水凝胶类软物质材料理论中的数学问题

 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.

MATHEMATICAL PROBLEMS IN SOFT MATTER LIKE HYDROGEL

Hydrogel is a kind of polymeric materials, have attracted some theoretical and experimental studies. The new hydrogel predominately consists of MMS (macromolecular microsphere), chains and water molecules, which shapes its well-defined structure and high mechanical 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 relationship? 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.