Analysis of Surfactants Adsorbed onto the Surface of Latex Particles

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Langmuir 2000, 16, 4094-4099

Analysis of Surfactants Adsorbed onto the Surface of Latex Particles by Small-Angle X-ray Scattering S. Seelenmeyer and M. Ballauff* Polymer-Institut, Universita¨ t Karlsruhe, Kaiserstrasse 12, 76128 Karlsruhe, Germany Received July 26, 1999. In Final Form: February 7, 2000 A comprehensive study of the process of adsorption of a nonionic surfactant C18E112 onto poly(styrene) (PS) latex particles by small-angle X-ray scattering (SAXS) is presented. The PS latexes (particle radii 35 and 71 nm) employed in this investigation bear no chemically bound surface charges. The analysis of the process of adsorption by SAXS demonstrates that the point of saturation of the surface may be determined directly from the scattering curves. Free micelles are formed beyond saturation, and no second layer of the surfactant is built up at higher concentrations of the surfactant. Any association of the micelles with the covered latex particle can be ruled out as well. Moreover, an analysis of the radial structure of the surface layer in terms the zeroth and the second moment of the electron density of the layers along the radial direction is given. Both moments can directly be obtained from the SAXS data. The zeroth moment of the excess electron density corroborates the finding that the surfactant is firmly adsorbed onto the surface of the particles. The average extension of the adsorbed layer (2-4 nm) as express through the second moment increases with the amount of adsorbed surfactant. This points to a stretching of the chains due to their mutual interaction when the point of saturation of the surfaced is approached.

Introduction Latex particles which have a spherical symmetry are nearly ideal objects for studies by small-angle neutron scattering (SANS)1 and small-angle X-ray scattering (SAXS).2 All structural information is embodied in the radial distribution F(r) of the scattering length density which determines the scattering amplitude B(q) through1

B(q) ) 4π

∫0R[F(r) - Fm]r2

sin(qr) dr qr

(1)

Here R is the radius of the particle whereas Fm denotes the scattering length density of the dispersion medium. Hence, for a system of noninteracting particles the scattering intensity I(q) (q ) (4π/λ) sin(θ/2), where θ is the scattering angle and λ is the wavelength) of one particle follows as I(q) ) B2(q) and can directly be used to determine the radial structure of the particles. The forward scattering I(0) is uniquely determined by the overall contrast Fj - Fm where Fj is the average scattering length density defined by

∫0R[F(r) - Fm]r2 dr Fj ) ∫0Rr2 dr

(2)

If the contrast of the latex particles against the surrounding medium is low, the process of adsorption of polymers or surfactants with higher scattering length density onto these particles can be studied easily by SANS or SAXS. When the contrast of the core particles is matched, the observed scattering intensity I(q) derives solely from the adsorbed layer. The scattering length density profile obtained from this analysis may be * To whom all correspondence should be addressed: e-mail, [email protected]. (1) Glatter, O., Kratky, O., Eds. Small Angle X-ray Scattering; Academic Press: London, 1982. (2) Higgins, J. S.; Benoit, H. C. Polymers and Neutron Scattering; Clarendon Press: Oxford, 1994.

