Collapse of a ring polymer: Comparison of Monte Carlo and Born–Green–Yvon integral equation results

Abstract

The equilibrium properties of an isolated ring polymer are studied using a Born–Green–Yvon (BGY) integral equation and Monte Carlo simulation. The model polymer is composed of n identical spherical interaction sites connected by universal joints of bond length σ. In particular, we study rings composed of up to n=400 square-well spheres with hard-core diameter σ and well diameter λσ (1⩽λ⩽2). Intramolecular site–site distribution functions and the resulting configurational and energetic properties are computed over a wide range of temperatures for the case of λ=1.5. In the high temperature (good solvent) limit this model is identical to a tangent-hard-sphere ring. With decreasing temperature (worsening solvent) both the radius of gyration and the internal energy of the ring polymer decrease, and a collapse transition is signaled by a peak in the single ring specific heat. In comparison with the Monte Carlo calculations, the BGY theory yields quantitative to semiquantitative results for T≳Tθ and is qualitatively accurate for T≲Tθ, where Tθ is the theta temperature. The thermal behavior of an isolated square-well ring is found to be quite similar to the behavior of an isolated 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 rings and chains becomes nearly identical.