Thermodynamic scaling and the characteristic relaxation time at the phase transition of liquid crystals

Derivation of coarse-grained force fields for buckling-induced topological defects of liquid crystals

Microscopic details of buckling-induced topological defects are required for molecular design of smectic liquid crystals to control buckling instability of the layers. In this study, we present a multiobjective optimization method to derive the coarse-grained (CG) force fields with sufficiently precise buckling characteristics including the molecular details for molecular dynamics (MD) simulations. We perform CGMD simulations of buckling deformation at sample points in the CG force field parameter space, from which the response surfaces of objective functions such as the scalar orientational order parameters, critical angles of layer collapse, and radial distribution functions are estimated. Since not all objective functions can be optimized simultaneously, we use a genetic algorithm to calculate the Pareto set of optimal solutions. We select the models with different molecular head-tail symmetries to study buckling deformation. The extracted CG model successfully reproduces the buckling deformation in terms of the collapse of smectic layers through the generation of dislocations with dipole disclinations. We also find that the molecular symmetry is a dominant factor to control the class of the buckling-induced dislocations.

Free volume in the smectic-E phase of 4-hexyl-4' isothiocyanatobiphenyl studied by positron annihilation spectroscopy

Positron annihilation lifetime spectroscopy has been used to study 4-hexyl-4'-isothiocyanatobiphenyl. Changes of the orthopositronium lifetime parameters with temperature have been observed for the supercooled smectic-E phase. The measurements confirm that positronium is created and annihilates in a layer of a lower electron density containing alkyl chains of molecules. The two-state bond-lattice model of glass transition explains the thermal activation of the centers where orthopositronium is created and annihilates when the glass of the smectic-E phase softens. However, the subsequent cold crystallization of the softened regions also influences the orthopositronium lifetime and intensity, which complicates the picture seen by positrons. The measurements during isothermal crystallization suggest that it progresses in two stages. The first stage can be described by the Avrami equation with the Avrami exponent close to unity, which indicates low-dimensional crystallization. Similarly to liquid n alkanes, the application of pressure is equivalent to temperature lowering with the similar equivalence relationship between pressure and temperature, which seems to confirm the structure of the smectic-E phase with sublayers containing alkyl chains in a molten state. The dependence of the orthopositronium lifetime on pressure for the smectic-E phase may be described by the bubble model where the positronium bubble is approximated with a finite square potential well with the depth of U=1.45eV.

Activation volume of selected liquid crystals in the density scaling regime

In this paper, we demonstrate and thoroughly analyze the activation volumetric properties of selected liquid crystals in the nematic and crystalline E phases in comparison with those reported for glass-forming liquids. In the analysis, we have employed and evaluated two entropic models (based on either total or configurational entropies) to describe the longitudinal relaxation times of the liquid crystals in the density scaling regime. In this study, we have also exploited two equations of state: volumetric and activation volumetric ones. As a result, we have established that the activation volumetric properties of the selected liquid crystals are quite opposite to such typical properties of glass-forming materials, i.e., the activation volume decreases and the isothermal bulk modulus increases when a liquid crystal is isothermally compressed. Using the model based on the configurational entropy, we suggest that the increasing pressure dependences of the activation volume in isothermal conditions and the negative curvature of the pressure dependences of isothermal longitudinal relaxation times can be related to the formation of antiparallel doublets in the examined liquid crystals. A similar pressure effect on relaxation dynamics may be also observed for other material groups in case of systems, the molecules of which form some supramolecular structures.

Thermodynamic consequences of the kinetic nature of the glass transition

In this paper, we consider the glass transition as a kinetic process and establish one universal equation for the pressure coefficient of the glass transition temperature, dTg/dp, which is a thermodynamic characteristic of this process. Our findings challenge the common previous expectations concerning key characteristics of the transformation from the liquid to the glassy state, because it suggests that without employing an additional condition, met in the glass transition, derivation of the two independent equations for dTg/dp is not possible. Hence, the relation among the thermodynamic coefficients, which could be equivalent to the well-known Prigogine-Defay ratio for the process under consideration, cannot be obtained. Besides, by comparing the predictions of our universal equation for dTg/dp and Ehrenfest equations, we find the aforementioned supplementary restriction, which must be met to use the Prigogine-Defay ratio for the glass transition.

Thermodynamic scaling of molecular dynamics in supercooled liquid state of pharmaceuticals: Itraconazole and ketoconazole

