New types of phase behaviour in binary mixtures of hard rod-like particles

The phase behaviour of binary mixtures of hard rod-like particles has been studied using Parsons—Lee theory (Parsons, J. D., 1979, Phys. Rev. A, 19, 1225); Lee, S. D., 1987, J. Chem. Phys., 87, 4972). The stability of the isotropic-nematic (I-N) transition with respect to isotropic—isotropic (I-I), and nematic—nematic (N-N) demixing is investigated. The individual components in the mixtures are modelled as hard cylinders of diameters D_i and lengths L_i (i = 1,2). The aspect ratios k_i = L_i/D_i of the components are kept fixed (with values of k ₁ = 15 and k ₂ = 150), and the phase behaviour of the mixtures is studied for varying diameter ratios d = D ₁/D ₂. When the diameter ratio is relatively large, e.g., for values of d = 50, component 1 may be considered a large colloidal particle, while the second component plays the role of a weakly interacting solvent. This mixture exhibits only an I-N phase transition which is driven by the excluded volume interaction between the large particles (no I-I or N-N demixing is seen). A decrease in the diameter ratio enhances the contribution of the smaller component to the free energy (especially in terms of the unlike excluded volume term), and I-I as well as N-N demixing transitions are observed. The character of the N-N transition is rather unusual, a single region bounded by a lower critical point (in the pressure—composition plane) is seen for a diameter ratio of d = 3.2, while two demixed nematic regions bounded by lower and upper critical points are observed for d = 3.13. A further decrease in the diameter ratio (e.g., to d = 3) leads to systems with a phase behaviour in which the two demixed N-N regions meet, giving rise to a large demixed region with very strong fractionation in composition, and no N-N critical points. The I-I demixing transition is always accompanied by a lower critical point and occurs for systems with intermediate size (diameter) ratios. A diameter ratio of d = 4.5 corresponds to systems with significant like and unlike excluded volume interactions, and in this case the I-N transition takes place over the whole composition range with weak fractionation and one azeotropic point. Surprisingly, the coexisting nematic phase is of lower packing fraction than the isotropic phase for some of the compositions, i.e., an inversion of packing fraction takes place. In addition to this, the longer rods can be less ordered that the shorter rods for certain values of the composition.     

A study of π states of H2 + in the one centre approach

The statistical theory of the elastic constants of nematic liquid crystals is applied to detailed calculations based on well-defined approximations for the direct correlation function of Ornstein and Zernike and for the singlet orientational distribution. The model of hard spherocylinders with superimposed r ^-6 attraction modulated by a Maier-Saupe P ₂(cos ?_{1 2}) term, is used. The dependence on temperature, on the order parameter and on the length to breadth ratio, of the reduced elastic constants K* _i (i=1, 2, 3), is discussed in some detail and comparison with experiment is included.     

Structure and elastic properties of a nematic liquid crystal: A theoretical treatment and molecular dynamics simulation

The Frank elasticity constants which describe splay (K ₁), twist (K ₂), and bend (K ₃) distortion modes are investigated for 4-n-pentyl-4'-cyanobiphenyl (5CB) in the nematic liquid crystal. The calculations rest on statistical-mechanical approaches where the absolute values of K _i (i=1,2,3) are dependent on the direct correlation function (DCF) of the corresponding nematic state. The DCF was determined using the pair correlation function by solving the Ornstein-Zernike equation. The pair correlation function, in turn, was obtained from molecular dynamics (MD) trajectory. Three different approaches for calculations of the elasticity constants were employed based on different level of approximation about the orientational order and molecular correlations. The best agreement with experimental values of elasticity constants was obtained in a model where the full orientational distribution function was used. In addition we have investigated the approximation about spherical distribution of the intermolecular vectors in the nematic phase, often used in derivation of various mean-field theories and employed here for the construction of the DCF. We found that this assumption is not strictly valid, in particular a strong deviation from the isotropic distribution is observed for short intermolecular distances. Received 22 March 2000 and Received in final form 9 June 2000     

Theoretical investigations of rotational phenomena and dielectric properties in a nematic liquid crystal

