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Unformatted text preview: Concentration and Solvency Effects on the Excess Amount and Surface Free Energy of a Colloidal Particle in a Solution of Nonadsorbing Polymer Remco Tuinier* ,² and Gerard J. Fleer ‡ Forschungszentrum Ju ¨ lich, Institut fu ¨ r Festko ¨ rperforschung, 52425 Ju ¨ lich, Germany, and Laboratory for Physical Chemistry and Colloid Science, Wageningen University, 6703 HB Wageningen, The Netherlands Received July 14, 2004; Revised Manuscript Received August 31, 2004 ABSTRACT: Analytical expressions are derived for the polymer excess amount and the grand potential (surface free energy) of flat and spherical surfaces immersed in a solution of nonadsorbing polymer chains in the meanfield approximation. We start from a recent meanfield expression for the depletion thickness δ which takes into account not only the effect of the chain length N but also that of the polymer concentration b and the solvency l . Simple expressions are obtained for the interfacial properties at a colloidal surface, using both the adsorption method and the osmotic route. For a sphere of radius a , the excess amount can be separated into a planar contribution Γ )  b δ and a curvature correction Γ c ) ( π 2 /12) b δ c 2 / a , where δ c is a “curvature thickness” which is close to (but smaller than) δ . The grand potential has a planar contribution Ω ) (2/9) b / δ and a curvature part Ω c ) ( π /18) b / a . We test the results against numerical lattice computations, taking care that the boundary conditions in the continuum and lattice models are the same. We find good agreement up to a polymer segment volume fraction of 10%, and even for more concentrated solutions our simple model is reasonable. For spherical geometry we propose a new equation for the segment concentration profile which excellently agrees with numerical lattice computations. The results can be used as a starting point for the pair interaction between colloidal particles in a solution containing nonadsorbing chains, which is discussed in the following paper. 1. Introduction When polymer chains are depleted from the surface of a colloidal particle, the socalled depletion interaction leads to an effective attraction between the colloidal particles in a colloid polymer dispersion. 1 In many theoretical studies on polymer depletion, the chains were considered as ideal (noninteracting random coils) 2,3 or even simplified further as dilute hard 4 or freely overlapping spheres. 5 In recent years depletion of (fully) interacting polymers in solution was studied using various theoretical methods, such as the polymer refer ence interaction site model (PRISM), 6,7 osmotic equilib rium theory (sometimes called free volume theory), 8 density functional theory, 9 a Gaussian core model, 10,11 and computer simulations....
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This note was uploaded on 07/20/2011 for the course EMA 6165 taught by Professor Brennan during the Spring '08 term at University of Florida.
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