Dissipative Particle Dynamics Particles Research Articles

Construction of Multiscale Dissipative Particle Dynamics (DPD) Models from Other Coarse-Grained Models.

We present a general scheme for converting coarse-grained models into Dissipative Particle Dynamics (DPD) models. We build the corresponding DPD models by analogy with the de novo DPD coarse-graining scheme suggested by Groot and Warren (J. Chem. Phys., 1997). Electrostatic interactions between charged DPD particles are represented though the addition of a long-range Slater Coulomb potential as suggested by González-Melchor et al. (J. Chem. Phys., 2006). The construction is illustrated by converting MARTINI models for various proteins into a DPD representation, but it not restricted to the usual potential form in the MARTINI model-viz., Lennard-Jones potentials. We further extended the DPD scheme away from the typical use of homogeneous particle sizes, therefore faithfully representing the variations in the particle sizes seen in the underlying MARTINI model. The accuracy of the resulting construction of our generalized DPD models with respect to several structural observables has been benchmarked favorably against all-atom and MARTINI models for a selected set of peptides and proteins, and variations in the scales of the coarse-graining of the water solvent.

Determination of interaction parameters in a bottom-up approach employed in reactive dissipative particle dynamics simulations for thermosetting polymers.

The limitations in previous dissipative particle dynamics (DPD) studies confined simulations to a narrow resin range. This study refines DPD parameter calculation methodology, extending its application to diverse polymer materials. Using a bottom-up approach with molecular dynamics (MD) simulations, we evaluated solubility parameters and bead number density governing nonbonded interactions via the Flory-Huggins parameter and covalent-bonded interactions. Two solubility parameter methods, Hildebrand and Krevelen-Hoftyzer, were compared for DPD simulations. The Hildebrand method, utilizing MD simulations, demonstrates higher consistency and broader applicability in determining solubility parameters for all DPD particles. The DPD/MD curing reaction process was examined in three epoxy systems: DGEBA/4,4'-DDS, DGEBA/MPDA and DGEBA/DETA. Calculations for the curing profile, gelation point, radial distribution function and branch ratio were performed. Compared to MD data for DGEBA/4,4'-DDS, the maximum deviation in secondary reactions between epoxy and amine groups according to DPD simulations with Krevelen-Hoftyzer was 14.8%, while with the Hildebrand method, it was 1.7%. The accuracy of the DPD curing reaction in reproducing the structural properties verifies its expanded application to general polymeric material simulations. The proposed curing DPD simulations, with a short run time and minimal computational resources, contributes to high-throughput screening for optimal resins and investigates mesoscopic inhomogeneous structures in large resin systems.

Representing the Fluid Particle Model to incorporate two non-central components for dissipation forces associated with random forces: A new integral algorithm in the modified Dissipative Particle Dynamics method

The standard formulation of dissipative particle dynamics (DPD) only considers centripetal forces acting on a single DPD particle, neglecting the eccentric cut-off forces between dissipation particles. Consequently, this model does not account for angular momentum and torque for individual DPD particles, whereas suspended particles in a stream exhibit both translational and rotational motion. To overcome this limitation, the fluid particle model (FPM) is proposed in this study, which incorporates two non-central cut-off components for dissipation forces that are associated with random forces via the fluctuation-dissipation theory. To accurately account for single particle hydrodynamics, a novel integration algorithm is introduced and assessed for its precision. Through simulations in low Reynolds number flows, this research determines the coefficients of the modified DPD formulation and validates its accuracy for simulating colloidal and polymeric solutions. Furthermore, this modified model can be employed for simulating currents passing through single DPD particles. The simulation results are compared with the analytical results, revealing the superior accuracy of the modified formulation. The findings also suggest an optimal choice of constants, time steps, and weight functions.

Novel multiscale simulations on the membrane formation via hybrid induced phase separation process based on dissipative particle dynamics