The molecular dynamics (MD) simulation, based on a realistic atom-atom interaction potential, was performed on 4-n-pentyl-4'-cyanobiphenyl (5CB) in the nematic phase. The rotational viscosity coefficients (RVCs) γ _i, (i = 1, 2) and the ratio of the RVCs λ = - γ ₂/γ ₁ were investigated. Furthermore, static and frequency-dependent dielectric constants and ε were calculated using parameters obtained from the MD simulation. Time correlation functions were computed and used to determine the rotational diffusion coefficient, D _⊥. The RVCs and λ were evaluated using the existing statistical-mechanical approach (SMA), based on a rotational diffusion model. The SMA rests on a model in which it is assumed that the reorientation of an individual molecule is a stochastic Brownian motion in a certain potential of mean torque. According to the SMA, γ _i are dependent on the orientational order and rotational diffusion coefficients. The former was characterized using: i) orientational distribution function (ODF), and ii) a set of order parameters, both derived from analyses of the MD trajectory. A reasonable agreement between the calculated and experimental values of γ _i and λ was obtained. Received 22 March 2000 and Received in final form 8 October 2000     

The McMillan parameter as an effective field variable for the nematic–smectic tricritical point in NO.M compounds

The dependence of the coupling of orientational and translational order parameters on the nematic-smectic A tricritical point (TCP), observed through birefringence experiments in the pure compounds and in the binary mixtures in the homologous series of N(p-n-alkyloxybenzylidene)p-n-alkylanilines, results in a mean field tricritical exponent. The McMillan parameter, M = T _NA/T _NI (where T _NA and T _NI are the smectic A—nematic (AN) and the nematic—isotropic (NI) phase transition temperatures respectively), is used as an effective and relevant field variable in analysing the TCP. The observed linear dependence of the jump in the orientational order parameter with new density variables in the tricritical region is found to be consistent with the results obtained from both the Landau mean field and the decoupled mean field models. The width of the mean field tricritical region is discussed in terms of the McMillan parameter. Further, the McMillan parameter is observed to be characteristic of chemical composition at the NA tricritical point.     

Kinetic analysis of the ionization ratio effects on a three‐species plasma

In partially ionized plasmas, the energy transferred to electrically charged species by the electromagnetic field can be partly channelized to the population of neutrals, due to interspecies collisional processes. Depending on the relative density of neutrals, these effects may govern the collective plasma dynamics by drastically modifying particle dynamics and energy‐transport processes with respect to the fully ionized plasma‐approximation models. In this work, the influence of the ionization ratio r_i on a partially ionized plasma is analysed by means of a three‐species one‐dimensional kinetic model to compute transient and steady state velocity‐dependent distribution functions. The conservative collision operators accounting for charge–charge and charge–neutral interactions allow studying several plasma scenarios with the same entire number of particles per unit of volume but for an increasing r_i parameter, in the presence of a modulated signal‐like electric field. For a sequence of plasma scenarios of fixed r_i, ranging from typical weakly ionized to highly ionized plasma values r_i ～ 10^?7–10^?4, the mass species flows are examined. These flows behave linearly with respect to r_i up to a value r_i ? 10^?5 from which the quasi‐linear dependence is critically altered. The convection–diffusion equations are solved with the semianalytical Propagator Integral Method, which behaves well to deal with conservative operators, density, and field discontinuities, allowing for the use of collision terms of disparate time and spatial characteristic scales. The results can be relevant to a wide class of plasma systems and to analyse the ionization ratio effects on transport coefficients.     

