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Register a new userSpace-Time Correlations in the Orientational Order Parameter and the Orientational Entropy of Water
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We introduce the spatial correlation function $C_Q(r)$ and temporal autocorrelation function $C_Q(t)$ of the local tetrahedral order parameter $Qequiv Q(r,t)$. Using computer simulations of the TIP5P model of water, we investigate $C_Q(r)$ in a broad region of the phase diagram. First we show that $C_Q(r)$ displays anticorrelation at $rapprox 0.32$nm at high temperatures $T>T_Wapprox 250$ K, which changes to positive correlation below the Widom line $T_W$. Further we find that at low temperatures $C_Q(t)$ exhibits a two-step temporal decay similar to the self intermediate scattering function, and that the corresponding correlation time $tau_Q$ displays a dynamic crossover from non-Arrhenius behavior for $T>T_W$ to Arrhenius behavior for $T<T_W$. Finally, we define an orientational entropy $S_Q$ associated with the {it local} orientational order of water molecules, and show that $tau_Q$ can be extracted from $S_Q$ using an analog of the Adam-Gibbs relation.
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Motivated by the structure of networks of cross-linked cytoskeletal biopolymers, we study the orientationally ordered phases in two-dimensional networks of randomly cross-linked semiflexible polymers. We consider permanent cross-links which prescribe a finite angle and treat them as quenched disorder in a semi-microscopic replica field theory. Starting from a fluid of un-cross-linked polymers and small polymer clusters (sol) and increasing the cross-link density, a continuous gelation transition occurs. In the resulting gel, the semiflexible chains either display long range orientational order or are frozen in random directions depending on the value of the crossing angle, the crosslink concentration and the stiffness of the polymers. A crossing angle $thetasim 2pi/M$ leads to long range $M$-fold orientational order, e.g., hexatic or tetratic for $theta=60^{circ}$ or $90^{circ}$, respectively. The transition is discontinuous and the critical cross-link density depends on the bending stiffness of the polymers and the cross-link geometry: the higher the stiffness and the lower $M$, the lower the critical number of cross-links. In between the sol and the long range ordered state, we always observe a gel which is a statistically isotropic amorphous solid (SIAS) with random positional and random orientational localization of the participating polymers.
Using scaled-particle theory for binary mixtures of two-dimensional hard particles with rotational freedom, we analyse the stability of nematic phases and the demixing phase behaviour of a variety of mixtures, focussing on cases where at least one of the components consists of hard rectangles or hard squares. A pure fluid of hard rectangles may exhibit, aside from the usual uniaxial nematic phase, an additional (tetratic) oriented phase, possessing two directors, which is the analogue of the biaxial or cubatic phases in three- dimensional fluids. There is computer simulation evidence that the tetratic phase might be stable with respect to phases with spatial order for rectangles with low aspect ratios. As hard rectangles are mixed with other particles not possessing stable tetratic order by themselves, the tetratic phase is destabilised, via a first- or second-order phase transition, to uniaxial nematic or isotropic phases; for hard rectangles of low aspect ratio tetratic order persists in a relatively large range of volume fractions. The order of these transitions depends on the particle geometry, dimensions and thermodynamic conditions of the mixture. The second component of the mixture has been chosen to be hard discs or disco-rectangles, the geometry of which is different from that of rectangles, leading to packing frustration and demixing behaviour, or simply rectangles of different aspect ratio. These mixtures may be good candidates for observing thermodynamically stable tetratic phases in monolayers of hard particles. Finally, demixing between fluid (isotropic--tetratic or tetratic--tetratic) phases is seen to occur in mixtures of hard squares of different sizes when the size ratio is sufficiently large.
The concept of symmetry breaking has been a propelling force in understanding phases of matter. While rotational symmetry breaking is one of the most prevalent examples, the rich landscape of orientational orders breaking the rotational symmetries of isotropic space, i.e. $O(3)$, to a three-dimensional point group remain largely unexplored, apart from simple examples such as ferromagnetic or uniaxial nematic ordering. Here we provide an explicit construction, utilizing a recently introduced gauge theoretical framework, to address the three-dimensional point-group-symmetric orientational orders on a general footing. This unified approach allows us to enlist order parameter tensors for all three dimensional point groups. By construction, these tensor order parameters are the minimal set of simplest tensors allowed by the symmetries that uniquely characterize the orientational order. We explicitly give these for the point groups ${C_n, D_n, T, O, I} subset SO(3)$ and ${C_{nv}, S_n, C_{nh}, D_{nh}, D_{nd}, T_h, T_d, O_h, I_h}subset O(3)$ for $n={1,2,3,4,6, infty}$. This central result may be perceived as a roadmap for identifying exotic orientational orders that may become more and more in reach in view of rapid experimental progress in e.g. nano-colloidal systems and novel magnets.
Motivated by experiments on colloidal membranes composed of chiral rod-like viruses, we use Monte Carlo methods to determine the phase diagram for the liquid crystalline order of the rods and the membrane shape. We generalize the Lebwohl-Lasher model for a nematic with a chiral coupling to a curved surface with edge tension and a resistance to bending, and include an energy cost for tilting of the rods relative to the local membrane normal. The membrane is represented by a triangular mesh of hard beads joined by bonds, where each bead is decorated by a director. The beads can move, the bonds can reconnect and the directors can rotate at each Monte Carlo step. When the cost of tilt is small, the membrane tends to be flat, with the rods only twisting near the edge for low chiral coupling, and remaining parallel to the normal in the interior of the membrane. At high chiral coupling, the rods twist everywhere, forming a cholesteric state. When the cost of tilt is large, the emergence of the cholesteric state at high values of the chiral coupling is accompanied by the bending of the membrane into a saddle shape. Increasing the edge tension tends to flatten the membrane. These results illustrate the geometric frustration arising from the inability of a surface normal to have twist.
Recent computational studies have reported evidence of a metastable liquid-liquid phase transition (LLPT) in molecular models of water under deeply supercooled conditions. A competing hypothesis suggests, however, that non-equilibrium artifacts associated with coarsening of the stable crystal phase have been mistaken for an LLPT in these models. Such artifacts are posited to arise due to a separation of time scales in which density fluctuations in the supercooled liquid relax orders of magnitude faster than those associated with bond-orientational order. Here, we use molecular simulation to investigate the relaxation of density and bond-orientational fluctuations in three molecular models of water (ST2, TIP5P and TIP4P/2005) in the vicinity of their reported LLPT. For each model, we find that density is the slowly relaxing variable under such conditions. We also observe similar behavior in the coarse-grained mW model of water. Our findings therefore challenge the key physical assumption underlying the competing hypothesis.e find that density relaxes significantly faster than bond-orientational order, as incorrectly predicted by this competing hypothesis.
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