A novel simulation methodology, that was based on dissipative particle dynamics (DPD) combined with information from molecular dynamics (MD) and calculations of an extended Maxwell-Stefan (MS) equations, was established to obtain multiscale analysis on the dynamics of hybrid induced phase separation (HIPS), taking polyvinylidene fluoride-diphenyl carbonate/water–ethanol (PVDF-DPC/water–ethanol) system as an example. Firstly, MS equations were derived to describe the heat transfer across the interface between the casting solution and coagulation to get the temperature profiles of the casting solution. Secondly, MD simulations for the PVDF-DPC solution were conducted to acquire bond and angle distributions of the PVDF chains. And compared to the DPD particle distributions, a novel DPD force field to describe the real flexibility of PVDF chains and a coarse-graining mapping between the MD and DPD were developed. Thirdly, based on the quenching time calculated by the MS equations and the DPD time scale, DPD simulations were carried out to demonstrate the dynamics of phase separation and membrane formation for different parts of the polymer solution via HIPS and compared to that via thermally induced phase separation (TIPS). The simulation results indicated that the mass transfer had a decisive effect on the phase separation of polymer solution near the interface and resulted in a highly asymmetric structure with a denser polymer top layer and porous sublayer, and this effect was together decided by the quenching rate and polymer solidification. For the inner parts of the polymer solution, a mainly isotropic structure was formed due to heat transfer. Based on experimental verification and simulation results, it can be known that the multiscale simulation was much closer to reality and can provide deep insights into the membrane formation prepared via the HIPS process.

Dissipative particle dynamics simulations for biological systems: From protein structures to cell mechanics

<p indent="0mm">Dissipative particle dynamics (DPD) is a mesoscopic coarse-grained simulation method developed in recent years, which is an important method for studying the dynamic behaviors of soft matter and complex fluids. In this method, each DPD particle represents a coarse-grained virtual cluster of a set of atoms or groups of matter. The position and momentum of the DPD particle are updated in a continuous phase but spaced at discrete time steps. The coarse-grained DPD particles are subject to simplified pairwise interacting conservative, dissipative, and random forces. Especially, the dissipative force and random force in the DPD method act as a heat sink and a source, respectively, and the combined effect of these two forces act as a thermostat, which conserves momentum and thus provides the correct description of hydrodynamic interactions for the model system. In addition, a common choice of the soft repulsion for the conservative force allows using larger integration time steps in DPD simulations than that usually allowed in classical molecular dynamics (MD) simulations. Hence, compared with the MD method, the computational cost of the DPD simulation is significantly reduced due to the smaller number of modeled particles and the larger computational time step, enabling the simulations of the static and dynamic behaviors of complex fluids and soft matter systems at physically attractive length scale and time scale. Moreover, the particle-based framework of the DPD method enables people to easily incorporate additional physical features into the model systems and extend its application to complex systems. For these reasons, the DPD method and its extension have been successfully applied to numerous soft matter and complex fluid systems such as oil/water/surfactant systems, chemical morphology, microscopic morphology, phase separation, as well as dynamics and rheological properties of polymer solutions and colloidal suspensions. In this paper, we first introduce the theoretical formulation and parameterization of the DPD method. Then, we review recent advances in DPD modeling of biological systems, focusing on its applications at the molecular and cellular scales. At the molecular scale, we highlight examples of successful simulations of the protein structures and their interactions, the structure and dynamics of amphiphilic lipid molecule membranes (e.g., the self-assembly of lipid molecules, the structure and properties of lipid membranes, the fusion of lipid membranes, and the budding and fission of lipid membranes), the interaction of lipid membranes with protein molecules, and the interaction of nanoparticles with lipid membranes; at the cellular scale, we focus on the DPD modeling of blood cell flow and blood rheological behaviors in the blood microcirculatory systems, including the shape deformation and flow dynamics of red blood cells, the margination and adhesion dynamics of white blood cells, the margination and aggregation behaviors of platelets, the hemorheological behavior of blood flow, as well as the separation of circulating tumor cells from blood flow using microfluidic devices. Additionally, we compare the advantages and disadvantages of the microscale blood flow simulations between the continuum-based methods and particle-based methods, including the DPD method. Finally, we briefly present the development trends and application prospects of DPD modeling in biological systems.

EH-DPD: a dissipative particle dynamics approach to electrohydrodynamics

Electrohydrodynamics is crucial in many nanofluidic and biotechnological applications. In such small scales, the complexity due to the coupling of fluid dynamics with the dynamics of ions is increased by the relevance of thermal fluctuations. Here, we present a mesoscale method based on the Dissipative Particle Dynamics (DPD) model of the fluid. Two scalar quantities, corresponding to the number of positive and negative ions carried by each DPD particle, are added to the standard DPD formulation. We introduced a general framework that, given the definition of the free-energy of the DPD particle, allows to derive a fluctuation-dissipation relation and the expression for ionic fluxes between the DPD particles. This provides a link between the dynamics of the system and its equilibrium properties. The model is then validated simulating a planar electroosmotic flow for the cases of overlapping and non overlapping electric double layers. It is shown that using a Van der Waals equation of state the effect of ionic finite size can be accounted, leading to significant effects on the concentration and velocity profiles with respect to the ideal solution case.Graphic abstract

Alternative expression for Boltzmann temperature of dissipative-particle-dynamics particles

