Applications of Dissipative Particle Dynamics

Abstract

Abstract. Dissipative Particle Dynamics (DPD) is one of the most promising simulation techniques for studies of mesoscopic properties of soft matter systems. Here, we discuss DPD, its parameterisation in simple systems, as well as in polymeric systems using the Flory-Huggins theory, and generalisations of DPD. Block copolymer mesophase separation, polymers and membranes in surfactant solutions, and biomembrane morphology and rupture will shown as specific examples. Why Mesoscopic Simulation?Over the last two decades most simulation studies have concentrated on the motion of individual atoms in systems of a few nanometers and a few nanoseconds. Other simulation methods concentrate exclusively on the macroscopic world of planes, trains and automobiles. However, between the nano-and macroscopic scale ranges some forty decades in volume and time. The holy grail of theoretical physics is to bridge this gap. This is due to the fact that in many cases simulation of this intermediate regime is essential for understanding macroscopic phenomena, e.g. molecules ordering spontaneously on mesoscopic length and time scales. This category of problems includes life and biological phenomena such as membrane structuring, perforation and trafficking. As a matter of fact, this list contains all soft condensed matter including surfactants, polymers and (multi)block copolymers that show microphase separation, or form gels or glassy systems, see Fig. 1.What could we expect if we would be able to extend the time scale over which we can simulate a physical system? If we take the example of lipid bilayers, we find that new phenomena occur every time we increase the time scale at which we look at our system [1]. On the shortest time scale of a few picoseconds the lipids show bond and angle fluctuations of dihedral angles within the same molecule. On larger time scales of a few tens of picoseconds, trans-gauche isomerizations of dihedrals occur [2]. On a time scale of a few nanoseconds the phospholipids rotate around their axis, and on the timescale of tens of nanoseconds two lipids switch place within a bilayer, giving rise to lateral diffusion. Within this time scale the individual lipids orient, and lipid membranes show protrusions [3]. Finally, on a time-scale of 100 ns peristaltic motions and undulations occur [4]. By virtue of parallelization over several processors or PC clusters, hardware developments have now pushed the limit of molecular simulations to 100 ns [4]. Nevertheless, there is a limit beyond which hardware developments cannot help us. For instance, phenomena such as co-operative motion in phase transitions, insertion of large molecules

Coarse graining and scaling in dissipative particle dynamics

“…This is in contrast to earlier publications. 12,20 Our result implies that, in reduced units, a DPD calculation performed for a system with small extensions and over a small time interval is numerically identical to one for a much larger system and covering a longer time range.…”

“…For a general discussion of the renormalization of diffusion, see, e.g., Kadanoff. 22 To what extent the trajectories of the particles in DPD can be understood as representing actual transport processes is discussed by Groot 20 and shown in the approach used, e.g., by Groot and Warren 3 and Jakobsen et al 23 These authors resolve the calibration problem by treating the natural time unit as undetermined and instead obtain the physical time scale t from calibrating diffusion constants measured in simulation to physical values. 3 Note that there are applications in which time scales are of minor interest; for example, for the investigation of static properties such as lipid phase diagrams only energy scales are relevant, and a direct physical interpretation is well possible.…”

Systematic coarse-graining of molecular models by the Newton inversion method

“…There is also a current interest to develop intermediate models in between atomistic and continuum models, presenting water as a liquid of particles, but without atomistic details. Example of such ''coarse-grained'' models may be the one-site model used in DPD simulations of water, 35 or the one used in the Martini force field. 8 These models are purely empirical.…”

Reverse Non-equilibrium Molecular Dynamics

“…This includes both the dissipative-particle method and the Malevanets-Kapral method (cf. Groot [1] and Español [2], and R. Kapral [3] in this volume, respectively). Applications of RNEMD on the mesoscale are therefore foreseeable.…”