003-4510, and Union Carbide Corporation, Cary, North Carolina 27551 Received October 28, 1996X A new technique, hydrodynamic fingerprinting, is presented for the characterization and study of expandable latex dispersions on the basis of their hydrodynamic behavior. In the hydrodynamic fingerprint the hydrodynamic size as measured by photon correlation spectroscopy is presented as a function of two colloidal state variables simultaneously, pH and pλ, where pλ is the logarithm of the conductivity. Hydrodynamic fingerprinting is applied to two methyl methacrylate-ethyl acrylate latexes, one of which contains 2% acrylic acid. It is shown that hydrodynamic fingerprinting can be used to measure expansion properties of colloids, time effects in colloidal solutions, colloidal stability, and the differences in chemistry of the colloid-solution interface.

Introduction Polymer latexes are widely used for coating and in many industrial applications. They have been used extensively as model systems in investigations of colloidal properties.1-7 Particle size measurements have been widely used in the study of polymer latexes and their associated behavioral properties, such as surface adsorption, steric and ionic stabilization, flocculation, surface chemistry, and particulate morphology.8-12 In many such investigations a measurable property is presented only for specific solution conditions or as a function of a single solution variable while other solution properties are assumed invariant. These assumptions are often incomplete, and a more revealing approach is illustrated in the present work. The hydrodynamic fingerprint is a global representation of the hydrodynamic size and is analogous to the electrophoretic fingerprint.13-15 The fingerprint is the twodimensional representation of a measured colloidal property, in this case the hydrodynamic size, as a function of †

Dedicated to the memory of Bruce J. Marlow. Advanced Magnetics Inc. § University of Massachusetts. | Union Carbide Corp. X Abstract published in Advance ACS Abstracts, March 15, 1997. ‡

(1) Ise, N.; Matsuoka, H.; Ito, K. Angew. Makromol. Chem. 1989, 166/167, 111-130. (2) Ise, N. Angew. Chem. Int. Ed. Engl. 1986, 25, 323. (3) Ise, N.; Okubo, T.; Ito, K.; Dosho, S. Journal of Colloid and Interface Science 1985, 103, 292. (4) Ise, N.; Okubo, T.; Kunugi, S.; Matsuoka, H.; Yamamoto, K.; Ishii, Y. J. Chem. Phys. 1984, 81, 3294. (5) Overbeek, J. T. G. J. Chem. Phys. 1987, 87, 4406. (6) Sogami, I. Phys. Lett. 1983, 96A, 199. (7) Thirumalai, D. J. Phys. Chem. 1989, 93, 5637. (8) Eshuis, A.; Harbers, G.; Doornink, D. J.; Mijnlieff, P. F. Langmuir 1985, 1, 289-293. (9) Goosens, J. W. S.; Zembrod, A. Colloid Polym. Sci. 1979, 257, 1979. (10) Couture, L.; van de Ven, T. G. M. Colloids Surf. 1991, 54, 245260. (11) Aksberg, R.; Einarson, M.; Berg, J.; Odberg, L. Langmuir 1991, 7, 43. (12) Rowell, R. L.; Farinato, R. S.; Parsons, J. W.; Ford, J. R.; Langley, K. H.; Stone, J. R.; Marshall, T. R.; Parmenter, C. S.; Bradford, E. B. J. Colloid Interface Sci. 1979, 69, 590-595. (13) Marlow, B. J.; Rowell, R. L. Langmuir 1991, 7, 2970. (14) Rowell, R. L. An Introduction to Polymer Colloids; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1990; pp 187-209. (15) Morfesis, A. A.; Rowell, R. L. Langmuir 1990, 6, 1088.

S0743-7463(96)01045-1 CCC: $14.00

the solution pH and pλ simultaneously. The corresponding three-dimensional surface is referred to as the hydrodynamic surface. In our earlier work on hydrodynamic fingerprinting, a study was made on two commercially available, surfactantfree, charge stabilized, polystyrene latexes.16 The previous work showed conditions of colloid instability and small changes of particle size for the commercial size standards. In the present work we apply the method to two surfactantstabilized copolymer latexes which were known to display interesting expandable properties because of differences in interfacial chemistry. Experimental Section Materials. The copolymer latexes were prepared at Union Carbide. The acidic latex, designated latex A170, is an ethyl acrylate, methyl methacrylate, acrylic acid copolymer latex. The composition of the monomer feed in the latex polymerization was 40 parts methyl methacrylate, 58 parts ethyl acrylate, and 2 parts acrylic acid, which was fed over the last half of the feed. Monomer was fed continuously into the reaction vessel at 80 °C in the presence of ammonium persulfate initiator and Aerosol OT.17 The mean particle diameter for latex A170, determined with the Microtrac UPA particle sizer, was 170 nm, with a standard deviation in the particle size distribution of 23 nm. The Microtrac measurements were made on the concentrated form of the latex, for which the solids weight fraction was 0.37 and the pH was approximately 3. Latex NA143 is the acid-free counterpart of latex A170. The polymerization procedure was the same as that used for latex A170, except that the composition of the monomer feed was 40 parts methyl methacrylate and 60 parts ethyl acrylate. No acrylic acid was present. Latex NA143 was found by the Microtrac UPA to be 143 nm in diameter with a standard deviation of 19 nm. The measurement was made at a pH of 3 and a solids weight fraction of 0.36. Latex NA143 was prepared as a control and was expected to be of constant size. All supporting solutions used for sample preparations were aqueous. The water to be used for solution preparations was distilled twice, the second time in an all glass apparatus. All of the salts were recrystallized from filtered aqueous solutions. The salts were KCl, LiCl, and NaCl, the acid was HCl, and the bases used were KOH, NaOH, and LiOH. (16) Prescott, J.; Rowell, R. L.; Shiau, S. J. Langmuir 1993, 9, 20712076. (17) Bassett, D. R.; Hoy, K. L. Polymer Colloids II; Fitch, R. M., Ed.; Plenum: New York, 1980; pp 1-26.

