Dielectric Effect In Charged Soft Matter Systems:Fast Algorithms And Computer Simulations

Electrostatic interaction is of fundamental importance for understanding the structure–function relationships of many physical and biological soft condensed matter systems,including liquid crystals,polymers,colloidal suspensions,membranes,foams and bio-materials such as DNA and proteins.The long-range nature of the electrostatic interaction lead to various challenges in the understanding of complex electrostatic phenomena.One of the central issues nowadays for charged many-body systems is the polarization effect due to the presence of complex dielectric interfaces.The presence of dielectric discontinuity will lead to induced charges on the dielectric interfaces,thus brings the so-called polarization effect,or dielectric effect.The dielectric effect is important in various systems,such as colloidal suspensions,liquid droplets in clouds,self-assembly of nanoparticles,and biopolymers.However,that part is usually missing in many computational works,because introducing the dielectric interfaces makes the simulation much more costly,since the calculation of polarization potential requires an efficient algorithm for solving 3D Poisson's equation with varying coefficient,which remains a technical difficulty for particle-based simulations.And this will also be our central problem to solve in this thesis.Therefore,this dissertation is divided into six chapters.We will first introduce the background in Chapter 1,and then discuss our own research work in the following five chapters.Specifically,from Chapter 2 to Chapter 4,we will emphasize the novel fast algorithms for simulating charged many-body systems with dielectric interfaces.Then from Chapter 5 to Chapter6,we will show the dielectric many-body effect in charged colloid systems,studied using the algorithms we developed.In Chapter 1,we will first introduce the basic knowledge about soft condensed matter systems,especially about colloidal suspensions: the basic concepts and mathematical models,conventional simulation techniques and fast algorithms that are popular currently.In Chapter 2,we will consider the Green's function problem for the Poisson equation in the presence of a simple dielectric sphere.The analytical image line-charge solution will be revisited first.Furthermore,since both the source charge,and the image charge interaction are in a very simple Coulomb form,treecode algorithm can be easily incorporated to accelerate our computation.We develop a new Barnes-Hut treecode algorithm tailored for the electrostatic evaluation in Monte Carlo simulations of Coulomb many-body systems.The computational cost of the Monte Carlo method with treecode acceleration scales as O(logN)in each move,where N is the number of charges.In Chapter 3,we will consider solving the electrostatic polarization effect in the presence of multiple dielectric interfaces.We will present two recently developed efficient approaches.The first is an extended image-charge method following Chapter 2,that can be applied to systems of spherical dielectric objects through multiple image-charge reflections and numerical evaluation of the resulting line integrals.The second is a boundary-element method(BEM)that computes the discretized surface bound charges through a combination of the generalized minimal residual method(GMRES)and a fast Ewald solver.We then discuss and compare in detail about the accuracy and efficiency of these two method.In Chapter 4,we will consider a more complicated case where multiple dielectric interfaces are densely packed.Both methods we presented in Chapter 3 are very efficient when the interfaces are well-separated,but performs much worse when interfaces are nearly touching.Thus,for the closely compacted interface case,a novel hybrid method is introduced,it has spectral accuracy,optimal scaling with system size,and does not suffer from contacting interfaces.At this stage,by combining all the algorithms presented from Chapter 2 ? 4 together,we obtain a set of accurate and efficient methods to deal with dielectric interface problems for charged many-body systems.And we have used these tools to further explore the dielectric effect in typical soft matter systems causing widely interest.These results will be presented in Chapter 5 and 6.In Chapter 5,we first use the algorithms to study the electric double layer structure near a dielectric spherical interface.Specifically,for a single dielectric sphere immersed in electrolyte,we investigate the effects of image charges,interfacial charge discreteness,and surface roughness on spherical electric double layer structures in electrolyte solutions under the settings of the primitive model.Systematic comparisons were carried out between three distinct models for interfacial charges,and we find that excluded volumes suppress charge inversion for monovalent interfacial charges and enhance charge inversion for multivalent interfacial charges.Finally in Chapter 6,we study the effect of polarization on the nano-particle self-assembly structure.We focus on the size-asymmetric binary nano-particle system.Through Molecular Dynamics simulations,we find that the dielectric many-body effect can qualitatively alter the predicted self-assembled structures,with surprising assembled rings,strings or crystal phases arising from the dielectric many-body effects.In conclusion,the scientific contribution and the novelty of this work can be summarized as follows.First,consider the dielectric interface problem in a variety of applications,we systematically developed a set of fast algorithms for computer simulation purpose,including analytical image-charge method,numerical boundary integral method,and semi-analytical image-moment hybrid method,enabling people to study spherical interface,arbitrary shape interface,or even densely packed interface problem.Then,we further couple these methods with other fast algorithms such as treecode,FMM or Ewald methods to achieve optimal scaling.Finally,we couple these algorithm in Monte Carlo and Molecular Dynamics simulations,revealing that polarization effect has important influence on the electric double layer structure,charge inversion,like-charge attraction,or the structure of nano-particle self-assembly.