The coarse graining parameter has been used to determine parameter values of the dissipative particle dynamics (DPD). However, it is known that the self-diffusivity obtained by the DPD simulation reduces with increasing the coarse graining parameter. In this study, an alternative expression for Boltzmann temperature of the DPD particles is proposed. The self-diffusivity and the dynamic viscosity of water were obtained by using the proposed expression for Boltzmann temperature of the DPD particles and the standard weight function. The obtained self-diffusivity was slightly higher than the measured value in the temperature range from 280 K to 330 K, however, it was independent of the coarse graining parameter. The obtained dynamic viscosity agreed well with value obtained by REFPROP in the temperature range from 280 to 370 K.

Closed-Form Coexistence Equation for Phase Separation of Polymeric Mixtures in Dissipative Particle Dynamics.

To date, no extensive study of the phase diagram for binary fluid mixtures in dissipative particle dynamics (DPD) has been published. This is especially pertinent for newer parameterization schemes where the self-self interaction, or the effective volume, of different particle types is varied. This work presents an exhaustive study of the parameter space concerning DPD particles with soft interaction potentials. Moreover, we propose a closed-form coexistence equation or binodal curve that is inspired by the Flory-Huggins model. This equation describes the phase diagram of all binary mixtures made up out of monomers, homopolymers, and the mixtures thereof when self-self interactions are varied. The mean absolute percentage error (MAPE) of the equation on simulated data, including validation simulations, is 1.02%. The equation can a priori predict the phase separation of mixtures using only DPD interaction parameters. The proposed coexistence equation can therefore be used to directly validate interaction parameters resulting from novel parameterization schemes, including coarse graining and equations of state, without the need for additional simulations. Finally, it is shown that the choice of bond potential markedly influences phase behavior.

A dissipative particle dynamics model for studying dynamic phenomena in colloidal rod suspensions.

A dissipative particle dynamics (DPD) model is developed and demonstrated for studying dynamics in colloidal rod suspensions. The solvent is modeled as conventional DPD particles, while individual rods are represented by a rigid linear chain consisting of overlapping solid spheres, which interact with solvent particles through a hard repulsive potential. The boundary condition on the rod surface is controlled using a surface friction between the solid spheres and the solvent particles. In this work, this model is employed to study the diffusion of a single colloid in the DPD solvent and compared with theoretical predictions. Both the translational and rotational diffusion coefficients obtained at a proper surface friction show good agreement with calculations based on the rod size defined by the hard repulsive potential. In addition, the system-size dependence of the diffusion coefficients shows that the Navier-Stokes hydrodynamic interactions are correctly included in this DPD model. Comparing our results with experimental measurements of the diffusion coefficients of gold nanorods, we discuss the ability of the model to correctly describe dynamics in real nanorod suspensions. Our results provide a clear reference point from which the model could be extended to enable the study of colloid dynamics in more complex situations or for other types of particles.

Towards bio-inspired artificial muscle: a mechanism based on electro-osmotic flow simulated using dissipative particle dynamics

One of the unresolved issues in physiology is how exactly myosin moves in a filament as the smallest responsible organ for contracting of a natural muscle. In this research, inspired by nature, a model is presented consisting of DPD (dissipative particle dynamics) particles driven by electro-osmotic flow (EOF) in micro channel that a thin movable impermeable polymer membrane has been attached across channel width, thus momentum of fluid can directly transfer to myosin stem. At the first, by validation of electro-osmotic flow in micro channel in different conditions with accuracy of less than 10 percentage error compared to analytical results, the DPD results have been developed to displacement of an impermeable polymer membrane in EOF. It has been shown that by the presence of electric field of 250 V/m and Zeta potential − 25 mV and the dimensionless ratio of the channel width to the thickness of the electric double layer or kH = 8, about 15% displacement in 8 s time will be obtained compared to channel width. The influential parameters on the displacement of the polymer membrane from DPD particles in EOF such as changes in electric field, ion concentration, zeta potential effect, polymer material and the amount of membrane elasticity have been investigated which in each cases, the radius of gyration and auto correlation velocity of different polymer membrane cases have been compared together. This simulation method in addition of probably helping understand natural myosin displacement mechanism, can be extended to design the contraction of an artificial muscle tissue close to nature.

Coarse-grained simulation of the translational and rotational diffusion of globular proteins by dissipative particle dynamics.