© 1997 American Chemical Society

Expandable Latex Dispersions Sample Preparations. The preparation of colloidal dispersions for accurate size determination by photon correlation spectroscopy (PCS) requires the solutions to be extremely clean and free of dust or stray particulates. To meet these requirements a multistage sample preparation procedure was developed. Diluted working stock solutions of the latexes were prepared by adding small measured volumes of the latex solutions as received to filtered, double-distilled water. Filtration was through 0.22 µm polycarbonate membranes from Gelman Scientific. The particle concentrations of the different working stock solutions were approximately 1% solids by weight. The working colloidal stock solutions were stored in HDPE bottles and refrigerated at 4 °C. Prior to the preparation of the samples for analysis, the working solutions were allowed to equilibrate to room temperature for 24 h. Stock solutions of the acids, bases, and salts were prepared. Samples for analysis were prepared by adding a small volume of a colloidal stock solution, typically less than 100 µL, to 4 mL of a filtered (0.22 µm) supporting solution in a sterile cuvette. The cuvette was then covered and sealed, and size measurements were made on the resultant solution directly. Final concentrations of the salts and either the acid or base were targeted. These values, however, were approximate since the solutions were to be characterized on the basis of measurable physical properties rather than calculated concentrations. The optimal solids weight fraction for accurate size determinations of these particles with our PCS instrumentation was found to be approximately 10-4. It was found that this concentration could be increased by a factor of greater than 2 without affecting the measured hydrodynamic size. PCS Measurements. All of the hydrodynamic size measurement used in this work were obtained by photon correlation spectroscopy (PCS) with a BI-90 from Brookhaven Instruments, Inc., of Holtsville, NY. The BI-90 utilizes a 5 mW He-Ne laser (632.8 nm) and a fixed detection angle of 90°. The temperature of the solutions was maintained at 25 ( 0.1 °C, and the solution viscosities were the same as that of water to better than 1%. Prior to the PCS measurements each sample cuvette was sonicated in an ultrasonic bath for 10 min and then allowed to stand for 10-15 min. Each reported value of the hydrodynamic diameter was the average of a minimum of five measurements. Data Presentation. The data are presented in the form of three-dimensional surfaces and the corresponding two-dimensional contour plots of the hydrodynamic diameter as a function of pH and pλ. The pλ is the conductivity variable, which is defined as the logarithm of the solution conductivity as measured in units of µS/cm. The pλ for double distilled water was approximately 0.3. The representation of the data in the form of three-dimensional hydrodynamic surfaces and two-dimensional contour diagrams, or “hydrodynamic fingerprints”, was accomplished using Surfer, a commercial software package from Golden Graphics of Golden, CO. The program creates a two-dimensional grid in the base plane (pH, pλ plane) of the three-dimensional surface and interpolates a z-coordinate (hydrodynamic diameter, dh) at each grid intersection on the basis of the values, distances, and the spatial distribution of neighboring data points. The two- and three-dimensional diagrams are then produced from the grid. Work was done on a well-characterized model system to optimize the variable parameters. The coded points on the hydrodynamic fingerprints represent data from individual latex solutions. Time Studies. Following the initial size measurements, the particulate samples were stored in their cuvettes at 4 °C. After 8 weeks the solutions were allowed to equilibrate to room temperature for 24 h. They were then sonicated for 10 min and allowed to stand for 15 min, and repeat size measurements were made.

