ABSTRACT
Perhaps the simplest theoretical approach to polymers in solution is molecular dynamics, i.e., the numerical integration of Newton’s equations of motion,
, where i extends over all n atoms in the simulation box. Common integrators like the Verlet or predictor corrector algorithms [1], yield
trajectories consisting of positions and velocities of the interaction centers (usually the nuclei) stored at regular time intervals on the picosecond time scale. Positions and
velocities can be tied to the thermodynamic quantities like pressure and temperature via the equipartition theorem. The forces in the above equations of motion may be derived
from a potential of the form
(1)
The first three terms describe potential energy variations due to bond (b), valence angle , and bond torsion angle deformations. The remaining (nonbonding) terms are
Lennard-Jones and Coulomb interactions between interaction sites separated by a distance . Nonbonded interactions usually exclude pairs of sites belonging
to the same bond or valence angle. A model of this type is appropriate to study the dynamics of a system with maybe 10,000 interaction centers in a time window of about 10ns, on current workstation computers. Figure 1 gives an impression of the typical size
of such a system. Figure 2 on the other hand shows how slow (global) conformation changes may be, even for a short oligomer, compared to the accessible time window. Clearly, Eq. (1) is a crude approximation to molecular interactions. It basically
constitutes the simplest level on which the chemical structure of a specific polymer can still be recognized. The development of more complex molecular and macromolecular force fields is still ongoing, and the reader is referred to the extensive literature (a good starting point is Ref. [2]).
