Fluctuation shift of the nematic–isotropic phase transition temperature

A macroscopic counterpart to the microscopic mechanism of the straightening dimer mesogens conformations, proposed recently by S.M. Saliti, M.G. Tamba, S.N. Sprunt, C. Welch, G.H. Mehl, A. Jakli, and J.T. Gleeson [Phys. Rev. Lett. 116, 217801 (2016)] to explain their experimental observation of the unprecedentedly large shift of the nematic–isotropic transition temperature is discussed. The proposed interpretation is based on singular longitudinal fluctuations of the nematic order parameter. Since these fluctuations are governed by the Goldstone director fluctuations, they exist only in the nematic state. External magnetic field suppresses the singular longitudinal fluctuations of the order parameter (similarly as is the case for the transverse director fluctuations, although with a different scaling over the magnetic field). The reduction of the fluctuations changes the equilibrium value of the magnitude of the order parameter in the nematic state. Therefore, it leads to additional (with respect to the mean field contribution) fluctuation shift of the nematic–isotropic transition temperature. Our mechanism works for any nematic liquid crystals, however the magnitude of the fluctuation shift increases with decrease in the Frank elastic moduli. Since some of these moduli supposed to be anomalously small for so-called bent-core or dimer nematic liquid crystals, just these liquid crystals are promising candidates for the observation of the predicted fluctuation shift of the phase transition temperature.     

Reexamining the phase diagram of the Gay—Berne fluid

This work reexamines and updates earlier investigations on the phase behaviour of the Gay-Berne liquid crystal model, concentrating on the effect of varying temperature. Constant volume and constant pressure Monte Carlo simulations are combined for systems consisting of N = 500 molecules along different isotherms over the reduced temperature range 0.60 ≤ T ≤ 1.25. As in previous simulation studies of the model, the study identifies nematic and smectic B phases on compressing the isotropic fluid, the particular phase sequence depending on temperature. The nematic phase is found to be stable with respect to the isotropic phase for reduced temperatures T ≥ 0.75. In the temperature range 0.75 ≤ T ≤ 1.25, the phase boundaries of the isotropic-nematic transition are obtained by computing the Helmholtz free energy of both phases from thermodynamic integration. From the simulation data, the relative volume change at the isotropic-nematic transition is about 2%, and this value appears to be rather insensitive to changes in temperature. On compressing the nematic phase, the Gay-Berne fluid undergoes a strong first-order transition to the smectic B phase. This transition is studied by using constant pressure simulation, and the coexistence properties are estimated from the limits of mechanical stability of the nematic phase. Larger relative volume changes are found at the transition than those suggested by previous studies, with typical values increasing up to 10.5% as the temperature is decreased. The results are consistent with the existence of strong coupling between nematic and smectic order parameters. For temperatures T ≤ 0.70 the nematic phase is no longer stable, and the phase sequence isotropic-smectic B is observed. Therefore, the Gay-Berne model exhibits an isotropic-nematic-smectic B triple point. Extrapolating the present simulation data, this triple point is located approximately at reduced temperature T_INB ? 0.70 and reduced pressure P_INB ? 1.825.     

Density functional theory of a Gay—Berne film between aligning walls

It is shown that the simple Onsager second-virial approximation of density functional theory can successfully describe the orientational structure of a Gay-Berne film confined between aligning plates. The theory takes as input the density profile as determined by computer simulation and semi-quantitatively reproduces the variation in the nematic order parameter throughout the film, at different temperatures and for different surface potential strengths, without any adjustable parameters. In this context the validity of an earlier analytical approach is discussed where the density, order parameter and tilt angle profiles were assumed to be step functions.     