Results The hydrodynamic surfaces and fingerprints for two polymer latexes are presented. The pH and pλ of the samples used to produce the fingerprints and to study the time dependence of the hydrodynamic size were controlled by the addition of aqueous stock solutions of either HCl of KOH to either water or aqueous KCl. Aqueous solutions containing either NaCl of LiCl were used for a consid-

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Figure 1. Hydrodynamic surface (a) and fingerprint (b) of latex A170, the expandable copolymer latex, in a KOH, HCl, KCl system. This latex possesses a carboxylated surface. All size measurements were made approximately 3 h after the solution preparations.

eration of the effect of monovalent cation identity on hydrodynamic behavior. (A) Hydrodynamic Fingerprints. (1) Latex A170. The hydrodynamic surface and fingerprint for latex A170 in a KOH, HCl, KCl system is shown in Figure 1. It can be seen from this figure that as the pH of the solution was increased from a pH of 2, the mean diameter was observed to increase by nearly 50%, going from 145 nm to a maximum of 205 nm. The maximum particle size of 205 nm occurs at conditions of a pH of 10.5 and a pλ of 2. This corresponds to a supporting solution which has had no KCl added. As the pH was increased further from this point, the hydrodynamic diameter was observed to decrease. The hydrodynamic diameter also shows a maximum value as the pH is held constant and pλ is increased. When the solution pH is varied from neutrality by the addition of either HCl or KOH in the absence of added KCl, the path traced in pH, pλ space is roughly parabolic. The boundary was approximated with Surfer using line segments. This defines the lower limits of the experimentally accessible conditions, since it is impossible to have low conductivity and either high or low pH simultaneously. Therefore this boundary represents the limits of the hydrodynamic surface also. The limits of experimentally accessible pH, pλ space are referred to as “system limited ionic strength”, or SLIS. No aggregation of latex was observed in the regions of pH, pλ space represented by Figure 1. Aggregation conditions found in earlier work could easily be identified by an increase in the polydispersity of the particle size distribution, accompanied by abrupt peaks on the hydrodynamic surface.16 The experimental fingerprint is a rapid and clear indication of the colloid stability in the pH-pλ domain. The BI-90 sizing algorithm generates a polydispersity index which is related to the sample

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Figure 3. Paths traced in pH, pλ space as the solution pH was adjusted by the addition of either HCl or KOH at constant concentrations of added KCl. Concentration of added KCl varies from low to high pλ as follows: 0, 0.1, 1.0, 10, and 30 mM KCl.

Figure 2. Hydrodynamic surface (a) and fingerprint (b) of latex NA143, the acid-free copolymer latex, in a KOH, HCl, KCl system. All size measurements were made approximately 3 h after the solution preparations.

polydispersity. The polydispersity index is the reduced second moment of a cumulant analysis of the scattering autocorrelation function and provides information on the relative width of the particle size distribution. Typically the polydispersity index ranges from 0 to 0.02 for monodisperse samples, from 0.02 to 0.08 for narrow distributions, and greater than 0.08 for broad or multimodal distributions. In these terms the size distributions of the solutions of latex A170 ranged from monodisperse to narrow. In general the size distributions of the copolymer latexes were found to be considerably narrower than the size distributions of the commercial polystyrene latexes which we studied previously.16 (2) Latex NA143. To our surprise, the no-acid latex (NA143) also displayed expandable behavior as shown in Figure 2, with a maximum in the hydrodynamic diameter at a pH of 5.5 and a pλ of 0.5. The maximum size of 136 nm corresponds to an aqueous dispersion of latex NA143 with no added acid, base, or salt. The hydrodynamic diameter was observed to decrease rather symmetrically along radial projections from this maximum into the experimentally accessible regions of pH, pλ space. Latex NA143 was stable against aggregation in all regions of pH, pλ space represented in Figure 2, and the size distributions ranged from monodisperse to narrow on the basis of the polydispersity index. (B) Profiles of the Dependence of the Size on the Colloid State Variables pH and pλ. Once a grid has been produced using Surfer, a curve can be specified in the x, y plane and a z-coordinate interpolated at every intersection this curve makes with the grid. The specific curves in the pH, pλ plane are referred to here as “paths”. The variation of the hydrodynamic diameter along specific paths was examined. These paths are representative of specific solution conditions. (1) Constant Salt Paths. Figure 3 shows the path in pH, pλ space made by solutions of the copolymer latexes

Figure 4. Hydrodynamic diameter of latex A170 as a function of pH at fixed concentrations of added KCl. Note the shoulder at a pH of approximately 6 in all of the curves except the 30 mM KCl curve. This represents a minor particle expansion on the order of 15 mM. Concentrations of added KCl are 0 (diamond), 0.10 mM (circle), and 1.0 mM (square).

A170 and NA143 when the pH was varied from neutrality by the addition of either KOH or HCl, while the molar concentration of KCl was held constant. These curves were the result of experimental measurements of pH and pλ. The pλ values were plotted as a function of pH, and the data were then smoothed using a second-order polynomial fit. The paths traced were the same for the two latexes. The variation in the hydrodynamic diameter with pH for latex A170 at various constant concentrations of added KCl is shown in Figure 4. These curves are interpolated from the hydrodynamic surfaces at small intervals in pH, as shown by the coded data points. It can be seen that the maximum in the hydrodynamic diameter for latex A170 is greatest for the supporting

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Figure 5. Variation in the hydrodynamic diameter of latex NA143 as a function of pH in solutions which had constant concentrations of added KCl. The maximum particle expansion is on the order of 15 nm. Concentrations of added KCl are 0 (diamond), 0.1 mM (circle), and 1.0 mM (square).

