兰州大学机构库 >土木工程与力学学院
受限空间聚合物链的统计热力学性质与布朗动力学仿真
Alternative TitleStatistical Mechanics Properties and Brownian Dynamics Simulations of Polymer Chains under Confinements
李润华
Thesis Advisor王记增
2014-05-24
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword聚合物 广义球棒模型 布朗动力学仿真 圆管约束 拉伸
Abstract聚合物链在复杂微环境中具有怎样的统计热力学性质,一直是近半个世纪以来软物质科学领域中既基础又非常具有挑战性的课题。相关的理论研究主要涉及到聚合物链受到圆管约束或者末端拉力作用下的平衡态性质,其中最为著名理论主要有针对受强拉伸或强几何约束链的偏转尺度理论(Deflection Scaling Theory)和针对受较弱拉伸或较弱几何约束链的链滴尺度理论(Blob Scaling Theory)。当聚合物链同时受到圆管约束和末端拉力作用时,其平衡态统计热力学性质的理论研究是非常困难的,目前仅有基于偏转尺度理论给出的关于强的综合作用下力与位移关系的尺度分析解。尤其令人遗憾的是,这一圆管等效拉力公式含有修正系数。另外,通过大量高精度的广义球棒模型(Generalized Bead-Rod, GBR; Wang and Gao, J. Chem. Phys., 123(8): 084906, 2005)的布朗动力学仿真发现:关于聚合物链在强圆管约束下伸展尺寸的经典公式相比于仿真结果偏大。针对于以上问题,本文通过尺度分析首次给出了关于聚合物链在强圆管约束下伸展尺寸的精确解析解,进而得到了新的不含任何待定系数高精度圆管等效拉力公式。与此同时,本文完善了GBR布朗动力学仿真模型及程序,大大扩展了其在复杂微环境下聚合物分子链统计热力学性质研究中的应用范围,并且采用C++语言开发完成了GBR模型布朗动力学仿真软件。
Other AbstractWhat 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 betw...
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Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225957
Collection土木工程与力学学院
Recommended Citation
GB/T 7714
李润华. 受限空间聚合物链的统计热力学性质与布朗动力学仿真[D]. 兰州. 兰州大学,2014.
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