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The dynamics of rigid polyatomic systems, either molecules or rigid portions of large molecules, is described by cartesian equations of motion for its atoms. In comparison with the original version of the method of constraint

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The dynamics of atactic polypropylene has been explored with quasielastic neutron scattering (QENS) measurements in the temperature range 4-460 K and momentum transfer range q) 0.2-2.25 Å-1. In parallel, molecular dynamics simulations of the same polymer have been conducted in the temperature range 260-600 K, using both a fully atomistic model and a model with united-atom methyl groups. In conjunction with the second model, a computational procedure for introducing the motion of methyl hydrogens a posteriori is proposed and tested against the fully atomistic simulation results. Simulated intermediate incoherent scattering functions I(q,t) reveal an initial exponentially decaying regime of duration ca. 1 ps, which is dominated by bond angle bending vibrations and torsional oscillations, as well as features attributable to torsional transitions of the methyl groups and to correlated conformational transitions of the backbone bonds at longer times. The time decay of I(q,t) beyond 1 ps is well-described by stretched exponential functions, the stretching exponent being around 0.5 at 600 K and decreasing with decreasing temperature. Analysis of the atomistic simulation trajectories yields distributions of relaxation times with a distinct log-Gaussian peak characteristic of methyl motion, from which a Gaussian distribution of activation energies for methyl torsional transitions with mean around 15 kJ/mol and standard deviation around 3 kJ/mol is extracted, in excellent agreement with QENS estimates. Torsional transitions of different methyls occur essentially independently of each other. QENS experiments reveal a nondecaying elastic contribution to the scattering over the time window of the measurement, which is not seen in the simulations. Apart from this, computed I(q,t) and incoherent dynamic structure factor S(q,ω) curves are in very favorable agreement with the measured QENS spectra and with earlier NMR data on atactic polypropylene.

The method of constant pressure molecular dynamics (MD), developed by Andersen for monoatomic fluids is extended to the MD, in Cartesian coordinates, of molecular systems with constraints. Andersen’s proof is easily generalized after decoupling internal degrees of freedom from the center-of-mass. Only these last degrees are directly affected by Andersen’s transformation (demon). The Cartesian equations of motion of individual atoms are derived from a generalized Andersen’s Lagrangian. The equations are quite similar to those of the usual MD simulation at constant volume apart from an additional term coupling the molecular center-of-mass and the volume of the sample. The volume appears now as a dynamical variable evolving from the imbalance between imposed external pressure and instantaneous values of the molecular stress tensor. Some numerical aspects are discussed and the technique is briefly illustrated for the case of rigid diatomic molecules.

A computer simulation method is devised whereby the change in location of a triple point is followed as one of the parameters of the interaction potential is modified. The method, a two-dimensional Clapeyron integration, is illustrated here for the case of a hard-core plus repulsive Yukawa potential of variable range. The latter is a crude model for charge-stabilized colloids. It is shown that the body-centered-cubic (bcc) phase becomes metastable when the range of the Yukawa term is smaller than, approximately, one-sixth of the hard-core diameter.