The inherent dynamics of isotropic- and nematic-phase liquid crystals

Abstract

The geodesic (shortest) pathways through the potential energy landscape of a liquid can be thought of as defining what its dynamics would be if thermal noise were removed, revealing what we have called the "inherent dynamics" of the liquid. We show how these inherent paths can be located for a model liquid crystal former, showing, in the process, how the molecular mechanisms of translation and reorientation compare in the isotropic and nematic phases of these systems. These mechanisms turn out to favor the preservation of local orientational order even under macroscopically isotropic conditions (a finding consistent with the experimental observation of pseudonematic domains in these cases), but disfavor the maintenance of macroscopic orientational order, even in the nematic phase. While the most efficient nematic pathways that maintain nematic order are indeed shorter than those that do not, it is apparently difficult for the system to locate these paths, suggesting that molecular motion in liquid-crystal formers is dynamically frustrated, and reinforcing the sense that there are strong analogies between liquid crystals and supercooled liquids.

What is special about how roaming chemical reactions traverse their potential surfaces? Differences in geodesic paths between roaming and non-roaming events

“…Moreover, since the kinetic energy has components associated with individual physical degrees of freedom such as vibration and rotation, we can define component lengths, as well, allowing us to ascertain how much these most efficient dynamical routes rely on each of the different kinds of degrees of freedom. 31,33 All of the published applications of these ideas, however, have been within the context of condensed matter problems, leaving us with the question of how relevant these particular most-efficient paths through the potential energy landscape are to high-energy intramolecular dynamics. While both kinds of applications have energies well above much of their potential surfaces' topography, the much higher dimensionality of many-body problems provides an additional measure of justification for using the landscape ensemble.…”

“…iterating, if necessary, until the boundary is reached. [29][30][31]33 Unlike the free-propagation steps, however, these particular steps are not guaranteed to leave the center of mass inviolate. Still, one can easily write a projected version of Eqs.…”

“…What distinguishes the tendency towards one kind of pathway or another is buried under the noise of the vibrational dynamics-which is why we need to compare the geodesic (inherent) pathways. [31][32][33]…”

“…(3.4) and (3.5), are a measure of the time we expect to be spent in moving the respective coordinates. 31,33 Even so, there would be no particular purpose served in comparing the geodesic lengths that the different channels traverse before they reach the asymptotic locations of their products. We already know that roaming involves far more wandering than the other channels do.…”

“…The suggestion then is that it is worth examining what is special about the prototypical coordinate-space pathways taken on (what may be) high-dimensional potential surfaces of systems that roam. A potential-landscape approach that has had some recent success in looking at such inherent paths in the context of slow liquid-state dynamics [28][29][30][31][32][33] offers a novel possibility for understanding some features of roaming. Instead of looking for transition-state surfaces through which some classical-trajectory flux is a maximum, this approach looks instead for paths through the potential landscape that are, in some sense, the most efficient.…”