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Influence of Particle Curvature on Polymer Adsorption Layer Thickness James A. Baker,’ Richard A. Pearson, and John C. Berg*t2 Department of Chemical Engineering BF-10, University of Washington, Seattle, Washington 98195 Received April 14, 1988. I n Final Form: November 3, 1988 The effect of particle radius ( R ) on the hydrodynamic thickness (6) of adsorbed polymeric stabilizers is determined by using photon correlation spectroscopy. Apparent adlayer thicknesses are reported for poly(ethy1ene oxide) homopolymers and ABA block copolymers (A = poly(ethy1ene oxide); B = poly(propylene oxide)) adsorbed on model polystyrene latices. For the poly(ethy1ene oxide) homopolymers, 6 shows a steady increase with particle radius that is greater than can be accounted for by the geometrical correction of Garvey et al., suggesting gradual structural changes with the radius of curvature. For the copolymers, the adlayer thickness generally increases with particle radius, but the dependence appears to be more complex. Introduction The use of adsorbed macromolecules to stabilize colloidal dispersions with respect to aggregation has motivated much research into the structure of adsorbed polymer^.^-'^ One aspect of the problem which has received relatively little attention is the apparent influence of particle size, or more generally, the radius of curvature of the adsorbent surface. Garvey et al.738reported apparent adlayer thicknesses of a fractionated, 88% hydrolyzed poly(viny1 alcohol)-poly(viny1 acetate) random copolymer (PVAA, M , = 67 000), adsorbed on a series of well-characterized polystyrene latex dispersions. The dispersions, all persulfate-initiated latices, ranged in radius from 40 to 260 nm. The technique used was photon correlation spectroscopy (PCS) (referred to by these authors as “intensity fluctuation spectroscopy, IFS”). One of the measured values was obtained by using ultracentrifugation. The results showed a steady increase in adlayer thickness with particle radius, although they displayed a scatter which was “outside the error that can be attributed to the mean value of [the radius] calculated from the Stokes-Einstein equation.” The value obtained by using ultracentrifugation fell comfortably on the line correlating the PCS data. (1) Present address: 3M Company, 3M Center, 208-1-01,St. Paul, MN 55144. (2) Author to whom correspondence should be addressed. (3) Sato, T.; Ruch, R. Stabilization of Colloidal Dispersions by Polymer Adsorption; Marcel Dekker: New York, 1980. (4) Napper, D. H. Polymeric Stabilization of Colloidal Dispersions; Academic Press: New York, 1983. (5) Hesselink, F. Th.; Vrij, A.; Overbeek, J. Th. G. J. Phys. Chem. 1971, 75, 2094. (6) Scheutjens, J. M. H. M.; Fleer, G. J. J.Phys. Chem. 1979,83, 1619; 1980, 84,178. (7) Garvey, M. J.; Tadros, Th. F.; Vincent, B. J. Colloid Interface Sci. 1974, 49, 57. (8) Garvey, M. J.; Tadros, Th. F.; Vincent, B. J. Colloid Interface Sci. 1976, 55, 440. (9) 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. (10) Cosgrove, T.; Vincent, B.; Crowley, T. L.; Cohen-Stuart, M. A. In Polymer Adsorption and Dispersion Stability; Goddard, E. D., Vincent, B., Eds.; ACS Symposium Series 240; American Chemical Society: Washington, DC, 1984; p 147. (11) Kato, T.; Nakamura, K.; Kawaguchi, M.; Takahashi, A. Polym. J. 1981, 13, 1037. (12) Technical Data o n PLURONIC Polyokr; BASF Wyandotte Corp.: Parsippany, NJ.
