Cooperative motion algorithm

Other moves are specific for dilute solutions (or single chain simulations) and very congested systems (as melts). Some complex rules involving different chains have been developed for the equilibrium study of melts of linear chains, such as the cooperative motion algorithm [105] where beads are moved cooper-... 

Pakula et al. [155] have used the cooperative motion algorithm to study melts of stars with up to 64 units. They studied the internal bead profiles and the correlations of the star centers of mass. They observed an ordering of the systems of stars with high functionalities. 

Gauger and Pakula [191] performed an MC simulation of comb polymers on the fee lattice in dilute and dense media, using the cooperative motion algorithm. It is shown that, unlike linear chains, the EV screening does not appear in the global mean size dependence on N. However, this screening is complete for the branches in the melt, which exhibit ideal behavior. 

Pakula and Zhulina [213] have simulated dry brushes at melt densities in contact with a repulsive wall. They used the cooperative motion algorithm. Their re-... 

It is beyond the scope of this chapter to review all the simulations in the literature, but recent work by Banaszak et al. [98,99] and Vassiliev and Matsen [100] is illustrative. Banaszak et al. did Monte Carlo simulations of ABA triblocks. Their systems contained 900 chains densely packed on a face-centered cubic (fee) lattice. The chains were moved by cooperative rearrangements, called the cooperative motion algorithm since all sites are occupied, a segment can be moved only if other segments are moved simiiltanp.on.sly. Their chains aU had 30 monomers, and they explored three different compositions, each with equal end block lengths. The first had 3 units of A on each end and 24 units of B in the middle this was labeled 3-24-3. The others were 7-16-7 and 10-10-10. The overall A-volume fractions for these are/ = 0.2,0.46, and 0.67. 

Fig. 7.10 Distribution function N s) of the volume fraction of stiff chains at several temperatures, for a subsystem of linear dimension f = 8 of a total system with linear dimension L = 30, using a face-centered cubic lattice with y = 0 and the cooperative motion algorithm. Both chain lengths of the stiff (s) and flexible (f) chmns are equal, N/— Ns = N = 10, and their volume fractions are equal and constant, — 1/2. For the stiff chains, energies 0, 0.5,...

Pakula T (1996) Simulation of copolymers by means of the cooperative-motion algorithm, J Computer-Aided Mater Design 3 329-340. 

The requirement of a detailed balance in the athermal polymer system, as considered here, reduces to showing that the transition probabilities between two neighboring states A and B are equal. In this algorithm, two such states are always reversible and are separated by cooperative rearrangements along loops of the same size and form but different motion directions. Because loops consist of vectors that are pointing equally probably at any direction, this condition is satisfied. Moreover, it remains valid for any polymer system because the loops are independent of the structure. 

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