COLLAPSE OF A POLYMER-CHAIN - A BORN-GREEN-YVON INTEGRAL-EQUATION STUDY

A Born-Green-Yvon (BGY) type integral equation is developed for the in tramolecular distribution functions of an isolated flexible polymer ch ain. The polymer is modeled as a linear array of n identical spherical interaction sites connected by universal joints of bond length sigma. In particular we study chains composed of up to n = 400 square-well s pheres with hard-core diameters sigma and well diameters lambda sigma (1 less than or equal to lambda less than or equal to 2). Intramolecul ar distribution functions and the resulting average configurational an d energetic properties are computed over a wide range of temperatures. In the high temperature (good solvent) limit this model is identical to the tangent hard-sphere chain. With decreasing temperature (worseni ng solvent) the square-well chain undergoes a collapse transition iden tified by a sudden reduction in chain dimensions and a peak in the sin gle chain specific heat. Extensive comparison is made between the BGY results and Monte Carlo results for square-well chains with lambda=1.5 . The BGY theory is extremely accurate for square-well 4-mers at all t emperatures. For longer chains the theory yields reasonably accurate r esults for reduced temperatures greater than Tapproximate to 1 (expan ded and theta states) and qualitatively correct behavior for T<1 (col lapsed state). Very accurate values for the theta temperatures for squ are-well chains with 1.25 less than or equal to lambda less than or eq ual to 2.0 are also obtained. (C) 1996 American Institute of Physics.