Effect of a uniaxially deformed aerogel on the orientation of the order parameter of superfluid 3He

The effect of a uniaxially deformed aerogel on the orientation of the order parameter of ³He has been analyzed with the inclusion of correlations in the positions of the particles forming the aerogel. The minimum strain for the B phase in the uniaxially stretched aerogel that can lead to the orientation of the orbital part of the order parameter different from the bulk case has been estimated. The orientational effect has been estimated for the A-like phase in the uniaxially compressed aerogel has been estimated. It has been shown that the dependence of the orientational effect on correlations in the mutual locations of the aerogel particles is stronger than that of the superconducting transition temperature.     

H and C NMR studies of molecular orientation and dynamics in liquid crystal 6BA

The dynamics and orientation of dimers accompanying the formation and destruction of hydrogen bonds in the nematic phases of 4-n-hexylbenzoic acid (6BA) were studied by ¹³C and ²H NMR. The orientational order parameter S in the nematic phase was estimated from the quadrupole splitting of the ²H NMR spectrum. The intermolecular interaction energy for the molecular order in the nematic phase decreased with increasing temperature. The flexibility of dimers due to the destruction of the hydrogen bond is closely related to a decrease in the intermolecular interaction energy. The proportion of ²H NMR spin-lattice relaxation time (T₁) to S, which reveals the coupling of the orientational fluctuations with the hydrogen bonding processes, was observed.     

Orientational order in three nO.m liquid crystalline compounds

Refractive index and density measurements have been carried out on three nO.m liquid crystalline compounds, namely, 4O.2, 4O.3 and 1O.10 belonging to the N-(p-n-alkoxybenzylidene)-p-n-alkylaniline series. From the data, the orientational order parameter has been estimated using Vuks and Neugebauer local field models. Furthermore, the orientational order parameter has been calculated directly from refractive index data employing the Vuks scaling factor method, Neugebauer f(B) parameter, effective geometry parameter and a method proposed by Kuczyński et al. It is observed that order parameter values estimated from different methods agree well near the nematic–isotropic transition and diverge as the nematic phase attains equilibrium. The temperature gradient of refractive indices and the nematic crossover temperatures have also been estimated for these compounds. The results obtained are compared and discussed.     

Deuteron NMR relaxometry applied to confined liquid crystals

We discuss the capability of deuteron nuclear magnetic resonance (NMR) spectroscopy and relaxometry to reveal molecular ordering and dynamics in confined liquid crystals. The attention is focused on the high-temperature phase above the nematic-isotropic transition, which is — in the absence of the long-range orientational order — very suitable for the study of surface interactions. Deuteron NMR spectra and relaxation rates are presented for two representatives of confined liquidcrystal systems: 8CB in cylindrical cavities of Anopore membranes and 5CB with an embedded polymer network. A substantial increase in the transverse spin relaxation rate, stimulated by the surface-induced order in enclosures, has been observed. In cylindrical cavities, it exhibits a strong temperature dependence on approaching the phase transition, whereas in the polymer network dispersion it is temperature-independent. The increase of T ₂ ^?1 provides information on the effect of spatial constraints on molecular mobility and on the surface orientational order parameter. Using deuteron relaxometry, one can measure the degree of orientational order in the isotropic phase not only in cylindrical but also in spherical cavities and enclosures of irregular shape, where the standard approach based on quadrupolar splitting of the NMR spectrum fails.     

Correlation of the molecular structure of discotic nematic liquid crystals with their orientational order and specific features of the nematic-isotropic phase transition

The orientational order parameter S of molecules in high-temperature discotic nematic liquid-crystal phases of triphenylene derivatives is investigated as a function of the length of side flexible molecular chains at different temperatures. It is established that the orientational order parameters S in the range of the transition from the nematic phase to the isotropic liquid phase (the N _D -I transition) are smaller than those predicted from the molecular-statistical theory and computer simulation. It is shown that the N _D -I transition is close to both the isolated Landau point and the tricritical point (regardless of the chemical structure of the molecules and the anisotropy of dispersion intermolecular interactions). Consistent explanations are offered for a number of experimental findings, such as the anomalously small changes in the enthalpy and entropy upon the N _D -I transition (as compared to those revealed upon the N-I transition in calamitic nematic liquid crystals), the anomalously strong response of the isotropic phase of discotic nematic liquid crystals to external fields (thermodynamically conjugate to the order parameter S) and the long relaxation times of this response, and the formation of cybotactic discotic molecular clusters in the isotropic phase in the vicinity of the N _D -I transition.     

