Comparison of the Effective Radius of Sterically Stabilized Latex

Langmuir 1998, 14, 5083-5087

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Comparison of the Effective Radius of Sterically Stabilized Latex Particles Determined by Small-Angle X-ray Scattering and by Zero Shear Viscosity A. Weiss, N. Dingenouts, and M. Ballauff*,† Polymer-Institut, Universita¨ t Karlsruhe, Kaiserstrasse 12, 76128 Karlsruhe, Germany

H. Senff and W. Richtering*,‡ Institut fu¨ r Makromolekulare Chemie, Universita¨ t Freiburg, Stefan-Meier-Strasse 31, 79104 Freiburg, Germany Received March 31, 1998. In Final Form: June 26, 1998 The influence of an adsorbed layer of a surfactant on the flow behavior of a latex is considered. The system studied consists of a poly(styrene) core latex without chemically bound charges (diameter: 146 nm) and a layer of poly(ethylene oxide) chains (length: 80 ethylene oxide units) affixed to the surface of the particles through adsorption of the surfactant Lutensol AT80 (C16-18EO80). Both the core latex as well as the latex covered by surfactant have been studied by small-angle X-ray scattering (SAXS). The hydrodynamic thickness of the layer was determined by rheology to be 11.7 nm whereas SAXS gives an extension of the layer of approximately 12 nm. The result demonstrates that realistic hydrodynamic radii of latex particles result from viscosimetric measurements. Relative viscosities measured at higher volume fractions compare favorable with a recent experimental master curve proposed for suspensions of hard spheres (Meeker, S. P.; Poon, W. C. K.; Pusey, P. N. Phys. Rev. E 1997, 55, 5718).

Introduction Up to now the rheology of sterically stabilized latex particles has been the subject of a number of studies.1-8 While the rheology of suspensions of hard spheres seems to be rather well understood by now,9,10 the flow behavior of particles stabilized by a surface layer of long polymer chains is still in need of further elucidation. The modification of the viscosity by an adsorbed layer of a surfactant or a polymer can be modeled in terms of an appropriate increase ∆ of the radius a of the particles. This leads to a concomitant rise of the volume fraction of the particles. Hence, an effective volume fraction φeff may be defined through

(

φeff ) φc 1 +

∆ ) φck a 3

)

where φc and a denote the volume fraction and the radius of the uncovered latex particles, respectively. In the dilute regime, the effective volume fraction φeff may be determined from the relative viscosity ηo/ηs by use of an expression derived by Batchelor11

η0 ) 1 + 2.5φeff + 5.9φ2eff ηs

(2)

where ηs denotes the viscosity of the solvent. The intrinsic viscosity is defined as

[η] ) lim φf0

η0 - ηs ηsφc

(3)

(1)

* To whom all correspondence should be addressed. † E-mail: [email protected]. ‡ E-mail: [email protected]. (1) Goodwin, J. W. In An Introduction to Polymer Colloids; Candau, F., Ottewill, R. H., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1990; p 209. (2) Goodwin, J. W.; Ottewill, R. H. J. Chem. Soc., Faraday Trans. 1991, 87, 357. (3) Prestidge, C.; Tadros, Th. F. J. Colloid Interface Sci. 1988, 124, 660. (4) Andrew, D.; Jones, R.; Leary, B.; Boger, D. V. J. Colloid Interface Sci. 1991, 147, 479. (5) Liang, W.; Tadros, Th. F.; Luckham, P. F. J. Colloid Interface Sci. 1992, 153, 131. (6) Andrew, D.; Jones, R.; Leary, B.; Boger, D. V. J. Colloid Interface Sci. 1992, 150, 84. (7) Liang, W.; Bognolo, G.; Tadros, Th. F. Prog. Colloid Polym. Sci. 1995, 98, 128. (8) Raynaud, L.; Ernst, B.; Verge, C.; Mewis, J. J. Colloid Interface Sci. 1996, 181, 11 and further references given therein. (9) Meeker, S. P.; Poon, W. C. K.; Pusey, P. N. Phys. Rev. E 1997, 55, 5718. (10) Phan, S.-E.; Russel, W. B.; Cheng, Z.; Zhu, J.; Chaikin, P. M.; Dunsmuir, J. H. Ottewill, R. H. Phys. Rev. E 1996, 54, 6633.

and follows from the initial slope when the relative viscosity is plotted against the volume fraction φc. For hard spheres [η] is given by 2.5; for particles covered by polymer chains [η] is greater because φeff > φc. At higher concentration the zero shear viscosity has often been described by the Dougherty-Krieger equation1,2

