Coarse-grained cubes

The bond fluctuation model (BFM) [51] has proved to be a very efficient computational method for Monte Carlo simulations of linear polymers during the last decade. This is a coarse-grained model of polymer chains, in which an effective monomer consists of an elementary cube whose eight sites on a hypothetical cubic lattice are blocked for further occupation (see... 

Let us divide the T-space somehow into very small, but finite cells Q Gi, Q , , Qx, , which might be, for instance, cubes of equal size. The average value which the fine-grained density p(q, p, <) has at time t over the cell Six we will call coarse-grained density P (t) (read capital p) of this cell. Because of Eq. (54) we have... 

Figure 1. Schematic illustration of the construction of a coarse-grained model for a macromolecule such as polyethylene. In the example shown here, the subchain formed by the three C-C bonds labeled 1,2,3 is represented by the effective bond labeled as I, the subchain formed by the three bonds 4,5,6 is represented by the effective bond labeled as II, etc. In the bond-fluctuation model the length b of the effective bond is allowed to fluctuate in a certain range 6min

An often-used coarse-grained Monte Carlo model is the bond-fluctuation model.In contrast to most other coarse-grained models, it lacks a fixed or quasi-fixed bond length. Instead, connected monomers can occupy all side and corner sites of an fee lattice if the monomer to which they are connected is in the center of the face-centered cube as shown in Figure 8. In this model, as in others, the solvent is typically ignored such that monomers are either occupying a site or the site is deemed to be empty. 

Therefore, the advantage of using a fine powder for densification is reduced because of fast grain growth. On the other hand, since densification time increases in proportion to the cube of powder size (G ), the use of coarse powder is also undesirable. In this regard it is useful to increase the relative densification rate and reduce G, as shown schematically in Figure 11.4(b). 

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