Statistical Mechanics Properties And Brownian Dynamics Simulations Of Polymer Chains Under Confinements

What the statistical thermodynamic properties of polymer under complicated loads and complex spatial constraints would be is the most fundamental and challenging problem in the field of soft matter science during half a century. The relevant theoretical researches are mainly related to the equilibrium nature of a single polymer trapped into a tube or stretched on its ends. There are two kinds of well-known theories:one is the deflection scaling theory for strong stretching force or strong tube confinement, the other is the blob scaling theory for weak stretching force or weak tube confinement. However, it becomes complex and difficult in theory for analyzing the equilibrium nature of a single polymer trapped into a tube as well as applied stretching force at ends. So far, there is only one scale analysis solution about the force-extension relation of that polymer for strong synthetic action, where the tube confinement is not couple with the stretching force and can be equivalent to the effective stretching force. Pitifully, the formula for the effective stretching force of the strong tube confinement contains one adjustable parameter, and that force-extension solution is only suitable for long polymer without specific scope definition. In addition, throughout Brownian simulations with the high-precision generalized Bead-Rod (GBR) model (Wang and Gao, J. Chem. Phys.,123(8):084906,2005), we find that the values given by the classical extension formula of a strongly tube-confined polymer are larger than the simulation results, and the deviations grow greatly as the tube dimension increasing slightly.To the above problems, we propose the accurate expression of the extension of a strongly tube-confined polymer following the scale analysis method. Then we give the specific application range for the force-extension relation of a strongly tube-confined polymer which is mentioned above, and obtain an accurate formula for the effective stretching force of the strong tube confinement without any undetermined coefficients.Meanwhile, we perfect the Brownian simulation method with the GBR model, greatly expanding its range of applications in polymer researches with complex environments. Firstly, we propose a generalized linear constraint solver which can achieve any kind of geometric constraints and external loads. Secondly, we make it clear that the GBR model with linear angle potential has the best performance on the approximation to the worm-like chain between the two common kinds of springs. Thirdly, we develop a software for the Brownian simulation with the GBR model based on the C++.