蒙特卡罗模拟中基于双向链表的元胞链表方法

较之分子动力学, 蒙特卡罗能够实现非局域的粒子移动, 从而解决一些分子动力学不容易模拟的问题. 非局域的粒子移动主要包括模拟化学反应时粒子产生和消失的过程, 高分子模拟时的扭折-跳跃、绕枢轴转动和蠕动以及位形偏倚蒙特卡罗中链的回溯和再生. 然而在蒙特卡罗方法处理非局域移动时, 并不存在一种计算短程作用的计算复杂度为 的算法, 从而限制了蒙特卡罗方法的应用. 本文基于双向链表的数据结构, 发展了蒙特卡罗模拟中因粒子删除和插入而引起的短程势能变化的计算复杂度为 的元胞链表方法. 所有非局域的粒子移动可以转化为粒子的删除和插入, 因此该方法适用于上述所有情形. 此外, 由于Metropolis算法中给某粒子一个随机位移的过程可以看成旧位置粒子的删除以及新位置粒子的插入, 因此该方法也适用于Metropolis算法中粒子的随机移动.     

Finite size effect of ions and dipoles close to charged interfaces

The modified dipolar Poisson-Boltzmann(MDPB) equation,where the electrostatics of the dipolar interactions of solvent molecules and also the finite size effects of ions and dipolar solvent molecules are explicitly taken into account on a mean-field level,is studied numerically for a two-plate system with oppositely charged surfaces.The MDPB equation is solved numerically,using the nonlinear Multigrid method,for one-dimensional finite volume meshes.For a high enough surface charge density,numerical results of the MDPB equation reveal that the effective dielectric constant decreases with the increase of the surface charge density.Furthermore,increasing the salt concentration leads to the decrease of the effective dielectric constant close to the charged surfaces.This decrease of the effective dielectric constant with the surface charge density is opposite to the trend from the dipolar Poisson-Boltzmann(DPB) equation.This seemingly inconsistent result is due to the fact that the mean-field approach breaks down in such highly charged systems where the counterions and dipoles are strongly attracted to the charged surfaces and form a quasi two-dimensional layer.In the weak-coupling regime with the electrostatic coupling parameter(the ratio of Bjerrum length to Gouy-Chapman length) Ξ 1,where the MDPB equation works,the effective dielectric constant is independent of the distance from the charged surfaces and there is no accumulation of dipoles near the charged surfaces.Therefore,there are no physical and computational advantages for the MDPB equation over the modified Poisson-Boltzmann(MPB) equation where the effect of dipolar interactions of solvent dipoles is implicitly taken into account in the renormalised dielectric constant.     

环形聚电解质电泳特征的分子动力学模拟

使用Langevin分子动力学模拟研究了环形聚电解质的电泳行为, 发现环形和线形链具有相似的临界电场强度. 当场强超出临界值, 平衡离子凝聚度急剧降低, 链构象明显溶胀. 相比线形分子, 环形链凝聚度降低的幅度较少, 源于环形链在电场中的构象拉伸度小于线形链. 在不考虑流体动力学相互作用的情况下, 2种分子链的电泳迁移率均满足“局部力平衡”关系. 在不同的溶液库仑强度下, 2种链的迁移率差异出现峰值, 电场增强导致峰值增大和峰位置右移.     

Self-consistent field theory of adsorption of flexible polyelectrolytes onto an oppositely charged sphere

The adsorption of flexible polyelectrolyte （PE） with the smeared charge distribution onto an oppositely charged sphere immersed in a PE solution is studied numerically with the continuum self-consistent field theory. The power law scaling relationships between the boundary layer thickness and the surface charge density and the charge fraction of PE chains revealed in the study are in good agreement with the existing analytical result. The curvature effect on the degree of charge compensation of the total amount of charges on the adsorbed PE chains over the surface charges is examined, and a clear understanding of it based on the dependences of the degree of charge compensation on the surface charge density and the charge fraction of PE chains is established.     

Numerical study of the interplay of monomer-surface electrostatic and non-electrostatic interactions in the adsorption of weak polyelectrolytes on oppositely charged surfaces

The adsorption of weak polybase on oppositely charged planar surfaces has been investigated numerically by using the self-consistent field theory (SCFT). Particular attention was paid to the interplay of monomer-surface electrostatic and non-electrostatic interactions in the adsorption behaviors of weak polybase. In this study, the strength of monomer-surface non-electrostatic interactions was set to be no more than the thermal energy k _B T. It was found from the numerical study that in the regime of low surface charge density of the substrate and low pH or high bulk degree of ionization, both the screening-enhanced and screening-reduced salt effects emerge. On the contrary, in the opposite regime, only the screening-reduced salt effect was observed. Moreover, the overall charge neutrality inside the adsorption layer was analyzed. The underlying mechanism governing the adsorption behaviors of weak polybase on oppositely charged surfaces was elucidated.     

四臂星型聚电解质刷在外加三价盐离子和电场下的塌缩

本文采用Langevin动力学模拟的方法,研究存在三价盐离子时,接枝在带相反电荷的极板上的部分带电的四个臂星型链呈现出的塌缩现象. 结果表明,在电场作用下,接枝星型链的平均带电分数和盐浓度在带电单体和三价盐离子的竞争性吸附中起关键作用. 对于接枝在带相反电荷的极板上的带电分数较高的星型链,刷子会塌缩到接枝极板上,并会产生极板表面电荷的过度补偿现象. 当带电分数较低时,如果星型链所带电荷数与三价盐离子电荷数相同,即使在很低的盐浓度下,极板对三价盐离子的吸引能力也高于对星型链中的带电单体的吸引. 结果表明,星型链在带电分数较低的情况下,三价盐离子的加入不会导致接枝电极表面电荷的过度补偿. 此外,本文还研究了三价盐离子对电场作用下星型刷的拉伸的影响.     

Molecular dynamics simulation of the response of bi-disperse polyelectrolyte brushes to external electric fields

Langevin dynamics simulations have been performed to investigate the response of bi-disperse and strong polyacid chains grafted on an electrode to electric fields generated by opposite surface charges on the polyelectrolyte(PE)-grafted electrode and a second parallel electrode. Simulation results clearly show that, under a negative external electric field, the longer grafted PE chains are more strongly stretched than the shorter ones in terms of the relative change in their respective brush heights. Whereas under a positive external electric field, the grafted shorter chains collapse more significantly than the longer ones. It was found that, under a positive external electric field, the magnitude of the total electric force acting on one shorter PE chain is larger than that on one longer PE chain, or vice versa. The effects of smeared and discrete charge distributions of grafted PE chains on the response of PE brushes to external electric fields were also examined.