Calculation Method And Parallel Optimization Of Simulating Self-avoiding Chain Based On Monte Carlo Method

Monte Carlo method, which is one of the most important scientific research methods for understanding laws of nature, is also widely used in the simulation of polymer science. This method can simulate not only stochastic problems in polymer science but aslo various microstates of polymer. The static and dynamic behavior of polymer can be simulated including the evolution of polymer conformation at the molecular level. Monte Carlo methods can freely control basic laws of physics in the computer simulation. Monte Carlo simulations not only can provide physical quantities of polymer, but also can find out some new physics laws. Therefore, the major issues, which remain unresolved by theoretical and experimental methods, are often hotspots in Monte Carlo method.Polymer adsorption on the surface plays a key role in a large number of industrial applications, including many bio-engineerings. On one hand, the surface changes conformation of polymer nearby. On the other hand, surface properties are related to the conformation and the shape of the polymer adsorbed on the surface. Therefor, many mechanisms of polymer adsorbed on the surface remain unclear. At present, the collection of conformational information is very limited in the experimental study, so it cannot fully reflect the conformation information of the polymer adsorbed on the surface. Theoretical calculations are often based on a certain formula, conformation information calculated by this way is also more limited, and it is beyond for slightly more complicated conditions. However, computer simulation can give more conformational information due to low cost and simple operation, which is given great attention from many researchers. People always adopt effective and fast algorithms to simulate the dynamic process of polymer, and to compute properties of adsorption and conformation in order to discover new laws of science. By using various methods and models for computer simulation of polymer science, a phase transition from a desorbed state to an adsorbed state occurs at the critical adsorption point with the change of temperature (or intensity) for an infinitely long polymer. There are differences for the critical adsorption point and the crossover exponent. There is also no unified scale calculation method. If you use different surface structures, different properties of components in polymer chains, they will produce more complicated effects. The new algorithm is worth to investigate for calculating critical adsorption point and conformation properties.This work was supported by the National Natural Science Fundation of China "dynamics simulation study on the critical phenomena of polymer chains adsorbed on surfaces (11304231)", the National Natural Science Foundation of China "simulation study on self-assembly of inorganic nanorods modified by polymer (21171145)", the Zhejiang Provincial Natural Science Foundation of China "study on the critical adsorption properties of copolymer polymer chain on the surface (LY14B040004)" and other research projects. We study some key computational technologies for modeling and scaling algorithms based on self-avoiding walk to simulate the critical phenomena of polymer chain on surface. The main work content and innovation are as follows:Firstly, we propose a model for simulating the critical phenomena of polymer chain on the surface by Monte Carlo method. Based on statistics mechanical method, we analyse simulation theory of polymer chain in dilute solution. We establish the growth model of polymer chain simulated by self-avoiding walk method. We simulate micro relaxation movement of self-avoiding walk chain by the bond fluctuations method. We propose the model of the critical phenomenon of polymer chain on surface by Monte Carlo method. We achieve numerical simulation calculation for the critical behavior of polymer chain on surface by statistical sampling physical quantities, such as system energy, mean square radius of gyration, mean square end-to-end distance and shape factor. We solve simulation problems of polymer science including the adsorption and conformation of polymer chains on surface.Secondly, we propose finite-size scaling algorithm for the critical adsorption of the homogeneous polymer and copolymer chain. First of all, dynamic Monte Carlo mehod is proposed to simulate adsorption properties of homogeneous polymer chain AN with one end grafted on the surface. The finite size scaling algorithm is proposed based on the critical adsorption of homogeneous self-avoiding walk chain. We found that the surface contact meet a uniform scale near the critical adsorption point and even in a wide temperature range. Then, we simulate copolymer which is formed by adding a weak adsorption (or no adsorption) segment B in the tail. We propose a scaling algorithm for the critical adsorption of copolymer AnBm. We analyse and compare the contact number, conformation and shape factor by using extrapolation method and approximatioss, respectively. We explained consistency problem of the critical adsorption points of copolymer chain AnBm and that of An. Finite-size scaling algorithm can solve computing problem of the critical temperature and crossover exponent even for the case that chain length is unknown in the experiment.Thirdly, we propose a calculation method for phase diagram of self-avoiding walk (SAW) chain on homogeneous or striped surfaces. Based on the model of two parallel surfaces, we propose scaling algorithm for the critical distance between parallel surfaces. We explain two different cases of SAW chain between two parallel surfaces:strong limiting state and weak one. Based on the model for stripe surface, we propose the calculation method for regional distribution of self-avoiding walks in space. The extrapolation method was used to build a phase diagram for an infinitely long chain on the surface with the finite stripe width:desorbed state, adsorbed on multi stripes and adsorbed on single stripe. Based on the different end-grafted location of diblock copolymer, we proposed two different models XAnBn and XBnAn, and explained the subtle conformation differences.Finally, we propose parallel optimization strategy of self-avoiding walks based on Monte Carlo simulation. Based on independence of samples, we present the model for simulating properties of self-avoiding walks on surface by parallel Monte Carlo. Each sample can be calculated at the same time, respectively, and the parallel computing achieve an ideal linear speedup. By modifying the relaxation functions, the relaxation times can be estimated in parallel computation, which can estimate the system balance system at each temperature and the runtime required for statistical analysis. Therefor, it is helpful to improve the precision of results and the utilization of computational resources.On the basis of this research, we will further study off-lattice model, Wang-Landau algorithm and further parallel optimization.