The Implementation Of Electrostatic Interactions In Dissipative Particle Dynamic Simulations And Related Applications

Soft matters are complex condensed matter systems that are composed of a va-riety of physical states. The main character of such systems, on one side is that they can response to external instant or weak stimulation, and on the other side is that the composition of these systems are too complex to describe at single scale. On microscopic level, the atomistic structures of soft matter systems are similar to fluid systems, and on macroscopic level, these systems do not have periodical features as crystals. But at mesoscopic level, molecules can form a series of complex sys-tems ranging from simply ordered assemblies to multi-functional organisms through particular intra-and intermolecular interactions.It is these complex assemblies that show completely different properties to solid and ideal fluid systems. In confined environment, they exhibit semi-ordered structures which is similar to solids, and the thermodynamic and dynamic proper-ties of these soft matter systems are strongly influenced by thermal fluctuations. Therefore, one can clarify that it is the environmental confinement and the thermal fluctuations that dominate the unique nature of these systems, and are responsible for the complexities and particularities in system compositions and interactions be-tween building blocks.Soft matter systems exhibit multiscale features in several aspects based on the complexities of compositions. In spatial and temporal multiscales, there are corre-sponding physical models and simulation methods for specific applications. These method include the quantum chemistry methods in investigating the electron be- haviors, the all-atomistic simulation methods at microscopic level in studying the specific interactions between molecules, the mesoscopic simulation method in de-scribing the structures and morphologies formed by soft matter systems, and the finite element methods for the description of the processing of polymeric materials.It is the particular interactions in soft matter systems that facilitate us to fabri-cate multi-functional assemblies by finely tuning the interactions between building blocks, such as the hydrophilic and hydrophobic interactions, as well as electrostatic interactions. In typical soft matter systems, such as polyelectrolytes and charged colloidals, the electrostatic interactions between charge groups dominate the unique behavior of such systems. Detailed and systematic studies on these systems enable us to control the structures and properties of assemblies, as well as to understand the complex behavior and functions of biomacromolecular organisms.In computer simulations, the electrostatic interactions between charges are long-range interactions, and the calculation of electrostatic interactions is the most time-consuming part. How to reduce the calculations with suitable parameters based on acceptable accuracy, is the main and principle issue one should consider before carrying out detailed simulations.In atomistic simulations, one can use Ewald summation method and corre-sponding derivative methods, such as particle-particle particle-mesh method and particle-mesh Ewald summation methods, to calculate electrostatic interactions. While the electrostatic interactions between charged colloid particles can be de-scribed by DLVO theory. But how to deal with electrostatic interactions between charged particles in moderate coarse-graining scheme is still an open question. Can the electrostatic interactions implicitly incorporated in other effective interactions, such as van der Waals interactions. In this thesis, We focus on how to accurately describe the electrostatic inter-action between charged groups on moderate coarse-grained simulations, especially in dissipative particle dynamics method, to avoid the formation of artificial ionic clusters due to the soft nature of short-range repulsive interactions between coarse-grained particles.With suitable algorithms to calculate electrostatic interactions between charged group in dissipative particle dynamic simulations, one can improve the computa-tional efficiency in dealing with electrostatic interactions based on acceptable accu-racy. With such coarse-graining scheme, one can study the complex behavior of soft matter systems on large spatial and long temporal scales, such as the polyelectrolyte conformations and the binding structures of dendrimer molecules on bilayer mem-branes. For these soft matter systems, one can study the thermodynamic, structural properties and dynamic behaviors, as well as the influence of external environmental stimulation on system properties, with which one can provide valuable information and reliable references for further experimental and theoretical analysis.The main research content of this thesis includes (1) The ENUF method, i.e., Ewald summation based on the Non-Uniform FFT (NFFT) technique, is implemented in Dissipative Particle Dynamics (DPD) simulation scheme to fast and