Some problems of the statistical physics of polymer chains with volume interaction

The present state of the theory of volume effects in a polymer chain is reviewed. The theory of coils (i.e., chains with predominately repulsive volume interaction of monomers) and the analogy between the excluded volume problem and the theory of second-order phase transitions are briefly described. The theory of globules, formed by attractive interaction of monomers or by external attractive fields, is considered in greater detail. The coil-globule transition under various conditions is analyzed. A theory is constructed for the simplest model of the polymer chain—the model of "interacting beads on a flexible string." The connection of this model with more realistic ones is discussed. This review is based on the approach proposed by I. M. Lifshitz in 1968. While attention is focused on the physical aspects of the problems, some questions concerning biological applications are discussed in the conclusion.