Constant-pressure and constant-surface tension simulations in dissipative particle dynamics

We present a method for constant-pressure and constant-surface tension simulations in dissipative particle dynamics using a Langevin piston approach. We demonstrate that the corresponding equations of motion lead to the relevant ensembles and propose an appropriate scheme of integration. After having identified a suitable set of parameters for the approach, we demonstrate the feasibility of the approach by applying it to two different systems, a simple isotropic fluid and an anisotropic fluid lipid-bilayer membrane in water. Results are presented for, respectively, isothermal bulk compressibility, tracer diffusion coefficient, lipid head-group area, and isothermal area compressibility. We find that our Langevin piston approach leads to improvements over other approaches in terms of faster equilibration and shorter correlation times of various system variables.     

Hydrodynamic interaction in polymer solutions simulated with dissipative particle dynamics

The authors analyzed extensively the dynamics of polymer chains in solutions simulated with dissipative particle dynamics (DPD), with a special focus on the potential influence of a low Schmidt number of a typical DPD fluid on the simulated polymer dynamics. It has been argued that a low Schmidt number in a DPD fluid can lead to underdevelopment of the hydrodynamic interaction in polymer solutions. The authors' analyses reveal that equilibrium polymer dynamics in dilute solution, under typical DPD simulation conditions, obey the Zimm [J. Chem. Phys. 24, 269 (1956)] model very well. With a further reduction in the Schmidt number, a deviation from the Zimm model to the Rouse model is observed. This implies that the hydrodynamic interaction between monomers is reasonably developed under typical conditions of a DPD simulation. Only when the Schmidt number is further reduced, the hydrodynamic interaction within the chains becomes underdeveloped. The screening of the hydrodynamic interaction and the excluded volume interaction as the polymer volume fraction is increased are well reproduced by the DPD simulations. The use of soft interaction between polymer beads and a low Schmidt number do not produce noticeable problems for the simulated dynamics at high concentrations, except for the entanglement effect which is not captured in the simulations.     

Finite-size effects in dissipative particle dynamics simulations

We have performed dissipative particle dynamics (DPD) simulations to evaluate the effect that finite size of transversal area has on stress anisotropy and interfacial tension. The simulations were carried out in one phase and two phases in parallelepiped cells. In one-phase simulations there is no finite-size effect on stress anisotropy when the simulation is performed using repulsive forces. However, an oscillatory function of stress anisotropy is found for attractive-repulsive interactions. In the case of liquid-liquid interfaces with repulsive interaction between molecules, there is only a small effect of surface area on interfacial tension when the simulations are performed using the Monte Carlo method at constant temperature and normal pressure. An important but artificial finite-size effect of interfacial area on surface tension is found in simulations in the canonical ensemble. Reliable results of interfacial tension from DPD simulations can be obtained using small systems, less than 2000 particles, when they interact exclusively with repulsive forces.     

Micellar polymerization: Computer simulations by dissipative particle dynamics

Nowadays, micellar polymerization is widely used in different fields of industry and research, including modern living polymerization technique. However, this process has many variables and there is no comprehensive model to describe all features. This research presents simulation methodology which describes key properties of such reactions to take a guide through a variety of their modifications. Dissipative particle dynamics is used in addition to Monte Carlo scheme to simulate initiation, propagation, and termination events. Influence of initiation probability and different termination processes on final conversion and molecular‐weight distribution are presented. We demonstrate that prolonged initiation leads to increasing in polymer average molecular weight, and surface termination events play major role in conversion limitation, in comparison with recombination. © 2018 Wiley Periodicals, Inc.     

