Collapse of a polymer chain: A Born–Green–Yvon integral equation study

Abstract

A Born–Green–Yvon (BGY) type integral equation is developed for the intramolecular distribution functions of an isolated flexible polymer chain. The polymer is modeled as a linear array of n identical spherical interaction sites connected by universal joints of bond length σ. In particular we study chains composed of up to n=400 square-well spheres with hard-core diameters σ and well diameters λσ (1≤λ≤2). Intramolecular distribution functions and the resulting average configurational and 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 (worsening solvent) the square-well chain undergoes a collapse transition identified by a sudden reduction in chain dimensions and a peak in the single chain specific heat. Extensive comparison is made between the BGY results and Monte Carlo results for square-well chains with λ=1.5. The BGY theory is extremely accurate for square-well 4-mers at all temperatures. For longer chains the theory yields reasonably accurate results for reduced temperatures greater than T*≊1 (expanded and theta states) and qualitatively correct behavior for T*<1 (collapsed state). Very accurate values for the theta temperatures for square-well chains with 1.25≤λ≤2.0 are also obtained.