Configurational statistics for isolated square-well chain molecules: exact results for short chains

Abstract

Exact results are obtained for the configurational statistical properties of isolated square-well chain molecules of lengths 3 and 4. The chain molecules considered here are composed of square-well spheres with hard-core diameter σ and well diameter λσ (1 ˇ- λ ˇ- 2) connected by ‘universal joints’ with bond length σ. Exact analytical and semi-analytical expressions are obtained for the intramolecular site-site distribution functions for these chain molecules. From the intramolecular distribution functions one can determine all average equilibrium configurational and energetic properties. In particular, the mean-square site-site separations, mean-square radius of gyration, average energy, and specific heat are calculated. With decreasing temperature the chain molecules undergo a collapse transition identified by a sudden reduction in chain dimensions and a peak in the specific heat. For both square-well 3-mers and 4-mers the reduced transition temperature is in the range 0·2 ≲T _c* ≲ 0·5.