With simplified interactions and degrees of freedom, coarse-grained (CG) simulations have been successfully applied to study the translational and rotational diffusion of proteins in solution. However, in order to reach larger lengths and longer timescales, many CG simulations employ an oversimplified model for proteins or an implicit-solvent model in which the hydrodynamic interactions are ignored, and thus, the real kinetics are more or less unfaithful. In this work, we develop a CG model based on the dissipative particle dynamics (DPD) that can be universally applied to different types of proteins. The proteins are modeled as a group of rigid DPD beads without conformational changes. The fluids (including solvent and ions) are also modeled as DPD beads. The electrostatic interactions between charged species are explicitly considered by including charge distributions on DPD particles. Moreover, a surface friction between the protein and fluid beads is applied to control the slip boundary condition. With this model, we investigate the self-diffusion of a single globular protein in bulk solution. The translational and rotational diffusion coefficients of the protein can be tuned by the surface frictional constant to fit the predictions of the Stokes-Einstein (SE) relation. We find that both translational and rotational diffusion coefficients that meet with the prediction of the SE relation based on experimental results of the hydrodynamic radius are reached at almost the same frictional constant for different types of proteins. Such scaling behavior indicates that the model can be applied to simulate the translational and rotational diffusion together for various types of proteins.

Dissipative particle dynamics simulation of cell entry into a micro-channel

Cell deformability is an important biomarker which can be used to distinguish and sort between healthy and cancer cells. In this paper, we presented a dissipative particle dynamics (DPD) model for investigating cell entry into micro-channels. The cell membrane is represented by a network of DPD particles (beads) connected by worm-like chain (WLC) springs, which is able to mimic the viscoelastic effect of the membrane. The entry process of benign breast epithelial cells (MCF-10A) and non-metastatic tumor breast cells (MCF-7) through a constricted micro-channel are comparatively investigated using this DPD model. It is shown that both the time histories of the cell displacement and the dynamic behaviors of cell entry agree with experimental observations. The entry time of MCF-10A cell is approximately four times of that of MCF-7 cell since MCF-10A cells are stiffer than MCF-7 cells. It is demonstrated that the presented DPD method is effective in modeling cell deformability, and the obtained results can be helpful in understanding how cells with different mechanical properties respond to physical loads.

Numerical Studies of Shape Recovery of a Red Blood Cell Using Dissipative Particle Dynamics

A biological cell exhibits viscoelastic behavior mainly because its components (membrane and cytoplasm) are viscoelastic, and this is clearly seen when it is stretched and released. The present work numerically studied the shape recovery of a red blood cell (RBC) based on a viscoelastic model at the meso-scale using Dissipative Particle Dynamics (DPD) method. In this model, the RBC membrane is represented by a triangular network of worm-like chains, while the cytoplasm is replaced by a system of DPD particles. This viscoelastic model is validated by examining the stretching deformation of an RBC and comparing with the existing experimental data. Viscoelastic properties of the RBC are then analyzed by stretching an RBC under a 20 pN stretching force, and allowing it to relax. The time to recover its shape upon removal of the stretching force is measured to be 111 and 92.6[Formula: see text]ms for an RBC with and without cytoplasm, and the corresponding membrane viscosity is [Formula: see text] and [Formula: see text] [Formula: see text], respectively. These values, for an RBC with cytoplasm, are closer to experimental data than those for an RBC without cytoplasm, lending support to the model with cytoplasm. Finally, parametric studies are conducted on the membrane elastic and bending moduli. The results show that the shape recovery time decreases with increasing the membrane elastic and bending moduli.

A new equation of state for homo-polymers in dissipative particle dynamics.

A chain-revised Groot-Warren equation of state (crGW-EOS) was developed and tested to describe systems of homo-oligomeric chains in the framework of dissipative particle dynamics (DPD). First, thermodynamic perturbation theory is applied to introduce correction terms that account for the reduction in pressure with an increasing number of bonds at constant bead number density. Then, this EOS is modified by introducing a set of switching functions that yields an accurate second virial coefficient in the low-density limit. The crGW-EOS offers several improvements over the revised Groot-Warren equation of state and Groot-Warren equation of state for chain molecules. We tested the crGW-EOS by using it to predict the pressure of oligomeric systems and the B2 virial coefficient of chain DPD particles for a range of bond lengths. Additionally, a method is developed for determining the strength of cross-interaction parameters between chains of different compositions and sizes and for thermal and athermal mixtures. We explored how different levels of coarse-graining affect the upper-critical solution temperature.

Tribological Behavior of Grafted Nanoparticle on Polymer-Brushed Walls: A Dissipative Particle Dynamics Study.