反气相色谱法测定环氧树脂的表面张力和溶解度参数

采用反气相色谱(IGC)测定了环氧E51树脂在30、40、50和60 ℃下的表面张力和溶解度参数。采用Schultz法,以正癸烷、正壬烷、正辛烷和正庚烷为非极性溶剂探针,计算了不同温度下环氧E51树脂的色散表面张力。根据Good-van Oss方程,以甲苯为碱性探针,二氯甲烷为酸性探针,计算得到环氧E51树脂的极性表面张力。结果表明,环氧E51树脂的色散表面张力和极性表面张力均随着温度的升高而线性降低。根据不同溶剂探针与树脂间的Flory-Huggins相互作用参数,采用DiPaola-Baranyi和Guillet方法计算得到环氧E51树脂在不同温度下的溶解度参数,其在30、40、50和60 ℃下分别为11.78、11.57、11.48和11.14 MPa1/2。根据表面张力、内聚能和溶解度参数的相互关系,计算得到不同温度下溶解度参数的色散和极性分量。结果发现,环氧E51树脂的溶解度参数的色散分量大于极性分量,且均随着温度的升高而降低。     

Configurational temperature in membrane simulations using dissipative particle dynamics

The use of excessively long time steps in dissipative particle dynamics simulations may produce simulation artifacts due to the generation of configurations which are not representative of the desired canonical ensemble. The configurational temperature, among other quantities, may be used to assess the extent of the deviation from equilibrium. This paper presents results for simulations of models of water and lipid bilayer membranes to illustrate the nature of the problems.     

Nanospheres in phase-separating multicomponent fluids: a three-dimensional dissipative particle dynamics simulation

The dynamics of phase separation of three-dimensional fluids containing nanospheres, which interact preferentially with one of the two fluids, is studied by means of large-scale dissipative particle dynamics simulations. We systematically investigated the effect of volume fraction, radius, and mass of the nanoparticles on both kinetics and morphology of the binary mixture. We found that nanospheres lead to a reduction of domain growth which is intensified as their volume fraction is increased for a given radius of nanoparticles, or as the nanoparticles radius is decreased for a given volume fraction. Up to moderate volume fractions of nanoparticles, the growth law, however, is found to be identical to that pure binary fluids, i.e., R(t) approximately t(n), with n=1. For relatively high volume fractions of nanoparticles, a diffusive growth regime was detected. The crossover to the slower growth regime as the nanoparticles volume fraction is increased or their radius is decreased is associated with the crystallization of the nanospheres within the preferred component. These results are qualitatively in good agreement with previous two-dimensional simulations using molecular dynamics [M. Laradji and G. MacNevin, J. Chem. Phys. 119, 2275 (2003)] and a time-dependent Ginzburg-Landau model [M. Laradji, J. Chem. Phys. 120, 9330 (2004)], as well as recent experiments.     

Anomalous solubility parameter and probe dependency of polymer-polymer interaction parameter in inverse gas chromatography

Inverse gas chromatography (IGC) has been widely used to measure the Flory-Huggins interaction parameters, χ, between two polymers. For over two decades studies have shown the polymer-polymer interaction parameter to be probe dependent. This study found that the solubility parameters of miscible polymer blends measured by IGC were lower than the volume average values of the components. This led to the conclusion that when specific interactions occur between two polymers the probes have less probability to contact the functional groups of the polymers, leading to a lower apparent solubility parameter. Using the solubility parameter model this deviation was shown to cause the probe dependency. Two methods were proposed to test the miscibility. One was to examine the deviation of the specific retention volume from the weight average rule. The other was to plot ?₂?₃RT(χ₂₃/V₂) vs. the solubility parameters of probes. For miscible blends a linear trend with negative slope was observed. The slope was proportional to the deviation of solubility parameter of the polymer mixtures from the volume average, which could be used as a measurement for miscibility.     

