Schmidt number effects in dissipative particle dynamics simulation of polymers

Simulation studies for dilute polymeric systems are presented using the dissipative particle dynamics method. By employing two different thermostats, the velocity-Verlet and Lowe's scheme, we show that the Schmidt number (S(c)) of the solvent strongly affects nonequilibrium polymeric quantities. The fractional extension of wormlike chains subjected to steady shear is obtained as a function of S(c). Poiseuille flow in microchannels for fixed polymer concentration and varying number of repeated units within a chain is simulated. The nonuniform concentration profiles and their dependence on S(c) are computed. We show the effect of the bounce-forward wall boundary condition on the depletion layer thickness. A power law fit of the velocity profile in stratified Poiseuille flow in a microchannel yields wall viscosities different from bulk values derived from uniform, steady plane Couette flow. The form of the velocity profiles indicates that the slip flow model is not useful for the conditions of these calculations.     

On the calculation of disjoining pressure isotherms for nonaqueous films

A review of the methods of London and Hamaker and of Lifshitz for calculating disjoining pressure isotherms of nonaqueous liquid films is presented. The disjoining pressure isotherms for films of n-octane and of three triglycerides (tributyrin, tricaprylin, and triolein) on glass were calculated using both methods. The disjoining pressure isotherms for films on silanized glass were calculated using only the London-Hamaker approach. The refractive indices and static dielectric constants, necessary for the calculations, were measured. The silanized glass was considered to be the original glass covered by a layer with the same characteristic frequency as the underlying glass and a smaller limiting value of the dielectric constant epsilon(0). The limiting dielectric constant epsilon(0) and the thickness of the surface layer were taken as adjustable parameters. The disjoining pressure isotherms indicate that all films are stable on glass. In contrast, the stability of the films formed on silanized glass was found to depend mainly on the value of epsilon(0) and, less strongly, on the thickness of the surface layer. The stability of the films decreased with the decrease of epsilon(0) and, for each value of epsilon(0), was maximal for the thinnest surface layer.     

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.     

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.     

Constant-pressure simulations with dissipative particle dynamics

Dissipative particle dynamics (DPD) is a mesoscopic simulation method for studying hydrodynamic behavior of complex fluids. Ideally, a mesoscopic model should correctly represent the thermodynamic and hydrodynamic properties of a real system beyond certain length and time scales. Traditionally defined DPD quite successfully mimics hydrodynamics but is not flexible enough to accurately describe the thermodynamics of a real system. The so-called multibody DPD (MDPD) is a pragmatic extension of the classical DPD that allows one to prescribe the thermodynamic behavior of a system with only a small performance impact. In an earlier paper [S. Y. Trofimov, E. L. F. Nies, and M. A. J. Michels, J. Chem. Phys. 117, 9383 (2002)] we much improved the accuracy of the MDPD model for strongly nonideal systems, which are of most practical interest. The ability to correctly reproduce the equation of state of realistic systems in turn makes simulations at constant pressure sensible and useful. This situation of constant-pressure conditions is very common in experimental studies of (soft) condensed matter but has so far remained unexplored with the traditional DPD. Here, as a proof of concept, we integrate a modified version of the Andersen barostat into our improved MDPD model and make an evaluation of the performance of the new model on a set of single- and multicomponent systems. The modification of the barostat suppresses the "unphysical" volume oscillations after a sudden pressure change and simplifies the equilibration of the system.     

Flow-induced translocation of polymers through a fluidic channel: a dissipative particle dynamics simulation study

The dynamics of flow-induced translocation of polymers through a fluidic channel has been studied by dissipative particle dynamics (DPD) approach. Unlike implicit solvent models, the many-body energetic and hydrodynamic interactions are preserved naturally by incorporating explicit solvent particles in this approach. The no-slip wall boundary and the adaptive boundary conditions have been implemented in the modified DPD approach to model the hydrodynamic flow within a specific wall structure of fluidic channel and control the particles' density fluctuations. The results show that the average translocation time versus polymer chain length satisfies a power-law scaling of τ ～N(1.152). The conformational changes and translocation dynamics of polymers through the fluidic channel have also been investigated in our simulations, and two different translocation processes, i.e., the single-file and double-folded translocation events, have been observed in detail. These findings may be helpful in understanding the conformational and dynamic behaviors of such polymer and/or DNA molecules during the translocation processes.     