0743-7463/S9/2405-0339$01.50/0
Table I. Mean Particle Radius of Model Polystyrene Latices latex PCS radius RH,nm B 28.5 f 3 D 72.0 f 6 E 223.0 f 13 F 361.5 f 28 I 549.5 f 58
The dependence of adlayer thickness on particle radius, together with independent measurements of specific adsorption, led Garvey et al. to conclude that the volume of adsorbed polymer per unit area was constant (independent of particle radius). The effect of surface curvature was purely geometrical, and an effective adlayer thickness, aeR, corresponding to adsorption on an equivalent flat surface, could be computed as [ ( R + 6)3 - R 3 ]
= constant (1) 3R2 where R is the particle radius and 6 is the apparent adlayer thickness. Quite different results, on the other hand, have been reported recently by Ahmed et al.? who examined the curvature dependence of adlayer thickness for a commercial PVAA copolymer (Vinol 107, M , = 23 000, 99% hydrolyzed). Measurements were carried out on three polystyrene latices having mean diameters of 190,400, and 1100 nm. Apparent adlayer thicknesses were determined by using capillary viscometry and, for the two smaller sizes, PCS. Both techniques yielded the same results. Adsorption density was found to be constant with particle radius, in agreement with Garvey et al., but apparent adlayer thickness depended much more steeply upon it than could be explained by the geometric correction of eq 1. The authors postulated changes in the configuration of the adsorbed polymer molecules with particle surface curvature. It thus remains unresolved whether or not the apparent increase in adsorption layer thickness with particle radius observed for PVAA random copolymers arises strictly from geometrical constraints, and the importance of particle curvature on the adsorption configuration adopted by stabilizers other than PVAA is untested. The objective of this work is to examine the importance of particle curvature on the adsorption layer thicknesses obtained for other classes of polymers, particularly linear homopolymers 6,ff
=
0 1989 American Chemical Society
Baker et al.
340 Langmuir, Vol. 5 , No. 2, 1989 Table 11. Properties of PEO Homopolymers and PEO-PPO Copolymers total molar mass M ,
PEO SE-2 SE-5 SE-8 SE-15 SE-30 SE-70 Pluronic F68 F98 P104 P105 F108
GPC 17 000 35 000 80 000 135 000 259 000 668 000
total molar mass 8 350 13 000 5 850 6 500 14 000
LS 18 000 39 000 86 000 145 000 252 000 594 000 PEO molar mass 6 600 10 250 2 600 3 250 10 750
MWIM,
1.10 1.07 1.02 1.03 1.04 1.04
PPO molar mass 1750 2750 3250 3250 3250
and block copolymers, and i n particular, t o assess the generality of t h e simple geometrical correction proposed by G a r v e y e t al.
Materials and Methods The model dispersions selected for study are listed in Table
I. They were polystyrene microspheres obtained from Polysciences, Inc. (Warrington, PA). The model dispersions were selected to cover a diameter range between 50 and lo00 nm. They were prepared by persulfate-initiated emulsion polymerization of styrene and thus were inherently electrostatistically stabilized by surface sulfate groups. All latices were supplied as aqueous dispersion a t 2.5 wt % solids and stated by the manufacturer to be "free of other electrolytes, residual styrene monomer and surfactants". Thus they were used as received, without additional cleaning. Water used in the preparation of dilute dispersions and polymer solutions was triply distilled. Two model polymer systems, listed in Table 11, were chosen for study: a family of monodisperse linear homopolymers and a series of commercial ABA block copolymers. Linear homopolymers of poly(ethy1ene oxide) (PEO), spanning a 3-decade range of molar mass, were obtained from Polymer Laboratories Ltd. (Nr. Shrewsbury, Shropshire, UK). These polymers, selected to serve as a reference system, were extremely well-characterized PEO fractions manufactured by Toyo Soda for use with gel permeation chromatography (GPC) standards. The molar masses and polydispersity indices (M,/M,,) were independently obtained by using GPC, light scattering, and viscosity measurements.'0." The molar masses referred to in the present study were determined by using GPC. All of the homopolymers exhibited a very narrow molar mass distribution (M,/M,, < Ll),with the highest degree of polydispersity indicated by the very low molar mass fractions (SE-2 and SE-5). The ABA block copolymers were