PHASE-TRANSITION BEHAVIOR OF THE ISOLATED POLYMER-CHAIN

A mean field theory of chain dimensions is formulated which is very similar to the van der Waals theory of a simple fluid. In the limit of infinite chain length, the chain undergoes a Landau-type second-order phase transition. For finite chains, the transition is pseudo-second-order. At low temperatures, the chain is in a condensed or globular state, and the mean square gyration radius (S2) varies as r2/3 where r is proportional to chain length. At high temperatures, the chain is in a gaslike or coil state where (S2) varies as r6/5. In the globular state, fluctuations in (S2) are very small, whereas they are very large in the coiled state. A characteristic feature of the theory is that ternary and higher order intramolecular interactions are approximated. At high temperatures, only binary interactions are important, but at low temperatures, many of the higher order terms contribute. An important conclusion of this study is that a polymer chain does not obey ideal chain statistics at Φ the temperature. Although the second virial coefficient vanishes at Φ, the third virial coefficient does not; its presence is responsible for the perturbation of the chain statistics. For an infinite chain, Φ and the second-order phase-transition temperature are identical. For finite chains, the pseudo-second-order transition temperature is less than Φ. When generalized to d dimensions, the theory yields at low temperatures (S2)d/2 ~ r for all d and at high temperatures (S2) ~ r6/(d+2), d < 4, and (S2) ~ r, d < 4. © 1979, American Chemical Society. All rights reserved.