胶体聚合物弹性模量的微观理论:键长的效应

Microscopic theory for elastic modulus of colloidal polymers:Effect of bond length

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.

Colloidal polymers have attracted increasing attention in condensed physics,statistical mechanics and polymer science and engineering due to their advances in synthesis and visualization.Many useful properties and applications of colloidal polymers make them an ideal model to explore fundamental problems in slow dynamics and rheology of chain-like molecules in supercooled regime.With temperature decreasing or density rapidly increasing,amorphous materials often exhibit nonzero shear moduli.In this article,we are to investigate the nonzero shear modulus and bulk modulus of colloidal polymer in supercooled regime based on recent microscopic theoretical development.At the segmental-scale level,an analytical derivation for elastic modulus of colloidal polymer is constructed based on the standard approximation in na?ve mode-coupling theory(NMCT).In the framework of nonlinear Langevin equation theory(NLET),the derivation combines the concept of dynamic free energy,localization and NMCT crossover volume fraction.Taking the chain connectivity into account,an explicit expression for shear modulus including intrachain structure factor,interchain correlation and localized length is formulated.Bulk modulus can be obtained by relating it to long wavelength part of static structure factor.Firstly,our calculation for discrete wormlike chain shows that intrachain structure factor has a power law decay at intermediate wavevector which is similar to flexible linear chain.Secondly,we find that colloidal polymer with long bond length has a lower NMCT crossover volume fraction.Furthermore,inputting the localized length,long wavelength density fluctuation and static intrachain and interchain structures into the theoretical expression,the effect of bond length on shear modulus and bulk modulus are investigated.Interestingly,we find the bond length plays a critical and unique role in localized length and bulk modulus.For instance,when the supercooling degree is used as an independent variable,the local length and bulk elastic modulus of the chain with the same bond length can be collapsed onto a universal curve,which is independent of chain length and local bending energy.However,in the aspect of shear modulus,the bond length is not a unique quantity and the above universal curve cannot be found.The shear modulus depends on other parameters of chain,such as chain length and rigidity.According to the universal behavior of zero-wavevector static structure factor versus bond length,we guess that the nonuniversal curve of shear modulus is due to the bond length effect on long wavevector static structure factor.This work provides a theoretical foundation for controlling various properties of chain-like supercooled materials in the future.