Molecular short trajectories

Figure 7 shows a Dimer calculation for the two-dimensional test problem. The initial configurations for the dimer searches were taken from the extrema of a short high temperature molecular dynamics trajectory (shown as a dashed line). 

G. A. Arteca, Biopolymers, 35, 393 (1995). Fluctuations in Molecular Size, Entanglement Complexity, and Anisometry Along Molecular Dynamics Trajectories of Short a-Helices. 

To compute the above expression, short molecular dynamics runs (with a small time step) are calculated and serve as exact trajectories. Using the exact trajectory as an initial guess for path optimization (with a large time step) we optimize a discrete Onsager-Machlup path. The variation of the action with respect to the optimal trajectory is computed and used in the above formula. 

It is appropriate to consider first the question of what kind of accuracy is expected from a simulation. In molecular dynamics (MD) very small perturbations to initial conditions grow exponentially in time until they completely overwhelm the trajectory itself. Hence, it is inappropriate to expect that accurate trajectories be computed for more than a short time interval. Rather it is expected only that the trajectories have the correct statistical properties, which is sensible if, for example, the initial velocities are randomly generated from a Maxwell distribution. 

Time reversibility. The third property of Newton s equation of motion is that it is reversible in time. Changing the signs of all velocities (or momenta) will cause the molecule to retrace its trajectory. If the equations of motion are solved correctly, then the numerical trajectory should also have this property. Note, however, that in practice this time reversibility can be reproduced by numerical trajectories only over very short periods of time because of the chaotic nature of large molecular systems. 

Finally, we were led to the last stage of research where we treated the crystallization from the melt in multiple chain systems [22-24]. In most cases, we considered relatively short chains made of 100 beads they were designed to be mobile and slightly stiff to accelerate crystallization. We could then observe the steady-state growth of chain-folded lamellae, and we discussed the growth rate vs. crystallization temperature. We also examined the molecular trajectories at the growth front. In addition, we also studied the spontaneous formation of fiber structures from an oriented amorphous state [25]. In this chapter of the book, we review our researches, which have been performed over the last seven years. We want to emphasize the potential power of the molecular simulation in the studies of polymer crystallization. 

Packing efficiency can also be described by the extent of short-range order in the amorphous state. Mitchell has shown through X-ray scattering studies that, while the local molecular organization of noncrystalline polymers is random, in many cases, there are additional correlations that do not perturb the chain trajectory but will impact polymer properties.15 These correlations have a limited spatial range (<50A) but will have a particular impact on bulk properties... 

---