converted into the volume profile of the adsorbed polymer or surfactant which extends into the aqueous phase. If the thickness d of the adsorbed layer is sufficiently large, scattering experiments will yield data at values of qd high enough to discern among different radial profiles of the layer. In principle, scattering methods are therefore capable of furnishing comprehensive information on the structure of the surface layer. Adsorption onto the surface of latex particles has been studied by a number of authors using SANS.3-7 By use of partially deuterated latex particles or mixtures of H2O and D2O, the contribution of the core particle to the measured scattering intensity can be minimized and the scattering signal is mainly due to the surface layer. The data obtained in this case may be analyzed according to the scheme devised by Auroy and Auvray8-10 for polymers affixed to flat surfaces. An important point of this analysis is the proper treatment of scattering arising from the fluctuations within the layer structure which may become the leading contribution at the high q-values. Up to now, SAXS has hardly been used to study the process of adsorption onto latex particles. The problem of SAXS is given by the fact that the contrast of dispersed particles cannot be changed as easily as in the case of SANS investigations. Recently it has been shown, however, that SAXS is well-suited to monitor the adsorption of surfactants onto poly(styrene) (PS) latex particles.11,12 (3) Ottewill, R. H. Prog. Colloid Polym. Sci. 1992, 88, 49 and further references given there. (4) Harris, N. M.; Ottewill, R. H. White, J. H. In Adsorption from Solution; Ottewill, R. H., Rochester, C. H., Smith, A. C., Eds.; Academic Press: London, 1983. (5) Ottewill, R. H.; Sinagra, E. MacDonald, I. P.; Marsh, J. F.; Heenan, R. K. Colloid Polym. Sci. 1992, 270, 602 and further references given therein. (6) Fleer, G. J.; Cohen Stuart, M. A.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B. Polymers at Interfaces; Chapman and Hall: London, 1993. (7) Griffiths, P. C.; Cosgrove, T.; Shar, J.; King, S. M.; Yu, G.-E.; Booth, C.; Malmsten, M. Langmuir 1998, 14, 1779. (8) Auroy, P.; Auvray, L. J. Phys. II 1993, 3, 227. (9) Auroy, P.; Auvray, L. Langmuir 1994, 10, 225. (10) Auroy, P.; Auvray, L. Macromolecules 1996, 29, 337. (11) Bolze, J.; Ho¨rner, K. D.; Ballauff, M. Langmuir 1996, 12, 2906.

10.1021/la990998f CCC: $19.00 © 2000 American Chemical Society Published on Web 04/03/2000

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Because of the low contrast of PS latexes in water (6.3 e-/nm3; refs 13 and 14) SAXS investigations of PS latexes are comparable to SANS studies in the immediate neighborhood of the match point. Previously, the adsorption of the nonionic surfactant Triton X-405 and of sodium dodecyl sulfate (SDS) on the surface of PS particles was studied by SAXS. The scattering curves measured at different concentrations of the added surfactant allowed us to follow the process of gradual coverage of the surface of the particles. In this paper we present a continuation of our previous SAXS studies11,12 of the adsorption of surfactants onto PS latex particles. We use the nonionic surfactant C18E112

which leads to adsorbed layers where the hydrophilic PEO chains extend into the water phase. The main emphasis lies on the analysis of the radial distribution of the hydrophilic PEO chains. In particular, we are interested in a possible stretching of the hydrophilic chains due to their mutual interaction. Two PS latexes differing widely in size (35 and 71 nm radii) will be studied here. A possible influence of the curvature of the surface onto the process of adsorption can hence be discussed. An improved Kratky camera presented recently15 allows measurement of the scattering intensity down to smaller scattering angles (q g 0.03 nm-1) with excellent resolution. This gives the opportunity to investigate particles up to a diameter of 200 nm. The particles used here bear no chemically bound surface charges16,17 as, e.g., sulfate or carboxyl groups, but are stabilized only by a small amount of SDS. Experimental Section

Figure 1. Comparison of the desmeared SAXS intensities obtained from the PS core latex (small core, R ) 35 nm) and from the same core latex covered with different amounts of the surfactant C18E112: (a) data taken up to saturation of the surface; (b) data taken beyond saturation of the surface.

