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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 mean-field approximation. We start from a recent mean-field 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 so-called 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.
- Spring '08