accurately calculate the electrostatic interac-tions at mesoscopic level. The Slater-type charge density distributions are adopted in simulations, which can effectively avoid the formation of artifi-cial ionic clusters due to the soft nature of short-range repulsive interactions between coarse-grained particles.The ENUF-DPD method is applied on simple model electrolyte systems to ex-plore suitable parameters, including the convergence parameter a, the NFFT approximation parameter p, and the cut-offs for real and reciprocal space con-tributions, are carefully determined. With these optimized parameters, The computational complexity of ENUF-DPD method is approximately described as O(N log N), which shows remarkably better efficiency than the traditional Ewald summation method with acceptable accuracy in treating long-range electrostatic interactions between charged particles at mesoscopic level.The ENUF-DPD method is further validated by investigating the influence of charge fraction of polyelectrolyte on corresponding conformational proper-ties. Meanwhile, the dependence of the conformations of fully ionized poly-electrolyte on ionic strength and valency of added salts are also studied. Sim-ulation results reveal that the polyelectrolyte conformation increase with the increase of charge fraction of polyelectrolyte, which reflects the transition of polyelectrolyte from collapse to fully extended conformation. When salts are added into solution, both ionic strength and valency of multivalent counte-rions of added salts can severely influence the conformational properties of polyelectrolyte due to the strong correlations between multivalent counterions and polyelectrolyte. Strong correlations between polyelectrolyte and counte-rions with high valency are observed. with the increase of counterion con-centrations, polyelectrolyte can undergo transitions from fully extended, to collapsed and then semi-swelled conformations, which emphasizes the impor-tant role of counterion valency. These applications show that the ENUF-DPD method is very robust and can be used to study charged complex systems at mesoscopic level.(2) The ENUF-DPD simulation method is used to study the specific binding struc-tures of polyamidoamine (PAMAM) dendrimers on amphiphilic membranes and the permeation mechanisms.Mutually consistent coarse-grained (CG) models both for PAMAM den-drimers and for dimyristoylphosphatidylcholine (DMPC) lipid molecules are constructed based on chemical identities. The PAMAM CG model describes correctly the conformational behavior of the dendrimers, and the DMPC CG model can properly give the surface tension of the amphiphilic membrane.Systematic simulations are performed to investigate the binding structures of the dendrimers on membranes with varied length of the hydrophobic tails of amphiphiles. Simulation results reveal that the sizes of PAMAM dendrimers influence the penetrability of dendrimers across membrane. Dendrimers with large generations can easily disrupt the membrane and introduce isolated pores on the surface of the membranes. The radius of gyration (Rg) of dendrimers on membranes are larger than corresponding reference values. With the in-crease of the dendrimer generations, the asphericity of dendrimers decreases, causing a transition from planar to spherical conformation. At the same time, the conformational and aspherical properties of PAMAM dendrimers are in-fluenced by the length of hydrophobic moieties of amphiphiles. By increasing the length of the hydrophobic tail of amphiphiles, the Rg and the asphericity of dendrimers increase and correspond to oblate conformation on membranes. The cavities on membranes indented by the PAMAM dendrimers are also in-fluenced by changing the dendrimer concentration. With high concentrations, there is a synergistic effect with PAMAM dendrimers enhancing their per-meability across membranes. We believe that these mesoscopic simulation results can provide valuable insight and guidelines for the future synthesis and applications of charged PAMAM dendrimers as nano-vehicles in gene and drug delivery processes.(3) A coarse-grained model, with three sets of effective pair potentials for l-butyl-3-methylimidazolium hexafluorophosphate ([Bmim][PF6]) ionic liquid, is intro-duced and used to study the structural and dynamical properties over extended length and time scales. Three sets of effective pair potentials between coarse-grained beads are obtained from the Reverse Monte Carlo (RMC) and the it-erative Boltzmann Inversion (IBI) methods, respectively, with different treat-ment of electrostatic interactions. The coarse-grained simulation results are compared systematically with corresponding atomistic simulation results on several thermodynamical and structural quantities together with charge den-sity distributions. In addition, the scattering and dynamical properties are also calculated and compared to both atomistic simulation results and experimental measurements.Compared to the experimental measurements, the atomistic simulations can generate