All solvents were analytical grade and used as received. Stearylic acid chloride (Fluka, >99%), pyridine (Fluka, >99%), and poly(ethylene) glycolmonomethyl ether 5000 (Fluka) were used without further purification. The surfactant C18E112 was synthesized by esterification of poly(ethylene) glycolmonomethyl ether with stearylic acid chloride in the presence of pyridine. The resulting surfactant was purified carefully by dialysis. Its purity was checked by reverse high-performance liquid chromatography (HPLC) (RP-18-column, solvent acetonitrile/dimethylformamide 74/26 by volume, isocratic) and by 1H NMR. Its critical micelle concentration (cmc) is located at approximately 10-6 M, which is much lower than the concentrations employed in this study. The PS latexes used here have been synthesized as described recently.16,17 The particles have no chemically bound surface charges and are solely stabilized by SDS. After synthesis the latexes are purified by extensive dialysis against H2O. This procedure ensures that only a small amount of SDS necessary to stabilized the particles is left in the latexes. The surfactant was added to the PS core latex with gentle shaking. Previous measurements had shown that equilibrium is established very quickly in these systems.11,12 In the following the concentrations of the surfactant are related to the mass of

the core latex. As an example, 60 mg/g indicates that the total amount of the surfactant C18H112 is 60 mg/g of PS particles in the latex. All SAXS measurements have been conducted using the improved Kratky camera described recently.15 The raw data have been corrected for the scattering of the serum and of the sample holder. Desmearing of the scattering curves was done as described in refs 14 and 15. In all cases to be discussed here absolute scattering intensities have been obtained.14 For better comparison with SANS data all intensities are expressed in cm-1. All intensities have been normalized to the volume fraction φ which follows from the weight concentration and the partial specific volume of the particles (0.95 cm3/g). As discussed in recent reviews,13,14 the effect of interparticular interference is restricted to the region of smallest q values. At higher q the influence of particle interaction can be safely dismissed.13 Hence, all measurements have been done at 7 wt % without the necessity of extrapolation to vanishing concentration (cf. the discussion of Figure 7 of ref 13). Densities of latexes and of solutions of the surfactant C18E112 have been measured using a DMA-60 densitometer (Paar, Graz, Austria).

(12) Bolze, J.; Ho¨rner, K. D.; Ballauff, M. Colloid Polym. Sci. 1996, 274, 1099. (13) Ballauff, M.; Bolze, J., Dingenouts, N.; Hickl, P.; Po¨tschke, P. Macromol. Chem. Phys. 1996, 197, 3043. (14) Dingenouts, N.; Bolze, J.; Po¨tschke, D.; Ballauff, M. Adv. Polym. Sci. 1999, 144, 1. (15) Dingenouts, N.; Ballauff, M. Acta Polym. 1998, 49, 178. (16) Ottewill, R. H.; Satguranthan, R. Colloid Polym. Sci. 1987, 265, 845. (17) Weiss, A.; Dingenouts, N.; Ballauff, M.; Senff, H.; Richtering, W. Langmuir 1998, 14, 5083.

Process of Adsorption. Two latexes have been investigated here: The smaller one had a radius of 35 nm whereas the larger one had a radius of 71 nm. Due to the method of synthesis,16,17 the latex particles bear no chemically bound charge and are stabilized solely by the adsorbed SDS molecules. To discuss the effect of added surfactant onto the measured scattering intensities, Figure 1a,b displays the comparison of I(q) of the small

Results and Discussion

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Figure 3. Analysis of the radial excess electron density distribution of the core latex (small core, R ) 35 nm). The squares give the measured intensities whereas the solid line represents the best fit obtained by the fit procedure described in ref 15. The respective radial profile of the excess electron density is shown in the inset. The higher electron density at the surface of the core particles indicates a thin layer of the surfactant SDS used for the synthesis of the core latex.

