Jain Aashish, Sunthar P, Dünweg B, Prakash J Ravi
Department of Chemical Engineering, Monash University, Melbourne, VIC 3800, Australia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 2):066703. doi: 10.1103/PhysRevE.85.066703. Epub 2012 Jun 11.
Simulating the static and dynamic properties of semidilute polymer solutions with Brownian dynamics (BD) requires the computation of a large system of polymer chains coupled to one another through excluded-volume and hydrodynamic interactions. In the presence of periodic boundary conditions, long-ranged hydrodynamic interactions are frequently summed with the Ewald summation technique. By performing detailed simulations that shed light on the influence of several tuning parameters involved both in the Ewald summation method, and in the efficient treatment of Brownian forces, we develop a BD algorithm in which the computational cost scales as O(N(1.8)), where N is the number of monomers in the simulation box. We show that Beenakker's original implementation of the Ewald sum, which is only valid for systems without bead overlap, can be modified so that θ solutions can be simulated by switching off excluded-volume interactions. A comparison of the predictions of the radius of gyration, the end-to-end vector, and the self-diffusion coefficient by BD, at a range of concentrations, with the hybrid lattice Boltzmann-molecular dynamics (LB-MD) method shows excellent agreement between the two methods. In contrast to the situation for dilute solutions, the LB-MD method is shown to be significantly more computationally efficient than the current implementation of BD for simulating semidilute solutions. We argue, however, that further optimizations should be possible.
用布朗动力学（BD）模拟半稀聚合物溶液的静态和动态特性需要计算通过排除体积和流体动力学相互作用相互耦合的大量聚合物链系统。在存在周期性边界条件的情况下，长程流体动力学相互作用通常用埃瓦尔德求和技术进行求和。通过进行详细的模拟，揭示了埃瓦尔德求和方法以及布朗力有效处理中涉及的几个调谐参数的影响，我们开发了一种BD算法，其计算成本按O(N(1.8)) 缩放，其中N是模拟盒中单体的数量。我们表明，贝纳克尔最初对埃瓦尔德和的实现仅对没有珠子重叠的系统有效，可以进行修改，以便通过关闭排除体积相互作用来模拟θ溶液。在一系列浓度下，将BD对回转半径、端到端向量和自扩散系数的预测与混合晶格玻尔兹曼 - 分子动力学（LB - MD）方法进行比较，结果表明两种方法之间具有极好的一致性。与稀溶液的情况相反，对于模拟半稀溶液，LB - MD方法在计算上比当前的BD实现效率显著更高。然而，我们认为进一步的优化应该是可行的。