(

)

φeff η0 ) 1ηs φmax

-[η]φmax

(4)

relating η0 to the effective volume fraction φeff. Here φmax is the volume fraction where η0 diverges. For hard spheres [η] ) 2.5. Given the validity of this concept, the zero shear viscosity is described through eq 4 by a single parameter φmax, which in principle should be a universal value independent of the particular system under consideration. A survey of experimental data shows, however, that φmax lies between 0.58 and 0.64.1-9 Apparently the choice of (11) Batchelor G. K. J. Fluid Mech. 1977, 83, 97; Brady, J. F.; Vicic, M. J. Rheol. 1995, 39, 545.

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5084 Langmuir, Vol. 14, No. 18, 1998

the “correct” volume fraction and its experimental determination is rather difficult. For suspensions of hard spheres this problem can be overcome by choosing the volume fraction of the disorderorder transition as reference.9,10 In case of particles stabilized through long polymeric chains which interact through a more complicated pair potential,12 the choice of the correct volume fraction to be used in fits of eq 4 may be more difficult. This is particularly true for systems for which an overlap or a compression of the hairy layer on the surface may occur at volume fractions around 0.5. Moreover, as discussed by Meeker et al.9 the data deriving from fits of eq 4 to experimental data may lead to unphysical values. These authors concluded from their experiments and a critical survey of data in the literature that the divergence of the viscosity is located rather at φeff ) 0.58, i.e., the volume fraction at which the glass transition occurs, rather than 0.64, the volume fraction of random-close-packing. To elucidate this problem further, a comparison of ∆ obtained from rheological data according to eqs 2 and 4 with structural data would clarify the physical significance of ∆. Small-angle scattering methods as small-angle neutron scattering (SANS)13 or small-angle X-ray scattering14 are suitable methods to obtain the radial structure of sterically stabilized particles. From these data a measure of the spatial extension of the steric layer may be derived and compared to ∆. Thus, the thickness of the shell consisting of poly(ethylene oxide) chains has been derived from a fit of the measured SANS data15,16 and compared3 to ∆. Several factors may render such a comparison rather difficult, however. In case of charged particles electroviscous effects may come into play.17 The size distribution will influence the static properties derived from SANS in a different manner than the hydrodynamic properties of the suspension. If the steric layer is affixed onto the surface of the particles by adsorption, the adsorbed surfactant may be in equilibrium with free surfactant or even micelles of the surfactant, which will further complicate the analysis.18,19 Here we give a systematic comparison of the thickness of an adsorbed layer measured by static and dynamic methods. A well-defined nonionic surfactant (Lutensol AT80) has been adsorbed onto the surface of a poly(styrene) model latex without chemically bound charges.20 Hence the effect of charges on the measured viscosity may be dismissed. The bare latex particles as well as the particles covered by the surfactant have been carefully studied by small-angle X-ray scattering (SAXS).14 Recent studies have demonstrated that SAXS is well-suited to analyze the internal structure of latex particles with very good (12) Genz, U.; D’Aguanno, B.; Mewis, J.; Klein, R. Langmuir 1994, 10, 2206. (13) Higgins, J. S.; Benoit, H. C. Polymers and Neutron Scattering, Clarendon Press: Oxford, England, 1994. (14) Ballauff, M.; Bolze, J.; Dingenouts, N.; Hickl, P.; Po¨tschke, D. Macromol. Chem. Phys. 1996, 197, 3043. Dingenouts, N.; Bolze, J.; Po¨tschke, D.; Ballauff, M. Adv. Polym. Sci., in press. (15) Cosgrove, T.; Crowley, T. L.; Vincent, B.; Barnett, K. G.; Tadros, Th. Faraday Symp. Chem. Soc. 1981, 16, 101. (16) Fleer, G. J.; Cohen Stuart, M. A.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B. Polymers at Interfaces; Chapman & Hall: London 1993. (17) Hunter, R. J. Foundations of Colloid Science; Oxford University Press: Oxford, England, 1987; Vol. I. (18) Kronberg, B.; Lindstro¨m, M.; Stenius, P. In Phenomena in Mixed Surfactant Systems; Scamehorn, J. F., Ed.; ACS Symposium Series 311; American Chemical Society: Washington, DC, 1986. (19) Bolze, J.; Ho¨rner, K. D.; Ballauff, M. Langmuir 1996, 12, 2906. (20) Ottewill, R. H.; Satguranthan, R. Colloid Polym. Sci. 1987, 265, 845.