Figure 2. Comparison of the desmeared SAXS intensities obtained from the PS core latex (large core, R ) 71 nm) and from the same core latex covered with different amounts of the surfactant C18E112: (a) data taken up to saturation of the surface; (b) data taken beyond saturation of the surface.

core latex to which various amounts of C18E112 per gram of PS have been added. Here Figure 1a gives the data below the point where saturation of the surface of the latex particles is reached. Figure 1b shows the data beyond the point of saturation. Figure 2 gives the same comparison for the latex with radius R ) 71 nm. It is directly obvious that the maxima of the scattering curves are shifted to smaller scattering angle (Figures 1a and 2a). Concomitantly, the intensity of the side maxima has raised considerably. Both effects are due to the adsorbed surface layer of the surfactant consisting mainly of poly(ethylene oxide), which has a much higher electron density (64 e-/nm3, determined from density measurements of the surfactant C18E112 in water) than PS (6.3 e-/nm3; taken from refs 13 and 14). Due to the increasing size of the layer, the radius of the particles is increased and the maxima of I(q) are shifted toward smaller q values. The point at which saturation of the surface of the core particles has been achieved is easily to detect by the constancy of the position of the maxima. This effect is clearly seen in Figures 1b and 2b. The point of saturation of the surface can be determined to ca. 70 mg/g PS in the case of the smaller latex which corresponds to an area of 10 nm2 per surfactant molecule of C18E112. In the case of the larger particles, a value of 38 mg/g PS results which corresponds to ca. 9 nm2 per molecule of the surfactant. Hence, despite the different diameters of both latexes, the surfactant molecules need the same area. This points to a minor influence of the curvature of the particles onto the process of adsorption in the case of C18E112. Further addition of surfactant will lead not only to an increase of the thickness of the surface layer but also to

the formation of free micelles.11,12 The present results shown in Figures 1 and 2 indicate that the free micelles formed beyond saturation will not stick to the surfaces or form hemimicelles on the surfaces. In this case the scattering intensity measured at small q would increase very much also beyond the point of saturation since the adsorbed micelles would contribute to the coherent scattering of the latex particles. Evidently, the scattering intensities of the surfactant-coated particles virtually superimpose throughout the q range shown in Figures 1b and 2b. The formation of hemimicelles can therefore be clearly ruled out. Structure of Adsorbed Layer. In the following the surface layer of the latex spheres will be analyzed with regard to the profile of the excess electron density derived from the SAXS data. The increase of the electron density of the surface layer is solely due to the hydrophilic tails of C18E112. Knowing the excess electron density of the PEO chain in aqueous solution, these data can be converted into profiles of the volume fraction of the PEO chains attached to the surface. For both latexes this analysis will be done for surfactant concentrations below the saturation of the surface. As shown further below, the strong adsorption of C18E112 allows disregarding of the contribution of free micelles to I(q) if the data are taken below saturation. This effect comes into play above the point of saturation as demonstrated in the previous section. Core Particles. As a first step in this analysis, the size and the polydispersity of the core latexes are determined by the method devised recently.15 For the smaller core latex the analysis of the SAXS intensities gives a numberaverage radius of 35 nm together with a standard deviation of the size distribution of 11.8%. The larger particles have a radius of 71 nm and a standard deviation of 6.0%. The residual SDS molecules used in the synthesis17 of the core latex leads to a thin shell of higher excess electron density on the surface which must be taken into account in all further analyses. This is in accord with recent findings on similar systems.11 As an example Figure 3 displays the scattering intensity of the large core particles together with the fitted intensity. The inset shows the profile of the excess electron density following from this fit. Covered Particles. We now turn to the analysis of the latex particles covered by the surfactant C18E112. The scattering intensity I(q) of a particle covered by a polymeric

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Figure 4. Determination of IPS(q) by a Porod plot of I(q) obtained from the PS core particles.

layer can in general be formulated as18

I(q) ) ICS(q) + ICS(q) + IPS(q)

(3)