Coil-to-globule transition by dissipative particle dynamics simulation

The dynamics of a collapsing polymer under a temperature quench in dilute solution is investigated by dissipative particles dynamics. Hydrodynamic interactions and many-body interaction are preserved naturally by incorporating explicit solvent particles in this approach. Our simulation suggests a four-stage collapse pathway: localized clusters formation, cluster coarsening in situ, coarsening involving global backbone conformation change into a crumpled globule, and compaction of the globule. For all the quench depths and chain lengths used in our study, collapse proceeds without the chain getting trapped in a metastable "sausage" configuration, as reported in some earlier studies. We obtain the time scales for each of the first three stages, as well as its scaling with the quench depths ξ and chain lengths N. The total collapse time scales as τ(c) ～ ξ(-0.46 ± 0.04)N(0.98 ± 0.09), with the quench depth and degree of polymerization.     

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.     

New parametrization method for dissipative particle dynamics

We introduce an improved method of parametrizing the Groot-Warren version of dissipative particle dynamics (DPD) by exploiting a correspondence between DPD and Scatchard-Hildebrand regular solution theory. The new parametrization scheme widens the realm of applicability of DPD by first removing the restriction of equal repulsive interactions between like beads, and second, by relating all conservative interactions between beads directly to cohesive energy densities. We establish the correspondence by deriving an expression for the Helmoltz free energy of mixing, obtaining a heat of mixing which is exactly the same form as that for a regular mixture (quadratic in the volume fraction) and an entropy of mixing which reduces to the ideal entropy of mixing for equal molar volumes. We equate the conservative interaction parameters in the DPD force law to the cohesive energy densities of the pure fluids, providing an alternative method of calculating the self-interaction parameters as well as a route to the cross interaction parameter. We validate the new parametrization by modeling the binary system SnI(4)SiCl(4), which displays liquid-liquid coexistence below an upper critical solution temperature around 140 degrees C. A series of DPD simulations were conducted at a set of temperatures ranging from 0 degrees C to above the experimental upper critical solution temperature using conservative parameters based on extrapolated experimental data. These simulations can be regarded as being equivalent to a quench from a high temperature to a lower one at constant volume. Our simulations recover the expected phase behavior ranging from solid-liquid coexistence to liquid-liquid coexistence and eventually leading to a homogeneous single phase system. The results yield a binodal curve in close agreement with the one predicted using regular solution theory, but, significantly, in closer agreement with actual solubility measurements.     

Improved dissipative particle dynamics simulations of lipid bilayers

The authors introduce a new parameterization for the dissipative particle dynamics simulations of lipid bilayers. In this parameterization, the conservative pairwise forces between beads of the same type in two different hydrophobic chains are chosen to be less repulsive than the water-water interaction, but the intrachain bead interactions are the same as the water-water interaction. For a certain range of parameters, the new bilayer can only be stretched up to 30% before it ruptures. Membrane tension, density profiles, and the in-plane lipid diffusion coefficient of the new bilayer are discussed in detail. They find two kinds of finite size effects that influence the membrane tension: lateral finite size effects, for which larger membranes rupture at a smaller stretch, and transverse finite size effects, for which tensionless bilayers are more compact in larger systems. These finite size effects become rather small when the simulation box is sufficiently large.     

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.     

Molecular dynamics simulation of pressure isotherms for nanofluids

Pressure isotherms have been constructed by the molecular dynamics method for nanofluids based on argon and zinc, aluminum, and lithium nanoparticles. Nanoparticle volume concentration is varied from 1 to 10%. Nanoparticles have sizes of 1 or 2 nm. The equation of state has been shown to essentially depend on the volume concentration, size, and material of the particles. Depending on the density of a carrier fluid, the pressure of a nanofluid (at a preset density) may be either higher or lower than the pressure of the basic fluid. On the other hand, the partial pressure of a pseudogas of nanoparticles decreases rapidly with an increase in their sizes (inversely proportional to the cubed particle radius).     

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.     

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.     

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.     

Multiple time step update schemes for dissipative particle dynamics

In dynamical simulations of coarse-grained models of soft matter in a solvent a considerable amount of the total simulation time is generically spent on updating the solvent particles, although their dynamics is in most cases not of primary interest. In order to speed up such simulations and as a consequence allow to extend them to cover larger system sizes, we propose and examine various multiple, specifically dual, time step update algorithms for dissipative particle dynamics simulations that are based on the velocity-Verlet scheme [Phys. Rev. 159, 98 (1967)]. Common to all update variants is that the solvent beads are updated with a lower frequency than the bonded interactions within the solute. As a test case we consider a coarse-grained model of a lipid bilayer in water. Our results demonstrate that a considerable saving of simulation time can be gained, while the obtained simulation data are within error brackets virtually identical to those obtained for the reference single time step update scheme.