The configurational statistics of a polymeric chain confined by impenetrable barriers

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Abstract
General expressions, applicable to any chain distribution function, are developed for the configurational statistics of a polymeric chain which is confined by any number of impenetrable barriers. The reflection principle, or method of images, is employed for this purpose. The procedure for obtaining approximate, analytical equations from these general expressions is then illustrated using the statistics of a real polymeric chain, to the order N−1, for the cases of: a loop (a chain with both ends attached to the same wall), a cilia (a chain with one end attached to a wall and the other end free), and a bridge (a chain with its ends attached to opposite walls), all between two walls.

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