Coarse-grained particle-based simulations

Coarse-Grained Particle-Based Simulations 1.16.4.3.1 Stochastic dynamics... 

Particle-based simulation techniques include atomistic MD and coarse-grained molecular dynamics (CG-MD). Accelerated dynamics methods, such as hyperdynamics and replica exchange molecular dynamics (REMD), are very promising for circumventing the timescale problem characteristic of atomistic simulations. Structure and dynamics at the mesoscale level can be described within the framework of coarse-grained particle-based models using such methods as stochastic dynamics (SD), dissipative particle dynamics (DPD), smoothed-particle hydrodynamics (SPH), lattice molecular dynamics (LMD), lattice Boltzmann method (IBM), multiparticle collision dynamics (MPCD), and event-driven molecular dynamics (EDMD), also referred to as collision-driven molecular dynamics or discrete molecular dynamics (DMD). 

Dissipative particle dynamics (DPD) is a meshless, coarse-grained, particle-based method used to simulate systems at mesoscopic length and timescales (Coveney and Espafiol 1997 Espafiol and Warren 1995). In simple terms, DPD can be interpreted as coarse-grained MD. Atoms, molecules, or monomers are grouped together into mesoscopic clusters, or beads, that are acted on by conservative, dissipative, and random forces. The interaction forces are pairwise additive in nature and act between bead centers. Connections between DPD and the macroscopic (hydrodynamic, Navier-Stokes) level of description (Espanol 1995 Groot and Warren 1997), as well as microscopic (atomistic MD) have been well established (Marsh and Coveney 1998). DPD has been used to model a wide variety of systems such as lipid bilayer membranes (Groot and Rabone 2001), vesicles (Yamamoto et al. 2002), polymersomes (Ortiz et al. 2005), binary immiscible fluids (Coveney and Novik 1996), colloidal suspensions (Boek et al. 1997), and nanotube polymer composites (Maiti etal.2005). 

Coarse-grained molecular d5mamics simulations in the presence of solvent provide insights into the effect of dispersion medium on microstructural properties of the catalyst layer. To explore the interaction of Nation and solvent in the catalyst ink mixture, simulations were performed in the presence of carbon/Pt particles, water, implicit polar solvent (with different dielectric constant e), and ionomer. Malek et al. developed the computational approach based on CGMD simulations in two steps. In the first step, groups of atoms of the distinct components were replaced by spherical beads with predefined subnanoscopic length scale. In the second step, parameters of renormalized interaction energies between the distinct beads were specified. 

Some of the coarse-grained parameters, i e and can be easily measured by experiments or in simulations. The other two parameters, %N and the suppression of density fluctuations, XqN, are thermodynamic characteristics, which are not directly related to the structure (i.e., they cannot be simply expressed as a function of the molecular coordinates). If density fluctuations of the polymeric liquid are small on the length scale of interest (e.g., width of an interface between domains), then the value of the compressibility has only a minor relevance and decreasing it even further will not significantly affect the behavior of the system. Thus, field-theoretic calculations often take the idealized limit of strict incompressibility. In particle-based simulations, however, one often softens the constraint in order to facilitate the motion of the interaction centers and, thereby, reduces the viscosity of the polymer liquid. The Flory-Huggins parameter, in turn, is a crucial coarse-grained parameter and different methods have been devised to extract it from experiments or simulations [16, 20-25]. We shall briefly discuss this important issue in Section 5.2.3, and further refer the reader to the literature, where computer simulations have been quantitatively compared with mean field predictions and where the role of fluctuations on the coarse-grained parameters is discussed [16, 22]. 

A large class of currently used CG models employs what some researchers call particle-based coarse-graining, in which a finite number of atoms of the molecular system are grouped into a single point mass (a CG particle, sometimes called a mesoparticle or a pseudo-particle). In the simulations of biomolecules, most commonly only a few heavy atoms (between 3 and 5) are replaced by a CG particle. 

In Equation 7.2, pt +i represents the probability of the system changing from current configuration i to a new configuration i + 1, AE the change in potential energy associated with the attempted move, the Boltzmann constant, and T the temperature of the system. MC simulations are often performed in NVT and pVT ensembles, and widely applied to polymers as well as polymers in contact with filler particles. Brownian dynamics (BD) and dissipative particle dynamics (DPD) are further particle-based coarse-grained simulation methods similar to MD simulation. BD employs a continuum solvent model rather than explicit solvent molecules in MD and the total force is ... 

Hybrid particle-field models combine single-cbain simulations with an appropriate field-theoretical approach. The corresponding class of multiscale techniques includes the single-chain-in-mean-field (SCMF) method, the theoretically informed coarse-grain (TICG) simulation scheme, self-consistent Brownian dynamics (SCBD), and the MD-SCF method, in which self-consistent field theory (SOFT) and particle-based MD are combined. 

Moving from particle-based and field-based simulations to continuum mechanics is a further step of coarse-graining, after which the effea of polymer dynamics are described only in a rather unspecific manner by a set of PDEs, employing the conservation laws and phenomenological constitutive relations. Continuum mechanics relies on the fundamental notion of a mesoscopic volume element in which properties averaged over disaete particles obey deterministic relationships. Continuum-level models assume naturally that matter is a continuum that is, it can be subdivided without limit. As a result, continuum simulations can in principle handle systems of any (maaoscopic) size and dynamic processes on long timescales. 

Some coarse-grained simulation methods have been estabHshed to understand the structure—property relationships of material interfaces, which include BD, dissipative particle dynamics (DPD), and CGMD based on MARTINI force field, and many efforts have focused on the protein adsorption, interfacial behavior and surface wettabihty, and so on. 

---