Dissipative Particle Dynamics Particles Research Articles

Interface of Hydrated Perfluorosulfonic Acid Electrolyte and Platinum Catalyst: Dissipative Particle Dynamics Simulation Model

Polymer electrolyte fuel cells (PEFC) are expected to be used widely in the future as a non-polluting power source in various applications. PEFC applications are only limited currently however, as PEFCs are still not competitive with existing power sources in energy efficiency and cost. One of the most popular forms of PEFC are composed of an electrolyte of hydrated perfluorosulfonic acid (PFSA), and carbon based electrodes that support small catalyst particles (typically Pt) on the surface. The global performance of PEFC of this type is governed by the rate of red-ox reactions on the catalyst surface, which are affected by molecular level dynamics of fuel, oxidants, and protons in the electrolyte near the catalyst surface. We need deeper understanding on this interfacial structures for new insights into the mechanisms that control the electrochemical surface processes. Several structure models have been proposed for the bulk electrolyte, while only little is understood as to its structure near the catalyst surface so far. In this study, to investigate the interfacial system of hydrated PFSA and platinum surface, we constructed models of this system for dissipative particle dynamics (DPD) simulations. DPD simulation is a kind of coarse-grained simulation which is used to study mesoscopic systems, typically consisting of macromolecules like polymers and biomolecules. We coarse grained the simulation system with DPD particles corresponding to PFSA segments A-C (see Fig.1), those grouping four water molecules (denoted as W), and those grouping ~8 platinum atoms (Pt). The catalyst surface was represented by a fixed slab of the Pt particles forming a simple lattice. We used soft potentials constructed via quantum chemical calculations by Okuwaki et al. [1] for interactions of DPD particles A-C and W; while we newly constructed soft potentials for the interactions of Pt with other DPD particles by analyzing their affinities via all-atom classical MD simulations for some small systems. For these all-atom MD simulations, we derived some intermolecular potential functions by first principles calculations. Details of our DPD simulations as well as the interaction model constructions will be presented in the conference session (a snapshot is displayed in Fig. 2). A portion of this research was supported by MEXT within the priority issue 6 of the FLAGSHIP2020 project (Project ID: hp160226, hp170253,hp180187). [1] K. Okuwaki et al., JSAP spring meeting (2016) 20a-W323-6. Figure 1

The Study of the Behavior of Nanocomposites Including Polymer Grafted Nanoparticles with Dissipative Particle Dynamics Simulation

Recently nanocomposites attract a lot of interests in the industry and the academic because the materials have a possibility to make their function much higher. The candidates of compositions are so many that it is the hard task that one finds the objective function. The insertion of inorganic nanoparticles like silica into polymers is one of the ways to make the material function higher. Controlling their dispersion is the important and difficult theme and the state of dispersion will have an influence on the physical properties like viscoelasticity. If the dispersive structure is necessary, grafting polymers onto nanoparticles is one of the methods. Computer simulation is a powerful tool to study the structure and physical properties of materials, but it is difficult to perform atomistic molecular dynamics simulations to understand the dispersion and slow dynamics of nanocomposites on account of the time and length scale. We therefore attempt to perform the Dissipative Particle Dynamics (DPD) simulation to study the behavior of nanocomposites including polymer grafted nanoparticles. The fundamental setup of the DPD simulation follows the method of Groot and Warren [1]. We make a sphere nanoparticle by collecting DPD particles with bond and angle potentials. The angle potential is considered to reproduce rigidity of the particle. We also make a linear chain polymer for the matrix polymers and the polymers grafting onto the particles. To assume the particle like silica and the polymer like polystyrene and not to penetrate the polymers into the particles, the interaction between the particles and polymers are more repulsive than that between particles and between polymers. The graft polymers are grafted onto the all surface of the particle to ignore the interactions on the interface between particles and matrix polymers. The modeling procedures are achieved with J-OCTA [2]. Fig. 1 shows the dispersion of the grafted nanoparticles with volume fraction of 3% of themselves. The lengths of both matrix polymers and grafted polymers are the same and each of these polymers is composed of 10 DPD particles with bonding, which assumes to ignore the entanglement effect. If no grafted polymers are on the particle, the particles are easy to aggregate. Next, with using the dispersive structure, we obtained the linear relaxation moduli G(t) by Green-Kubo formula. Figure 2 shows the comparison of G(t) with nanocomposites and pure polymers. The polymer chain length in pure polymers is also 10. By inserting the nanoparticles, the modulus is increasing and the terminal relaxation time is longer compared to those of pure polymers. These results would indicate that DPD simulation reproduces the effect of reinforcement of nanoparticles in the polymer system. If the molecular weight of polymers is larger than the molecular weight between entanglements, the entanglement effect would appear and have influence on the physical properties. Recently to reproduce the entanglement effect with DPD, the slip-spring model is suggested [3]. In the presentation, we would discuss the application of the model to the nanocomposites.

