We critically review dissipative particle dynamics (DPD) as a mesoscopic simulation method. We have established useful parameter ranges for simulations, and have made a link between these parameters and χ-parameters in Flory-Huggins-type models. This is possible because the equation of state of the DPD fluid is essentially quadratic in density. This link opens the way to do large scale simulations, effectively describing millions of atoms, by firstly performing simulations of molecular fragments retaining all atomistic details to derive χ-parameters, then secondly using these results as input to a DPD simulation to study the formation of micelles, networks, mesophases and so forth. As an example application, we have calculated the interfacial tension σ between homopolymer melts as a function of χ and N and have found a universal scaling collapse when σ/ρkBTχ0.4 is plotted against χN for N>1. We also discuss the use of DPD to simulate the dynamics of mesoscopic systems, and indicate a possible problem with the timescale separation between particle diffusion and momentum diffusion (viscosity).

A new simulation method, dissipative particle dynamics, is applied to model biological membranes. In this method, several atoms are united into a single simulation particle. The solubility and compressibility of the various liquid components are reproduced by the simulation model. When applied to a bilayer of phosphatidylethanolamine, the membrane structure obtained matches quantitatively with full atomistic simulations and with experiments reported in the literature. The method is applied to investigate the cause of cell death when bacteria are exposed to nonionic surfactants. Mixed bilayers of lipid and nonionic surfactant were studied, and the diffusion of water through the bilayer was monitored. Small transient holes are seen to appear at 40% mole-fraction C(9)E(8), which become permanent holes between 60 and 70% surfactant. When C(12)E(6) is applied, permanent holes only arise at 90% mole-fraction surfactant. Some simulations have been carried out to determine the rupture properties of mixed bilayers of phosphatidylethanolamine and C(12)E(6). These simulations indicate that the area of a pure lipid bilayer can be increased by a factor 2. The inclusion of surfactant considerably reduces both the extensibility and the maximum stress that the bilayer can withstand. This may explain why dividing cells are more at risk than static cells.

The dissipative particle dynamics (DPD) simulation method has been used to study mesophase formation of linear (AmBn) diblock copolymer melts. The polymers are represented by relatively short strings of soft spheres, connected by harmonic springs. These melts spontaneously form a mesocopically ordered structure, depending on the length ratio of the two blocks and on the Flory–Huggins χ-parameter. The main emphasis here is on validation of the method and model by comparing the predicted equilibrium phases to existing mean-field theory and to experimental results. The real strength of the DPD method, however, lies in its capability to predict the dynamical pathway along which a block copolymer melt finds its equilibrium structure after a temperature quench. The present work has led to the following results: (1) As the polymer becomes more asymmetric, we qualitatively find the order of the equilibrium structures as lamellar, perforated lamellar, hexagonal rods, micelles. Qualitatively this is in agreement with experiments and existing mean-field theory. After taking fluctuation corrections to the mean field theory into account, a quantitative match for the locations of the phase transitions is found. (2) Where mean-field theory predicts the gyroid phase to be stable, the simulations evolve toward the hexagonally perforated lamellar phase. (3) When a melt is quenched the stable structure emerges via a nontrivial pathway, where a series of metastable phases can be formed before equilibrium is reached. The pathway to equilibrium involves a percolation of the minority phase into a network of tubes, which is destabilized by a nematic or smectic transition. (4) We conclude that either hydrodynamic interactions, or the precise form of the Onsager kinetic coefficient play an important role in the evolution of the mesophases.

Electrostatic interactions have been incorporated in dissipative particle dynamics (DPD) simulation. The electrostatic field is solved locally on a grid. Within this formalism, local inhomogeneities in the electrostatic permittivity can be treated without any problem. Key issues like the screening of the potential near a charged surface and the Stillinger–Lovett moment conditions are satisfied. This implies that the method captures the essential features of electrostatic interaction. For the direct simulation of mixed surfactants near oil–water interfaces, or for the simulation of Coulombic polymer–surfactant interactions, this method has all the advantages of DPD over full atomistic molecular dynamics (MD). DPD has proven to be faster than MD by many orders of magnitude, depending on the precise scaling factor chosen for the simulation. This brings phenomena of microseconds in reach of routine simulation, while maintaining a fairly accurate representation of the structure of the molecules. As an example of this simulation tool, the interaction between a cationic polyelectrolyte and anionic surfactant is discussed. Without a surfactant, the polyelectrolyte shows a fractal dimensionality that is in line with the theoretical and experimental values cited in literature, it behaves as a fairly stiff rod, df∼1.1. When salt is replaced by anionic surfactant, the polymer wraps around one or more discrete surfactant micelles, in line with the current understanding of these systems, and scaling invariance in the correlation function is broken.

The most efficient way to pack equally sized spheres isotropically in three dimensions is known as the random close packed state, which provides a starting point for many approximations in physics and engineering. However, the particle size distribution of a real granular material is never monodisperse. Here we present a simple but accurate approximation for the random close packing density of hard spheres of any size distribution based upon a mapping onto a one-dimensional problem. To test this theory we performed extensive simulations for mixtures of elastic spheres with hydrodynamic friction. The simulations show a general (but weak) dependence of the final (essentially hard sphere) packing density on fluid viscosity and on particle size but this can be eliminated by choosing a specific relation between mass and particle size, making the random close packed volume fraction well defined. Our theory agrees well with the simulations for bidisperse, tridisperse, and log-normal distributions and correctly reproduces the exact limits for large size ratios.