Fast Algorithms And Computer Simulations In Multi-scale Hybrid Model For Electrolyte Solutions | Posted on:2021-06-29 | Degree:Doctor | Type:Dissertation | Country:China | Candidate:J Fu | Full Text:PDF | GTID:1481306503482654 | Subject:Computational and applied mathematics | Abstract/Summary: | PDF Full Text Request | Nanoparticles occur widely in nature,which are an important component of atmospheric pollution.They are also crucial components of many industrial products such as paint and metal,and play an important role in our lives.Nanoparticles attract increasing interest in the fields of medicine,chemistry,physics,and materials science.The core-shell dielectric nanomaterials draw extensive research in the field of electrochemical supercapacitors.Electrostatic interactions play an important role in the aggregation and self-assembly of nanoparticles,and are critical to understanding the structure and function of many physical and biological soft matter systems.For a large many-body system,numerical calculations are generally prohibitively expensive due to the long-range nature of electrostatic interaction.In systems made up of spatially non-uniform dielectric constant,due to dielectric discontinuities,polarized charges are generated at the dielectric interface,which results in polarization effects or dielectric effects.Dielectric effects have certain effects for the electric field,such as protein folding,nanochannel transport,nanoparticle aggregation and self-assembly.In actual calculations,it is difficult to estimate polarization charge accurately.The calculation of polarization potential requires an effective algorithm to solve the three-dimensional Poisson equation with variable coefficients.In the molecular dynamics simulation or Monte Carlo simulation,the entire simulation process requires millions of time steps,since the force or energy needs to be calculated in each time step,thus increasing the computational difficulty.By introducing an appropriate electrolyte multi-scale hybrid model,we systematically investigate the dielectric effects of charged manybody systems,and develop appropriate fast algorithms to transform the polarization potential and perform molecular dynamics or Monte Carlo simulations.An accurate image-charge method(ICM)is developed for ionic interactions outside a coreshell structured dielectric sphere.Core-shell particles have wide applications,for which the theoretical investigation requires efficient methods for the Green’s function used to calculate pairwise interactions of ions.The ICM is based on an inverse Mellin transform from the coefficients of spherical harmonic series of the Green’s function such that the polarization charge due to dielectric boundaries is represented by a series of image point charges and an image line charge.The residue theorem is used to accurately calculate the density of the line charge.At the same time,using Monte Carlo simulations,we investigated the influence of the core-shell structure dielectric boundary on the electric double layer structure and capacitance.For the interaction of two core-shell structure dielectric spheres,we develop a general image charge method for multipole sources and combine it with the method of moment to develop a hybrid method.It does not require a large number of reflection layers when the two dielectric core-shell structure dielectric spheres are close to each other,which is importmant for the image charge method.Also,it does not need to truncate many terms,which is importmant for the method of moment.At the same time,this method can be extended to a system of many-body core-shell structure dielectric spheres.For the multi-scale model of electrolytes which combines the strengths of atomistic/continuum electrolyte representations,a harmonic surface mapping algorithm is developed for fast and accurate evaluation of the electrostatic reaction potentials.This method reformulates the reaction potential into a sum of image charges for the near-field,and a charge density on an auxiliary spherical surface for the far-field,which can be further discretized into point charges.The fast multipole method is used to accelerate the pairwise Coulomb summation,such that this method can reach linear complexity.Using molecular dynamics simulations,we investigate the self-assembly behavior of twoconfiguration nanoparticles on a two-dimensional plane.The molecular dynamics simulations consider two systems with different radii and dielectric constants,or asymmetrically charged nanoparticles.By adjusting the size of the asymmetric coefficient,we investigate the selfassembled structure.In conclusion,we mainly introduce a fast algorithm for the multi-scale hybrid model.For the water solvent,the image charge method is developed for the core-shell structure nanoparticle.For the ionic solvent,the harmonic surface mapping algorithm is developed for evaluation of the electrostatic reaction potentials.We also perform molecular dynamics simulations to explore the dielectric effects of the self-assembly. | Keywords/Search Tags: | Dielectric effect, Poisson equation, Image charge, Multi-scale hybrid modeling, Linearized Poisson-Boltzmann equation, Harmonic surface mapping, Molecular dynamics simulation, Self-assembly | PDF Full Text Request | Related items |
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