Mesoscopic modelling of microbubble in liquid with finite density ratio of gas to liquid

A microbubble model is developed with the mesoscopic simulation tool, dissipative particle dynamics (DPD) and many-body dissipative particle dynamics (MDPD). Standard DPD particles are employed to represent bubble phase at low density, and MDPD particles are for the liquid phase. The microbubble can be stable in liquid, in contrast to the vacuum bubble model. Gas-liquid interface is well presented with density and pressure jumps. The density ratio of gas to liquid can be lower than 0.1 by increasing the cut-off radius of bubble particles. Oscillating behavior of the microbubble model is investigated and validated by comparing with the Rayleigh-Plesset equation. The current model shows correct dynamic response, and the fluctuating behavior is captured as well. The lower the density ratio of the microbubble model, the closer the oscillating frequency to that of continuum theory.

DPD of diffusion-weighted MRI

Diffusion weighted magnetic resonance imaging (DW-MRI) experiments can be simulated by coupling dissipative particle dynamics (DPD) with Bloch equations. DPD gives hydrodynamics with thermal fluctuations at a well-defined temperature by introducing momentum conserving particle interaction forces and a fluctuation dissipation theorem. The Bloch equations are a set of differential equations that describe the evolution of nuclear magnetization as a function of time. Here we successfully simulate DW-MRI by using the solution of Bloch equations for each DPD particle while computing its trajectories through DPD forces. To this end, a spin echo sequence combined with different diffusion-weighting gradients was implemented and tested for the diffusion of a fluid bound by different diffusion regimes. Fluid confinement was easily incorporated, which enabled investigating different diffusion regimes and the performance of different pulse sequences. The three different sequences applied were: spin echo single-sided bipolar gradient, spin echo two-sided bipolar gradient and spin echo uni-polar gradient; and the three imaged diffusion regimes of interest were: free diffusion, localization and motional narrowing.

Anisotropic single-particle dissipative particle dynamics model

We have developed a new single-particle dissipative particle dynamics (DPD) model for anisotropic particles with different shapes, e.g., prolate or oblate spheroids. In particular, the conservative and dissipative interactions between anisotropic single DPD particles are formulated using a linear mapping from the isotropic model of spherical particles. The proper mapping operator is constructed between each interacting pair of particles at every time step. Correspondingly, the random forces are properly formulated to satisfy the fluctuation-dissipation theorem (FDT). Notably, the model exactly conserves both linear and angular momentum. We demonstrate the proposed model's accuracy and efficiency by applying it for modeling colloidal ellipsoids. Specifically, we show it efficiently captures the static properties of suspensions of colloidal ellipsoids. The isotropic-nematic transition in an ellipsoidal suspension is reproduced by increasing its volume fraction or the aspect ratio of ellipsoid particles. Moreover, the hydrodynamics and diffusion of a single colloidal ellipsoid (prolate or oblate with moderate aspect ratios) are accurately captured. The calculated drag force on the ellipsoid and its diffusion coefficients (both translational and rotational) agree quantitatively with the theoretical predictions in the Stokes limit.