Orientational order in CO and N2 monolayers on graphite studied by X-ray diffraction

X-ray diffraction has been used to study the structure and orientational phase transitions of CO and N₂ adsorbed on graphite (Papyex). Both form orientationally ordered 2√3 × 2√3 R30° commensurate phases on graphite at low temperatures (10 K). The in-plane herringbone structure of N₂ has been confirmed but CO has more orientational disorder than N₂, which may be associated either with tilting, random static or systematic, of the molecules away from the surface and/or with orientational order of shorter range than the centre of mass order. In the first case the average tilt would have to be about 26° and in the second case the orientational correlation length would have to be 200 Å compared with 450 Å for the translational order. The orientational phase transition is sharp for N₂, occurring over the range 27–30 K, in agreement with previous work. For CO the transition is broad and starts at lower temperatures. This and the structural data indicate that a point quadrupolar interaction is not a suitable model for comparing the properties of N₂ and CO layers. The orientational phase transition in the incommensurate phase of N₂ is found to be broad and occurs below 20 K. For CO it is sharper than for the commensurate phase and occurs at a higher temperature. The lattice parameter changes by 0.75% across the orientational phase transition. For both N₂ and CO there is evidence of translational disorder in the commensurate phases but it cannot be interpreted quantitatively.     

Pressure dependence of the rotational ground state tunnel splitting in Ni(NH3)6I2

Inelastic neutron scattering techniques have been used to determine the rotational tunnel splitting of the librational ground state of ammonia molecules in Ni(NH₃)₆I₂ as a function of hydrostatic pressure up to 5.6 kbar at 8 K. The resulting exponential dependence of the tunnel splitting on pressure was interpreted with the help of a concurrent measurement of the compressibility to suggest a dependence on the interatomic distance as r^?9 of the orientational potential. The phase transition temperature at 5.6 kbar was determined to be 27 K compared with 19.9 K at atmospheric pressure.     

Der Einfluß des elastischen Gitters auf den Orientierungsübergang von festem Ortho-Wasserstoff in Molekularfeldnäherung

We calculate the influence of the elastic lattice on the orientational order-disorder transition in fcc solid ortho-hydrogen. The angular momentaJ = 1 of the molecules are coupled by quadrupole-quadrupole interaction which we reduce within the space group Pa 3 to the Ising model approximation. Local mechanical equilibrium requires the lattice to adjust itself to the forces caused by the inhomogeneous fluctuations in the angular momentum configuration. Following Wagner [6] this results in a 4-angular-momentum interaction with long range and short range contributions depending on the one-phonon Green function of the lattice. We use a Debye phonon spectrum and the molecular field approximation in order to obtain numerical results. According to the first order nature of the phase transition we get a pressure drop at the critical pointT ^c of 9.7 bar. The experimental value is estimated to be 8 bar. Compared to the rigid lattice the phase transition on the elastic lattice is smoothed out by the short range contribution. This corresponds to a reduction of the discontinuity of the order parameter at the critical pointT ^c by about 13%. The phase transition will vanish completely if we increase the magnitude of the short range terms by a factor of three.     

EPR study of the ferroelastic phase transition in CsLiSO4

EPR spectra of SO^-₃ ion-radical in X-ray irradiated CsLiSO₄ single crystals were used for the study of the ferroelastic phase transition at T_c = 203.0 K. The splitting (ΔH) of the SO₃ line in the low-temperature ferroelastic phase has been interpreted as proportional to the square of the order parameter. The splitting shows the temperature dependence ΔH ∞ (T_c ? T) 1.01^± 0.01     

Fluctuations of orientational order in a uniaxial nematic liquid crystal with biaxial molecules and its response to an external field

Homogeneous thermal fluctuations of the orientational order parameters S and G of biaxial molecules in a uniaxial nematic liquid crystal are investigated in the framework of the molecular-statistical theory. It is demonstrated that the molecular biaxiality significantly affects the order parameters S and G, their temperature dependences in the nematic phase, the amplitude and the temperature dependence of the order parameter fluctuations in the nematic and isotropic phases, and the character of the transition from the nematic phase to the isotropic liquid phase. It is established that the fluctuations of the parameters S and G in the nematic phase are related to the temperature dependences of S and G and the susceptibilities χ_S and χ_G of the nematic liquid crystal to external fields, which leads to a change in the parameters S and G at a fixed director orientation. Explanations are offered for the known experimental data on the orientational ordering of biaxial molecules under the action of external fields in the isotropic phase of nematic liquid crystals.     