solution without any added KCl, at a pH of about 10. The maximum in the hydrodynamic diameter decreases in magnitude and shifts to a higher pH value as the concentration of added KCl in the supporting solution is increased. This is consistent with earlier work as discussed below. Two maximum are found in both the 0 mM KCl and 0.1 mM KCl curves. The first maximum (acid maximum) is smaller in magnitude than the second maximum (alkaline maximum) and occurs near a pH of 6. This is the first report of an acid maximum. The magnitude of the first maximum is 15-17 nm. The alkaline maximum occurs near a pH of 10 and is 50 nm larger than the acid maximum. At KCl concentrations of 10 mM and greater the acid maximum is suppressed. The dependence of the hydrodynamic diameter on pH for solutions of latex NA143 with constant concentrations of added KCl is shown in Figure 5. The magnitude of the maximum in the hydrodynamic diameter is observed to decrease as the concentration of KCl in the supporting solution is increased. The total variation in the hydrodynamic diameter with pH for solutions of latex NA143 without added KCl was on the order of 15 nm, while for concentrations of added KCl of 10 mM or greater the variation in the hydrodynamic diameter was less than 5 nm. The maximum of the curves from Figure 5 lie at pH values of about 5.8. (2) Cation Effect. The dependence of the hydrodynamic diameter on pH was also considered for a unique path in pH, pλ space that was traced by solutions containing several different monovalent alkali metal cations. The path chosen corresponds to a constant added salt concentration of approximately 0.1 mM. Three different supporting systems were considered: an HCl, KOH, KCl system, an HCl, NaOH, NaCl system, and an HCl, LiOH, LiCl system. The dependence of the hydrodynamic diameter on Latex A170 pH along this path for the three different electrolyte solutions was very similar. This dependence is shown in Figure 6. The values of the hydrodynamic diameter posted for the HCl, KOH, KCl system were extrapolated from the grid of the hydrodynamic surface which was used to create Figure 2.

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Figure 6. Hydrodynamic diameter of latex A170 as a function of pH for solutions containing different monovalent cations. The concentration of added salt was 0.10 mM in each solution, and the pH was adjusted from neutrality by the addition of either HCl or the appropriate alkali metal hydroxide. Systems are KOH, HCl, KCl (cross), NaOH, HCl, NaCl (square), and LiOH, HCl, LiCl (circle).

Figure 7. Hydrodynamic diameter of latex A170 as a function of pH under conditions of constant pλ (or constant solution conductivity) in a KOH, HCl, KCl system. pλ values are 1.0 (diamond), 2.0 (cross), 2.5 (triangle), 3.0 (square), and 3.5 (circle).

(3) Constant Conductivity. Profiles were also taken of the hydrodynamic surfaces of latexes A170 and NA143 under conditions of constant pλ or constant solution conductivity. The profiles of the surface of latex A170 as a function of pH for different constant values of pλ are presented in Figure 7. The concentration of added KCl varies from point to point along a path of constant pλ in pH, pλ space, but the conductivity of the supporting solution does not. The variation in the hydrodynamic diameter with pH for a few different values of pλ is shown in Figure 7. The magnitude of the maximum in the hydrodynamic diameter decreases and shifts to higher pH values as pλ increases.

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Figure 8. Hydrodynamic diameter of latex NA143, the acidfree copolymer latex, as a function of pH under conditions of constant pλ in a KOH, HCl, KCl system. pλ values are 1.0 (cross), 1.5 (diamond), 2.0 (square), 2.5 (triangle).

The constant pλ profiles of latex NA143 as a function of pλ are shown in Figure 8. Distinct maximum at pλ values between 5.5 and 6.0 are found for all of the curves except the curve representing a pλ value of 2.5. This was the highest pλ value considered in the figure. The magnitude of the maximum decreased as the pλ values increased. Time Dependence of the Hydrodynamic Size. The effect of time on the hydrodynamic size of solutions of latexes A170 and NA143 was followed. Differential hydrodynamic fingerprints, produced by subtracting one grid from another to generate a differential grid, are presented as a means of studying changes in the hydrodynamic behavior with time. The results are described below. (1) The Expandable Copolymer Colloid, Latex A170. A study of the hydrodynamic diameter was made 8 weeks after the preparation of the solutions of latex A170. The resulting hydrodynamic surface and fingerprint of latex A170 after 8 weeks time had elapsed are presented in Figure 9. Comparison with Figure 1 shows a striking decrease in size over much of the pH-pλ domain. A differential fingerprint and surface were generated by subtracting the original grid for latex A170 from the grid generated from the size measurements after 8 weeks time had elapsed and are shown in Figure 10. It can be seen from Figure 10 that in much of the region where latex A170 had initially exhibited expansion the latex now appears to have collapsed or grown smaller. In the region were the maximum expansion had been observed the hydrodynamic diameter has decreased by approximately 50 nm. It can also be seen from the differential surface and fingerprint that when the solution pH was less than about 6, the latex exhibited little or no change in the hydrodynamic diameter over the 8 weeks. The overall result then is that the alkaline maximum collapsed while the acid maximum was retained. (2) The Acid-Free Copolymer Colloid, Latex NA143. Figure 11 shows the hydrodynamic surface and fingerprint of latex NA143 after 8 weeks time had elapsed. The similarity to the hydrodynamic surface and fingerprint of latex NA143 shortly after solution preparation, shown in Figure 2, is striking.