A dissipative particle dynamics model for thixotropic materials exhibiting pseudo-yield stress behaviour

Many materials (e.g., gels, colloids, concentrated cohesive sediments, etc.) exhibit a stable solid form at rest, and liquify once subjected to an applied stress exceeding a critical value – a yield-stress behaviour. This can be qualitatively explained by the forming and destruction of the fluid microstructure [1], and it may be modelled as a thixotropic and yield stress material. In this paper, we propose a mesoscopic model which is able to mimic a thixotropic and yield stress behaviour using a particle-based technique known as dissipative particle dynamics (DPD). The DPD technique satisfies conservation of mass and momentum and it has been applied successfully for a number of problems involving complex-structure fluids, such as polymer solutions, suspensions of rigid particles, droplets, biological fluids, etc. In this work, an indirect linkage dissipative particle model (ILDP) is proposed based on qualitative microstructural physics, which results in a non-Newtonian fluid with observed yield stress and thixotropic properties. The model comprises of two types, or species, of DPD particles – with only repulsive conservative force between the same species, and with repulsive force at short range and attractive force at long range between different species. Numerical results show that the proposed DPD fluid can represent some observed complex behaviours, such as yield stress and thixotropic effects.

Electrostatics in dissipative particle dynamics using Ewald sums with point charges

A proper treatment of electrostatic interactions is crucial for the accurate calculation of forces in computer simulations. Electrostatic interactions are typically modeled using Ewald-based methods, which have become some of the cornerstones upon which many other methods for the numerical computation of electrostatic interactions are based. However, their use with charge distributions rather than point charges requires the inclusion of ansatz for the solutions of the Poisson equation, since there is no exact solution known for smeared out charges. The interest in incorporating electrostatic interactions at the scales of length and time that are relevant for the study the physics of soft condensed matter has increased considerably. Using mesoscale simulation techniques, such as dissipative particle dynamics (DPD), allows us to reach longer time scales in numerical simulations, without abandoning the particulate description of the problem. The main problem with incorporating electrostatics into DPD simulations is that DPD particles are soft and those particles with opposite charge can form artificial clusters of ions. Here we show that one can incorporate the electrostatic interactions through Ewald sums with point charges in DPD if larger values of coarse-graining degree are used, where DPD is truly mesoscopic. Using point charges with larger excluded volume interactions, the artificial formation of ionic pairs with point charges can be avoided and one obtains correct predictions. We establish ranges of parameters useful for detecting boundaries where artificial formation of ionic pairs occurs. Lastly, using point charges we predict the scaling properties of polyelectrolytes in solvents of varying quality, and obtain predictions that are in agreement with calculations that use other methods and with recent experimental results.

Dissipative Particle Dynamics interaction parameters from ab initio calculations

Dissipative Particle Dynamics (DPD) is a commonly employed coarse-grained method to model complex systems. Presented here is a pragmatic approach to connect atomic-scale information to the meso-scale interactions defined between the DPD particles or beads. Specifically, electronic structure calculations were utilized for the calculation of the DPD pair-wise interaction parameters. An implicit treatment of the electrostatic interactions for charged beads is introduced. The method is successfully applied to derive the parameters for a hydrated perfluorosulfonic acid ionomer with absorbed vanadium cations.

Structure–Property Relationship of Sulfosuccinic Acid Diester Sodium Salt Micelles: 3D-QSAR Model and DPD Simulation