Surface-induced weak orientational order and role of isotropic-nematic interface fluctuations in the appearance of an induced nematic film

Recently the nontrivial spatial and temperature dependence of the surface-induced weak planar orientational order parameter Q(z, T) was determined just above the isotropic-nematic (IN) phase transition point (Ji-H. Lee et al., Phys. Rev. Lett. 102, 167801 (2009)). In this paper we present a theoretical explanation of the observed behaviour. We obtain expressions for the short-range and long-range contributions to the interface potential of the induced nematic film and specify the repulsive character of the interaction between the soft IN interface and the external bounding substrate. It is shown that the small value of the IN interfacial tension results in the renormalization of the repulsive interaction potential due to the thermal fluctuations of the soft IN interface. This leads to an increase of the equilibrium thickness of the induced nematic film and the appearance of a step-like orientational order parameter profile. We find that only renormalized short-range and thermal pseudo-Casimir interactions are essential for the appearance of the induced nematic film, which provide the observed thickness, h ?? 30 nm, of this film. The long-range van der Waals interaction is shown to be negligibly small and the dominant role is played by the renormalized short-range repulsion. Fitting of the experimental order parameter profiles (Ji-H. Lee et al. (2009)) with the expressions based on these interactions makes it possible to determine the material parameters of the system, including the amplitudes of the surface interaction, the IN interfacial tension and the interfacial coherence length. The agreement between theory and experiment confirms the importance of the interface fluctuation renormalization of the interface potentials for soft interfaces.      

Orientational order and polarizability of molecules in a nematic liquid crystal

The influence of the orientational order of molecules in a nematic liquid crystal on the mean value $\bar \gamma$ and anisotropy Δγ of the molecular polarizability has been studied in the framework of the molecular statistical approach with allowance for the perturbation of the electronic structure of molecules due to the change in the conformation of their aromatic core and intermolecular interactions. Experimental dependences of $\bar \gamma$ and Δγ on the molecular orientational order parameter S have been derived, and their specific features for the known objects have been explained. The possibility of separating the contributions of opposite signs to the dependence Δγ(S) due to the change in the conformation of molecules and intermolecular interactions has been shown using nematic MBBA as an example.     

Momentenanalyse derR 2-Nullphononen-Linie in NaF unter einaxialem Druck

The R₂ zero-phonon absorption line 4480 Å in NaF at 4.2 °K and 23 °K is studied under uniaxial stress along 〈100〉 and 〈100〉. According to the F₃ model of theR center the R₂ line is found to be due to a transition between a degenerate ground state (²E) and a nondegenerate excited state (²A) of this center. Instead of a splitting into single components under stress, changes in line shape are observed which are analyzed by means of the method of moments. The zeroth and first moment of the line are calculated as functions of the magnitude of stress and temperature. The theoretical moments are found to be in good agreement with those determined from the experimental data. From a comparison of the measured moments with the theoretical expressions the stress splitting parameters are obtained which describe the removal of both the orientational and the orbital degeneracy of theR center under uniaxial stress. The corresponding strain parameters of the R² line in NaF are compared with those in other alkali halides.     

Decay of bcc-structure and of bond-orientational order in a fluid

The decay of an initially prepared bcc structure and the bond-orientational order (anisotropy of the first coordination shell) are studied in a non-equilibrium molecular dynamics simulation for a fluid of 1024 particles interacting with a repulsive r^-12 potential. Data are presented for pair-correlation functions and order parameters associated with an angle dependence described by cubic harmonics of the ranks 4, 6 and 8. These cubic pair-correlation functions and cubic order parameters are defined by the expansion of the pair-correlation function and of the bond orientational distribution function with respect to Cartesian tensors. The relaxation of the local anisotropy shows a pretransformational slowing down for densities approaching the freezing point.     

