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By Matchett J.R., et al. (eds.)

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These properties inlcude the internal energy or the size of the polymer chains as determined from the radius of gyration of the chains,78 both of which are readily accessible via computation. When using an atomic scale MD simulation of this cooling process, the integration time step dt is typically as small as 1 fs (10À15 s), and accordingly, even very long runs (on the order of 107 or 108 time steps) will not exceed a time interval of 100 ns. It is not even clear that on such short time scales the true physical traits of the glass transition can emerge fully.

One example of each bond vector class is shown in the sketch. Simulation Methods 13 allows for a physical interpretation of the obtained stochastic dynamics41 that generates Rouse-like motion of the chains12 in the simulation of dense polymer melts. SIMULATION METHODS The simulation methods most commonly used for atomistic or coarsegrained molecular models are MD simulations and MC simulations. In MD simulations, Newton’s equations of motion are integrated to generate a trajectory (a history) of the model system.

19]. This requires the suggestion probabilities to be reversible W0 ðx ! x0 Þ ¼ W0 ðx0 ! , Metropolis rates, Glauber rates, or heat-bath,51 but there is an unlimited variety of possible choices for W0 , and this is the great advantage of the MC method. Only some choices for W0 result in physically reasonable dynamics (in general, local moves like selecting a monomer at random and then moving it into a randomly chosen direction by a small distance), but all reversible choices lead to the correct equilibrium distribution of states.

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