The objective of this study was to develop structure–property relationship of a series of sulfosuccinic acid diester sodium salts required for industrial purposes. In this paper, three-dimensional quantum structure–activity relationship (3D-QSAR) method studies are performed to elucidate the relationship between critical micelle concentration (CMC) activity and molecular 3D structural features. Two regression models are developed by partial least squares (PLS) and genetic function approximation (GFA), respectively. The training set of PLS-QSAR model generates a correlation coefficient (R2) = 0.94539300 and sum of square of residues (S2) = 0.32764200. For the GFA-QSAR model, the training set yields R2 = 1.00000000. It is shown that the GAF method effectively improves the test accuracy significantly. Dissipative particle dynamics (DPD) mesoscopic molecular simulation method is carried out on the aggregation behavior of polyoxyethylene (n) stearyl ether sodium sulfosuccinate (PSSE-n) surfactant micelles. In the DPD simulation, water molecular (solvent) and colloidal particles are replaced by a set of DPD particles. The results demonstrated that sensitive PSSE-n molecules can assemble into special structures in specific solution concentration, such as star-shaped micelle, spherical micelle, rodlike micelle, and lamellar phase. DPD simulation can be used as an efficient method for studying the structure–property relationship of sulfosuccinic acid diester sodium salts.

New modified weight function for the dissipative force in the DPD method to increase the Schmidt number

To simulate liquid fluid flows with high Schmidt numbers (Sc), one needs to use a modified version of the Dissipative Particle Dynamics (DPD) method. Recently the modifications made by others for the weight function of dissipative forces, enables DPD simulations for Sc, up to 10. In this paper, we introduce a different dissipative force weight function for DPD simulations that allows achieving a solution with higher values of Sc and improving the dynamic characteristics of the simulating fluid. Moreover, by reducing the energy of DPD particles, even higher values of Sc can be achieved. Finally, using the new proposed weight function and , the Sc values can reach up to 200.

Liquid-liquid equilibria for soft-repulsive particles: improved equation of state and methodology for representing molecules of different sizes and chemistry in dissipative particle dynamics.

Three developments are presented that significantly expand the applicability of dissipative particle dynamics (DPD) simulations for symmetric and non-symmetric mixtures, where the former contain particles with equal repulsive parameter for self-interactions but a different repulsive parameter for cross-interactions, and the latter contain particles with different repulsive parameters also for the self-interactions. Monte Carlo and molecular dynamics simulations for unary phases covering a wide range of repulsive parameters and of densities for single-bead DPD particles point to deficiencies of the Groot and Warren equation of state (GW-EOS) [J. Chem. Phys. 107, 4423 (1997)]. A revised version, called rGW-EOS, is proposed here that is significantly more accurate over a wider range of parameters/densities. The second development is the generalization of the relationship between the Flory-Huggins χ parameter and the repulsive cross-interaction parameter when the two particles involved have different molecular volumes. The third aspect is an investigation of Gibbs ensemble Monte Carlo simulation protocols, which demonstrates the importance of volume fluctuations and excess volumes of mixing even for equimolar symmetric mixtures of DPD particles. As an illustrative example, the novel DPD methodology is applied to the prediction of the liquid-liquid equilibria for acetic anhydride/(n-hexane or n-octane) binary mixtures.

An efficient dissipative particle dynamics-based algorithm for simulating electrolyte solutions.

We propose an efficient simulation algorithm based on the dissipative particle dynamics (DPD) method for studying electrohydrodynamic phenomena in electrolyte fluids. The fluid flow is mimicked with DPD particles while the evolution of the concentration of the ionic species is described using Brownian pseudo particles. The method is designed especially for systems with high salt concentrations, as explicit treatment of the salt ions becomes computationally expensive. For illustration, we apply the method to electro-osmotic flow over patterned, superhydrophobic surfaces. The results are in good agreement with recent theoretical predictions.

Investigation of particles size effects in Dissipative Particle Dynamics (DPD) modelling of colloidal suspensions

In the Dissipative Particle Dynamics (DPD) simulation of suspension, the fluid (solvent) and colloidal particles are replaced by a set of DPD particles and therefore their relative sizes (as measured by their exclusion zones) can affect the maximal packing fraction of the colloidal particles. In this study, we investigate roles of the conservative, dissipative and random forces in this relative size ratio (colloidal/solvent). We propose a mechanism of adjusting the DPD parameters to properly model the solvent phase (the solvent here is supposed to have the same isothermal compressibility to that of water).