Figure 9. Hydrodynamic surface (a) and fingerprint (b) of latex A170, the expandable copolymer latex, in a KOH, HCl, KCl system, 8 weeks after the solutions were prepared.

Figure 10. Differential hydrodynamic surface (a) and fingerprint (b) between the aged and recently prepared samples of latex A170, the expandable copolymer latex, in a KOH, HCl, KCl system.

A differential fingerprint has also been carried out for latex NA143, and the results are presented in Figure 12. The differential fingerprint for latex NA143 shows an increase in the hydrodynamic diameter in some regions of pH, pλ space by as much as 2 nm and a decrease by as much as 4 nm. It should be noted that the greatest

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unchanged over the 8 weeks. We conclude that the acid expansion was stable in both the acid and the acid-free latex. Discussion

Figure 11. Hydrodynamic surface (a) and fingerprint (b) of latex NA143, the acid-free copolymer latex, in a KOH, HCl, KCl system, eight weeks after the solutions were prepared.

Figure 12. The differential hydrodynamic surface (a) and fingerprint (b) between the aged and recently prepared samples of latex NA143, the acid-free copolymer latex, in a KOH, HCl, KCl system.

differences in the hydrodynamic diameter of latex NA143 as a function of time occur near the boundaries of the fingerprint, which represent the approximate limits of the experimentally accessible conditions. The differences observed in the differential fingerprint are comparable to the uncertainty in the measurement, so that the hydrodynamic surface was, within the experimental error,

Valuable information regarding a colloidal system can be obtained from a careful consideration of the system microstate variables. The use of an electrical variable (pλ) and a chemical variable (pH) to describe an aqueous solution provides a self-consistent description of the solution, assuming that other variables, such as the temperature or the presence of soluble neutral materials, are either invariant or do not effect the colloidal property of interest. The hydrodynamic size and the variational trends in the hydrodynamic size throughout pH, pλ space are unique for each of the systems considered in this work. Comparison of the present results with earlier work16 suggests that the observed patterns, such as expandable behavior or aggregation peaks, are found to be characteristic of particular surface structures and of the surface chemistries. (A) Hydrodynamic Fingerprinting as a Characterization Technique. The hydrodynamic surfaces and fingerprints of latexes A170 and NA143 in Figures 1 and 2 show that both of these colloids display expandable behavior. This was a surprise since NA143 was designed as a control and was expected to have a constant size, independent of pH and pλ. However, the magnitude of the expansion is much greater for latex A170 than for latex NA143. Other control systems such as surfactantfree, charge-stabilized polystyrene latex dispersions were found to be much more sensitive to pH and pλ in terms of their bulk stability16 than were latexes A170 and NA143. It is apparent from the observation of particle expansion that the present copolymer latexes owe some of their stability to steric factors resulting from their surface compositions. Residual surfactant from the latex preparations also contributes to the steric and electrostatic stability of the latexes. The copolymer latexes were stable in all of the experimentally accessible regions of pH, pλ space represented in Figures 1 and 2. This was not the case for previously reported, commercially available, surfactant-free polystyrene latexes where pronounced aggregation was observed. The acid expansion found in the present work is similar to that found earlier in acidfree latexes.16 Previous angular intensity light scattering studies on a latex having the same composition as latex A170 have shown that the latex displayed a bilayer morphology.18,19 The latex consists of a dense core, with an approximately constant diameter of 140-150 nm, with a less dense outer layer. It is this outer layer that expands strongly as the pH is increased. As the carboxyl functional groups of the tangled chains that comprise the surface layer deprotonate, the surface develops a negative charge. Repulsion between neighboring charges causes the surface layer to expand in order to minimize repulsive interactions.17 The expansion in latex NA143 is possible due to repulsive interactions between the polymer chains residing at the latex surface due to localized regions of polarity. Localized charges on neighboring polymer chains would be interactive and would be greater in solutions of low electrolyte concentration than in solutions with high concentrations of electrolytes.20-23 This is analogous to (18) Rowell, R. L.; Ford, J. R.; Parsons, J. W. Polymer Colloids II; Fitch, R. M., Ed.; Plenum: New York, 1980; pp 27-35. (19) Ford, J. R.; Morfesis, A. A.; Rowell, R. L. J. Colloid Interface Sci. 1985, 105, 516. (20) Flory, P. J. J. Chem. Phys. 1949, 17, 303. (21) Olander, D. S.; Holtzer, A. J. Am. Chem. Soc. 1968, 90, 4549.

