Consequences for the excluded-volume problem in polymers at rigid boundaries

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Abstract
On the basis of a previously reported diagrammatic convolution technique, the internal spatial probability distributions of segments within a sequence of N hard-sphere segments are determined in particular, the diameter of the first segment is progressively increased, and the properties of the remainder of the chain investigated which rapidly attain asymptotic form, and which we qualitatively identify with those of a hard-sphere chain terminally attached to a rigid plane. The analysis is repeated for various chain–plane offset distances, and for a range of attractive segment–plane interactions whilst excluded-volume processes continue to operate within the chain. Configurational properties are determined as a function of chain length, offset distance and interaction strength, and a subsequent analysis investigates the development of loops, trains and tails for a terminally attached sequence, again as a function of chain length and interaction strength. Finally, the stabilization of dispersed colloidal systems by polymeric solvents is investigated. The central role of purely geometric entropic effects is emphasised throughout the discussions.

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