Weiss et al. Table 1. Characterization of the Latexesa DN(DCP) (nm) Dw/DN(DCP) DN(TEM) (nm) Dw/DN(TEM) DN(SAXS) (nm) Dw/DN(SAXS)

core latex

covered latex

145 1.02 141 1.003 146 1.007

172 1.007

a D ; D : number- and weight-average diameter, respectively. N w DCP: disk centrifugation. TEM: transmission electron microscopy. SAXS: small-angle X-ray scattering.

resolution.14,19,21 Since the size of the steric layer is precisely known from a comparison of the SAXS data obtained before and after adsorption, the value of ∆ derived through application of eqs 2 and 4 to viscosimetric data may now be compared to structural data. In addition to this, the viscosity measured at higher volume fractions may be compared to data deriving from hard-sphere systems.9,10 Experimental Section Materials. Styrene (BASF) was washed three-times with 3 M aqueous NaOH and then with H2O and subsequently dried and distilled in vacuo. Ascorbic acid, KCl, H2O2 (35 wt %), and sodium dodecyl sulfate (SDS) have been obtained from Fluka and used without further purification. Lutensol AT80 is a poly(oxyethylene ether) C16-18EO80 and was obtained from BASF AG. The surfactant was used as received. To avoid chemically bound surface charges on the latex particles, the emulsion polymerization was initiated20 by use of the redox initiator ascorbic acid/H2O2. In a typical run 550 g of styrene, 6.0 g of SDS, and 0.64 g of ascorbic acid were dispersed in 2 L of deionized water and the emulsion polymerization stared through addition of 1.1 mL of 35% hydrogen peroxide. The core latex thus obtained was purified through dialysis against a 0.002 M KCl solution for approximately 2 weeks. Dilution of the latex was effected through a 0.002 M KCl solution. Adsorption of the surfactant was achieved through stirring of 100 mL of the purified core-latex with 2.0 g of Lutensol AT80 for several hours. The excess of the surfactant was removed through extensive serum-replacement with a 0.002 M KCl solution. The latex thus obtained is stable against 0.7 M aqueous CaCl2 and can be concentrated up to weight fractions of ca. 45 wt % without coagulation. Methods. The density of the latexes was measured by a DMA60 densitometer supplied by PAAR (Graz, Austria). The size distribution was determined using Brookhaven DCP disk centrifuge. Details of the measurements have been given elsewhere.22 Transmission electron microscopy was done using a Phillips EM 400 microscope with the image analysis system IBAS from Kontron (Mu¨nchen, Germany). SAXS measurements were done using a modified Kratky camera having an improved resolution. The details of the measurement, the subsequent desmearing of the data, and the fit procedures have been presented recently.23 Concentrations of the latexes were ca. 10 wt %. An automatic Schott Mikro Ostwald viscometer was used to determine the intrinsic viscosity. Rheological properties of concentrated dispersions were investigated with a stress controlled rheometer CVO (Bohlin Instruments) in cone/plate geometry. All measurements were performed at 20 °C. Table 1 summarizes the diameters of both latexes as obtained by different methods.

Results and Discussion Analysis of the Particles by SAXS. Figure 1 displays the SAXS intensities I(q) of the core latex and the latex (21) Bolze, J.; Ho¨rner, K. D.; Ballauff, M. Colloid Polym. Sci. 1996, 274, 1099. (22) Weiss, A.; Po¨tschke, D.; Ballauff, M. Acta Polym. 1996, 47, 333. (23) Dingenouts, N.; Ballauff, M. Acta Polym. 1998, 49, 178.

Sterically Stabilized Latex Particles

Figure 1. SAXS intensities of the core latex (lower curve) and the latex covered by Lutensol AT80 (upper curve). The upper curve has been multiplied by 10 to preserve the clarity. The solid lines display the theoretical intensities deriving from the profiles of the excess electron densities shown in Figure 2. For the details of the SAXS measurements and the evaluation, see ref 23.