Here ICS(q) is the part of I(q) due to the core-shell structure of the covered particles. It is given by the scattering intensity calculated according eq 1 for a particle having a homogeneous core and a shell with an excess electron density varying according to the volume profile of the adsorbed surfactant. In the case discussed here the PS core has a low electron density whereas the shell consisting of poly(ethylene oxide) chains is characterized by a high electron density, i.e., by a high contrast toward the dispersion medium water. Here model calculations showed that ICS(q) is dominated by the contribution of the shell except for smallest q values. The term Ifl(q) refers to the contribution by the thermal density fluctuations within the adsorbed layer. This term has first been discussed by Auroy and Auvray8-10 and may give an appreciable contribution at high q values if the layer is not too thin. For polymeric networks affixed to PS latex particles it may even become the leading term at highest scattering angles.18 In the q range employed here, however, its influence is expected to be negligible, in particular for the thin layers investigated in this study.6,8,19 Hence, this term will be disregarded in the present investigation. The third term IPS(q) denotes the scattering intensity which originates from the density fluctuations of the solid PS of the core.15 This term can easily be determined by SAXS measurements of the core particles and subtracted from I(q) of the covered particles. It must be noted that all three terms add up independently; there is no cross term. This is due to the fact that these intensities originate from statistically independent fluctuations of the electron density in the scattering volume. Hence, the respective cross terms of the scattering amplitude cancel out and solely the intensities of the different contributions add up. The analysis of the scattering intensity according to eq 3 will be demonstrated using the data which corresponds to nearby saturation of the surface by the surfactant (63 mg/g PS in the case of R ) 35 nm; 29 mg/g PS in the case of R ) 71 nm). The determination of the volume fraction profile proceeds along the following steps: 1. The contribution IPS(q) caused by the PS cores can be easily obtained by a Porod plot of the intensity obtained from the core particles. Figure 4 shows the Porod plot1 of I(q) of the PS-core latex with the smaller diameter (35 (18) Dingenouts, N.; Norhausen, Ch.; Ballauff, M. Macromolecules 1998, 31, 8912.

Figure 5. Subtraction of IPS(q) (see eq 3) from the scattering intensity I(q) of the small core particles (a, R ) 35 nm; covered by 63 mg of C18E112 per gram core of the particles) and of the large particles (b, R ) 71 nm; covered by 29 mg of C18E112 per gram core of the particles). The squares denote the uncorrected intensities whereas the crosses display I(q) - IPS(q) (cf. eq 3). IPS(q) has been taken from the slope of the Porod plot of the core particles (see Figure 4).

nm). The slope taken from this plot leads directly to IPS(q), which may be assumed as constant throughout the q range under consideration here (q < 1 nm-1). The same procedure is done using the scattering intensity of the large core particles. Subtracting this part of I(q) according to eq 3 gives the corrected intensity displayed in Figure 5a; Figure 5b gives the same comparison for the larger latex particles. Here it becomes obvious that IPS(q) is negligible at small q but becomes an appreciable contribution at qR > 25. 2. The radial structure of the covered particle can be analyzed using these data which refer to I(q) - IPS(q) (cf. eq 3). This analysis can be done by the method described recently.14,15 The polydispersity of the core particles has been determined from the scattering intensity of the PScore particles (see the discussion of Figure 3). It may be assumed in good approximation that there is no polydispersity of adsorbed shells; i.e., the polydispersity of the covered particles is determined by the size distribution of the core particles. 3. The radial excess electron density within the adsorbed layer now may be discussed in terms of models suggested by literature:5 For a dense layer of polymer chains attached terminally to a hard wall, a parabolic profile of the volume fraction is expected (see the discussion in ref 6). If attractive interactions between the hydrophilic chains and the particles must be taken into account, an exponential volume profile is expected.6 Given the excess electron density of the PEO chains in water, the volume fractions

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Figure 7. Correspondence of the calculated amount of adsorbed molecules nA,SAXS per unit area of the surface and the corresponding figure nA,cal obtained from the total amount of surfactant in the system. nA,cal has been determined under the assumption that all molecules of the added surfactant C18E112 adsorb onto the surface of the core particles: hollow symbols, small latex (R ) 35 nm); filled symbols, large latex (R ) 71 nm). The zeroth moment of both latexes as calculated from the profiles F(r) - Fm by eq 4 together with the excess electron density of PEO in water served for the calculation of nA,SAXS. See text for further explanation.