Study of dipole dynamics and pre-transitional effects at isotropic to nematic phase transition by low-frequency dielectric relaxation measurements

Thermal microscopy (TM) as well as low-frequency (LF) dielectric relaxation studies are carried out on a nematic liquid crystal (NLC), viz E7 (Merck Ltd, UK). The isotropic to nematic (IN) transition temperatureT _IN determined by TM and LF-dielectric permittivity measurements agrees with the available data. Dielectric loss studies in the frequency region of 5–10?MHz indicate a relaxation (in the kHz region) akin to Debye type off-centered dispersion. The observed nematic relaxation is found to correspond to reorientation (about the short axis) of the nematic dipole to the external field. The temperature variation of the nematic relaxation frequencyf _R is found to follow an Arrhenius shift, with an activation energy of 1.7?eV. Temperature variation of the dielectric strength (Δε = ε _o ? ε_∞) and the distribution parameter α in the nematic phase are discussed. The dynamic response of the nematic dipoles and growth of pre-transitional fluctuations are found to be nonlinear in the vicinity of the IN transition. The value of the exponent α_eff = 0.072 indicates weak growth of transitional fluctuations across the IN transition.     

Influence of the nematic order on the rheology and conformation of stretched comb-like liquid crystalline polymers

We have studied the rheology and the conformation of stretched comb-like liquid-crystalline polymers. Both the influence of the comb-like structure and the specific effect of the nematic interaction on the dynamics are investigated. For this purpose, two isomers of a comb-like polymetacrylate polymer, of well-defined molecular weights, were synthesized: one displays a nematic phase over a wide range of temperature, the other one has only an isotropic phase. Even with high degrees of polymerization N, between 40 and 1000, the polymer chains studied were not entangled. The stress-strain curves during the stretching and relaxation processes show differences between the isotropic and nematic comb-like polymers. They suggest that, in the nematic phase, the chain dynamics is more cooperative than for a usual linear polymer. Small-angle neutron scattering has been used in order to determine the evolution of the chain conformation after stretching, as a function of the duration of relaxation t _r. The conformation can be described with two parameters only: , the global deformation of the polymer chain, and p, the number of statistical units of locally relaxed sub-chains. For the comb-like polymer, the chain deformation is pseudo-affine: is always smaller than (the deformation ratio of the whole sample). In the isotropic phase, has a constant value, while pincreases as tr. This latter behavior is not that expected for non-entangled chains, in which p varies as t _r ^1/2 (Rouse model). In the nematic phase, decreases as a stretched exponential function of t _r, while p remains constant. The dynamics of the comb-like polymers is discussed in terms of living clusters from which junctions are produced by interactions between side chains. The nematic interaction increases the lifetime of these junctions and, strikingly, the relaxation is the same at all scales of the whole polymer chain. Received 5 May 1999 and Received in final form 18 October 1999     

Investigation of the mass dependence of self-diffusion coefficients by molecular dynamics calculations: binary and ternary isotopic mixtures of atoms

Extensive molecular dynamics calculations have been used to study for the first time systematically the dependence of the self-diffusion coefficients D_i (i = 1, 2, 3) in binary and ternary atomic isotopic mixtures on the particle mass ratios m*₂ = m ₂/m ₁ and m*₃ = m ₃/m ₁ at different reduced temperatures T* and reduced particle number densities n*, using a Lennard-Jones 12-6 potential and a hard-soft-spheres potential. In addition, the dependence of D_i values of binary mixtures on the mole fraction x ₁ = 1—x ₂ was also investigated for some thermodynamic states. The calculated values of D_i can be represented quantitatively by exponential estimates of the form D_i = D* _i (m*₂)^ex _i in the case of binary mixtures and D_i = D ⁰ _i (m*₂)^{ex _i} (m ₃)^{ext _i} in the case of ternary mixtures. D ⁰ _i are the self-diffusion coefficients in reference mixtures of mass ratios m*₂ = m*₃ = 1. The dependence of the exponents ex _i (m*₂, T*, n*, x ₁) of binary mixtures on m*₂, T*, n*, and x ₁ and the dependence of the exponents ext _i (m*₂, m*₃, n*) of equimolar ternary mixtures at T* = 1.8 on the exponents ex _i of the constituent binary mixtures and on m*₂, m*₃, and n* are discussed.     

