The Statistical Mechanics of Lattice Models of Polymers
聚合物晶格模型的统计力学
基本信息
- 批准号:RGPIN-2019-06303
- 负责人:
- 金额:$ 1.24万
- 依托单位:
- 依托单位国家:加拿大
- 项目类别:Discovery Grants Program - Individual
- 财政年份:2020
- 资助国家:加拿大
- 起止时间:2020-01-01 至 2021-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Polymers appear in
many different forms, namely as soft or hard solids, as liquids,
glues, or melts, or as networks of covalently bonded monomers, or
adsorbed onto a surface, or twisted and entangled in knotted
conformations. Underlying this rich set of forms and thermodynamic phases is
the notion of polymer entropy, which is related to the number of
conformations of a polymer molecule. In this application I shall give
an overview of my ongoing work in this field and explain several
avenues for continuing my research program. I will also explain the current involvement of students in my research program and their contributions, as well as future projects which are suitable for training students in Monte Carlo simulations and statistical mechanics.
Polymer entropy was
studied by Nobel prize winners Flory in the 1940s, and de Gennes in
the 1970s. A rich mathematical theory to model the entropy of
string-like objects was built on their work. This includes the
self-avoiding walk and related models, directed path models in
combinatorial mathematics, percolation, networks, as well as
numerical methods including Monte Carlo methods. These models are
ubiquitous in the statistical mechanics of random clusters and in the
theory of phase transitions and are related to classical models of
spin system models of magnetic materials. This area of research straddles rigorous and applied
statistical mechanics, combinatorial mathematics, probability theory,
and mathematical physics. There is also a connection to experimental
and theoretical polymer physics and chemistry. Research in this area is important because it adds to the understanding of phase behaviour and scaling in models of interacting and dense polymers and on networks.
Over the last cycle
my students and I have worked on mean field scaling for networks in
molecular biology and on a self-avoiding walk model of compressed dense polymers. With other collaborators I have worked on the phase
diagrams of linear and branched polymers and on partition function
zeros of adsorbing self-avoiding walks. My short term goals are to
expand my research into the partition function zeros of models of
self-avoiding walks and directed lattice paths, to apply
Flory-Huggins theory (a theory of dense polymer solutions) to models
of copolymer melts, and to perform simulations of lattice spin
systems using the GARM algorithm. In addition, I am investigating the phase diagram of pulled adsorbing models of branched polymers using self-avoiding walk models. Studies on partition function
zeros and models of dense polymers will be done with graduate students.
The longer term goals are to consider the usefulness of Flory-Huggins theory in creating a framing for understanding the phase diagram of dense polymer systems on the one hand, and on the other hand to examine the mathematical properties of
partition function zeros and the role they play in creating critical points in self-avoiding walk models of interacting polymers.
聚合物出现在
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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JansevanRensburg, Esaias的其他文献
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{{ truncateString('JansevanRensburg, Esaias', 18)}}的其他基金
The Statistical Mechanics of Lattice Models of Polymers
聚合物晶格模型的统计力学
- 批准号:
RGPIN-2019-06303 - 财政年份:2022
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
The Statistical Mechanics of Lattice Models of Polymers
聚合物晶格模型的统计力学
- 批准号:
RGPIN-2019-06303 - 财政年份:2021
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
The Statistical Mechanics and Combinatorics of Self-Avoiding Walk and Directed Path Models of Polymers
聚合物自回避行走和有向路径模型的统计力学和组合学
- 批准号:
RGPIN-2014-04731 - 财政年份:2018
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
The Statistical Mechanics and Combinatorics of Self-Avoiding Walk and Directed Path Models of Polymers
聚合物自回避行走和有向路径模型的统计力学和组合学
- 批准号:
RGPIN-2014-04731 - 财政年份:2017
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
The Statistical Mechanics and Combinatorics of Self-Avoiding Walk and Directed Path Models of Polymers
聚合物自回避行走和有向路径模型的统计力学和组合学
- 批准号:
RGPIN-2014-04731 - 财政年份:2016
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
The Statistical Mechanics and Combinatorics of Self-Avoiding Walk and Directed Path Models of Polymers
聚合物自回避行走和有向路径模型的统计力学和组合学
- 批准号:
RGPIN-2014-04731 - 财政年份:2015
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
The Statistical Mechanics and Combinatorics of Self-Avoiding Walk and Directed Path Models of Polymers
聚合物自回避行走和有向路径模型的统计力学和组合学
- 批准号:
RGPIN-2014-04731 - 财政年份:2014
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
The statistical mechanics of lattice paths and lattice walk models of polymers
聚合物晶格路径和晶格行走模型的统计力学
- 批准号:
122237-2008 - 财政年份:2013
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
The statistical mechanics of lattice paths and lattice walk models of polymers
聚合物晶格路径和晶格行走模型的统计力学
- 批准号:
122237-2008 - 财政年份:2011
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
The statistical mechanics of lattice paths and lattice walk models of polymers
聚合物晶格路径和晶格行走模型的统计力学
- 批准号:
122237-2008 - 财政年份:2010
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
相似国自然基金
Science China-Physics, Mechanics & Astronomy
- 批准号:11224804
- 批准年份:2012
- 资助金额:24.0 万元
- 项目类别:专项基金项目
相似海外基金
The Statistical Mechanics of Lattice Models of Polymers
聚合物晶格模型的统计力学
- 批准号:
RGPIN-2019-06303 - 财政年份:2022
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
The Statistical Mechanics of Lattice Models of Polymers
聚合物晶格模型的统计力学
- 批准号:
RGPIN-2019-06303 - 财政年份:2021
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
The Statistical Mechanics of Lattice Models of Polymers
聚合物晶格模型的统计力学
- 批准号:
RGPIN-2019-06303 - 财政年份:2019
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
The statistical mechanics of lattice paths and lattice walk models of polymers
聚合物晶格路径和晶格行走模型的统计力学
- 批准号:
122237-2008 - 财政年份:2013
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
The statistical mechanics of lattice paths and lattice walk models of polymers
聚合物晶格路径和晶格行走模型的统计力学
- 批准号:
122237-2008 - 财政年份:2011
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
Combinatorial approaches to problems in lattice statistical mechanics
解决晶格统计力学问题的组合方法
- 批准号:
341844-2007 - 财政年份:2011
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
The statistical mechanics of lattice paths and lattice walk models of polymers
聚合物晶格路径和晶格行走模型的统计力学
- 批准号:
122237-2008 - 财政年份:2010
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
Combinatorial approaches to problems in lattice statistical mechanics
解决晶格统计力学问题的组合方法
- 批准号:
341844-2007 - 财政年份:2010
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
The statistical mechanics of lattice paths and lattice walk models of polymers
聚合物晶格路径和晶格行走模型的统计力学
- 批准号:
122237-2008 - 财政年份:2009
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
Combinatorial approaches to problems in lattice statistical mechanics
解决晶格统计力学问题的组合方法
- 批准号:
341844-2007 - 财政年份:2009
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual














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