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the conformational changes of some water borne polymers as the electrolytic composition of the supporting solution is varied or to the unfolding of polylysine as the acid/base character or nonspecific electrolyte concentration is varied.24-28 The existence of a hydrated surface layer can be deduced from the contraction of carboxyl-free latexes upon the addition of a neutral salt of NaOH to the solution. The thickness of this surface layer depends to some extent on the hydrophilicity of the particle surface.17 It is possible that the surface of latex NA143 possesses some discrete charge character which was acquired by hydrogen bonding or adsorption of anionic species from the solution. The anionic species could be surface sulfate groups, residual surfactant (Aerosol OT) remaining from the latex preparation, or the (anionic) products of the dissolution of carbonic acid in the latex solution, which can partition to the latex surface. The interactions between the electronegative regions on a latex surface would be expected to diminish at higher electrolyte concentrations due to the shielding of the neighboring localized asymmetric charge distributions by both counterions and co-ions.17,19,21,29 Consistent with the experimental observations is the fact that the measured hydrodynamic size is proportional to the dielectric constant of the solution. The measured hydrodynamic size decreased as the dielectric constant decreased (due to the increase in the bulk electrolyte concentration). It is possible that the relationship between the latex size and the dielectric constant is due to intraparticle interactions. While the presence of ions may decrease the repulsive interactions between electronegative regions of the surface, it would also be expected to unscreen the attractive intermolecular van de Waals interactions within a particle. Therefore, as the dielectric constant was lowered, the attractive forces within the particles increased, causing a decrease in the size of the latex. This explanation is consistent with the observation that the transmission electron microscopy (TEM) sizes for some commercial polystyrene latexes were considerably less than for the PCS sizes of the latexes in aqueous solution.16 The dielectric constant of the environment of latex samples during TEM measurements is approximately 1, while in solution values of the dielectric constant of the medium are greater by 1 to 2 orders of magnitude. The expandable outer layers of latexes A170 and NA143 impart a steric stability to these particles. For the latexes to aggregate, the outer layers of two particles would have to come in contact and overlap, which would be entropically unfavorable.30 Latex A170 also has a carboxylated surface which contributes an electrostatic component to its stabilization mechanism as the carboxyl groups are deprotonated. The outer expandable layer is modeled as a hydrated acid rich shell surrounding a dense polymer core. Such a layer is expected to posess steric stability properties of an adsorbed polymer as well as electrostatic repulsion due to the presence of charged acid groups. The combined idea was termed “electrosteric” by one of us (D.R.B.) at (22) Karplus, M.; Weaver, D. L. Nature 1976, 260, 404. (23) Levitt, M.; Chothia, C. Nature 1976, 261, 552. (24) Creighton, T. E. Prog. Biophys. Mol. Biol. 1978, 33, 231. (25) Derjaguin, B. V.; Landau, L. Acta Physicochim. URSS 1941, 14, 633. (26) Verwey, E. J. W.; Overbeek, J. T. G. Theory of Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1948. (27) Elimelech, M.; O’Melia, C. R. Colloids Surf. 1990, 44, 165. (28) Napper, D. H. J. Colloid Interface Sci. 1977, 58, 390. (29) Martell, A. E.; Smith, R. M. Critical Stability Constants; Plenum Press: New York, 1974. (30) Darvell, B. W.; Leung, V. W. H. Chem. Br. 1991, 1, 29.

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the 1972 Gordon Conference on Coatings and subsequently published in a book arising from the 1978 ACS Miami meeting.17 Since that time the term has been widely accepted in the literature.31 (B) Dependence of the Size on the Colloid State Variables pH and pλ. At sufficiently high salt concentrations the variation in the ionic strength as the solution pH is adjusted becomes very small. This can be seen in Figure 3, where the relationship between pH and pλ for solutions with fixed concentrations of added electrolytes is presented. As has been shown thus far in this work, much of the most interesting hydrodynamic behavior occurs when little or no extraneous salt has been added to the solution, and where the conductivity of the solution can change by as much as 3 orders of magnitude as the pH is varied while the ionic strength with respect to KCl is constant. The fingerprinting method reveals an interesting pattern that is not shown by the classical method of a single pH-sweep at high and nearly constant pλ. The solution conductivity is representative of the electrolytic composition of a particular solution, while the ionic strength is a calculated quantity and does not necessarily represent the complete nature of the ionic distribution in solution. Some implicit assumptions are made in determining the ionic strength, such as the electrolyte being fully dissociated and the ions being independent. It is further assumed that the ions are distributed uniformly throughout the medium independent of colloidal content and composition.13 Also, the in situ ionic strength will differ from the calculated ionic strength if specific ion adsorption occurs. The conductivity variable (pλ) represents the dynamic electrolytic nature of the colloidal medium since the solids concentration is very small. The ionic strength does not reflect the change in electrolytic environment caused by changes in salt concentration from changing pH. (1) Constant Added KCl Concentrations. The paths traced in pH, pλ space for solutions of latexes A170 and NA143 which have constant concentrations of added KCl were presented in Figure 3. Each curve represents a different constant concentration of KCl which had been added to the solutions, while the pH has been controlled by adding either HCl or KOH to the solutions. Also shown in the figure is the SLIS (system limited ionic strength) curve. The measured solution conductivity varied by over 3 orders of magnitude as the pH was varied in the absence of added KCl. The magnitude of the variation in the conductivity with pH decreased with increasing concentrations of added KCl. When the concentration of added KCl was held constant at 30 mM, the conductivity was virtually constant over the pH range from 2 to 12. A theoretical treatment of the relationship between solution conductivity and the bulk electrolyte concentration has been published by Marlow and Rowell.13 To a first approximation the conductivity is proportional to the bulk electrolyte concentration. However, the condition of a constant concentration of an added salt to a series of solutions with different pH values and the case of constant ionic strength are not the same. Profiles of the hydrodynamic diameter for latexes A170 and NA143 along the path representing constant concentrations of added KCl are presented in Figures 4 and 5. The expandable nature of the particles can be clearly seen from these profiles. In the case of SLIS and 0.1 mM KCl, latex A170 exhibits a two-stage expansion as the pH increases from a value (31) Napper, D. Polymeric Stabilization of Colloidal Dispersions; Academic Press, New York, 1983.

