Structural Coarse-Graining

The Iterative Boltzmann Method (IBM) was developed to circumvent the problems encountered with the simplex technique. It is designed to optimize coarse-graining parameters against the structure of an atomistic simulation, and it lifts the limitation of needing analytical potentials. 

In the limit of infinite dilution, one could use the potential of mean force (PMF) by Boltzmann inverting the pair distribution function from a simulation or an experiment to get an interaction potential between monomers, which is 

When working with iterative structural coarse-graining techniques, we limit ourselves to potentials and distribution functions that depend only on a single coordinate like radial distribution functions (RDFs), bond distance, bond angle, or dihedral angle distributions. These distribution functions are convenient for describing the structure of polymers, and they enable the use of the to reproduce the structure. As this procedure is iterative, 

It is noteworthy to point out that, in any system, optimization of the bonded and the nonbonded parameters can be performed either together in one combined procedure or they can be done separately because the mutual effects between the two types of interactions are negligible. Because the intrachain optimization can be achieved much more quickly than can the interchain optimization, most modelers choose to optimize the two separately. 

It has been shown recently, with a comparative study of melts and solutions of polyisoprene, that the environment has a strong effect on the coarsegrained model. Because polymers in the melt have a different scaling behavior than in solution, we cannot use the same model when we remove the solvent. For polyisoprene, it was possible to calibrate the meso-scale model at chains of length 10 and then to perform simulations for chain lengths up to 120. The scaling for the melt and the solution cases were well in agreement with experiments and with theoretical expectations. 

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Figure 4 Scheme of the iterative procedure used in structural coarse-graining based on... 

Figure B3.6.3. Sketch of the coarse-grained description of a binary blend in contact with a wall, (a) Composition profile at the wall, (b) Effective interaction g(l) between the interface and the wall. The different potentials correspond to complete wettmg, a first-order wetting transition and the non-wet state (from above to below). In case of a second-order transition there is no double-well structure close to the transition, but g(l) exhibits a single minimum which moves to larger distances as the wetting transition temperature is approached from below, (c) Temperature dependence of the thickness / of the enriclnnent layer at the wall. The jump of the layer thickness indicates a first-order wetting transition. In the case of a conthuious transition the layer thickness would diverge continuously upon approaching from below.

The coarse-graining approach is commonly used for thermodynamic properties whereas the systematic or random sampling methods are appropriate for static structural properties such as the radial distribution function. 

In coarse-grained microscopic models, the amphiphiles, oil, and water molecules are still treated as individual particles, but their structure is very much... 

The mechanical properties of Watts deposits from normal, purified solutions depend upon the solution formulation, pH, current density and solution temperature. These parameters are deliberately varied in industrial practice in order to select at will particular values of deposit hardness, strength, ductility and internal stress. Solution pH has little effect on deposit properties over the range pH 1 0-5-0, but with further increase to pH 5 -5, hardness, strength and internal stress increase sharply and ductility falls. With the pH held at 3-0, the production of soft, ductile deposits with minimum internal stress is favoured by solution temperatures of 50-60°C and a current density of 3-8 A/dm in a solution with 25% of the nickel ions provided by nickel chloride. Such deposits have a coarse-grained structure, whereas the harder and stronger deposits produced under other conditions have a finer grain size. A comprehensive study of the relationships between plating variables and deposit properties was made by the American Electroplaters Society and the results for Watts and other solutions reported... 

Solid metals obtained upon solidification of the molten metal exhibit grain structure. They consist of fine crystallites randomly oriented in space. The size of the individual crystallites (grains) is between 10 m (fine-grained structure) and 10 m (coarse-grained structure). The crystal stracture of the individual grains as a rule is not ideal. It contains various types of defects vacant sites, interstitial atoms or ions, and dislocations (lattice shearing or bending). Microcracks sometimes evolve in the zones between crystallites. 

There are various ways to check the quality of the resulting structures with respect to experiment. A typical check would be to compare the mean square end-to-end distance with results from scattering experiments. However, since the experimental samples are highly polydisperse, the results from scattering experiments are somewhat questionable [195]. Furthermore, a crucial check is the direct comparison of conformations of systems. In order to be able to compare the conformations resulting from simulations unanimously to experiment we reintroduce the chemical details into the coarse-grained chain. This is one of the reasons why it is so important to device a mapping procedure which stays close to the chemical structure of the objects. We have a one-... 

As for any modeling of continuum structures, the properties of the phases must be known for this kind of approach to work. Here, estimates obtained by atomistic methods of other techniques, described in the earlier chapters of this review, may be employed, or empirically known values may be used. It is hoped that the co-development of these continuum techniques and atomistic and coarse-grained approaches will lead to a seamless integration of the different techniques. 

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