Figure 6. Analysis of the radial excess electron density of the adsorbed layer: (a) small core, R ) 35 nm (covered by 63 mg/g surfactant); (b) large core, 71 nm (covered by 29 mg/g surfactant). By use of the radial profiles shown in the inset, the experimental I(q) corrected for IPS(q) (see the discussion of Figure 5) can be fitted by variation of the respective model parameters. The cores consist of solid PS having a constant excess electron density of 6 e-/nm3. The core also comprises also the short hydrophobic part of the surfactant. The radial structures of the hydrophilic tails of the surfactant are modeled in terms of two assumed profiles: (1) parabolic profile (dashed line); (2) exponential profile (solid line).

can directly be converted into the respective radial excess electron densities. Fit parameters are the extension of the layer and the value of F(r) - Fm at the surface of the particles. From analyses of similar systems6,18,19 it is obvious that Ifl(q) may only be important at the highest q values accessible. Hence, the profile of the excess electron density will be derived taking into account the intermediate q range in which the minima and maxima of ICS(q) are clearly visible. Figure 6a,b displays the resulting fit for the two possible volume fraction profiles for both latexes. It is obvious that the present q range is too small to fully discern between these two models. There is a slightly better fit by the exponential profile, however. This is in agreement with previous analyses of comparable systems6 and a previous SANS study of poly(ethylene oxide) chains adsorbed onto PS particles.19 Moreover, a comparison between the maximum extension of the profile and the hydrodynamic radius measured by viscosimetry done for a related system gives an additional argument in favor of the exponential profile. The exponential profile used there describes correctly the maximal extension of the layer as determined by the hydrodynamic radius.17 (19) Mears, S. T.; Cosgrove, T.; Obey, T.; Thomson, L.; Howell, I. Langmuir 1998, 14, 4997.

While the present q range does not allow extraction of the full distribution of excess electron density of the surface layer in an unambiguous manner, the present data lead to a reliable zeroth and second moment of F(r) - Fm. Hence, the profiles F(r) - Fm obtained for different coverage of the surface below the below the point of saturation may be evaluated according to

M0,layer ) 4π

∫R∞[F(r) - Fm]r2 dr 0

(4)

Here M0,layer is the zeroth moment of the surface layer where R0 denotes the core radius. Given the excess electron density of poly(ethylene oxide), this quantity may directly be converted into the amount of the surfactant adsorbed onto the surface. Two problems must be considered when discussing the dependence of M0,layer on the concentration of added surfactant. (i) The radius R0 has been derived from a fit of I(q) of the core particles (cf. the discussion of Figure 3) and has a small but negligible error of the order of 0.5 nm. This error afflicts the magnitude of M0,layer but not its dependence of the concentration of added surfactant. (ii) The core particles have a thin but non-negligible shell. As discussed above in conjunction with Figure 3, this thin shell of higher electron density at the surface of the core particles may be traced back to the residual SDS molecules used in the synthesis of the core latex which may remain on the surface. Hence, M0,layer does not vanish at vanishing concentrations of added surfactant. For these reasons the zeroth moment of the shell of the core particles was subtracted from M0,layer. From M0,layer thus corrected the number of adsorbed molecules per unit area nA,SAXS has been calculated. These data in turn can be compared to the number nA,cal calculated under the assumption that all surfactant molecules added to the latex will adsorb onto the surface of the particles. Figure 7 displays a plot of nA,SAXS vs nA,cal