Mesoscale study of particle sedimentation with inertia effect using dissipative particle dynamics

Mesoscale dispersed two-phase flows often involve complicated dynamic behaviors. Grid-based methods within the framework of continuum mechanics are usually difficult to capture certain degree of molecular-level effect, while the molecular dynamics is only practical at extremely small temporal and spatial scales. In this paper, dissipative particle dynamics (DPD) is extended to the investigation of a fluid–solid sphere system with inertia effect within two parallel plates through the modification of DPD weighting function and hence the dynamic parameters. The sphere and walls are composed of frozen DPD particles that are first treated to reach equilibrium state in the simulation. The force on the solid sphere is obtained from all the particles included in the sphere. The drag coefficient of the frozen sphere is evaluated and compared with the classical correlations. The initial value problem for the sedimentation of the sphere is then solved at certain Reynolds numbers, which is consistent with our direct numerical simulation results.

Structural analysis of telechelic polymer solution using dissipative particle dynamics simulations

A telechelic polymer is an amphiphilic polymer that can form micellar structures when dissolved in water. A telechelic polymer solution shows viscoelastic behaviour owing to the formation of characteristic networks, i.e. loops, bridges and dangling chains. For industrial purposes, telechelic polymers have many applications as thickening agents, such as in paints and cosmetics. Thus, it is desirable to predict and control the rheological properties of telechelic polymers. However, detailed studies at the molecular level have not yet been performed. In this study, I use the dissipative particle dynamics (DPD) method to investigate the relationship between the characteristic structural properties and the molecular structure in telechelic polymer solutions. I show that the morphology of telechelic polymer solutions depends on the concentration and chain length, the distribution of the end-to-end distance, the mean square end-to-end distance, the mean square radius of gyration and the time-averaged mean square displacement. Although an effect of entanglement is important for properties of polymer melts, the polymer chain composed of DPD particles cannot reproduce it. Therefore, I compare telechelic polymer solutions with and without the segmental repulsive potential (SRP), which can simulate the effect of entanglement in DPD simulations. The results indicate that it is necessary to include the SRP in DPD simulations to correctly analyse the behaviour of telechelic polymer solutions.

A spring model for suspended particles in dissipative particle dynamics

This paper is concerned with the use of oscillating particles instead of the usual frozen particles to model a suspended particle in the dissipative particle dynamics (DPD) method. A suspended particle is represented by a set of basic DPD particles connected to reference sites by linear springs of very large stiffness. The reference sites, collectively modeling a rigid body, move as a rigid body motion calculated through their Newton-Euler equations, using data from the previous time step, while the velocities of their associated DPD particles are found by solving the DPD equations at the current time step. In this way, a specified Boltzmann temperature (specific kinetic energy of the particles) can be maintained throughout the computational domain, including the region occupied by the suspended particles. This parameter can also be used to adjust the size of the suspended and solvent particles, which in turn affect the strength of the shear-thinning behavior and the effective maximal packing fraction. Furthermore, the suspension, comprised of suspended particles in a set of solvent particles all interacting under a quadratic soft repulsive potential, can be simulated using a relatively large time step. Several numerical examples are presented to demonstrate attractiveness of the proposed model.

Distortion and flow of nematics simulated by dissipative particle dynamics.