Kinetics of the isotropic–nematic phase transition in melted multi-component liquid crystal mixtures upon cooling

The kinetics of the phase separation and the nematic phase growth in two melted commercial multi-component liquid crystal mixtures upon cooling was studied using polarising optical microscopy and IR spectrometry. The droplets of the nematic phase revealed in the optical images across the phase transition were segmented and treated statistically. In the resulting size histograms of mixture B, two overlapping statistical ensembles related to two co-existing nematic phases were recognised; these phases were shown to be different in their chemical structures. In mixture A, any separation within the nematic phase was not found. The statistical ensembles of the nematic droplets were successfully described using the principles of irreversible thermodynamics. Analysis of the mean droplet diameter as a function of time allowed recognition of two regimes of the nematic phase evolution: (1) nucleation and rapid nucleus growth and (2) nucleus coalescence. Both the regimes were quantitatively described with the universal law for the cluster growth.     

Evidence of pressure dependence tricritical point at the nematic–smectic-A transition

We examine the effect of pressure on the nematic to smectic-A N–SmA) transition within the Landau phenomenological theory. The influence of pressure on the N–SmA transition is discussed by varying the coupling between the orientational and translational order parameters. The possibility of the tricritical point at the N–SmA transition is discussed in a phenomenological way. The theoretical predictions are found to be in good qualitative agreement with experimental results.     

Liquid–vapour transition of the long range Yukawa fluid

Two liquid state theories, the self-consistent Ornstein–Zernike equation (SCOZA) and the hierarchical reference theory (HRT) are shown, by comparison with Monte Carlo simulations, to perform extremely well in predicting the liquid–vapour coexistence of the hard-core Yukawa (HCY) fluid when the interaction is long range. The long range of the potential is treated in the simulations using both an Ewald sum and hyperspherical boundary conditions. In addition, we present an analytical optimized mean field theory which is exact in the limit of an infinitely long-range interaction. The work extends a previous one by C. Caccamo, G. Pellicane, D. Costa, D. Pini, and G. Stell, Phys. Rev. E 60, 5533 (1999) for short-range interactions.     

Ionization of molecules at the fluid–fluid phase transition in warm dense hydrogen

The problem of the fluid–fluid phase transition in warm dense hydrogen/deuterium has been studied experimentally and theoretically in the best laboratories in the last decade. However, the nature of the phase transition remains unclarified. In this paper we put forward the new idea that H₂ molecules are ionized at the phase transition to produce molecular H ₂ ⁺ and H ₃ ⁺ ions     

A comparative coupled cluster and density functional theory study of the HOCI → HCIO transition state

The structural features of the HOCl → HClO isomerization mechanism, including all stationary points, and one saddle point, were examined by use of coupled cluster and the B3LYP density functional theory methodology. To improve the results a very large 6–311++G (3df, 3pd) Gaussian-type basis set was employed in the presented calculations. In addition, Gaussian-3 theory was tested against our coupled cluster (with single, double and triple excitations) results, and they were found to correlate closely with one another by around 1–2 kcal mol^?1. The energy change for this isomerization reaction is predicted to be 54.5 kcalmol^?1 and 52.5 kcalmol^?1 with the B3LYP and CCSD (T) methods, respectively, and the activation barrier is 76.1 kcal mol^?1 and 70.1 kcalmol^?1 with the same methods.     

Study of the first-order transition in the spin-1 Blume–Capel model by using effective-field theory

The spin-1 Blume–Capel model on a square lattice is studied by using an effective-field theory (EFT) with correlation. We propose an expression for the free energy within the EFT. The phase diagram is constructed in the temperature (T) and single-ion anisotropy amplitude (D) plane. The first-order transition line is obtained by Maxwell construction (comparison between free energies). Our results predict first-order transitions at low temperatures and large anisotropy strengths, which correspond in the phase diagram to the existence of a tricritical point (TCP). We compare our results with mean-field approximation (MFA), that show a qualitative correct behavior for the phase diagram.     

Critical point and mechanism of the fluid–fluid phase transition in warm dense hydrogen

The density functional theory is used to calculate the equation of state and the proton–proton pair correlation functions in the range of hydrogen temperatures and densities where the fluid–fluid phase transition is expected. The metastable states are considered. The critical temperature has been estimated to be ~4000 K. We propose a two-step mechanism: the partial ionization of molecules to produce H ₂ ⁺ ions at the phase transition followed by the formation of H ₃ ⁺ ions.     