commercial poly(ethy1ene oxide-co-propylene oxide) (PEO-PPO) ABA block copolymers manufactured by BASF Wyandotte Corp. (Wyandotte, MI) and marketed as nonionic, water-soluble surfactants named Pluronics.'2 These materials were expected t o adsorb on hydrophobic polystyrene with the central P P O block attached as a train to the surface and the PEO tails extending out into bulk solution under good solvency conditions. The primary disadvantage of the Pluronics as model systems is that they are commercial samples of unknown purity. Accordingly, the molar masses presented in Table I1 are only approximate, calculated on the basis of the stoichiometry of the polymerization (the two PEO blocks in the Pluronic molecular formula are assumed to be statistically equal in length). In addition, the polydispersities of these samples are unknown. Photon correlation spectroscopy (PCS) was used to determine the mean diffusion coefficient for all model dispersions in the presence and absence of adsorbed stabilizer. The diffusion coefficient was evaluated by using a cumulants fit t o the normalized autocorrelation function obtained for each sample. A relative estimate of the spread of the distribution of diffusion coefficients (polydispersity index) was obtained by normalizing
F i g u r e 1. Schematic illustration of the geometrical component of the curvature dependence of adlayer thickness. the value of the second cumulant by the square of the first cumulant.13 The apparent hydrodynamic radius (RH) of the particles (or polymer-coated particles) was calculated from the mean diffusion coefficient (D)by application of the Stokes-Einstein equation: RH = kT/(GapD) (2) where k is the Boltzmann constant, Tis the absolute temperature, and p is the viscosity of the dispersion medium. Equation 2 provides a direct method for evaluating the mean hydrodynamic radius of a collection of colloidal particles undergoing Brownian motion. Measurements carried out on both bare and polymercoated particles yield the apparent adsorption layer thickness as the difference in apparent hydrodynamic radii between polymer-covered and bare particles. The PCS measurements were carried out on a Brookhaven Model B1-2030,72-channel digital correlator. The correlator was used in conjunction with a Spectra-Physics Model 124B 15-mW He-Ne laser and a Model BI-2OOSM motorized goniometer. Reference PCS conditions (scattering angle = 90°, latex cong/mL, p H 3.0, T = 25 "C) were used for centration = 1.5 X all measurements. The p H value of 3.0 corresponded to a solution ionic strength equivalent to the 0.001 M 1:l electrolyte added by Garvey et al. and Ahmed et al. to suppress electroviscous effects. Determinations were made 1 and 24 h after polymer addition. The values obtained a t 24 h, which correspond t o equilibrium adsorption configurations for all polymers listed in Table 11,were used in evaluating polymer adlayer thicknesses. Measurements were carried out at as a function of polymer molar mass a t a fixed bulk polymer concentration corresponding to a position on the adsorption plateau for each class of polymer. These concentrations were determined from measurements of the adsorption thickness isotherms for each polymer on the smallest diameter latex and corresponded to 5 x g/mL for the Pluronics and 5 X g/mL for the PEO homopolymer^.'^
Results and Discussion Mean h y d r o d y n a m i c radii (RH),determined b y using PCS for e a c h of the model dispersions, a r e summarized i n T a b l e I. Standard deviations about the mean r a d i u s ( a t the 95% confidence level) are r e p o r t e d f o r all model dispersions. In general, all dispersions m a y be considered monodisperse (polydispersity index < 1.05), although t h e spread about the mean radius increases with particle size. Measurements of the a d s o r p t i o n layer thicknesses on each of the model dispersions were carried out as a function of molar mass for the PEO linear homopolymers and Pluronic ABA copolymers listed i n Table 11. The results are plotted in Figure 2 for the linear homopolymers and Figure 3 for the Pluronic ABA Copolymers. N o t e that the data for the Pluronics are plotted as a function of the molar m a s s of hydrophile, since the PPO block is assumed t o interact strongly with the surface, and contribute negligibly to the a d s o r p t i o n layer thickness. These data, which were all o b t a i n e d b y the same opera t o r o n a single instrument using reproducible techniques, i n d i c a t e t h e relatively s t r o n g dependence of a d l a y e r thickness o n particle size. Least-squares lines for all the latices are sketched in Figure 2 on logarithmic coordinates. (13) Weiner, B. B. In Modern Methods Barth, H. G.; Ed.; Wiley: New York. (14) a
