水凝胶类软物质材料中的数学问题  

MATHEMATICAL PROBLEMS IN SOFT MATTER LIKE HYDROGEL

作　　者：张辉[1] 

机构地区：[1]北京师范大学数学科学学院,数学与复杂系统教育部重点实验室

出　　处：《计算数学》2018年第1期1-23,共23页Mathematica Numerica Sinica

基　　金：国家自然科学基金(11471046,11571045);教育部中心高校基础研究基金

摘　　要：水凝胶是一种具有广泛应用前景的软物质材料，一直是材料学家、物理化学家们关心的热点，目前有很多实验和专利产品．其机理和模型的研究处于初期阶段，本文综述该领域的部分进展，包括形变、微结构和宏观性质等的数学模型和相关计算方法，一并列出一些亟待解决的问题．Hydrogel is a kind of polymeric materials, have attracted some theoretical and experi- mental studies. The new hydrogel predominately consists of MMS （macromolecular micro- sphere）, chains and water molecules, which shapes its well-defined structure and high mechan- ical strength. But, how is it phase transition and forming these well-defined micro-structure？ Why the hydrogels have such high mechanical strengths？ what is the structure-property re- lationship？ How do the structural factors affect, such as nanoparticle size, grafting density, polymer chain length, entanglement, and so on？ Here we will review some mathematical progress to partly answer them, including phase transition, micro-structure, macro-property and related numerical methods. Meanwhile, we also present some mathematical problems to be solved.

关 键 词：水凝胶类软物质 相变 微结构 宏观性质 可计算建模 计算方法 

分 类 号：O648.17[理学—物理化学]