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Register a new userV-T Theory of Self Dynamic Response in a Monatomic Liquid
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Added by
Giulia De Lorenzi-Venneri
Publication date
2008
fields
Physics
and research's language is
English
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A new theoretical model for self dynamic response is developed using Vibration-Transit (V-T) theory, and is applied to liquid sodium at all wavevectors q from the hydrodynamic regime to the free particle limit. In this theory the zeroth-order Hamiltonian describes the vibrational motion in a single random valley harmonically extended to infinity. This Hamiltonian is tractable, is evaluated a priori for monatomic liquids, and the same Hamiltonian (the same set of eigenvalues and eigenvectors) is used for equilibrium and nonequlibrium theory. Here, for the self intermediate scattering function Fself(q,t) we find the vibrational contribution is in near perfect agreement with molecular dynamics (MD) through short and intermediate times, at all q. This is direct confirmation that normal mode vibrational correlations are present in the motion of the liquid state. The primary transit effect is diffusive motion of the vibrational equilibrium positions, as the liquid transits rapidly among random valleys. This motion is modeled as a standard random walk, and the resulting theoretical Fself(q,t) is in excellent agreement with MD results at all q and t. In the limit for q to infinity, the theory automatically exhibits the correct approach to the free-particle limit. Also in the limit for q to zero, the hydrodynamic limit emerges as well. In contrast to the benchmark theories of generalized hydrodynamics and mode coupling, the present theory is near a priori, while achieving modestly better accuracy. Therefore, in our view, it constitutes an improvement over the traditional theories.
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In V-T theory the atomic motion is harmonic vibrations in a liquid-specific potential energy valley, plus transits, which move the system rapidly among the multitude of such valleys. In its first application to the self intermediate scattering function (SISF), V-T theory produced an accurate account of molecular dynamics (MD) data at all wave numbers q and time t. Recently, analysis of the mean square displacement (MSD) resolved a crossover behavior that was not observed in the SISF study. Our purpose here is to apply the more accurate MSD calibration to the SISF, and assess the results. We derive and discuss the theoretical equations for vibrational and transit contributions to the SISF. The time evolution is divided into three successive intervals: the vibrational interval when the vibrational contribution alone accurately accounts for the MD data; the crossover when the vibrational contribution saturates and the transit contribution becomes resolved; and the diffusive interval when the transit contribution alone accurately accounts for the MD data. The resulting theoretical error is extremely small at all q and t. Comparison of V-T and mode-coupling theories for the MSD and SISF reveals that, while their formulations differ substantially, their underlying atomic motions are in logical correspondence.
We examine the distinct part of the density autocorrelation function Fd(q,t), also called the intermediate scattering function, from the point of view of the vibration-transit (V-T) theory of monatomic liquid dynamics. A similar study has been reported for the self part, and we study the self and distinct parts separately because their damping processes are not simply related. We begin with the perfect vibrational system, which provides precise definitions of the liquid correlations, and provides the vibrational approximation Fdvib(q,t) at all q and t. Two independent liquid correlations are defined, motional and structural, and these are decorrelated sequentially, with a crossover time tc(q). This is done by two independent decorrelation processes: the first, vibrational dephasing, is naturally present in Fdvib(q,t) and operates to damp the motional correlation; the second, transit-induced decorrelation, is invoked to enhance the damping of motional correlation, and then to damp the structural correlation. A microscopic model is made for the transit drift, the averaged transit motion that damps motional correlation on 0 < t < tc(q). Following the previously developed self-decorrelation theory, a microscopic model is also made for the transit random walk, which damps the structural correlation on t > tc(q). The complete model incorporates a property common to both self and distinct decorrelation: simple exponential decay following a delay period, where the delay is tc(q, the time required for the random walk to emerge from the drift. Our final result is an accurate expression for Fd(q,t) for all q through the first peak in Sd(q). The theory is calibrated and tested using molecular dynamics (MD) calculations for liquid Na at 395K; however, the theory itself does not depend on MD, and we consider other means for calibrating it.
Crystallization from a supercooled liquid initially proceeds via the formation of a small solid embryo (nucleus), which requires surmounting an activation barrier. This phenomenon is most easily studied by numerical simulation, using specialized biased-sampling techniques to overcome the limitations imposed by the rarity of nucleation events. Here, I focus on the barrier to homogeneous ice nucleation in supercooled water, as represented by the monatomic-water model, which in the bulk exhibits a complex interplay between different ice structures. I consider various protocols to identify solidlike particles on a computer, which perform well enough for the Lennard-Jones model, and compare their respective impact on the shape and height of the nucleation barrier. It turns out that the effect is stronger on the nucleus size than on the barrier height. As a by-product of the analysis, I determine the structure of the nucleation cluster, finding that the relative amount of ice phases in the cluster heavily depends on the method used for classifying solidlike particles. Moreover, the phase which is most favored during the earlier stages of crystallization may happen, depending on the nucleation coordinate adopted, to be different from the stable polymorph. Therefore, the quality of a reaction coordinate cannot be assessed simply on the basis of the barrier height obtained. I explain how this outcome is possible and why it just points out the shortcoming of collective variables appropriate to simple fluids in providing a robust method of particle classification for monatomic water.
We report a molecular dynamics simulation demonstrating that the Smectic B crystalline phase (Cr-B), commonly observed in mesogenic systems of anisotropic molecules, can be formed by a system of identical particles interacting via a spherically symmetric potential. The Cr-B phase forms as a result of a first order transition from an isotropic liquid phase upon isochoric cooling at appropriate number density. Its structure, determined by the design of the pair potential corresponds to Cr-B structure formed by elongated particles with the aspect ratio 1.8. The diffraction pattern, and the real-space structure inspection demonstrate dominance of the ABC-type of axial layer stacking. This result opens a general possibility of producing smectic phases using isotropic interparticle interaction both in simulations and in colloidal systems.
Liquid crystal networks exploit the coupling between the responsivity of liquid-crystalline mesogens, e.g., to electric fields, and the (visco)elastic properties of a polymer network. Because of this, these materials have been put forward for a wide array of applications, including responsive surfaces such as artificial skins and membranes. For such applications, the desired functional response must generally be realized under strict geometrical constraints, such as provided by supported thin films. To model such settings, we present a dynamical, spatially-heterogeneous Landau-type theory for electrically-actuated liquid crystal network films. We find that the response of the liquid crystal network permeates the film from top to bottom, and illustrate how this affects the time scale associated with macroscopic deformation. Finally, by linking our model parameters to experimental quantities, we suggest that the permeation rate can be controlled by varying the aspect ratio of the mesogens and their degree of orientational order when cross-linked into the polymer network, for which we predict a single optimum. Our results contribute specifically to the rational design of future applications involving transport or on-demand release of molecular cargo in liquid crystal network films.
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