Coarse-Grained Particle Methods

Coarse-grained particle methods Huid particle model Mesoscopic method... 

Mesoscopic method Fluid particle model Coarse-grained particle methods... 

Coarse graining may be combined with a confinement of the conformational space by placing the coarse grain particles on a cubic lattice. For example, Kurcinski and Kolinski (76) (CABS-REMC) represented the polypeptide chains by strings of Ca beads on a cubic lattice. Side chains were represented by up to two interaction centers, which correspond to Cp and the centers of mass of the remaining portions of the side groups, respectively. The conformational space of this model is sampled by means of a multicopy Monte Carlo method. 

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 ... 

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). 

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. 

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). 

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... 

Secondly, we might mention that there are two possible attitudes to a theory of valence based on the AO expansion method. The chemist uses the electron-pair model essentially as one of his axioms or, at least, as a good working hypothesis. This model is extremely familiar and useful any theory of such a model of valence should be capable of providing at least some foundation for and extension of his qualitative concepts. To the physicist, however, the simplest molecules are quite complex many-particle systems and he would perhaps find it surprising if we are able to obtain any useful results from our coarse-grained minimal basis model in view of the complexity of the interactions involved. We must try to balance these views in any evalution we make. 

Processing conditions are known to play a critical role in establishment of morphology and final properties of the materials. Balazs and coworkers [245, 246] designed a multiscale method (coarse-grained Cahn-Hilliard approach and Brownian dynamics) and found that addition of solid particles significantly... 

Grain growth of zinc oxide occurs at much lower temperatures than in titania, so that production of fairly crystalline ZnO nanopowders needs special precautions. The thermal decomposition of freeze-dried Zn(N03)2 at 260 to 270°C results in the formation of poorly crystalline, but coarse-grained ZnO powders. " At the same time, insulation of ZnO particles in the inert NaCl matrix by the method described before - led to no change in the size of the ZnO particles. The ZnO particles were obtained from freeze-dried precipitate of zinc hydroxide of 15 to 20 nm, and this size was maintained at least up to 600°C. "... 

These principles ensure correct hydrodynamic behavior of DPD fluid. The advantage of DPD over other methods lies in the possibility of matching the scale of discrete-particle simulation to the dominant spatio-temporal scales of the entire system. For example, in MD simulation the timescales associated with evolution of heavy colloidal particles are many orders of magnitude larger than the temporal evolution of solvent particles. If the solvent molecules are coarse-grained into DPD droplets, they evolve much more slowly and are able to match the time scales close to those associated with the colloidal particles. 

With the aim of coarse-graining DPD, the fluid particle method (FPM), a non-central force has been introduced that is proportional to the difference between the velocities of the particles (Espan ol 1998). This force exeits additional drag, which produces rotational... 

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