Messungen des γi-Koeffizienten,der Zündspannung und des normalen Katodenfalls der Glimmentladung an gasbedeckten Mo- und Fe-Oberflächen in Edelgasen

Measurements of the γ_i-coefficient, the ignition voltage and the normal cathode fall of the glow discharge on gas-covered cathode surfaces for the combinations Mo—Ne⁺, Ar⁺, Kr⁺, Xe⁺ and Fe—Ne⁺ are described. H₂, N₂ and O₂ are used for covering the cathodes with a monomolecular adsorption layer. Measurements are carried out with a dynamic method according to VARNEY in the range 30 ? X/p₀ ? 400 V cm^?1 Torr^?1.     

Quantum Motion on 2D Surfaces of Spherical Topology

When the motion of a particle is constrained on the two-dimensional surface, excess terms exist in usual kinetic energy 1/(2μ) ∑ p _i ² with hermitian form of Cartesian momentum p _i (i = 1,2,3), and the operator ordering should be taken into account in the kinetic energy which turns out to be 1/(2μ) ∑ (1/f _i )p _i f _i p _i where the functions f _i are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this article, the explicit forms of the dummy functions f _i for quantum motion on some 2D surfaces of revolution of spherical topology are given. PACS numbers: 03.65.-w Quantum mechanics, 04.60.Ds Canonical quantization.     

Structure,elasticity and phase transitions in liquid crystals with deformations

ABSTRACT

A molecular-statistical theory describing the nematic liquid crystals (LCs) with spherical inclusions (or point defects) is proposed. At given size of inclusions and nematic order parameters at the surfaces of inclusions (zero in the case of point defects) and far from inclusions (where the nematic LC is almost uniform), the distribution of nematic order parameters in the bulk of LC with inclusions was found to be fully determined by the elastic constants of LC. We have found and explained the two-step heat-driven transformation from the nematic phase into the isotropic phase, with the intermediate phase in between. The nematic order parameters and the elastic constants are evaluated in the framework of a unified approach based on the features of pair interaction potentials of the individual LC molecules. It is shown that, in the case of K₃₃ < K₁₁, the point defects should destroy the conventional nematic phase.     

Investigation of the mass dependence of self-diffusion coefficients by molecular dynamics calculations: binary non-isotopic mixtures of atoms

Extensive molecular dynamics calculations have been used to study systematically for the first time the dependence of the self-diffusion coefficients D_i (i = 1,2) in binary equimolar non-isotopic atomic mixtures (mole fractions x ₁ = x ₂ = 0.5, reduced temperature T? = 1.6) on the particle mass ratio m?₂ = m ₂/m ₁ (1 ≤ m?₂ ≤ 16.5) in the ranges of reduced particle number density 0.15 ≤ n? ≤ 0.85 and reduced length parameter 0.5 ≤ σ?₂₂ ≤ 2.0 for a Lennard-Jones 12-6 potential. The calculated D_i values can be represented quantitatively by an exponential estimate of the form: D_i = D ⁰ _i (m?₂) ^ex _i . D ⁰ _i are the self-diffusion coefficients in reference mixtures with m?₂ = 1. The observed dependence of the exponents ex _i (m?₂, n?, σ?₂₂) on m?₂, n? and σ?₂₂ is discussed in this paper.     

Universality of Operator Ordering in Kinetic Energy Operator for Particles Moving on two Dimensional Surfaces

When the motion of a particle is constrained on the two-dimensional surface, excess terms exist in usual kinetic energy 1/(2m)∑ p _i ² with hermitian form of Cartesian momentum p _i (i = 1,2,3), and the operator ordering should be taken into account in the kinetic energy which turns out to be 1/(2m)∑ (1/f _i )p _i f _i p _i where the functions f _i are dummy factors in classical mechanics and nontrivial in quantum mechanics. The existence of non-trivial f _i shows the universality of this constraint induced operator ordering in quantum kinetic energy operator for the constraint systems.     

