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

Abstract

Monte Carlo simulation of polymer chain collapse in an athermal solventThe equilibrium properties of an isolated ring polymer are studied using a Born-Green-Yvon ͑BGY͒ integral equation and Monte Carlo simulation. The model polymer is composed of n identical spherical interaction sites connected by universal joints of bond length . In particular, we study rings composed of up to nϭ400 square-well spheres with hard-core diameter and well diameter ͑1рр2͒. Intramolecular site-site distribution functions and the resulting configurational and energetic properties are computed over a wide range of temperatures for the case of ϭ1.5. In the high temperature ͑good solvent͒ limit this model is identical to a tangent-hard-sphere ring. With decreasing temperature ͑worsening solvent͒ 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 TտT and is qualitatively accurate for TՇT , where T 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 state͒ the microscopic structure of rings and chains becomes nearly identical.

The phase behavior of polyethylene ring chains

“…The radius of gyration is an important parameter to describe the collapse transition of the polymer systems. The behavior of ͗S 2 ͘ / N is different from square-well 34 and LJ ͑Ref. As seen in Fig.…”

“…34,69 We have plotted the ratio of 1 / g for the 80-bond chain as a function of temperature in the inset graph of Fig. In fact, the ratio of ͗S 2 ͘ linear / ͗S 2 ͘ ring ͑ϵ1 / g͒ is 2 for the Gaussian chains.…”

“…In fact, the ratio of ͗S 2 ͘ linear / ͗S 2 ͘ ring ͑ϵ1 / g͒ is 2 for the Gaussian chains. 34 We may expect that the properties of the square-well chains are similar to those of the ideal or Gaussian chains because both of them should be flexible chains. 1.…”

“…However, most of the previous studies 12,13,19,20 have only considered single linear chains, and a collapse transition is also expected for polymers of more complex molecular architecture. [32][33][34] However, the structural properties of the linear and ring chains are different and the ring polymer chain exhibits certain features of the crumpled globule. Indeed, the properties of ring polymers have been the interest of studies in recent years.…”

Effects of solvent on polymer chain dimensions: a Born–Green–Yvon integral equation study

“…With these approximations, Eq. (7) This BGY theory has been used to study both isolated hard-sphere and square-well chain and ring polymers [9,13]. The success of the theory in these cases provides validation of the above approximations.…”