Concentration and solvency effects on the excess amount and surface free energy of a colloidal particle in a solution of nonadsorbing polymer

R. Tuinier, G.J. Fleer

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)

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 φb and the solvency χ. 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 = -φbδ and a curvature correction Γc = -(π2/12)φbδc 2/a, where δc is a "curvature thickness" which is close to (but smaller than) δ. The grand potential has a planar contribution ω = (2/9)φb/δ and a curvature part ωc = (π/18)φb/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.

Original languageEnglish
Pages (from-to)8754-8763
Number of pages10
JournalMacromolecules
Volume37
Issue number23
DOIs
Publication statusPublished - 16 Nov 2004
Externally publishedYes

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