A small-angle X-ray scattering study of the isotropic and nematic phases of V2O5 suspensions

We report small-angle X-ray scattering experiments performed in both the isotropic and nematic phases of aqueous V₂O₅ suspensions. We show that the scattering in the isotropic phase can be well described in the whole accessible q-range by only considering the form factor of non-interacting ribbons. We investigate the influence of concentration and pH on the dimensions of V₂O₅ ribbons and show that these parameters do not have any significant effect, as long as the system stays well within the chemical stability domain of the ribbons. We then show that nematic single domains display an anisotropic small-angle scattering pattern, even at scattering vectors small compared to that at which a characteristic correlation peak is observed. This feature is expected for a nematic phase, but was rarely observed. We finally try to describe this scattering within the framework of theories developed for the structure factor of a nematic polymer, and we reach the conclusion that chain ends are certainly important to understand this pattern. Received 21 July 1999 and Received in final form 17 December 1999     

Refractive index and orientational order parameter of a polar–polar binary system showing induced smectic Ad and re-entrant nematic phases

Refractive index measurements have been done on a polar–polar binary system, 4-cyanophenyl [4′(4″-n-heptylphenyl)] benzoate (7CPB)?+?4-cyanophenyl-4-nonylbenzoate (9.CN), exhibiting nematic–smectic A_d–re-entrant nematic phase sequence using thin prism technique. From refractive index as well as density data, the polarizability anisotropy in the mesomorphic state has been calculated from the standard Vuks model and the orientational order parameter (?P ₂?) values have been determined. By measuring the refractive indices and density in the solid phase, the validity of the Haller's extrapolation method for systems having higher order phases has been verified. The temperature variation of the density, birefringence, and ?P ₂? values at the nematic–smectic A_d and smectic A_d–re-entrant nematic transitions for all the mixtures are found to be continuous. The experimental ?P ₂? values have been compared with our previous X-ray data and also those calculated from the Luckhurst and Timimi model.     

Using the full Raman depolarisation in the determination of the order parameters in liquid crystal systems

The depolarisation ratio for the Raman-active phenyl stretching mode has been measured over the whole of the mesophase range, and the orientational order parameters deduced, in the uniaxial nematic liquid crystal octylcyanobiphenyl (8CB). Linearly polarised light was incident normally on a homogeneously aligned sample and a χ² minimisation routine performed on the 360^° depolarisation ratio profile. The order parameters 〈P ₂₀₀〉 and 〈P ₄₀₀〉 , together with the differential polarisability ratio, r , are used as fitting parameters and measured as a function of temperature. Interestingly, we show that the value for r , conventionally measured in the isotropic phase and assumed to remain constant, has a clear temperature dependence, ranging from -0.032±0.008 in the isotropic phase through to -0.245±0.015 at the nematic-to-smectic A phase transition. The measured order parameters 〈P ₂₀₀〉 and 〈P ₄₀₀〉 varied from 0.35- 0.55±0.02 and 0.180- 0.245±0.02 , respectively, across the 8 ^° C wide nematic phase range. The values of both 〈P ₂₀₀〉 and 〈P ₄₀₀〉 are in excellent agreement with theory, but it is noteworthy that 〈P ₄₀₀〉 shows a much better quantitative match than has been reported in previous work. Crucially the temperature dependence of r is shown to be a contributing factor in the low 〈P ₄₀₀〉 values that have been conventionally reported from Raman scattering measurements. The potential for fitting the entire angular depolarisation ratio distribution in liquid crystalline systems that are described by more order parameters, specifically biaxial materials, is discussed.     

Neutrons produced by 1.22 GeV antiproton interactions with nuclei

Inclusive neutron energy spectra were measured by time of flight using 1.22 GeV antiprotons from LEAR, CERN, as projectiles and targets from natural Al, Cu, Ag, Ho, Ta, Au, Pb, Bi, U. The sum of two Maxwellian distributions was fitted to the spectra obtained at several forward and backward angles yielding neutron multiplicities M_i and slope or temperature parameters T _i for the low-energy (evaporative, i=1) and high-energy (pre-equilibrium,i=2) parts, respectively. M ₁ increases with A, proportional to the nuclear volume, and M ₂ is growing with A , proportional to the nuclear radius. The T parameters are nearly independent of A. The results are compared with previous multiplicity measurements with a neutron detector, intranuclear cascade calculations and neutron spectra from stopped antiproton annihilation on nuclei. With the measured proton spectra also the ratio of emitted neutrons to protons was determined for Au. Received: 25 February 2000 / Accepted: 19 May 2000