Two contacting surfaces grafted with polymer brushes have potential applications due to their extraordinary lubricating behavior. However, the polymer brushes may have poor mechanical stability under high normal and shear stresses, which is a challenge for practical usage of polymer brush systems. In this study, we propose the use of grafted nanoparticles as nanobearings on polymer-brush-coated surfaces to alleviate the harsh working conditions of polymer brushes and to improve their mechanical stability. We have performed dissipative particle dynamics (DPD) simulations to investigate the tribological interaction between grafted nanoparticle and parallel walls with noncharged polymer brushes in the presence of explicit solvent. The influences of several parameters (solvent quality, brush miscibility, etc.) on the tribological behavior of the system are investigated. The grafted nanoparticle obviously acts as a nanobearing that partially replaces the sliding contact between two brushed walls with rolling contact between the grafted nanoparticle and two brushed walls and reduces the number of DPD particles withstanding high force. Although the introduction of the grafted nanoparticle into polymer-brushed walls increases the friction coefficient by 20-30%, it does not greatly decrease lubrication of the brushed walls, while still helping in stabilizing the system of polymer brushes to be used with liquids with low viscosity, such as water. The DPD simulation results and analysis performed in this study would be beneficial in designing systems with polymer-brushed surfaces and grafted nanoparticles.

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

To investigate a morphological structure of hydrated perfluorosufuonic acids (PFSA) in contact with a platinum surface, we constructed a model of this interfacial system for dissipative particle dynamics (DPD) simulations. The model consists of a bead-spring model of hydrated PFSA molecules and a rigid slab of DPD particles that represents a platinum surface. We applied previously proposed soft potentials for the interactions of DPD particles of hydrated PFSA, while we constructed new ones for the interactions between those of platinum and hydrated PFSA, based on first principles calculations and all-atom classical molecular dynamics simulations. A set of DPD simulations were performed with the constructed simulation model. The calculated results suggest that hydrated PFSA tends to form layers of hydrophilic and hydrophobic components near the platinum surface.

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

To investigate a morphological structure of hydrated perfluorosufuonic acids (PFSA) in contact with a platinum surface, we constructed a model of this interfacial system for dissipative particle dynamics (DPD) simulations. The model consists of a bead-spring model of hydrated PFSA molecules and a rigid slab of DPD particles that represents a platinum surface. We applied previously proposed soft potentials for the interactions of DPD particles of hydrated PFSA, while we constructed new ones for the interactions between those of platinum and hydrated PFSA, based on first principles calculations and all-atom classical molecular dynamics simulations. A set of DPD simulations were performed with the constructed simulation model. It was suggested that hydrated PFSA tends to form layers of hydrophilic and hydrophobic components near the platinum surface.

Improvement of Dissipative Particle Dynamics method by taking into account the particle size

In this paper, flow past a single Dissipative Particle Dynamics (DPD) particle with low Reynolds number is investigated and it is inquired that whether a single DPD particle immersed in a fluid, has an intrinsic size. Then a minimum length scale is determined such that the hydrodynamic behavior based on standard DPD formulation is modeled correctly. Almost all of the previous studies assume the DPD particles as point centers of repulsion with no intrinsic size. Hence to prescribe the size of a simulating sphere, a structure of frozen DPD particles is created. In this paper two effective radii, Stokes-Einstein radius and a radius based on the Stokes law, for DPD particles are introduced. For small Reynolds numbers; it is proved that the two radii approach each other. Finally in spite of the typical simulations which assume DPD particles as point centers of repulsion, it is concluded that each of the individual DPD particles interact with other particles as a sphere with non-zero radius. It results the reduction of the required number of particles and eventuates more economical simulations. Moreover contemplating the radius of the particles is necessary for the new Low-Dimensional model which is derived based on the DPD method.

A note on dissipative particle dynamics (DPD) modelling of simple fluids

In this paper, we show that a dissipative particle dynamics (DPD) model of a viscous Newtonian fluid may actually produce a linear viscoelastic fluid. We demonstrate that a single set of DPD particles can be used to model a linear viscoelastic fluid with its physical parameters, namely the dynamical viscosity and the relaxation time in its memory kernel, determined from the DPD system at equilibrium. The emphasis of this study is placed on (i) the estimation of the linear viscoelastic effect from the standard parameter choice; and (ii) the investigation of the dependence of the DPD transport properties on the length and time scales, which are introduced from the physical phenomenon under examination. Transverse-current auto-correlation functions (TCAF) in Fourier space are employed to study the effects of the length scale, while analytic expressions of the shear stress in a simple small amplitude oscillatory shear flow are utilised to study the effects of the time scale. A direct mechanism for imposing the particle diffusion time and fluid viscosity in the hydrodynamic limit on the DPD system is also proposed.

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