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Additional resources for Simulation Methods For Polymers
In other words, that no particular region in phase space is excluded from sampling by the algorithm. Such an exclusion would render the simulation wrong, even if the simulated object itself is ergodic. As an extreme example consider an algorithm to simulate various conformations of the freelyjointed chain in three dimensions, which, for some reason, such as a programming error, never selects bonds parallel to the z axis. Evidently, many representative conformations will be erroneously excluded.
An approach for tracking electronic degrees of freedom in parallel with a numerical integration of the classical equations of motion for the nuclei, and therefore determining V(rn) ‘‘on the fly,’’ has been devised by Car and Parrinello . This extended ensemble molecular dynamics method, termed ‘‘ab initio molecular dynamics,’’ solves the electronic problem approximately using the Kohn–Sham formulation of Density Functional Theory. This approach proved useful for covalent systems; it still has to be applied to the systems where the properties of interest are defined by Lennard-Jones interactions.
As we discussed above, polymer chains are not rigid bodies, and there is an entropy associated with the different polymer chain conformations. Polymer chains usually contain very large numbers of monomers (thousands or more), and, provided that environmental conditions ensure the same excluded volume exponent , all polymers with the same chain topology are similar at the length scales comparable to the chain radius of gyration. Flory’s model is the simplest; it assumes that chain conformation does not change upon mixing, and therefore there is no conformational entropy contribution in Eq.