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Table 1. Relative Dissociation Ratios for Surface Bound Carboxyl Groups as a Function of pHa pH 2 3 4 5 6 6.25 8 12

[(surface)-COO-]/[(surface)-COOH] 5.62 × 10-3 5.62 × 10-2 0.562 5.62 56.2 100 5.62 × 103 5.62 × 107

a The surface carboxyls are assumed to have a pK of 4.25, which a is the pKa of acrylic acid.

of 2. The first expansion occurs around a pH value of 5.5, followed by a greater expansion around a pH of 10. For latex A170 it was also observed (Figure 4) that as the concentration of added KCl was increased, the magnitude of the alkaline maximum in the hydrodynamic size decreased and shifted to higher pH values, while the acidic maximum was suppressed. The magnitude of the maximum expansion of latex NA143 (no-acid) was also observed to decrease with increasing concentrations of added KCl (Figure 5). The total variation in the hydrodynamic diameter of latex NA143 was as much as 17 nm. This was a 14% increase in diameter for a control sample which was expected to be of constant size. This is the magnitude of the change in size as the pH is increased from 2 to 5.8 along the SLIS curve of Figure 5. The hydrodynamic diameter of latex A170 exhibited nearly identical behavior under the same conditions (acidic maximum). As the pH increased from 2 to 5.8 at SLIS, the hydrodynamic size increased by about 15 nm. This expansion between a pH value of 2 and a value of 5.5 was suppressed for both latexes A170 and NA143 as the concentration of added KCl to the supporting solution was increased. As previously mentioned, the mechanism of expansion in latex A170 occurs in two stages as the pH is increased from a value of 2. The dominant mechanism in the range from 2 to 6 is similar to the expansion mechanism for solutions of latex NA143 in the same pH range. The pKa of acrylic acid is 4.25.32 If the pKa of the surface bound acrylic acid is assumed in the first approximation to behave the same as the free acid in solution, the ratio of surface carboxylate ion to undissociated surface carboxyls would increase from 0.562 to 56.2 as the pH was increased from 4 to 6. The calculated ratios of ionized surface carboxyls to protonated surface carboxyls, assuming that the surface carboxyl has the same pKa as free acrylic acid, are listed in Table 1. The proposed mechanism for this acid to neutral expansion of latex A170 is the repulsive interaction between charged or partially charged (polar) regions of the surface layer that are not acidic as well as from dissociation of acidic groups. Under conditions of higher pH the acid/base chemistry of the surface layer is the primary source of expandable behavior. The cited ratio of unprotonated carboxyls to protonated carboxyls would increase from 56 to greater than 100 as the pH is increased from 6 to 6.25, based on a pKa value for acrylic acid of 4.25. The acid latex (A170) expands dramatically as the pH is increased from 6 to 10. This is due to the acidic nature of the outer layer of this latex, specifically to the deprotonation of surface carboxyl groups. In the highest pH range the hydrodynamic diameter of the acid-free latex decreased due to bulk ion effects rather than to a particular acidic or basic surface functionality. (32) Tjipangandjara, K. F.; Somasundaran, P. Colloids Surf. 1991, 55, 245-255.

