Monte Carlo simulation of the crystal structure of the rotator phase of n-paraffins. II. Effects of rotation and translation of the rigid molecules

Abstract

Structures and molecular motions in the rotator phases of n-paraffins are simulated by use of the Monte Carlo method—both rotational and translational degrees of freedom of the molecules being taken into account. Molecules of rigid trans-planar structure are assumed to be placed in a two-dimensional orthorhombic or orthohexagonal lattice with lattice parameters a and b. A model of the nearly continuous molecular motion is adopted in this work; each molecule is assumed to have 36 discrete orientations (in 10° intervals) and 10 discrete translations (in 0.128 Å intervals) around and along the molecular axis, respectively. Molecular packing modes in various lattice systems of different a/b values are examined ranging from that of the ordinary orthorhombic phase (a/b=1.50) to that of the rotator-II (R-II) phase (a/b=31/2). It is found that the crystals in the rotator phases are generally composed of many domains within which molecules are packed more or less in order. In the rotator-I (R-I) phase, fairly large structural changes are observed with the change in a/b value; the structure of the R-I phase reported in our previous MC work should be slightly modified. The structure of the R-II phase, on the other hand, is found to be essentially the same as that of our previous MC work. Modes of the molecular motion in the R-II phase are studied by monitoring the time evolution of the rotational and translational states of all molecules in the system. It is found that the molecules are making fairly active rotational oscillation around one of the six equivalent directions connecting nearest neighbor molecular pairs. The molecules are also making sporadic large rotations to the different directions. The translational motion of the molecules is found to be very active and evidently independent of the rotational motion. The overall molecular motions in the rotator phase are found to be described in terms of the movement of the boundaries of the ordered domains.

A comparison of computer models for the simulation of crystalline polyethylene and the long n-alkanes.

“…Refs. [26][27][28][29]). Simulations of the orthorhombic phases of short n-alkanes have been reported by McGann and Lacks [30] and Mavrantza et al [31].…”

Pressure effect on the solid–liquid equilibrium forms of odd normal alkanes

“…Eventually, the five ''rotator phases'' and the transition between them were discovered [13]. These phases and transitions were supported by computer simulations using the molecular dynamics method [14,15] and the Monte Carlo method [16,17].…”

X-ray-diffraction study of the superliquid region of the phase diagram of a Langmuir monolayer

“…) These results can be compared to the finding of Copeland, Harkins, and Boyd [2] and Abraham et al [3] that the "viscosity" and shear modulus have a minimum in this region; our results provide a microscopic basis for the anomalous mechanical properties. Of course the xray studies do not tell us why the monolayer is so poorly ordered in the rotator-I phase, but experiments [16], molecular-dynamics simulations [17], and Monte Carlo simulations [18] indicate that the rotator-I phase in lamellar paraSns has small domains, large numbers of gauche bonds, large amplitudes for motion normal to the layers, increased tilt disorder, and layer roughening. Roughening and large vertical motions are unlikely in lipid monolayers on water, but this still leaves a number of mechanisms that might be associated with the observed behavior in monolayers.…”