Length Scales and Structural Dynamics in Nematogen Pseudonematic Domains Measured with 2D IR Vibrational Echoes and Optical Kerr Effect Experiments

Long-time relaxation dynamics in nematic and smectic liquid crystals of soft repulsive colloidal rods

Understanding the relaxation dynamics of colloidal suspensions is crucial to identifying the elements that influence the mobility of their constituents, assessing their macroscopic response across the relevant time and length scales, and thus disclosing the fundamentals underpinning their exploitation in formulation engineering. In this work, we specifically assess the impact of long-ranged ordering on the relaxation dynamics of suspensions of soft repulsive rodlike particles, which are able to self-organize into nematic and smectic liquid-crystalline phases. Rods are modeled as soft repulsive spherocylinders with a length-to-diameter ratio L^{★}=5, interacting via the truncated and shifted Kihara potential. By performing dynamic Monte Carlo simulations, we analyze the effect of translational and orientational order on the diffusion of the rods along the relevant directions imposed by the morphology of the background phases. To provide a clear picture of the resulting dynamics, we assess its dependence on temperature, which can dramatically determine the response time of the system relaxation and the self-diffusion coefficients of the rods. The computation of the van Hove correlation functions allows us to identify the existence of rods that diffuse significantly faster than the average and whose concentration can be accurately adjusted by a suitable choice of temperature.

Measuring order in disordered systems and disorder in ordered systems: Random matrix theory for isotropic and nematic liquid crystals and its perspective on pseudo-nematic domains

Surprisingly long-ranged intermolecular correlations begin to appear in isotropic (orientationally disordered) phases of liquid crystal forming molecules when the temperature or density starts to close in on the boundary with the nematic (ordered) phase. Indeed, the presence of slowly relaxing, strongly orientationally correlated, sets of molecules under putatively disordered conditions ("pseudo-nematic domains") has been apparent for some time from light-scattering and optical-Kerr experiments. Still, a fully microscopic characterization of these domains has been lacking. We illustrate in this paper how pseudo-nematic domains can be studied in even relatively small computer simulations by looking for order-parameter tensor fluctuations much larger than one would expect from random matrix theory. To develop this idea, we show that random matrix theory offers an exact description of how the probability distribution for liquid-crystal order parameter tensors converges to its macroscopic-system limit. We then illustrate how domain properties can be inferred from finite-size-induced deviations from these random matrix predictions. A straightforward generalization of time-independent random matrix theory also allows us to prove that the analogous random matrix predictions for the time dependence of the order-parameter tensor are similarly exact in the macroscopic limit, and that relaxation behavior of the domains can be seen in the breakdown of the finite-size scaling required by that random-matrix theory.

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

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.