Comparison of Monte Carlo and quasi-Monte Carlo technique in structure and relaxing dynamics of polymer in dilute solution

Abstract

Structure and dynamics of polymer in solvent solution is an important area of research since the functional properties of polymer are largely dependent on the morphology of the polymers in solution. This structure related properties are especially important in case of surface science where the phase-separated morphology in the micro/nano scale dictates the properties of the product. Modeling polymers in solution is an efficient way to determine the morphology and thus the properties of the products. It saves time as well as helps to design novel materials with desired properties. Polymers in solution systems are generally modeled with bead spring model and Monte Carlo or importance sampling Monte Carlo simulations is used to find the optimal configuration where the energy of the system is minimized. Often in these simulations, random numbers are used in the Monte Carlo steps. Normally random numbers try to form clusters and do not cover the entire dimension of the system. Thus the minimum energy structures obtained from simulations with random numbers are not optimal configuration of the system. In the present work a lattice-based model is used for polymer solution system and importance sampling Monte Carlo is used for simulation. Quasi-random numbers generated from Hammersley sequence sampling (HSS) are used in the simulation steps for stochastic selection polymers and its movements. Quasi-random numbers obtained from HSS are random in nature and they have n-dimensional uniformity. They do not form clusters and the structural configuration obtained using quasi-random numbers are optimal in nature. The optimal configurations of the polymers as obtained from random number and quasi-random number are compared. The result shows that simulation with HSS attains a lower energy state after initial quench. At the late stage of spinodal decomposition, the structure factor decrease-showing Ostwald ripening which is not observed from simulation with random numbers.