The rolling transition of a Gaussian chain end-grafted at a penetrable surface

A Gaussian chain at a liquid-liquid interface is considered. The solvents are represented by an external potential field u that has a constant value in one half-space and is zero elsewhere. One end of the chain is fixed at the boundary where the external potential field changes its value. For this model the exact partition function is available. The system features a first-order phase transition for which the external potential is the control parameter; the chain rolls from one half-space to the other upon changing the sign of the external potential. The chain distributes its N segments over both regions when the external potential difference between the two regions \u\much less than 1/N, otherwise the chain puts virtually all its segments in the region with the lowest potential. The relation between the problem of a Gaussian chain at a solid/liquid boundary and that of a chain at a liquid/liquid interface, is illustrated. Applications of the model are discussed. (C) 2000 American Institute of Physics. [S0021-9606(00)50616-3].