(2) Cation Effect. The dependence on the hydrodynamic diameter of three different monovalent cations (K+, Na+, and Li+) along the same path in pH, pλ space is presented in Figure 6. The pH was controlled in the three systems studied by the addition of either HCl or the hydroxide of the particular cation, and each solution was 0.1 mM in the particular cation chloride salt. The general behavior of the hydrodynamic size as a function of pH was very similar for all three systems. More extensive data would have to be taken to establish a clear dependence on cation type. (3) Constant Solution Conductivity. It is shown in Figure 3 that holding the concentration of an added salt constant while the pH is varied is not the same as constant ionic strength. Calculated ionic strengths assume that all of the ions in solution are in the same electrochemical state and are insensitive to ion-specific interactive behavior, such as ion pairing or specific surface interactions. Assuming that the electrolyte is totally dissociated and that all the ions have identical electric potentials makes no allowances for complex ion formation or solvation effects. The contributions from weak acids or bases and slightly soluble salts also pose difficulties in calculating the ionic strength. This problem is greatest in dilute solutions and diminishes as the bulk concentration of strong electrolyte increases. It is apparent from the constant conductivity profiles of the hydrodynamic surface for latex NA143 shown in Figure 8 that the hydrodynamic diameter passes through a maximum at a pH between 5.5 and 6.0. This is indicative of a neutral surface layer with some inherent polarity. The direct proportionality between the concentration of KCl and the solution conductivity as discussed by Marlow and Rowell has been verified for solutions of a commercial polystyrene latex with a carboxylated surface.13 This suggests that a measured characteristic property (such as size) is better represented as a function of the measured solution conductivity than on the general and possible misleading quantity of ionic strength, which would not distinguish between HCl and KCl. The dependence of the hydrodynamic diameter of latex A170 on pH under conditions of constant solution conductivity (or constant pλ) shown in Figure 7 is similar to the dependence of size on pH under conditions of constant concentration of added KCl. The maximum expansion was seen in the curve of minimum pλ, and the magnitude of the maximum decreased and shifted to higher pH as pλ increased. A limitation of this approach is that profiles of the hydrodynamic diameter at lower values of pλ scan increasingly narrower regions of pH space. In Figure 7 the minimum pλ value represented was 2.0. The twostage expansion mechanism is not seen because pλ values less than 2 were not considered. This point is quite clear in the profiles of Figure 3. By considering the functional dependence of individual PCS measurements on the pH and pλ of the sample solution in the fingerprinting approach, a fuller understanding of the surface chemistry and surface properties is achieved. Such a global representation of the measured hydrodynamic diameter gives a great deal of information on the colloidal systems studied in this work. (C) Time Study. (1) Latex NA143. It can be seen from a comparison of the hydrodynamic surface of latex NA143 that was generated from size measurements made 3 h after the solutions were prepared (Figure 2) and the surface generated after 8 weeks (Figure 11) that there was little change in the overall hydrodynamic behavior. The differential analysis of latex NA143 which is presented in Figure 12 shows that the range of the variation in the hydrodynamic size with time was 5 nm or less, which is

1986 Langmuir, Vol. 13, No. 7, 1997

close to the experimental error. This is not much of a difference in comparison to the time effects that were observed with the acidic copolymer latex. The least reliable regions of any of the hydrodynamic surfaces are the edges, which represent the limits of the experimentally accessible conditions. The greatest variation found in the differential analysis of latex NA143 occurs at the edges of the surface and fingerprint. (2) Latex A170. It is apparent from a comparison of the hydrodynamic surface for the initially prepared solutions of latex A170 (Figure 1) and the hydrodynamic surface for the same samples after they have aged for 8 weeks (Figure 9) that some extraordinary changes have occurred. Over the same time period the change in the hydrodynamic diameter that was observed for solutions of latex A170 with pH values of 6.5 or less was quite small (less than 5 nm) with the hydrodynamic diameter being about 145 nm. This represents a variation in the diameter of less than 4% over 8 weeks. The low pH expansion in the acid latex appeared to be the same as the low pH expansion in the no-acid latex. This suggests that the low pH expansion in both latexes is the same. Further research should be carried out to explore the low pH expansion since the same pattern appears in the surfactant-free latexes studied in other work.16 Previous work did not resolve the low pH expansion, but a re-examination of earlier work provides added evidence of a real change in size: (1) In the ultracentrifuge

Prescott et al.

work of Bassett and Hoy17 Ba(OH)2 caused a compression below core size at pH 5.5 and higher; NaOH showed similar core compression above pH 8 on a no-acid standard latex and a polystyrene latex; and two latexes designed to be nonexpanding were compressed in a similar manner at high pH. (2) The angular intensity light scattering, which measures the core size, clearly showed that the core was smaller at high pH than at low pH,19 but only four pH values were sampled so that the details of the trend were not clear within the limits of experimental error. The self-consistency of the present work, revealed by the fingerprinting approach, is the strongest evidence to date for the changes in hydrodynamic size reported. There was a considerable change, however, in the regions of pH, pλ space where the maximum expansion in the 3 h old samples had been observed. The maximum size on the hydrodynamic surface for the 3 h old samples was 209 nm at a pH of 10 and a pλ of 2. After 8 weeks the hydrodynamic size at the same point in pH, pλ space was 160 nm. The slow depletion of low molecular weight species from the latex surface could result in a decrease of the electrostatic charge and subsequent contraction of the surface layer. Acknowledgment. We are grateful to the Brookhaven Instrument Corporation for the use of a BI-90. The accuracy and self-consistency of Surfer were tested in some detail by Peter Tsang. LA961045+