High Temperature Isotropic Phase Research Articles

Order-disorder transition in a two-dimensional associating lattice gas.

We study an associating lattice gas (ALG) using Monte Carlo simulation on the triangular lattice and semianalytical solutions on Husimi lattices. In this model, the molecules have an orientational degree of freedom and the interactions depend on the relative orientations of nearest-neighbor molecules, mimicking the formation of hydrogen bonds. We focus on the transition between the high-density liquid (HDL) phase and the isotropic phase in the limit of full occupancy, corresponding to chemical potential μ→∞, which has not yet been studied systematically. Simulations yield a continuous phase transition at τ_{c}=k_{B}T_{c}/γ=0.4763(1) (where -γ is the bond energy) between the low-temperature HDL phase, with a nonvanishing mean orientation of the molecules, and the high-temperature isotropic phase. Results for critical exponents and the Binder cumulant indicate that the transition belongs to the three-state Potts model universality class, even though the ALG Hamiltonian does not have the full permutation symmetry of the Potts model. In contrast with simulation, the Husimi lattice analyses furnish a discontinuous phase transition, characterized by a discontinuity of the nematic order parameter. The transition temperatures (τ_{c}=0.51403 and 0.51207 for trees built with triangles and hexagons, respectively) are slightly higher than that found via simulation. Since the Husimi lattice studies show that the ALG phase diagram features a discontinuous isotropic-HDL line for finite μ, three possible scenarios arise for the triangular lattice. The first is that in the limit μ→∞ the first-order line ends in a critical point; the second is a change in the nature of the transition at some finite chemical potential; the third is that the entire line is one of continuous phase transitions. Results from other ALG models and the fact that mean-field approximations show a discontinuous phase transition for the three-state Potts model (known to possess a continuous transition) lends some weight to the third alternative.

Orientational order at finite temperature on curved surfaces

We study the effect of thermal fluctuations in the XY model on surfaces with unequal principal curvatures. Unlike Gaussian curvature that typically frustrates orientational order, the extrinsic curvature of the surface can act as a local field that promotes long-range order at low temperature. We find numerically that the transition from the high temperature isotropic phase to the true long-range ordered phase is characterized by critical exponents consistent with those of the flat space Ising model in two dimensions, up to finite size effects. Our results suggest a versatile strategy to achieve geometric control of liquid crystal order by suitable design of the underlying curvature of a substrate.

Glassiness of Thermotropic Liquid Crystals across the Isotropic−Nematic Transition

The orientational dynamics of thermotropic liquid crystals across the isotropic-nematic phase transition have traditionally been investigated at long times or low frequencies using frequency domain measurements. The situation has now changed significantly with the recent report of a series of interesting transient optical Kerr effect (OKE) experiments that probed orientational relaxation of a number of calamitic liquid crystals (which consist of rod-like molecules) directly in the time domain, over a wide time window ranging from subpicoseconds to tens of microseconds. The most intriguing revelation is that the decay of the OKE signal at short to intermediate times (from a few tens of picoseconds to several hundred nanoseconds) follows multiple temporal power laws. Another remarkable feature that has emerged from these OKE measurements is the similarity in the orientational relaxation behavior between the isotropic phase of calamitic liquid crystals near the isotropic-nematic transition and supercooled molecular liquids, notwithstanding their largely different macroscopic states. In this article, we present an overview of the understanding that has emerged from recent computational and theoretical studies of calamitic liquid crystals across the isotropic-nematic transition. Topics discussed include (a) single-particle as well as collective orientational dynamics at a short-to-intermediate time window, (b) heterogeneous dynamics in orientational degrees of freedom diagnosed by a non-Gaussian parameter, (c) fragility, and (d) temperature-dependent exploration of underlying energy landscapes as calamitic liquid crystals settle into increasingly ordered mesophases upon cooling from the high-temperature isotropic phase. A comparison of our results with those of supercooled molecular liquids reveals an array of analogous features in these two important classes of soft matter systems. We further find that the onset of growth of the orientational order in the parent nematic phase induces translational order, resulting in smectic-like layers in the potential energy minima of calamitic systems if the parent nematic phase is sandwiched between the high-temperature isotropic phase and the low-temperature smectic phase. We discuss implications of this startling observation. We also discuss recent results on the orientational dynamics of discotic liquid crystals that are found to be rather similar to those of calamitic liquid crystals.

Orientational relaxation in a discotic liquid crystal

We investigate orientational relaxation of a model discotic liquid crystal, consisting of disclike molecules, by molecular dynamics simulations along two isobars starting from the high temperature isotropic phase. The two isobars have been so chosen that (a) the phase sequence isotropic- (I-) nematic- (N-) columnar (C) appears upon cooling along one of them and (b) the sequence isotropic- (I-) columnar- (C) along the other. While the orientational relaxation in the isotropic phase near the I-N phase transition in system (a) shows a power law decay at short to intermediate times, such power law relaxation is not observed in the isotropic phase near the I-C phase boundary in system (b). In order to understand this difference (the existence or the absence of the power law decay), we calculated the growth of the orientational pair distribution functions (OPDFs) near the I-N phase boundary and also near the I-C phase boundary. We find that the OPDF shows a marked growth in long range correlation as the I-N phase boundary is approached in the I-N-C system (a), but such a growth is absent in the I-C system, which appears to be consistent with the result that I-N phase transition in the former is weakly first order while the I-C phase transition in the latter is not weak. As the system settles into the nematic phase, the decay of the single-particle second-rank orientational time correlation function follows a pattern that is similar to what is observed with calamitic liquid crystals and supercooled molecular liquids.