Pressure-Volume-Temperature (PVT) measurements and broadband dielectric spectroscopy were carried out to investigate molecular dynamics and to test the validity of thermodynamic scaling of two homologous compounds of pharmaceutical activity: itraconazole and ketoconazole in the wide range of thermodynamic conditions. The pressure coefficients of the glass transition temperature (dT(g)/dp) for itraconazole and ketoconazole were determined to be equal to 183 and 228 K/GPa, respectively. However, for itraconazole, the additional transition to the nematic phase was observed and characterized by the pressure coefficient dT(n)/dp = 258 K/GPa. From PVT and dielectric data, we obtained that the liquid-nematic phase transition is governed by the relaxation time since it occurred at constant τ(α) = 10(-5) s. Furthermore, we plotted the obtained relaxation times as a function of T(-1)v(-γ), which has revealed that the validity of thermodynamic scaling with the γ exponent equals to 3.69 ± 0.04 and 3.64 ± 0.03 for itraconazole and ketoconazole, respectively. Further analysis of the scaling parameter in itraconazole revealed that it unexpectedly decreases with increasing relaxation time, which resulted in dramatic change of the shape of the thermodynamic scaling master curve. While in the case of ketoconazole, it remained the same within entire range of data (within experimental uncertainty). We suppose that in case of itraconazole, this peculiar behavior is related to the liquid crystals' properties of itraconazole molecule.

Scaling of the dynamics of flexible Lennard-Jones chains

The isomorph theory provides an explanation for the so-called power law density scaling which has been observed in many molecular and polymeric glass formers, both experimentally and in simulations. Power law density scaling (relaxation times and transport coefficients being functions of ρ(γ(S)), where ρ is density, T is temperature, and γ(S) is a material specific scaling exponent) is an approximation to a more general scaling predicted by the isomorph theory. Furthermore, the isomorph theory provides an explanation for Rosenfeld scaling (relaxation times and transport coefficients being functions of excess entropy) which has been observed in simulations of both molecular and polymeric systems. Doing molecular dynamics simulations of flexible Lennard-Jones chains (LJC) with rigid bonds, we here provide the first detailed test of the isomorph theory applied to flexible chain molecules. We confirm the existence of isomorphs, which are curves in the phase diagram along which the dynamics is invariant in the appropriate reduced units. This holds not only for the relaxation times but also for the full time dependence of the dynamics, including chain specific dynamics such as the end-to-end vector autocorrelation function and the relaxation of the Rouse modes. As predicted by the isomorph theory, jumps between different state points on the same isomorph happen instantaneously without any slow relaxation. Since the LJC is a simple coarse-grained model for alkanes and polymers, our results provide a possible explanation for why power-law density scaling is observed experimentally in alkanes and many polymeric systems. The theory provides an independent method of determining the scaling exponent, which is usually treated as an empirical scaling parameter.

Thermodynamic properties and entropy scaling law for diffusivity in soft spheres

The purely repulsive soft-sphere system, where the interaction potential is inversely proportional to the pair separation raised to the power n, is considered. The Laplace transform technique is used to derive its thermodynamic properties in terms of the potential energy and its density derivative obtained from molecular dynamics simulations. The derived expressions provide an analytic framework with which to explore soft-sphere thermodynamics across the whole softness-density fluid domain. The trends in the isochoric and isobaric heat capacity, thermal expansion coefficient, isothermal and adiabatic bulk moduli, Grüneisen parameter, isothermal pressure, and the Joule-Thomson coefficient as a function of fluid density and potential softness are described using these formulas supplemented by the simulation-derived equation of state. At low densities a minimum in the isobaric heat capacity with density is found, which is a new feature for a purely repulsive pair interaction. The hard-sphere and n = 3 limits are obtained, and the low density limit specified analytically for any n is discussed. The softness dependence of calculated quantities indicates freezing criteria based on features of the radial distribution function or derived functions of it are not expected to be universal. A new and accurate formula linking the self-diffusion coefficient to the excess entropy for the entire fluid softness-density domain is proposed, which incorporates the kinetic theory solution for the low density limit and an entropy-dependent function in an exponential form. The thermodynamic properties (or their derivatives), structural quantities, and diffusion coefficient indicate that three regions specified by a convex, concave, and intermediate density dependence can be expected as a function of n, with a narrow transition region within the range 5 < n < 8.

Phase behavior and dynamics of a cholesteric liquid crystal

The synthesis, equation of state, phase diagram, and dielectric relaxation properties are reported for a new liquid crystal, 4(')-butyl-4-(2-methylbutoxy)azoxybenzene (4ABO5*), which exhibits a cholesteric phase at ambient temperature. The steepness of the intermolecular potential was characterized from the thermodynamic potential parameter, Γ = 4.3 ± 0.1 and the dynamic scaling exponent, γ = 3.5 ± 0.2. The difference between them is similar to that seen previously for nematic and smectic liquid crystals, with the near equivalence of Γ and γ consistent with the near constancy of the relaxation time of 4ABO5* at the cholesteric to isotropic phase transition (i.e., the clearing line). Thus, chirality does not cause deviations from the general relationship between thermodynamics and dynamics in the ordered phase of liquid crystals. The ionic conductivity of 4ABO5* shows strong coupling to the reorientational dynamics.