In this study, we simulated distortion and flow of nematics by dissipative particle dynamics (DPD). The nematics were modeled by a binary mixture that contained rigid rods composed of DPD particles as mesogenic units and normal DPD particles as solvent. Elastic distortions were investigated by monitoring director orientation in space under influences of boundary anchoring and external fields. Static distortion demonstrated by the simulation is consistent with the prediction of Frank elastic theory. Spatial distortion profile of the director was examined to obtain static elastic constants. Rotational motions of the director under influence of the external field were simulated to understand the dynamic process. The rules revealed by the simulation are in a good agreement with those obtained from dynamical experiments and classical theories for nematics. Three Miesowicz viscosities were obtained by using external fields to hold the orientation of the rods in shear flows. The simulation showed that the Miesowicz viscosities have the order of ηc > ηa > ηb and the rotational viscosity γ1 is about two orders larger than the Miesowicz viscosity ηb. The DPD simulation correctly reproduced the non-monotonic concentration dependence of viscosity, which is a unique property of lyotropic nematic fluids. By comparing simulation results with classical theories for nematics and experiments, the DPD nematic fluids are proved to be a valid model to investigate the distortion and flow of lyotropic nematics.

Simulation of a single red blood cell flowing through a microvessel stenosis using dissipative particle dynamics.

The motion and deformation of a single red blood cell flowing through a microvessel stenosis was investigated employing dissipative particle dynamics (DPD) method. The numerical model considers plasma, cytoplasm, the RBC membrane and the microvessel walls, in which a three dimensional coarse-grained spring RBC. The suspending plasma was modelled as an incompressible Newtonian fluid and the vessel walls were regarded as rigid body. The body force exerted on the free DPD particles was used to drive the flow. A modified bounce-back boundary condition was enforced on the membrane to guarantee the impenetrability. Adhesion of the cell to the stenosis vessel surface was mediated by the interactions between receptors and ligands. Firstly, the motion of a single RBC in a microfluidic channel was simulated and the results were found in agreement with the experimental data cited by [1]. Then the mechanical behavior of the RBC in the microvessel stenosis was studied. The effects of the bending rigidity of membrane, the size of the stenosis and the driven body force on the deformation and motion of red blood cell were discussed.

Rheology of bubble suspensions using dissipative particle dynamics. Part I: A hard-core DPD particle model for gas bubbles

In this paper, the rheology of dilute bubble suspensions is studied using dissipative particle dynamics (DPD). Each gas bubble is modeled by a hard-core DPD particle. The approach addresses the issue of zero-viscosity arising from modeling of a gas bubble by a set of DPD particles. Moreover, it helps to reduce significantly the computational demand due to a much less number of DPD particles required in the simulation. A dissipative layer is created outside the effective region of the hard-core DPD particle to manage the hydrodynamic force acting on it, and different phases can be defined accordingly. The model is further examined in the simulation of dilute bubble suspensions, and measurements on the Newtonian viscosity for the volume fraction less than 15% are consistent with experimental results and results from theoretical models in continuum mechanics at low Ca limit.

Dissipative particle dynamics study of translational diffusion of rigid-chain rodlike polymer in nematic phase

In this study, dissipative particle dynamics (DPD) method was employed to investigate the translational diffusion of rodlike polymer in its nematic phase. The polymer chain was modeled by a rigid rod composed of consecutive DPD particles and solvent was represented by independent DPD particles. To fully understand the translational motion of the rods in the anisotropic phase, four diffusion coefficients, D∥(u), D⊥(u), D∥(n), D⊥(n) were obtained from the DPD simulation. By definition, D∥(n) and D⊥(n) denote the diffusion coefficients parallel and perpendicular to the nematic director, while D∥(u) and D⊥(u) denote the diffusion coefficients parallel and perpendicular to the long axis of a rigid rod u. In the simulation, the velocity auto-correlation functions were used to calculate the corresponding diffusion coefficients from the simulated velocity of the rods. Simulation results show that the variation of orientational order caused by concentration and temperature changes has substantial influences on D∥(u) and D⊥(u). In the nematic phase, the changes of concentration and temperature will result in a change of local environment of rods, which directly influence D∥(u) and D⊥(u). Both D∥(n) and D⊥(n) can be represented as averages of D∥(u) and D⊥(u), and the weighted factors are functions of the orientational order parameter S2. The effect of concentration and temperature on D∥(n) and D⊥(n) demonstrated by the DPD simulation can be rationally interpreted by considering their influences on D∥(u), D⊥(u) and the order parameter S2.