Mp. Taylor et al., COLLAPSE OF A RING POLYMER - COMPARISON OF MONTE-CARLO AND BORN-GREEN-YVON INTEGRAL-EQUATION RESULTS, The Journal of chemical physics, 106(12), 1997, pp. 5181-5188
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.