胶体聚合物弹性模量的微观理论:键长的效应

Using the mode-coupling theory and combining the concepts of dynamic free energy, local size and glass transition point in the theory of nonlinear Langevin equations, the elasticity problem of colloidal polymers is studied. Based on the microscopic static structure, the explicit expression of the shear elastic modulus is theoretically derived. This expression includes the single-chain structure factor, the static structure of monomers between chains and the dynamic local size. It is first reported that the increase in bond length has a reducing effect on the volume fraction of the supercooled liquid transition. Later, taking the static structure of the colloidal chain as an input function and based on the relationship between the bond length and the local size, the influence of the bond length on the shear elastic modulus and the bulk elastic modulus is mainly explored. The research findings are as follows: When using the supercooling depth as an independent variable, the local size and the bulk elastic modulus of chains with the same bond length can be described by a universal curve, while the shear elastic modulus cannot collapse onto a universal curve. Based on the universal curve of the zero-wavevector static structure factor, we conjecture that this comes from the influence of the bond length on the long-wavevector static structure. This work provides theoretical guidance for the regulation of the elastic properties of polymer materials in the future.

使用模耦合理论,并结合非线性朗之万方程理论中的动力学自由能、局域尺寸和玻璃化转变点的概念,研究胶体聚合物的弹性问题.以微观的静态结构为基础,在理论上推导出剪切弹性模量的显式表达.该表达式包含了单链结构因子、链间单体的静态结构与动力学局域尺寸.首先报道了键长的增加对过冷液体转变体积分数有降低作用.之后,将胶体链的静态结构作为输入函数,基于键长对局域尺寸的关系,重点探索了键长对剪切弹性模量和体积弹性模量的影响.研究发现:当使用过冷深度作为自变量时,同一键长的链的局域尺寸和体积弹性模量能被一条普适曲线刻画,而剪切弹性模量则不能塌缩到一条普适曲线上.基于零波矢静态结构因子的普适曲线,我们猜想这来自于键长对长波矢静态结构的影响.该工作为日后对聚合物材料的弹性性质的调控提供了理论指导.