Universal shape characteristics for the mesoscopic polymer chain via dissipative particle dynamics

In this paper we study the shape characteristics of a polymer chain in a good solvent using a mesoscopic level of modelling. The dissipative particle dynamics simulations are performed in the $3D$ space at a range of chain lengths $N$. The scaling laws for the end-to-end distance and gyration radius are examined first and found to hold for $N\geq 10$ yielding reasonably accurate value for the Flory exponent $\nu$. Within the same interval of chain lengths, the asphericity, prolateness, size ratio and other shape characteristics of the chain are found to become independent of $N$. Their mean values are found to agree reasonably well with the respective theoretical results and lattice Monte Carlo simulations. Broad probability distributions for the shape characteristics are found resembling in form the results of lattice Monte Carlo simulations. By means of analytic fitting of these distributions the most probable values for the shape characteristics are found to supplement their mean values.