Decoupling phenomena in supercooled liquids: Signatures in the energy landscape

A significant deviation from the Debye model of rotational diffusion in the dynamics of orientational degrees of freedom in an equimolar mixture of ellipsoids of revolution and spheres is found to begin precisely at a temperature at which the average inherent structure energy of the system starts falling with drop in temperature. We argue that this onset temperature corresponds to the emergence of the alpha-process as a distinct mode of orientational relaxation. Equally important, we find that the coupling between the rotational and translational diffusion breaks down at a still lower temperature where a sharp change occurs in the temperature dependence of the average inherent structure energy.Comment: Submitted for publicatio

Anisotropic translational diffusion in the nematic phase: Dynamical signature of the coupling between orientational and translational order in the energy landscape

We find in a model system of thermotropic liquid crystals that the translational diffusion coefficient parallel to the director $D_{\parallel}$ first increases and then decreases as temperature drops through the nematic phase, and this reversal occurs where the smectic order parameter of the underlying inherent structures becomes significant for the first time. We argue, based on an energy landscape analysis, that the coupling between orientational and translational order can play a role in inducing the non-monotonic temperature behavior of $D_{\parallel}$. Such a view is likely to form the foundation of a theoretical framework to explain the anisotropic translation diffusion.Comment: 10 pages, 4 figure

Frequency dependent heat capacity within a kinetic model of glassy dynamics

There has been renewed interest in the frequency dependent specific heat of supercooled liquids in recent years with computer simulation studies exploring the whole frequency range of relaxation. The simulation studies can thus supplement the existing experimental results to provide an insight into the energy landscape dynamics. We here investigate a kinetic model of cooperative dynamics within the landscape paradigm for the dynamic heat capacity behavior. In this picture, the beta-process is modeled as a thermally activated event in a two-level system and the alpha-process is described as a beta-relaxation mediated cooperative transition in a double well. The model provides a description of the activated hopping in the energy landscape in close relation with the cooperative nature of the hopping event. For suitable choice of parameters, the model predicts a frequency dependent heat capacity that reflects the two-step relaxation behavior. Although experimentally obtained specific heat spectra of supercooled liquids till date could not capture the two-step relaxation behavior, this has been observed in a computer simulation study by Scheidler et. al. [Phys. Rev. B 63, 104204 (2001)]. The temperature dependence of the position of the low-frequency peak, due to the alpha-relaxation, shows a non-Arrhenius behavior as observed experimentally by Birge and Nagel [Phys. Rev. Lett. 54, 2674 (1985)]. The shape of the alpha-peak is, however, found to be temperature independent, in agreement with the simulation result. The high-frequency peak appears with considerably larger amplitude than the alpha-peak. We attempt a plausible reason for this observation that is in contrast with the general feature revealed by the dielectric spectroscopy.Comment: 10 pages, 10 figure

Nonmonotonic temperature dependence of heat capacity through the glass transition within a kinetic model

The heat capacity of a supercooled liquid subjected to a temperature cycle through its glass transition is studied within a kinetic model. In this model, the β process is assumed to be thermally activated and described by a two-level system. The a process is described as a β relaxation mediated cooperative transition in a double well. The overshoot of the heat capacity during the heating scan is well reproduced and is shown to be directly related to delayed energy relaxation in the double well. In addition, the calculated scan rate dependencies of the glass transition temperature Tg and the limiting fictive temperature TLf show qualitative agreement with the known results. Heterogeneity is found to significantly reduce the overshoot of heat capacity. Furthermore, the frequency dependent heat capacity has been calculated within the present framework and found to be rather similar to the experimentally observed behavior of supercooled liquids

Waiting time distribution and nonexponential relaxation in single molecule spectroscopic studies: realization of entropic bottleneck in a simple model