The phase-transition order parameter, fluctuations, and nanoclusters in benzil crystals

Bragg and diffuse X-ray reflections from the M points of the Brillouin zone boundary of a benzil crystal paraphrase, the integral intensity of which is associated with the order parameter and its fluctuations, are studied. Original data on the temperature behavior of the order parameter and diffuse scattering are obtained. The relevant critical exponents are determined. A conclusion is drawn as to the proximity of the phase transition in these crystals to the tricritical point. A phase transition model is discussed.     

On the applicability of mode coupling theory to a ϕ 4-model with first order phase transition

A ? ⁴-model with symmetric double-well-like on-site potential and anharmonic, infinite range interactions is investigated. This model exhibits a first order phase transition at a temperature T _c. The time-dependent displacement correlation function is studied in the framework of the mode coupling theory (MCT). Depending on the choice of slow modes, MCT makes qualitatively different predictions which are compared with MD-results. These numerical results suggest that only the order parameter mode {ie1-1} should be considered as slow. In that case it is shown that MCT yields a dynamical transition in the supercooled high-temperature phase {ie1-2} at a temperature T* which coincides with the spinodal temperature T _s (T _s = 0 for our model) where the metastable supercooled phase becomes instable.     

Influence of nematic and smectic orders on polarizability of molecules of ethyl-p-(4-ethoxybenzylideneamino-)α-methyl cinnamate liquid crystals

Experimental values of the polarizability tensor γ components of molecules of ethyl-p-(4-ethoxybenzylideneamino-)α-methyl cinnamate liquid crystals in the nematic and smectic A phases have been obtained. Quadratic dependences of the longitudinal, γ _l , and transverse, γ _t , components, the mean value $\bar \gamma $ , and anisotropy Δγ in both phases have been established as functions of the orientational order parameter S of molecules in a maximally wide range of S. The nematic-smectic A phase transition with a continuous variation of S manifests itself as kinks in the linear dependences of $\bar \gamma $ , Δγ, and γ _l on S ² and does not influence the dependence γ _t (S ²). The observed dependences have been derived in the framework of the theory of the nematic-smectic A phase transition. The factors responsible for different influences of the orientational and positional orderings of molecules on the polarizability parameters have been determined.     

基于Gay-Berne势能模型的粗粒化动力学模拟研究正丁醇的玻璃态相变

通过基于Gay-Berne势能模型的粗粒化动力学模拟,研究液态正丁醇体系的冷却过程. 采用密度泛函计算,拟合出适合正丁醇体系的GB势能参数. 体系的密度、平均势能等性质随温度的降低(由290 K降至50 K,间隔为10 K)发生特殊变化,即体系发生玻璃态相变,相变温度为T_g=120±10 K,与实验值110±1 K符合很好.     

Effects of fluctuations in the orientational order parameter in the cyanobiphenyl (nCB) homologous series

Photopyroelectric measurements of the anisotropy in the thermal conductivity Deltak vs temperature in the nCB (n=5,ellipsis,9) series are reported. The data have been used to deduce the behavior of the orientational order parameter Q close to the nematic-isotropic (N-I) and smectic A-nematic (A-N) phase transitions, respectively. It has been shown that near the N-I transition the data for 5CB and 6CB are consistent with the so-called "tricritical hypothesis," which predicts beta=0.25. This is not true for 7CB and 8CB in which the order parameter exhibits a behavior that could be caused by the presence of fluctuations that become increasingly important when the transition temperature is approached. A very simple model, which takes into account the contribution of fluctuations to the orientational order, has been developed close to the A-N transition and it has been shown that it is in good agreement with the experimental results. A semiquantitative explanation for the observed behavior in compounds with different nematic range has been also given.     

On the behavior of indicators of melting: Lennard-Jones system in the vicinity of the phase transition

Various indicators of melting for a system of particles whose pair interaction is described by the Lennard-Jones potential have been considered. The behavior of the radial distribution function g(r) and the associated criteria of melting, modified Lindemann criterion, and criteria based on the properties of short-range orientational order (rotational invariants q _l and w _l of various orders l) has been analyzed in detail in the vicinity of the melting phase transition. A parameter based on the loss of the nearest neighbors of an atom/particle has been proposed to characterize the melting transition. All considered indicators of melting for the Lennard-Jones system have been compared. It has been shown that the indicators of melting derived from the properties of the short-range orientational order are much more sensitive to the melting phase transition and can be used to construct new phenomenological criteria of melting similar to the Lindemann criterion. An additional important advantage of such indicators is the relatively small number of configurations of the system necessary for their calculation.