of
Particle Size Andysis;
Langmuir, Vol. 5, No. 2, 1989 341
Influence of Particle Curvature on Polymers I
I
I
,I
I
7
4
J
size are, within experimental error, constant at 0.52 f 0.06. Scatter in the data prevents determination of any dependence of the slope on particle size. In order to test the hypothesis that the influence of particle radius on adlayer thickness is purely geometrical, eq 1was used to evaluate effective adlayer thicknesses (aeE) for the data presented in Figure 2. The resulting effective adlayer thickness data are plotted in Figure 3. The effect of the curvature correction tends to bring the data together, but a significant degree of particle radius dependence remains. The net effect, illustrated schematically in Figure 1,is for particles of smaller radius (lower radius of curvature) to allow polymer segments greater access to the regions immediately adjacent to the particle surface, resulting in an effectively higher segment density near the surface but a lower adsorption layer thickness. In the limit of a flat surface, polymer adsorption at full surface coverage will act to exclude some of the segments from the region adjacent to the adsorbent surface. Consequently, the local segment density will be lower, but the mean extension of the polymer chains away from the particle surface will be effectively greater. The curvature correction is also seen to strengthen the dependence of apparent adlayer thickness on molar mass, as indicated by the higher average slope of the data in Figure 3 relative to Figure 2. The data in Figure 3 can be least-sqaures fit to yield a Mw0,65 dependence of the effective adlayer thickness. The increase in magnitude of the molar mass proportionality constant is greatest for the smallest particle sizes, as expected from the form of eq 1. Garvey et al. reported a Mw0.5dependence of 6 and a MW1.l4 dependence of 6,, for partially hydrolyzed PVAA adsorbed on p o l y ~ t y r e n e . ~ - ~ JThey ~ - l ~ attributed much significance to the MW1,l4 dependence for effective PVAA adlayer thicknesses evaluated by using eq 1. This molar mass dependence was theoretically predicted by using specific adsorption data for PVAA/latex systems and an intrinsic viscosity correlation for polymer radius of gyration obtained for isolated chains in free ~ o l u t i o n .In ~ addition to the problems associated with using free polymer statistics to predict the configuration of adsorbed polymers, there is no physical basis for expecting a first-power molar mass dependence of the layer thickness. Indeed, recent statistical thermodynamic theories of polymer adsorption5@ predict a Mw0.5 dependence of adlayer thickness in both athermal solution and 0 solvents. The data obtained for the Pluronics, while exhibiting greater scatter, indicate trends similar to the homopolymers, with adlayer thickness increasing with both total molar mass and molar mass of PEO. Interestingly, the PEO molar mass dependence of the Pluronic adlayer thickness apparently decreases with increasing particle size, starting at a Mw(PE0)0.69 dependence for the smallest latex and becoming essentially independent of PEO molar mass for the largest particles. The decreasing dependence of thickness on molar mass for the largest diameter particles suggests that the PEO tails may adopt a flatter conformation on these particles. It should be noted, however, that there are relatively large experimental errors involved in determining the small adlayer thicknesses involved in the copolymer systems, particularly for the relatively (15) Vincent, B. In Science and Technology of Polymer Colloids; Poehlein, E. W., Ottewill, R. H., Goodwin, J. W., Eds.; NATO AS1 Series; Nijhoff Boston, 1983; Vol. 2, p 335. (16) Cowell, C.; Vincent, B. In T h e Effect of Polymers on Dispersion Properties; Tadros, Th. F., Ed.; Academic Press: New York, 1982;p 263. (17) Tadros, Th. F. In T h e Effect of Polymers on Dispersion Properties; Tadros, Th. F., Ed.; Academic Press: New York, 1982; p 1. (18) Lips, A.; Staples, E. Faraday Discuss. Chem. SOC.1978, 65, 325.
Baker et al.