A self-consistent approach for the SmA–SmC* phase transition

By using an analogy with the Maier–Saupe theory of the nematic phase, a mean field theory of the chiral smectic-C (SmC*) phase is constructed. As an order parameter of the SmC* phase, the tilt angle θ is selected, and the feedback effect of θ is introduced into the hindered rotational potential about the molecular long axis. By solving the self-consistent equation for the order parameter θ, the second-order phase transition appears. Also, to describe the SmA–SmC* phase transition under an electric field, a coupling term between a molecular dipole moment and an external electric field is introduced to the potential function. The electroclinic effect in the SmA phase and the hysteresis effect in the SmC* phase, which were described phenomenologically in the past, are found directly from the microscopic theory.     

A study of particle number fluctuation under BCS theory

Particle number fluctuations in BCS theory are studied with the relativistic mean-field theory and the shell effects of particle number fluctuations are first discovered. By analyzing the relative errors of the particle number fluctuations, we find that the particle number fluctuations are relevant with the odd-even character. We later apply this method to the examination of the new shell structure, showing that N = 184 for the neutron is indeed a new closed shell.     

Relaxation dynamics near the sol–gel transition: From cluster approach to mode-coupling theory

A long standing problem in glassy dynamics is the geometrical interpretation of clusters and the role they play in the observed scaling laws. In this context, the mode-coupling theory (MCT) of type-A transition and the sol–gel transition are both characterized by a structural arrest to a disordered state in which the long-time limit of the correlator continuously approaches zero at the transition point. In this paper, we describe a cluster approach to the sol-gel transition and explore its predictions, including universal scaling laws and a new stretched relaxation regime close to criticality. We show that while MCT consistently describes gelation at mean-field level, the percolation approach elucidates the geometrical character underlying MCT scaling laws.     

Anomalous dielectric behavior in the nematic and isotropic phases of a strongly polar–weakly polar binary system

We report permittivity studies in the isotropic liquid and anisotropic liquid crystalline (nematic or N) phases of a binary system, in which one component has molecules with a strongly polar longitudinal group, and the other has a weakly polar transverse group. The dielectric constant in the isotropic phase as well as its anisotropy in the N phase show, surprisingly, an anomalous non-monotonic dependence with concentration having a peak-like behavior for 10.2 mol% concentration of the weakly polar constituent. The transition between the two phases, being weakly first order, exhibits pretransitional effects signifying the appearance of the N-like regions in the isotropic phase. The coordinates of the maximum point of the convex shaped temperature-dependence of the dielectric constant in the isotropic phase, characteristic of strongly polar systems, also exhibit a non-monotonic dependence with concentration. Possible causes for these observations are discussed.     

Structural and electronic properties of SbnAl(0,±1) (n = 1–10) clusters using density-functional theory

We used the density functional theory (DFT) with the unrestricted B3LYP exchange-correlation potential and LanL2DZ basis sets to optimize the geometries of Sb_nAl and Sb_nAl^±1 (n = 1–10) clusters. We mainly utilized Gaussian 03 W software to calculate the data. In order to find the most stable structure of each isomer, we calculated the total energy, the spin multiplicity (S), point group symmetry (PG), the electronic state (State), and the average bond lengths of Sb-Al bond and Sb-Sb bond (R₁ and R₂). Through the calculations and analysis of these data, we found the ground state structure of each group isomer. By discussing the average binding energy (E_b), fragmentation energy (E_f), and the second-order energy difference (Δ₂E), the stabilities of the Sb_nAl ^(0,±1) clusters were studied. The results of the electron transfer show that the Sb₄Al and Sb₈Al clusters are different with the other neutral clusters. In order to study the electric properties of Sb_nAl ^(0,±1) clusters, the energy gap (E_g) between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), AEA, VDE, AIP, and VIP were calculated. Besides, the magnetic moment of the positive and negative clusters have the same effects when n = 2–9.