good results on density profiles and volumetric properties. The screening length of the charge structure existing in [Bmim][PF6] RTIL system, estimated from charge radial distributions, is approximately25A. This im-plies that the long-range electrostatic interactions should be explicitly treated in coarse-grained simulations if the coarse-graining level is not too high. The experimental scattering results calculated from simulations match well to the experimental measurements. But the direct comparison of the dynamical be-havior over a large temperature range is not easy since the current atomistic force field is limited to room temperature range. Hence the current atomistic force field parameters should be further refined to meet specific requirement in studying the dynamical properties of [Bmim][PF6] RTIL system over large temperature range.For coarse-grained simulations, we find that although the forms of the inter-action potentials derived from the RMC and the IBI iteration procedures with explicit treatment of electrostatic interactions are different, two sets of effec-tive potentials can reproduce exactly the same radial distribution functions (RDFs) as obtained in the atomistic reference simulations. For other proper-ties, such as thermodynamical, structural and dynamical properties, both two sets of effective potentials can generate similar results and reproduce gener-ally good results from atomistic simulations. While for the interaction poten-tials deduced from the RMC iteration scheme without explicit incorporation of electrostatic interactions but implicitly included in tabulated potentials, the coarse-grained simulation results reveal that all the agreements for thermody-namical, structural, scattering and dynamical properties are rather poor. We can conclude that in the development of effective potentials with the RMC and the IBI methods, the long-range electrostatic interactions between the ionic groups are important and should be treated explicitly to improve the reliabil-ity of the simulation results.(4) Polyethylene oxide (PEO) of different oligomer lengths but with fixed total number of ether units in aqueous dilute solution has been simulated using various differently developed FFs. These FFs, characterized with different interaction strengths between ether units and water molecules, are evaluated together with flexible SPC/E water model. The performance of five differ-ently parameterized force fields (denoted as GEN FF, EMP FF, CZMP FF, QC FF and CHARMM FF, respectively) in describing the behavior of PEO oligomers in dilute solution is critically and systematically studied using all- atomistic molecular dynamic simulations and compared with the available ex-perimental data.The GEN FF underestimate and QC FF overestimates the interactions between ether units and water molecules, resulting in lower and higher densities com-pared with experimental data. The CHARMM FF can properly reproduce the solution densities, while the EMP and CZMP FFs gave the densities in reason-able agreement with the experimental density. The solvation free energies for ether unit can be qualitatively reproduced by CZMP, QC and CHARMM FFs. The Rg of PEO oligomers differ between different force field. Both CZMP and QC FFs generate the relationship between Rg and molecular weight consid-erably well and are better than the CHARMM FF. All FFs show rather large fluctuations for end-to-end distance (Ree), which may be attributed to the ex-trapolated experimental data from long PEO chains, as well as that the confor-mation of PEO oligomers change continuously in dilute solution. Close exam-ination of RDFs reveals that the interaction strengths between ether units and water molecules in different force fields affect the formation of hydrogen bond network differently. PEO oligomers, described by GEN FF, show a consider-ably amount of hydrophobicity, while CHARMM FF gives semi-hydrophobic behaviors. The remaining three FFs can reproduce the PEO hydrophilic prop-erties qualitatively. The O-C-C-O segments on PEO chains are dominated by gauche conformation. Self-diffusion coefficients for PEO oligomers de-scribed by CZMP and CHARMM FFs are in good agreement with experimen-tal measurements. All EMP, GEN and QC FFs describe PEO oligomers with slower mobilities, even the power-law exponent fitted from QC FF is in con-sistence with nuclear magnetic resonance and analytical ultracentrifuge exper- imental measurements. The dependence of the dilute PEO solution propertieson particular water models is also investigated. In the water-rich regime (di-lute solution), both structural and conformer properties are found to be nearlyindependent on the water model.Overall, the CZMP FF performs best in reproducing PEO thermodynamic,chain dimension, structural characteristics and dynamic behavior. The QC FFdescribes the chain dimension and the hydrophilic behavior properly, also asdemonstrated in several other simulations. Simulation results obtained fromCHARMM FF are much better than those obtained from EMP and GEN FFs.