COLLAPSE OF A RING POLYMER - COMPARISON OF MONTE-CARLO AND BORN-GREEN-YVON INTEGRAL-EQUATION RESULTS

The equilibrium properties of an isolated ring polymer are studied usi ng a Born-Green-Yvon (BGY) integral equation and Monte Carlo simulatio n. The model polymer is composed of n identical spherical interaction sites connected by universal joints of bond length sigma. In particula r, we study rings composed of up to n = 400 square-well spheres with h ard-core diameter sigma and well diameter lambda sigma (1 less than or equal to lambda less than or equal to 2). Intramolecular site-site di stribution functions and the resulting configurational and energetic p roperties are computed over a wide range of temperatures for the case of lambda = 1.5. In the high temperature (good solvent) limit this mod el is identical to a tangent-hard-sphere ring. With decreasing tempera ture (worsening solvent) both the radius of gyration and the internal energy of the ring polymer decrease, and a collapse transition is sign aled by a peak in the single ring specific heat. In comparison with th e Monte Carlo calculations, the BGY theory yields quantitative to semi quantitative results for T greater than or similar to T-theta and is q ualitatively accurate for T less than or similar to T-theta, where T-t heta is the theta temperature. The thermal behavior of an isolated squ are-well ring is found to be quite similar to the behavior of an isola ted square-well chain. The BGY theory indicates that rings and chains have comparable theta and collapse transition temperatures. In the low temperature limit (collapsed state) the microscopic structure of ring s and chains becomes nearly identical. (C) 1997 American Institute of Physics.