Stiff-Chain Macromolecules

TLDR: In this paper, a review of various aspects of equilibrium and nonequilibrium properties of stiff chains without excluded volume in dilute solution is presented, focusing on molecular models, theoretical methods, and adaptation to real chains or determination of model parameters.

Abstract: Ordinary flexible-chain polymers such as polymethylene and polystyrene may be characterized by the proportionality ofthe mean-square end-to-end distance to the molecular weight (or the number of skeletal bonds) over a wide range in the unperturbed state with vanishing excluded volume effects (1). This property characteristic of the random-flight chain is violated by (static) chain stiffness arising from structural constraints and hindrances to internal rotation. This leads to the definition of semiflexibleor stiff-chain macromolecules in a broad sense (1 , 2); they include not only typical stiff chains such as DNA, a-helical polypeptides, and cellulose derivatives but also short chains of ordinary flexible polymers. The present review is intended to cover various aspects of equilibrium and nonequilibrium properties of such stiff chains without excluded volume in dilute solution. Emphasis is focused on molecular models, theoretical methods, and adaptation to real chains (or determination of model parameters). Among a number of models presented for chain molecules, the rotational isomeric state model (3) can best mimic the equilibrium conformational behavior of real chains of arbitrary length since it takes account of the details of the chain structure. However, for many equilibrium and steady-state transport problems on stiff chains, such details are not amenable to mathematical treatments, and moreover are often unnecessary to consider. Some coarse-graining may then be introduced to replace this discrete chain by continuous models, although the discreteness must be, to some extent, retained in a study of dynamic properties, especially local chain motions. The foremost of these models is the worm-like chain proposed by Kratky & Porod (4) in 1949 and its numerous, subsequent modifications. Those theoretical developments made before the early 1970s