Excluded volume effects for polymers in presence of interacting surfaces: Chain conformation renormalization group

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Abstract
The chain conformational space renormalization group method is extended to consider excluded volume effects in polymer chains interacting with surfaces. The general theory is illustrated primarily by considering a system with a single impenetrable flat interface. The presence of boundaries, while breaking the translational invariance of the full-space theory, introduces a number of novel theoretical features into the renormalization group treatment. A parameter δ is introduced to describe the strength of the polymer chain–surface interaction, and previous expansions in powers of δ or δ−1 are not required. We evaluate several moments of the end-vector distribution such as 〈zn〉, 〈‖ρ‖2〉, etc. to first order in the excluded volume. Our work differs essentially from previous studies because the full dependence on the polymer–surface interaction parameter δ is retained to all orders, the crossover dependence on excluded volume is incorporated and the generalized crossover (i.e., excluded volume dependent) exponents are corrected through second order. Previous results, such as power law exponents, scaling forms for distributions, end-vector distributions in the absence of excluded volume, etc., are obtained simply as particular limiting cases upon the values of the excluded volume and the interaction parameter δ.