Thermodynamic scaling of dynamic properties of liquid crystals: verifying the scaling parameters using a molecular model

The thermodynamic scaling of molecular dynamic properties of rotation and thermodynamic parameters in a nematic phase was investigated by a molecular dynamic simulation using the Gay-Berne potential. A master curve for the relaxation time of flip-flop motion was obtained using thermodynamic scaling, and the dynamic property could be solely expressed as a function of TV(γτ) , where T and V are the temperature and volume, respectively. The scaling parameter γτ was in excellent agreement with the thermodynamic parameter Γ, which is the logarithm of the slope of a line plotted for the temperature and volume at constant P2. This line was fairly linear, and as good as the line for p-azoxyanisole or using the highly ordered small cluster model. The equivalence relation between Γ and γ(τ) was compared with results obtained from the highly ordered small cluster model. The possibility of adapting the molecular model for the thermodynamic scaling of other dynamic rotational properties was also explored. The rotational diffusion constant and rotational viscosity coefficients, which were calculated using established theoretical and experimental expressions, were rescaled onto master curves with the same scaling parameters. The simulation illustrates the universal nature of the equivalence relation for liquid crystals.

Relationship between thermodynamic parameter and thermodynamic scaling parameter for orientational relaxation time for flip-flop motion of nematic liquid crystals

Thermodynamic parameter Γ and thermodynamic scaling parameter γ for low-frequency relaxation time, which characterize flip-flop motion in a nematic phase, were verified by molecular dynamics simulation with a simple potential based on the Maier-Saupe theory. The parameter Γ, which is the slope of the logarithm for temperature and volume, was evaluated under various conditions at a wide range of temperatures, pressures, and volumes. To simulate thermodynamic scaling so that experimental data at isobaric, isothermal, and isochoric conditions can be rescaled onto a master curve with the parameters for some liquid crystal (LC) compounds, the relaxation time was evaluated from the first-rank orientational correlation function in the simulations, and thermodynamic scaling was verified with the simple potential representing small clusters. A possibility of an equivalence relationship between Γ and γ determined from the relaxation time in the simulation was assessed with available data from the experiments and simulations. In addition, an argument was proposed for the discrepancy between Γ and γ for some LCs in experiments: the discrepancy arises from disagreement of the value of the order parameter P2 rather than the constancy of relaxation time τ1(*) on pressure.

Determination of the orientational order parameter of the homologous series of 4-cyanophenyl 4-alkylbenzoate (n.CN) by different methods

The orientational order parameters of a homologous series of 4-cyanophenyl 4-alkylbenzoates have been determined at different temperatures from (13)C-NMR, x-ray diffraction, optical birefringence, high resolution density and diamagnetic susceptibility anisotropy measurements. To determine the temperature dependence of the orientational order parameter from the (13)C chemical shift values, the two-dimensional polarization inversion spin exchange at the magic angle (PISEMA) method was also used for the measurement of (13)C-(1)H dipolar couplings at different sites in the oriented phase. The nematic order parameters determined from each of these methods have been compared. Apart from a slight shift in their values their trends with temperature are very similar. The differences among the results obtained by these five different methods have been discussed. From the high resolution density data, the values of the critical exponents near the T(N-I) transition are found to lie between the Ising model and tricritical behaviour.

Connection between dynamics and thermodynamics of liquids on the melting line

The dynamics of a large number of liquids and polymers exhibit scaling properties characteristic of a simple repulsive inverse power-law potential, most notably the superpositioning of relaxation data as a function of the variable TV^{γ}, where T is temperature, V the specific volume, and γ a material constant. A related scaling law T{m}V{m}{Γ}, with the same exponent Γ = γ, links the melting temperature T{m} and volume V{m} of the model IPL liquid; liquid dynamics is then invariant at the melting point. Motivated by a similar invariance of dynamics experimentally observed at transitions of liquid crystals, we determine dynamic and melting-point scaling exponents γ and Γ for a large number of nonassociating liquids. Rigid, spherical molecules containing no polar bonds have Γ = γ; consequently, the reduced relaxation time, viscosity, and diffusion coefficient are each constant along the melting line. For other liquids γ > Γ always; that is, the dynamics is more sensitive to volume than is the melting point, and for these liquids the dynamics at the melting point slows down with increasing T{m} (that is, increasing pressure).

Interaction potential in nematogenic 6CHBT

Pressure-volume-temperature (PVT) measurements were carried out on the nematic liquid crystal 4(trans-4'-n-hexylcyclohexyl)isothiocyanatobenzene (6CHBT). In combination with previous dielectric relaxation measurements at elevated pressure and new measurements extending to GHz frequencies, the characteristics of the anisotropic interaction potential were determined. The thermodynamic potential parameter, gamma, which measures the variation of the interaction energy with volume, equals 5.03 +/- 0.06, with a barrier height equal to approximately 7 kJ/mol. Thus, there is a low potential barrier to reorientations of the 6CHBT molecule about its short axis; however, the retarding potential is strongly volume-dependent. The longitudinal reorientational times determined for various thermodynamic conditions superpose using a scaling exponent equal to gamma within the experimental error. It then follows, as found recently for other liquid crystals, that this relaxation time must be constant along the pressure-dependent clearing line. Thus, the control parameter (e.g., Gibbs free energy) governing the competition between the anisotropic energy and the entropy must also govern the rotational dynamics in the ordered phase of this liquid crystal.