Structure matching, coarse-grained

So far, CG approaches offer the most viable route to the molecular modeling of self-organization phenomena in hydrated ionomer membranes. Admittedly, the coarse-grained treatment implies simplifications in structural representation and in interactions, which can be systematically improved with advanced force-matching procedures however, it allows simulating systems with sufficient size and sufficient statishcal sampling. Structural correlations, thermodynamic properties, and transport parameters can be studied. 

Equations (8.10)—(8.12), tensorial ranks and boundary conditions (8.14)-(8.15) notwithstanding, embody a structure similar in format and symbolism to their counterparts for the transport of passive scalars, e.g., the material transport of the scalar probability density P (Brenner, 1980b Brenner and Adler, 1982), at least in the absence of convective transport. As such, by analogy to the case of nonconvective material transport, the effective kinematic viscosity viJkl of the suspension may be obtained by matching the total spatial moments of the probability density Pu to those of an equivalent coarse-grained dyadic probability density P j, valid on the suspension scale, using a scheme (Brenner and Adler, 1982) identical in conception to that used to determine the effective diffusivity for material transport at the Darcy scale from the analogous scalar material probability density P. In particular, the second-order total moment M(2) (sM, ) of the probability density P, defined as... 

This is a sequential method, the simulations at atomistic and CG levels are treated separately. Potentials for collection of atoms i.e., CG beads) are derived from the all atomistic MD simulations. There are different ways to get the potentials for the coarse grained systems. Derivation of potentials from Boltzmann inversion of several bonded and non-bonded distributions (structure based) and force matching from all atomistic MD trajectories followed by their applications will be discussed in the following sections. 

Voth et al. in the same work also reported CG MD of methanol by FC potentials. They coarse grained the system as one site and two sites model. The structural properties matched well with the atomistic reference calculations. Other than structural properties thermodynamical properties such as average configurational energy, isochoric heat capaeity was less than the experimental values for both the models. However the thermal expansion coefficient and isothermal coefficients were in good agreement with experimental values. 

The idea of a minimal coarse-grained model for polymer-solid contacts consists in not describing the structural details of the polymer-solid contact on the length scale of Angstroms because this length scale is not resolved. Instead, the aim is to tailor the interactions at the surface in order to match the difference in surface tension, Ay, of the coarse-grained model to the experimental data. In this way, the macroscopic interfacial thermodynamics is parameterized. 

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