Monte Carlo Simulation In Conformational Statistics Of Polymer Chain

In 1940's the Monte Carlo method has been applied in polymer science. With the development of computer, the Monte Carlo method application has been concerned with most research areas of polymer science, and made the particular effort in many important theory research areas. The Monte Carlo method provides approximate solutions to a variety of mathematical problems by performing statistical sampling experiments on a computer. It is not only popular used in theory research, but also used in practice area. Although the Monte Carlo method was popular applied in polymer areas, but now there is no systematic and full solutions on it. In this paper, the research area is Monte Carlo application in conformational statistic of polymer chain. Comparing with other methods, there is no common program in Monte Carlo method, so there are variety skills and methods in program. In this paper the basic thinking of Monte Carlo method will be described. The Monte Carlo simulating the polymer chain's statistical sampling method and examples will be given. In the process of Monte Carlo simulation, producing kinds of probability distributing random variable is required. The character of Monte Carlo method is the use of random numeral, and the basic important random variables are uniform distributing in [0, 1]. A high quality random numeral generator will be described; also a checkout method will be used in this paper. In polymer dilute solution, polymer chains exist individually. So there is no effect among them, we can deal with them as single chain. Polymer can not exist as gases, and we study the single polymer chain character from dilute solution firstly. In polymer dilute solution theory, generally the solvent was considered as continuous medium. Making the continuous medium discretization, it will be better for computer simulation. In lattice model, just several particular lattice sites can be used as the chain unit. Although, there are big differences between the simulated polymer chain by lattice model and polymer chain, but the statistics on most characters of polymer chain would not be depended on details of the chain model. In this paper, Gennes's BLOB model and lattice model will be applied together to achieve the lattice model applied in computer program and the polymer chain simulation on lattice module. Also, the theory of "individual inner circumvolve"and off-lattice model will be compositely used for deeply research in the method of computer simulating real polymer chain. For getting the statistic of polymer chain by the Monte Carlo method, conditional sampling is needed. Base on the enough samples, the mean of polymer chain's conformational statistics will be calculated. Actually, the sampling process of the chain is the growing process of the chain. In the polymer statistical sampling problem, the RW and SAW will be the revelatory examples. These two kinds of chain model are used to research in big scale character of soft polymer chain in dilute solution. Based on the lattice model, this paper will describe the sampling method for RW chain and SAW chain. And relation of the RW and SAW chains'R 2...