8.8. Simulation in dilute solution and melt (on-lattice simulation)
.......Dilute solution: Randomly select one monomer and look for a vacant site. The vacant site can be assigned as occupied by solvents. Calculate energy and follow Metropolis scheme as previously discussed.
......Melt: In melt simulation, instead of selecting a monomer randomly, select a vacant site randomly and find an occupied site nearest to that vacant site. This is because, in melt, most of the sites are occupied by the polymer. Thus, finding an occupied site next to a vacant site is more probable than finding a vacant site next to an occupied site. Once a pair of occupied and vacant site is found, apply suitable MC move to run the simulation. Flow diagrams of a typical simulation method in lattice are given in Figure 8.13 and 8.14 for dilute solution and melt respectively.
8.9. Simulation of polymers with complex architectures
.........So far we have discussed the simulation methodology largely applicable for linear polymers. There are many polymers with complex structural features, such as, ring polymer, branched polymer. Branched polymer can be of grafted polymer (branches are grafted on a main chain), star branched polymer (branches are originating from a single branch point), dendrimer (many branch point) etc. Some of them are illustrated in Figure 8.12.
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Ring Polymer.............. Branched................................. Star polymer .........................Dendrimer
Figure 8.12: Schematic representation of polymers with complex architecture
In these branched polymers, single site bond fluctuation is possible, but reptation move is not possible. However, a partial reptation is possible for ring polymer and branches. The reptation move will be initiated by the terminal unit of a branch and terminated at the branch point, subject to the bond length constraint and no-bond crossing criteria. R2 is no longer an equilibrium properties due to the non-existence of two open ends, but R2g can be used universally to all such polymers.
................Special measure needs to be taken in moving the branch point. Movement of branch point is associated with the movement of at least 3 bonds. Bond length and bond crossing of all the bonds needs to be checked – time consuming steps and many of the moves get rejected as the number of branching increases. As an example, branch point of a star polymer with more than 16 arms may remain static throughout the simulation.