A practical method to avoid bond crossing in two-dimensional dissipative particle dynamics simulations

Dissipative particle dynamics (DPD) simulation technique is an effective method targeted on mesoscopic simulations in which the interactions between particles are soft. As a result, it inevitably causes bond crossing and interpenetration between particles. Here we develop a practical method based on the two-dimensional DPD model which can extremely reduce the possibility of bond crossing. A rigid core is added to each particle by modifying the form of the conservative force in DPD so that the particles cannot penetrate each other. Then by adjusting the spring constant of the bond, we can impose a simple geometry constraint so that the bond crossing can hardly take place. Furthermore, we take into account an analytic geometry constraint in the polymerization model of DPD by which we can successfully avoid the severe bond crossing problem during bond generation in two dimensions. A parabola fitting between the pressure and the particle number density shows that our modified DPD model with small rigid cores can still be mapped onto the Flory-Huggins model, and the mesoscopic length scale of our simulations does not change. By analyzing the mean-square displacement of the innermost monomer and the center of mass of the chains, we find a t(8/15) power law of the polymer dynamics in our model instead of the Rouse prediction supporting the recent results in literature.     

Trotter derivation of algorithms for Brownian and dissipative particle dynamics

This paper focuses on the temporal discretization of the Langevin dynamics, and on different resulting numerical integration schemes. Using a method based on the exponentiation of time dependent operators, we carefully derive a numerical scheme for the Langevin dynamics, which we found equivalent to the proposal of Ermak and Buckholtz [J. Comput. Phys. 35, 169 (1980)] and not simply to the stochastic version of the velocity-Verlet algorithm. However, we checked on numerical simulations that both algorithms give similar results, and share the same "weak order two" accuracy. We then apply the same strategy to derive and test two numerical schemes for the dissipative particle dynamics. The first one of them was found to compare well, in terms of speed and accuracy, with the best currently available algorithms.     

Electrostatic interactions in dissipative particle dynamics using the Ewald sums

The electrostatic interactions in dissipative particle dynamics (DPD) simulations are calculated using the standard Ewald [Ann. Phys. 64, 253 (1921)] sum method. Charge distributions on DPD particles are included to prevent artificial ionic pair formation. This proposal is an alternative method to that introduced recently by Groot [J. Chem. Phys. 118, 11265 (2003)] where the electrostatic field was solved locally on a lattice. The Ewald method is applied to study a bulk electrolyte and polyelectrolyte-surfactant solutions. The structure of the fluid is analyzed through the radial distribution function between charged particles. The results are in good agreement with those reported by Groot for the same systems. We also calculated the radius of gyration of a polyelectrolyte in salt solution as a function of solution pH and degree of ionization of the chain. The radius of gyration increases with the net charge of the polymer in agreement with the trend found in static light scattering experiments of polystyrene sulfonate solutions.     

Mesoscopic simulation of self-assembly in surfactant oligomers by dissipative particle dynamics

Self-assembling properties of surfactant oligomers in an aqueous medium is simulated by dissipative particle dynamics (DPD). The critical micellar concentration (CMC) of dimeric (oligomerization = 2) and trimeric (oligomerization = 3) surfactant is much lower than their single-chain counterpart. All surfactants form spherical micelles at the concentration not far above their CMC. The transition from spherical to cylindrical micelles exhibits with increasing surfactant concentration. Lamellar micelles will appear with further increasing the surfactant concentration. For dimeric and trimeric surfactants, cylindrical micelles transform into extremely long “wormlike” or “threadlike” micelles before the transition to lamellar micelles. These results are in qualitative agreement with laboratory experiment. Average aggregation numbers (AN) of micelles increase with a power law of AN  c when the surfactant concentration c CMC. The self-diffusion coefficients will drop with a power law of D  c⁻ when wormlike micelles are formed.     

Two-component membrane material properties and domain formation from dissipative particle dynamics

The material parameters (area stretch modulus and bending rigidity) of two-component amphiphilic membranes are determined from dissipative particle dynamics simulations. The preferred area per molecule for each species is varied so as to produce homogeneous mixtures or nonhomogeneous mixtures that form domains. If the latter mixtures are composed of amphiphiles with the same tail length, but different preferred areas per molecule, their material parameters increase monotonically as a function of composition. By contrast, mixtures of amphiphiles that differ in both tail length and preferred area per molecule form both homogeneous and nonhomogeneous mixtures that both exhibit smaller values of their material properties compared to the corresponding pure systems. When the same nonhomogeneous mixtures of amphiphiles are assembled into planar membrane patches and vesicles, the resulting domain shapes are different when the bending rigidities of the domains are sufficiently different. Additionally, both bilayer and monolayer domains are observed in vesicles. We conclude that the evolution of the domain shapes is influenced by the high curvature of the vesicles in the simulation, a result that may be relevant for biological vesicle membranes.     