covered by the surfactant as function of the magnitude of the scattering vector q (q ) (4π/λ)sin(θ/2); λ, wavelength of radiation, θ, scattering angle). For the sake of clarity the scattering intensity of the covered latex has been multiplied by 10. The pronounced maxima of I(q) immediately demonstrate the narrow size distribution of both latexes; i.e., modification of the surface of the core latex did not change the breath of the distribution. This points to the fact that Lutensol AT80 is a well-defined surfactant with the ethylene oxide chains having approximately the same degree of polymerization. The fit of radial electron density profiles to I(q) obtained from both latexes have been achieved through the procedure described recently.14,23 The solid lines in Figure 1 show the good agreement between the measured and calculated intensities for both the core latex as well as for the latex covered by surfactant. Minor deviations at smallest angles may be traced back to the residual influence of particle interaction and are of no concern for the comparison of experimental data with calculated intensities (see ref 14 for a discussion of this point). The resulting profiles are displayed in Figure 2 together with a sketch of the structure of the particles derived therefrom. The core latex is already characterized by a small surface layer of ca. 1 nm size. As discussed recently,21 the origin of this layer may be ascribed to adsorbed SDS molecules. In the context of this work, it could be demonstrated that nonionic surfactants as used herein fully replace SDS because of the longer hydrophobic moiety.19,21 The result obtained here (Figures 1 and 2) corroborates this analysis. The profile of the excess electron density of the latex covered by surfactant (see Figure 2) demonstrates that the poly(ethylene oxide) chains are rather tightly attached to the surface of the particles. This can be understood from the fact that poly(ethylene oxide) itself will be adsorbed on the surface of PS particles.24 A more detailed study of the structure of adsorbed surfactants is under way at present.24 For the sake of clarity, Figure 1 displays the comparison of the experimental data with the respective fits only up to q ) 0.5 nm-1. The agreement of theory and experiment (24) Seelenmeyer, S.; Dingenouts, N.; Ballauff, M. Manuscript in preparation.

Langmuir, Vol. 14, No. 18, 1998 5085

Figure 2. Scheme of the radial structure of the core latex and the latex covered by the surfactant Lutensol AT80 (left-hand side) and profiles of the excess electron density deriving from the SAXS intensities shown in Figure 1. For the details of the evaluation of the SAXS data and the fit procedure, see ref 23.

Figure 3. Relative zero shear viscosity η0/ηS of the sterically stabilized latex covered by the surfactant Lutensol AT80 as function of the volume fraction of the latex core. The dashed lines displays the fit according to eq 5 in order to obtain the effective volume fraction φeff (see text for further explanation).

persists up to q ) 1.0 nm-1, however. This fact demonstrates the absence of micelles formed by nonadsorbed surfactant. As shown in previous studies,19,21 a surplus of nonadsorbed surfactant forms free micelles which give a distinct scattering signal at higher q values. Hence, the suspension of the covered particles present a suitable model system for the subsequent rheological study. Rheological Characterization. Figure 3 shows the relative viscosity of the sterically stabilized latex in the dilute regime plotted vs latex concentration. The volume fraction φc of the polystyrene core was calculated using the density of polystyrene and by taking into account the mass of the adsorbed surfactant. The intrinsic viscosity was determined by a fit according to the equation

η0 ) 1 + 2.5(φck) + 5.9(φck)2 ηs

(5)

using k (see eq 1) as the only adjustable parameter. A k value of 1.56 was obtained from the fit leading to [η] ) 3.9. A linear fit would result to [η] ) 4.39 which underscores the necessity of taking into account the quadratic term of eq 2 even at small volume fractions.9

5086 Langmuir, Vol. 14, No. 18, 1998

Weiss et al.

Figure 4. Shear viscosity η as function of shear rate for three different weight fractions of the latex covered by the surfactant Lutensol AT80. The respective weight fractions are indicated in the graph. The lines display the fits according to Cross,25 which has been used to evaluate the zero shear viscosity η0.

The deviations from the hard sphere value [η] ) 2.5 are due to the adsorbed layer. To calculate the thickness of this adsorbed polymer layer following eq 1, one has to know the core radius. From SAXS the radius of the polystyrene core was determined as a ) 73 nm which leads to ∆ ) 11.7 nm by use of the experimental value k ) 1.56. The fit of the SAXS intensities has led to the conclusion that the steric layer has an extension of ca. 12 nm. Hence, the SAXS result and the effective diameter taken from the dilute shear viscosity (cf. Figure 3) agree very well for the system under consideration here. It is evident that this comparison must be done for surfactants having different lengths of the hydrophilic moiety before drawing general conclusions. The present result, however, suggests that the relative viscosity in the dilute regime leads to meaningful data for ∆ which can be used for subsequent evaluations. In particular, it demonstrates that [η] ) 2.5 if a meaningful φeff has been used. Hence, [η] should not be used as a fit parameter when comparing eq 4 to experimental data at higher concentrations. At higher concentrations shear thinning may seriously hamper the comparison of experiment and theory which requires zero shear viscosities.9 Shear thinning was indeed observed with more concentrated samples. Nevertheless, the low shear rate plateau was experimentally accessible and the zero shear viscosity was obtained from a fit with the expression given by Cross25