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.

Orientational order and finite strain in nematic elastomers

Nematic elastomers exhibit large, spontaneous shape changes at the transition from the high-temperature isotropic phase to the low-temperature nematic phase. These finite deformations are studied here in the context of a nonlinear, properly invariant, variational theory that couples the orientational order and elastic deformation. The theory is based on the minimization of a free-energy functional that consists of two contributions: a nematic one due to the interaction of the mesogenic units and an elastic one arising from the stretching of the cross-linked polymer chains. Suitable choices for these two contributions allow for large, reversible, spontaneous shape changes in which the elastic deformation can affect the isotropic-nematic transition temperature. The change in transition temperature as well as the magnitude of the resulting spontaneous deformation is illustrated for various parameter values. The theory includes soft elasticity as a special case but is not restricted to it.

Pretransitional Effects Near the Hexagonal−Micellar Phase Transition of the C12EO6/H2O Lyotropic Mixture

The transition hexagonal phase/fluid isotropic phase in the nonionic binary system C12EO6/water is studied. The birefringence of a planar monodomain and the water deuterium NMR splitting are measured as functions of the temperature in the hexagonal phase, at the azeotropic concentration. The planar monodomain is obtained by directional solidification. It is shown that important pretransitional effects exist on approaching the transition. These effects are interpreted as due to the appearance of defects which announce the high-temperature isotropic phase. These defects may consist either of a fragmentation of the columns in segments of finite length or of bridges connecting neighboring cylinders. The activation energy associated with these defects is estimated to be of the order of 0.13 eV/surfactant molecule. The mean length between defects along a column at the transition is estimated to be of the order of 80 nm. Finally an estimate is given for the curvature and saddle splay elastic constants of the monolayer.

Optical studies of supramolecular tubular structures generated by taper-shaped side groups in the columnar hexagonal phase

Birefringence measurements in the columnar hexagonal phase (Φ h ) and turbidity measurements in the high temperature isotropic phase (I) have been performed on a polymethacrylate (12-AG-4EO-PMA) having taper-shaped side groups; the same measurements wer also performed on a self-assembling monomeric precursor (12-AG-4EO-OH). We found that the optical retardation increases strongly with decreasing temperature in the Φ h -I phase transition temperature T Φh1 from above

Statistical mechanics of solutions of semiflexible chains: A path integral formulation

A path integral formulation has been used to study the behavior of a single chain in the solution of many semiflexible chains. The Flory–Huggins approximation on lattices suggests that the chains undergo a phase transition from a high temperature isotropic phase to an anisotropic phase where the chains are rod-like. Using a self-consistent approximation, we, however, find that, at any stiffness, long chains (in the limit of the chain length going to infinity) remain in the disordered state.

Thermally induced cholesteric‐isotropic transition in lyotropic polypeptide liquid crystals

AbstractThe thermally induced cholesteric to isotropic transition of lyotropic polybenzylglutamate liquid crystals in six solvent combinations was examined optically. The solvents chosen for study support both low and high pitch values, positive and negative pitch temperature coefficients, and polypeptide denaturation. The biphasic zone below the clearing temperature is broad and solvent dependent. Unusual large‐scale phase separations and solution morphologies occur in some solvents. No evidence was found for pretransitional chiral orientational ordering near the clearing point in the high‐temperature isotropic phase.

Phase Transitions in Polypeptide Liquid Crystals: A Reentrant Isotropic Phase

Abstract Optical and C-13 NMR examinations of concentrated solutions of poly-γ-benzyl-L-glutamate (PBLG) in a mixed solvent system containing a denaturant acid, show that this polymer liquid crystal has both a low and high temperature isotropic phase. The latter is due to thermal disruption of long range orientational order of the elongated macromolecules. The former reentrant isotropic phase is a result of an intramolecular helix to random coil transition, which leads to a macromolecular conformation inconsistent with liquid crystallinity.

Re-entrant isotropic phase of a polypeptide liquid crystal

Optical and C-13 NMR examinations of concentrated solutions of poly-γ-benzyl-L-glutamate (PBLG) in a mixed solvent system containing a denaturant acid, show that this polymer liquid crystal has both a low and high temperature isotropic phase. The latter is due to thermal disruption of long-range orientational order of the elongated macromolecules. The former re-entrant isotropic phase is a result of an intramolecular helix to random coil transition, which leads to a macromolecular conformation inconsistent with liquid crystallinity.