Self-consistent-field theory for hard-sphere chains close to hard walls

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Abstract
A continuum theory for confined hard-sphere polymers is presented. Starting from fundamental relations and applying defined approximations, a constitutive relation for the conformation probability (analogous to the result in mean-field lattice theories) is developed. The main problem of hard-sphere correlations is attacked by two approximate methods: First, using the Carnahan–Starling equation of state and local volume fractions (CS). Second, by an extension of the lattice theory to spherical components with unequal volumes (LATT). The agreement with Monte Carlo simulations is good for both approximations at low densities, but becomes only qualitative at the higher concentrations. The CS approximation seems to be favored over the LATT approach at the higher concentrations when correlation becomes more important. Both free and grafted chains are treated. The influence of chain length, grafting density, solvent concentration, solvent chain length, and surface curvature on the segment distribution is investigated.