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for both latexes employed in this study. Here both the parabolic as well as the exponential profile have been used for the calculation according to eq 4. From the definition of M0,layer it is obvious that both profiles must lead to the same zeroth moment since this quantity is proportional to the total amount of adsorbed material. The differences between nA,SAXS obtained from both sets of the data may therefore be taken as a measure of the experimental error. Within these limits of error, all data lie on the diagonal below the point of saturation which corresponds to ca. one molecule per 10 nm2 (cf. above). Deviations at small coverage may be due to the problems in the determination of R0 (see above). Beyond the point of saturation no additional surfactant is adsorbed anymore and the measured value of nA,SAXS levels off as expected. Moreover, data obtained from particles having widely different diameters practically coincide. This leads to the conclusion that the different curvature has no marked influence on the process of adsorption of the surfactant C18E112. This must be traced back to the fact that the radius of the particles is considerably greater than the spatial extension of the layer. The good correlation of nA,SAXS and nA,cal shows that the adsorption of the surfactant C18E112 onto the surface of the charge-free PS-core latex is strong. The same conclusion has been drawn from recent data related to the flow behavior of latexes covered by surfactants related to C18E112 used here.17 These systems proved to be stable against high shearing forces up to effective volume fractions of the order of 0.5. Therefore PS latex spheres covered by suitable nonionic surfactants may be regarded as model systems of purely sterical stabilized particles. Besides M0,layer the present data allow calculation of the 2 which may be normalized moment of the layer Rg,layer defined as

2 Rg,layer

∫R∞[F(r) - Fm](r - R0)2r2 dr ) ∫R∞[F(r) - Fm]r2 dr 0

(5)

0

This quantity may be regarded as a measure for the average height of the adsorbed layer above the surface of 2 the particles. By virtue of its normalization, Rg,layer remains practically constant if the maximal extension of the surface layer does not change with increasing surface coverage. If, however, the extension of F(r) - Fm increases with an increasing number nA,SAXS of adsorbed molecules, 2 Rg,layer will increase as well. Hence, this quantity allows discussion of the overall extensions of the surface layer. Figure 8 displays the values of Rg,layer as function of nA,SAXS. As already observed in the case of M0,layer a finite value of this quantity is found for the core particles as well. Therefore the present discussion will be restricted to the discussion of the variation of Rg,layer with increasing nA,SAXS and disregard its absolute magnitude. As expected the data obtained from both types of profiles coincide. Despite the considerable scatter of the data, Rg,layer is seen to be virtually constant below nA,SAXS ) 0.05 nm-2. Beyond

Figure 8. Dependence of the second moment Rg,layer (see eq 5) on the number of adsorbed molecules nA,SAXS per unit area (cf. Figure 7): hollow symbols, small latex (R ) 35 nm); filled symbols, large latex (R ) 71 nm). The calculation of Rg,layer has been done using the exponential profile (circles) as well as the parabolic profile (squares) F(r) - Fm. See text for further explanation.

this point there is an increase of Rg,layer which indicates a stretching of the hydrophilic chains of the surfactant as expected. Within the present limits of error, both sets of data do not differ with regard to their slope. This again demonstrates that for the thin layer under consideration here there is no marked influence of the curvature of the core particles: Rg,layer was found between 2 and 4 nm whereas the radii of the latexes were 35 and 71 nm, respectively. Conclusion The present discussion has shown that SAXS is wellsuited for the investigation of the process of adsorption onto the surface of PS latex spheres. The adsorption of the surfactant onto the surface of the charge-free PS latexes is strong, but no second layer of the surfactant is built up at higher concentrations of the surfactant. Moreover, any association of the micelles with the covered latex particle can be ruled out completely. From the present data the zeroth moment M0,layer and the normalized second moment Rg,layer of the profile can be obtained with good accuracy. The dependence of Rg,layer on the amount of adsorbed surfactant indicates a weak stretching of the hydrophilic part of the chains when the coverage of the surface approaches saturation. This demonstrates that SAXS can furnish valuable data on the spatial structure of surface layers that have average extensions of a few nanometers only. Acknowledgment. Financial support by the Bundesministerium fu¨r Bildung und Forschung, Projekt “Konzentrierte Kunststoffdispersionen”, and of the AIF is gratefully acknowledged. We are indebted to N. Dingenouts for helpful discussions and to H. Ku¨hn for skilful technical assistance in the course of the SAXS investigations. LA990998F