Dissipative particle dynamics method

DPD is a mesoscopic simulation method, introduced in 1992 by Hoogerbrugge and Koelman [22]. It is a simple but intrinsically promising simulation method that allows the study of the phase behaviors of block copolymers. In a DPD simulation, a particle represents the center of mass in a cluster of atoms, and the position and momentum of the particle are updated in a continuous phase but spaced at discrete time steps. Particles i and j at positions r, and Tj interact with each other via pairwise conservative, dissipative, and random forces, which are given by 

To model the block copolymers, the total force can also have an elastic contribution, which is derived from the harmonic force used to connect two consecutive particles in the chains of polymer [10]. This contribution is expressed as 

The dynamics of the DPD particles are followed by solving Newton s equation of motion, with the forces above using a 

DYNAMICS SIMULATIONS OF MICROPHASE SEPARATION IN BLOCK COPOLYMERS 

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ScWijper, A., Hoogetbragge, R, Manke, C. Computer simulation of dilute polymer solutions with the dissipative particle dynamics method. J. Rheol. 39, 567 (1995). doi 10.1122/1. 550713... 

Gibson, J. B., Chen, K., and Chynoweth, S. Simulation of particle adsorption onto a polymer-coated surface using the dissipative particle dynamics method. J Colloid Interface 5cz., 206,464-74 (1998). 

While the evaluation of the interactions in a dense system is computationally beneficial, the underlying lattice structure requires the usage of special simulation techniques to accurately calculate the contribution of the nonbonded interactions to the pressure. These difficulties can be mitigated by using a soft, coarse-grained, off-lattice model. Since forces are well defined in off-lattice models, one can use Brownian dynamics or dissipative particle dynamics methods [97-103]. Also, simulations under constant pressure or surface tension are feasible. 

A fiirther theme is the development of teclmiques to bridge the length and time scales between truly molecular-scale simulations and more coarse-grained descriptions. Typical examples are dissipative particle dynamics [226] and the lattice-Boltzmaim method [227]. Part of the motivation for this is the recognition that... 

During the past few decades, various theoretical models have been developed to explain the physical properties and to find key parameters for the prediction of the system behaviors. Recent technological trends focus toward integration of subsystem models in various scales, which entails examining the nanophysical properties, subsystem size, and scale-specified numerical analysis methods on system level performance. Multi-scale modeling components including quantum mechanical (i.e., density functional theory (DFT) and ab initio simulation), atom-istic/molecular (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational... 

Simulation techniques suitable for the description of phenomena at each length-scale are now relatively well established Monte Carlo (MC) and Molecular Dynamics (MD) methods at the molecular length-scale, various mesoscopic simulation methods such as Dissipative Particle Dynamics (Groot and Warren, 1997), Brownian Dynamics, or Lattice Boltzmann in the colloidal domain, Computational Fluid Dynamics at the continuum length-scale, and sequential-modular or equation-based methods at the unit operation/process-systems level. 

Molecular Dynamics simulation is one of many methods to study the macroscopic behavior of systems by following the evolution at the molecular scale. One way of categorizing these methods is by the degree of determinism used in generating molecular positions [134], On the scale from the completely stochastic method of Metropolis Monte Carlo to the pure deterministic method of Molecular Dynamics, we find a multitude and increasingly diverse number of methods to name just a few examples Force-Biased Monte Carlo, Brownian Dynamics, General Langevin Dynamics [135], Dissipative Particle Dynamics [136,137], Colli-sional Dynamics [138] and Reduced Variable Molecular Dynamics [139]. 

Computer simulations in the mesoscopic regime are now possible using methods such as Lattice Bolztmann, Dissipative Particle Dynamics, MesoDyn and Cell Dynamics Simulations. MesoDyn is a commercial package (from... 

Dissipative particle dynamics or Lattice Boltzman methods also may be used here. Inside the small spheres are reactive water molecules modeled using tight-binding (TB) approaches. TB is also used to treat reactive surface functional groups. 

Transition state searching and kinetic Monte Carlo techniques MULTISCALE COMPUTATIONAL METHODS FOR FLUIDS Dissipative particle dynamics Agglomeration of particles... 

Dissipative Particle Dynamics (DPD) is a coarse graining method that groups several atoms into simulation sites whose dynamics is governed by conservative and frictional forces designed to reproduce thermodynamics and hydrodynamics [132,133]. Since the effective interactions are constmcted to reproduce macroscopic properties soft repulsive forces can be used, thereby avoiding the small MD step sizes needed to integrate the system when full interactions are taken into account. In addition, random... 

The molecular dynamics methods that we have discussed in this chapter, and the examples that have been used to illustrate them, fall into the category of atomistic simulations, in that all of the actual atoms (or at least the non-hydrogen atoms) in the core system are represented explicitly. Atomistic simulations can provide very detailed information about the behaviour of the system, but as we have discussed this typically limits a simulation to the nanosecond timescale. Many processes of interest occur over a longer timescale. In the case of processes which occur on a macroscopic timescale (i.e. of the order of seconds) then rather simple models may often be applicable. Between these two extremes are phenomena that occur on an intermediate scale (of the order of microseconds). This is the realm of the mesoscale Dissipative particle dynamics (DPD) is particularly useful in this region, examples include complex fluids such as surfactants and polymer melts. 

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