η)

η0 - η∞ 1 + (κγ˘ )n

+ η∞

(6)

which is known to provide a good description of the viscosity of colloidal suspensions.26 η∞ is the high shear viscosity. The respective fits are shown in Figure 4. Only at the highest volume fractions does the measured viscosity exhibit a marked dependence on shear rate, and η0 can be extrapolated in good accuracy by using the procedure of Cross. Figure 5 shows a plot of the zero shear viscosity vs the effective volume fraction φeff calculated from the viscometry results in dilute solution, i.e., with a layer thickness ∆ ) 11.7 nm. The full line in Figure 5 represent the experimental hard-sphere data by Meeker et al.,9 which could be described by the Doughtery-Krieger equation, eq 4, (25) Cross, M., M. J. Colloid Sci. 1965, 20, 417. (26) Ferguson, J.; Kemblowski, Z. Applied Fluid Rheology, Elsevier: London, 1991.

Figure 5. Relative zero shear viscosity ηo/ηs as function of the effective volume fraction φeff (cf. the discussion of Figure 3) for the latex covered by the surfactant Lutensol AT80. The solid line displays the master curve for suspensions of hard spheres according to Meeker et al.9 The dashed line shows the fit by the Dougherty-Krieger eq 4 where [η] has been fixed to the hardsphere value of 2.5.

with [η] ) 3.2 and φmax ) 0.55. Our data are very close to those of the hard sphere system. Note that no factor has been introduced to compare the present data to the data of ref 9. The dashed line in Figure 5 shows the result of a fit with the Dougherty-Krieger equation when [η] is fixed at the hard sphere value 2.5. The fit gives φmax ) 0.54, but as demonstrated by Figure 5, the fit does not describe the data very well. A much better fit is obtained when [η] is used as second fit parameter resulting in [η] ) 2.85 and φmax ) 0.548 (not shown in Figure 5). However, we believe that [η] cannot be used as a fit parameter in the course of a meaningful analysis of the rheological data. Small deviations between our data and the data of ref 9 are found in the region of intermediate volume fractions. This might be due to the larger ratio of a/∆ which is ca. 6 in our case. The hard sphere model systems used by Meeker et al.9 and by Phan et al.10 typically have core diameters in the range of 600 nm and ratios of the core diameter to ∆ much higher than those in our system. Given the margin of error (cf. Figure 5), however, the present data lie close to the master curve of the hard-sphere system of ref 9. Despite these minor differences the present data corroborate the analysis of Meeker et al. by suggesting that the divergence of ηo occurs at volume fractions below 0.6. Therefore all these results cast general doubt only the validity of the conclusions drawn from the DoughertyKrieger fit or by similar approaches which assume the divergence at volume fractions above 0.6. It is hence evident that the strong raise of ηo will take place at the glass transition rather than at the volume fraction of random-close packing. Conclusions A sterically stabilized aqueous polystyrene dispersion with a core diameter of 146 nm was investigated by SAXS and viscosimetry. On one hand, the thickness of the adsorbed polymer layer can be determined directly by SAXS and ∆ ) 12 nm was found. Viscosimetry, on the other hand, led to a value of ∆ ) 11.7 nm by using the core diameter obtained through SAXS. The good agreement demonstrates that the values of ∆ deriving from measurements of the viscosity in the dilute regime may indeed be regarded as a good measure for the thickness of the steric layer. The relative viscosities determined at higher volume fractions lie close to the master curve derived recently for suspensions of hard spheres.9 This finding suggests that

Sterically Stabilized Latex Particles

the divergence of the zero shear viscosity of the present system will occur in the vicinity of the volume fraction where the glass transition occurs (ca. 0.58). All results cast doubt on procedures using the Dougherty-Krieger equation, eq 4, for determination of the thickness ∆ of the steric layer.

Langmuir, Vol. 14, No. 18, 1998 5087

Acknowledgment. Financial support by the Bundesministerium fu¨r Bildung und Forschung, Projekt “Konzentrierte Kunststoffdispersionen”, and by the Deutsche Forschungsgemeinschaft is gratefully acknowledged. LA980356C