342 Langmuir, Vol. 5, No. 2, 1989 large-diameter particles (since a difference technique is used). Data obtained for the PEO homopolymers, for which the measured adlayer thicknesses are typically of the order of 20-100 nm, were not affected by this problem. Measurements of specific adsorption for Pluronics F68 and F108 on the 550-nm latex yielded plateau adsorption values of 9 X g/m2 and 1.35 X g/m2, re~pective1y.l~ These are comparable to the values of 9.2 X lo4 g/m2 and 1.15 X g/cm2 obtained by Kayes and Rawlinslg for adsorption of these polymers on a 312-nm polystyrene latex. It thus seems reasonable to conclude that the specific adsorption for Pluronics on polystyrene latex dispersions is independent of particle size. It is clear for both the homopolymers of poly(ethy1ene oxide) and the block copolymers studied that the geometrical correction for particle curvature suggested by Garvey et al. is not sufficient to explain the results obtained and that additional structural changes are indicated. There may, for example, be specific polymer/particle interactions that can affect the adsorption configuration. Such interactions include the hydrogen bonding which can occur between PEO ether groups and surface hydroxyl or sulfonic acid groups. They can also include specific polymer segment/surface and segment/solvent interactions, as exhibited by the PPO and PEO blocks of the Pluronics. Ahmed et al.9120recently offered the following explanation for an increase adlayer thickness with increasing particle radius, even when the adsorption per unit area remains a constant. The same adsorption per unit area could result for different particle sizes if the total number of loops decreases, such that the loops are, on the average, longer and thicker on the larger particles. Alternatively, the same adsorption per unit area could arise if tail or train segments are thrown into loops on the larger particles. It is also possible that both of these mechanisms are simultaneously involved in increasing the loop size (and hence the hydrodynamic thickness) with increasing particle radius. The implication of these mechanisms, if they are in fact at work, is that polymer adsorption on larger particles is relatively weaker than for the smaller particles. Direct evidence in support of this theory was obtained by Ahmed?O who measured the strength of adsorption of low molar mass ( M , = 35 SOO), 99% hydrolyzed PVAA (Vinol 107) on polystyrene by using microcalorimetry. The exothermic heat of adsorption was found to decrease from 0.4377 J / m 2 on a 190-nm-diameterlatex, to 0.3233 J / m 2 for a 400-nm latex, with a further decrease to 0.2717 J/m2 on a 1100-nm latex. In addition, Ahmed noted that the PVAA achieved adsorption equilibrium more rapidly on the larger particles compared to the smaller particle sizes, suggesting that the adsorption process was diffusion limited. A similar effect of particle size, polymer structure, and polymer molar mass on the time required to attain equilibrium polymer conformation at the solid/liquid interface (19)Kayes, J. B.; Rawlins, D. A. Colloid Polym. Sci. 1979, 257, 622. (20) Ahmed, M. S. 'Adsorption and Stabilization of Polymers and Latex Particles"; Ph.D. Dissertation Lehigh University, 1984.
was observed in the present work. The Pluronics achieved their equilibrium adsorption configuration, as reflected by the adsorption layer thickness, within a few hours. The higher molar mass linear homopolymers, however, required 24 h or longer to reach an equilibrium thickness. This slow approach to an equilibrium conformation was exacerbated by decreasing the particle radius. For example, SE-150 linear homopolymer ( M , = 1190000) required almost 1 week to acquire an equilibrium adsorption layer thickness when adsorbed on latex B (RH = 28.5 nm) but achieved an equilibrium conformation in less than 24 h on latex I (RH = 550 nm).14 The experimentally observed decrease in adsorption layer thickness with time is consistent with a change in adsorption configuration. Thus, high molar mass PEO homopolymers initially adsorb as loops, trains, and highly extended tails, regardless of particle size. On large particles, where close packing of adsorbed train segments effectively precludes access of extended tail segments to surface regions (Figure l),the initial adsorption configuration will not change significantly with time. On the smaller particles, however, the high curvature allows access of tail segments to regions near the surface. Tail segments continue to undergo three-dimensional diffusion until they access unsaturated surface sites and adsorb additional segments in trains. Such rearrangements, which do not change the adsorbed amount, will only occur if the free energy change of adsorption, as governed by the energetics of segment-surface, segment-segment, and segment-solvent interactions, is negative. The net result for favorable adsorption energetics will be a shift from an extended tail configuration to loops and shorter terminal tails, accompanied by a decrease in equilibrium adsorption layer thickness.
Conclusions A significant effect of particle radius on the measured adsorption layer thickness has been demonstrated for both PEO linear homopolymers and PEO-PPO-PEO copolymers. The general effect of increasing particle curvature is to increase the measured adlayer thickness for all of the polymers studied. The molar mass dependence of adlayer thickness varies with radius of curvature, and the range of this variation appeared to depend upon polymer structure and adsorption configuration. The first-order geometrical correction proposed by Garvey et al. has been shown to systematically undercorrect for the total effect of changing particle radius for the PEO homopolymers, while the effect of particle radius on the copolymer adlayer thicknesses (for the systems studied) is more complex. These results suggest that more elaborate corrections are needed to quantify the influence of particle curvature on adlayer thickness.
Acknowledgment. This research was supported in part by a grant from the IBM Corp., the Washington Technology Center, and the UW Center for Surfaces, Polymers and Colloids. Registry No. PEO, 25322-68-3; (EO) (PO) (block copolymer), 106392-12-5; polystyrene, 9003-53-6.