The phase behavior, structure, and dynamics of rodlike mesogens with various flexibility using dissipative particle dynamics simulation

We present a systematic dissipative particle dynamics (DPD) study on the phase behavior, structure, and dynamics of rodlike mesogens. In addition to a rigid fused-bead-chain model with RATTLE constraint method, we also construct a semirigid model in which the flexibility is controlled by the bending constant of k(φ). Using this notation, the rigid model has an infinite bending constant of k(φ)=∞. Within the parameter space studied, both two kinds of models exhibit the nematic and smectic-A phases in addition to the isotropic and solid phases. All of the phase transitions are accompanied by the discontinuities in the thermodynamical, structural, and dynamical quantities and the hysteresis around the transition points, and are therefore first order. Note that the obtained solid state exhibits an in-layer tetragonal packing due to the high density. For the rigid model, the simulations show that the liquid crystal phases can be observed for mesogens with at least five beads and the nematic phase is the first one to appear. More importantly, the phase diagram of seven-bead-chain models is obtained as a function of k(φ) and temperature. It is found that decreasing the value of k(φ) reduces the anisotropy of molecular shape and the orientational ordering, and thereby shifts the liquid crystal phases to the lower temperature end of the phase diagram. Due to the different k(φ) dependence of phase transition temperatures, the nematic phase range exhibits a more marked narrowing than the smectic-A phase as k(φ) is reduced, implying that the flexibility has a destabilizing effect on the nematic and smectic-A phases. We also have investigated the anisotropic translational diffusion in liquid crystal phases and its temperature and flexibility dependence. In our study, we find that the phases formed, their statical and dynamic properties, as well as the transition properties are in close accord with those observations in real thermotropic liquid crystals. It is clear that both the rigid and semirigid models we used are valuable models with which to study the behavior of thermotropic liquid crystals using DPD algorithm.     

A comparative study between dissipative particle dynamics and molecular dynamics for simple- and complex-geometry flows

The purpose of this study is to compare the results from molecular-dynamics and dissipative particle dynamics (DPD) simulations of Lennard-Jones (LJ) fluid and determine the quantitative effects of DPD coarse graining on flow parameters. We illustrate how to select the conservative force coefficient, the cut-off radius, and the DPD time scale in order to simulate a LJ fluid. To show the effects of coarse graining and establish accuracy in the DPD simulations, we conduct equilibrium simulations, Couette flow simulations, Poiseuille flow simulations, and simulations of flow around a periodic array of square cylinders. For the last flow problem, additional comparisons are performed against continuum simulations based on the spectral/hp element method.     

A many-body dissipative particle dynamics study of forced water-oil displacement in capillary

The forced water-oil displacement in capillary is a model that has important applications such as the groundwater remediation and the oil recovery. Whereas it is difficult for experimental studies to observe the displacement process in a capillary at nanoscale, the computational simulation is a unique approach in this regard. In the present work, the many-body dissipative particle dynamics (MDPD) method is employed to simulate the process of water-oil displacement in capillary with external force applied by a piston. As the property of all interfaces involved in this system can be manipulated independently, the dynamic displacement process is studied systematically under various conditions of distinct wettability of water in capillary and miscibility between water and oil as well as of different external forces. By analyzing the dependence of the starting force on the properties of water/capillary and water/oil interfaces, we find that there exist two different modes of the water-oil displacement. In the case of stronger water-oil interaction, the water particles cannot displace those oil particles sticking to the capillary wall, leaving a low oil recovery efficiency. To minimize the residual oil content in capillary, enhancing the wettability of water and reducing the external force will be beneficial. This simulation study provides microscopic insights into the water-oil displacement process in capillary and guiding information for relevant applications.