We study a dynamical disorder model for environmental modulation of rate processes where a need of dynamical cooperativity presents an entropy barrier, rather than an energy barrier. The rate depends on a control variable, Q, that describes the collective instantaneous state of the environment and is itself a random walker in finite discrete space with continuous time. We obtain the waiting time distribution for the relaxation by simulating the model. The time dependence of the average survival probability is derived there from and also by a numerical solution through the Liouville-master equation approach to the theoretical problem. We present an analytical treatment of the first passage time problem that is posed by a limiting case of our model. As the rate of the environmental fluctuation, τ-1env, slows down, the decay of the average survival probability is found to be more and more nonexponential in short times, but to change to exponential at longer times. The average survival time, τ, exhibits a fractional power law dependence on κ( = τenvk0), where time is scaled in terms of k-10, k0 being the intrinsic rate coefficient for the relaxation. The mean first passage time in the limiting case of the model exhibits an exponential dependence on the total number of the environmental subsystems N and a non-Arrhenious temperature dependence over the temperature range studied. We note the likely relevance of a part of this result to single molecule spectroscopic studies that reveal a tail in the waiting time distribution at long times

Engineering Rings in Network Materials

Network materials can be crystalline or amorphous solids, or even liquids, where typically directional interactions link the building blocks together, resulting in a physical representation of a mathematical object, called a graph or equivalently a network. Rings, which correspond to a cyclic path in the underlying network, consisting of a sequence of vertices and edges, are medium‐range structural motifs in the physical space. This Perspective presents an overview of recent studies, which showcase the importance of rings in the emergence of crystalline order as well as in phase transitions between two liquid phases for certain network materials, comprised of colloidal or molecular building blocks. These studies demonstrate how the selection of ring sizes can be exploited for programming self‐assembly of colloidal open crystals with an underlying network and elucidate rings as a vehicle for entanglement that distinguishes the two liquid phases of different densities involved in liquid–liquid phase transitions of network liquids with local tetrahedral order. In this context, an outlook is presented for engineering rings in network materials composed of colloidal and molecular building blocks, with implications also for metal‐organic frameworks, which have been extensively studied as porous crystals, but, more recently, as network‐forming liquids and glasses as well

Energy landscape view of phase transitions and slow dynamics in thermotropic liquid crystals

Thermotropic liquid crystals are known to display rich phase behavior on temperature variation. Although the nematic phase is orientationally ordered but translationally disordered, a smectic phase is characterized by the appearance of a partial translational order in addition to a further increase in orientational order. In an attempt to understand the interplay between orientational and translational order in the mesophases that thermotropic liquid crystals typically exhibit upon cooling from the high-temperature isotropic phase, we investigate the potential energy landscapes of a family of model liquid crystalline systems. The configurations of the system corresponding to the local potential energy minima, known as the inherent structures, are determined from computer simulations across the mesophases. We find that the depth of the potential energy minima explored by the system along an isochor grows through the nematic phase as temperature drops in contrast to its insensitivity to temperature in the isotropic and smectic phases. The onset of the growth of the orientational order in the parent phase is found to induce a translational order, resulting in a smectic-like layer in the underlying inherent structures; the inherent structures, surprisingly, never seem to sustain orientational order alone if the parent nematic phase is sandwiched between the high-temperature isotropic phase and the low-temperature smectic phase. The Arrhenius temperature dependence of the orientational relaxation time breaks down near the isotropic-nematic transition. We find that this breakdown occurs at a temperature below which the system explores increasingly deeper potential energy minima

Design principles for Bernal spirals and helices with tunable pitch

Using the framework of potential energy landscape theory, we describe two in silico designs for self-assembling helical colloidal superstructures based upon dipolar dumbbells and Janus-type building blocks, respectively. Helical superstructures with controllable pitch length are obtained using external magnetic field driven assembly of asymmetric dumbbells involving screened electrostatic as well as magnetic dipolar interactions. The pitch of the helix is tuned by modulating the Debye screening length over an experimentally accessible range. The second design is based on building blocks composed of rigidly linked spheres with short-range anisotropic interactions, which are predicted to self-assemble into Bernal spirals. These spirals are quite flexible, and longer helices undergo rearrangements via cooperative, hinge-like moves, in agreement with experiment