Depletion effects in smectic phases of hard-rod-hard-sphere mixtures

It is known that when hard spheres are added to a pure system of hard rods the stability of the smectic phase may be greatly enhanced, and that this effect can be rationalised in terms of depletion forces. In the present paper we first study the effect of orientational order on depletion forces in this particular binary system, comparing our results with those obtained adopting the usual approximation of considering the rods parallel and their orientations frozen. We consider mixtures with rods of different aspect ratios and spheres of different diameters, and we treat them within Onsager theory. Our results indicate that depletion effects, and consequently smectic stability, decrease significantly as a result of orientational disorder in the smectic phase when compared with corresponding data based on the frozen-orientation approximation. These results are discussed in terms of the τ parameter, which has been proposed as a convenient measure of depletion strength. We present closed expressions for τ, and show that it is intimately connected with the depletion potential. We then analyse the effect of particle geometry by comparing results pertaining to systems of parallel rods of different shapes (spherocylinders, cylinders and parallelepipeds). We finally provide results based on the Zwanzig approximation of a fundamental-measure density-functional theory applied to mixtures of parallelepipeds and cubes of different sizes. In this case, we show that the τ parameter exhibits a linear asymptotic behaviour in the limit of large values of the hard-rod aspect ratio, in conformity with Onsager theory, as well as in the limit of large values of the ratio of rod breadth to cube side length, d, in contrast to Onsager approximation, which predicts τ ∼ d ³. Based on both this result and the Percus-Yevick approximation for the direct correlation function for a hard-sphere binary mixture in the same limit of infinite asymmetry, we speculate that, for spherocylinders and spheres, the τ parameter should be of order unity as d tends to infinity.     

A kinetic theory and benchmark predictions for polymer-dispersed, semi-flexible macromolecular rods or platelets

The goals of this paper are: to present a mean-field kinetic theory for the hydrodynamics of macromolecular high aspect ratio rods or platelets dispersed in a polymeric solvent; and, to apply the formalism to predict the impact due to a polymeric versus viscous solvent on the classical Onsager isotropic-nematic equilibrium phase diagram and on the monodomain response to imposed steady shear. The kinetic theory coupling between the nanoscale rods or platelets and the polymeric solvent is incorporated through a mean-field potential that reflects the enormous particle-polymer surface area and the particle-polymer interactions across this interfacial area. To determine predictions of this theory on the equilibrium and sheared monodomain phase diagrams, we present a reduction procedure which approximates the coupled Smoluchowski equations for the polymer chain probability distribution function (PDF) and the nano-particle orientational PDF in favor of a coupled system of equations for the rank 2 second-moment tensors for each PDF. The reduced model consists of an 11-dimensional dynamical system, which we solve using continuation software (AUTO) to predict the modified Onsager equilibrium phase diagram and the modified Doi-Hess shear phase diagram due to the physics of polymer-particle surface interactions.     

Polar nano-rods under shear: From equilibrium to chaos

The orientational dynamics of rod-like particles with permanent (electric or magnetic) dipole moments in a plane Couette shear flow is investigated using mesoscopic relaxation equations combined with a generalized Landau free energy. The free energy contribution due to the coupling between average alignment and dipole orientation is derived on a microscopic basis. Numerical results of the resulting eight-dimensional dynamical system are presented for the case of longitudinal dipoles and thermodynamic conditions where the equilibrium state is a (polar or non-polar) nematic. Solution diagrams reveal presence of a large variety of periodic, transient chaotic, and chaotic dynamic states of the average alignment and dipole moment, respectively, appearing as a function of Deborah number and tumbling parameter. Compared to rods without dipoles we observe a significant preference of out-of-plane kayaking-tumbling states and, generally, a higher sensitivity to the initial conditions including bistability. We also demonstrate that the average (electric) dipole moment characterizing most of the observed states yields electrodynamic (magnetic) fields of measurable strength.     

Long-range order and dynamic structure factor of a nematic under a thermal gradient

We use a fluctuating hydrodynamic approach to calculate the orientation fluctuations correlation functions of a thermotropic nematic liquid crystal in a nonequilibrium state induced by a stationary heat flux. Since in this nonequilibrium stationary state the hydrodynamic fluctuations evolve on three widely separated times scales, we use a time-scale perturbation procedure in order to partially diagonalize the hydrodynamic matrix. The wave number and frequency dependence of these orientation correlation functions is evaluated and their explicit functional form on position is also calculated analytically in and out of equilibrium. We show that for both states these correlations are long-ranged. This result shows that indeed, even in equilibrium there is long-range orientational order in the nematic, consistently with the well known properties of these systems.We also calculate the dynamic structure of the fluid in both states for a geometry consistent with light scattering experiments. We find that as with isotropic simple fluids, the external temperature gradient introduces an asymmetry in the spectrum shifting its maximum by an amount proportional to the magnitude of the gradient. This effect may be of the order of 7 per cent. Also, the width at half height may decrease by a factor of about 10 per cent. Since to our knowledge there are no experimental results available in the literature to compare with, the predictions of our model calculation remains to be assessed.     

Onsager model for the structure of rigid rods confined on a spherical surface

Recent studies have suggested that a monolayer of self-avoiding hard rods confined on a spherical surface may display a distribution texture corresponding to splay, tennis-ball, rectangle, or cut-and-rotate splay symmetries. We investigate the system on the basis of a generalized Onsager model which includes both excluded-volume and entropic effects. The numerical solution indicates that the splay state, where on average rods line up in parallel to the longitudinal lines on the spherical surface, is the only stable state.     

Shearing of planar smectic C chevrons

We have theoretically investigated chevron formation in smectic C materials and the transformation of this chevron structure to a tilted layer structure as the cell is sheared. We find a series of transition temperatures at which the behaviour of the cell critically changes. As the cell is cooled from the smectic A phase past the first critical temperature there is a second order transition which forms two tilted layer states with lower energy than the smectic A bookshelf structure. Although these low energy tilted structures exist the bookshelf structure is the stable state for zero shear. However, upon further cooling this bookshelf structure becomes unstable to the formation of a chevron state. Now when the cell is sheared the chevron structure smoothly transforms into the tilted layer structure. As each further critical temperature is passed an additional multiple chevron solution is formed which although a high energy, unstable state may be observed transiently. For sufficiently low temperatures the transition from chevron to tilted layer becomes first order. This first order transition occurs as the chevron interface merges with the surface alignment region to form the tilted layer structure. Received 28 December 1998 and Received in final form 8 April 1999     

External field induced tricritical phenomenon in the isotropicnematic phase transition of hard non-spherical particle systems

The effect of static external field is studied on the isotropic–nematic phase transition of a system of hard non-spherical particles (rods or platelets) with negative anisotropic polarizability (susceptabilities). On the basis of Onsager theory, the phase coexistence curve is calculated numerically without any approximation. It is found that a weakly ordered nematic phase (uniaxial planar) is in coexistence with a highly ordered biaxial nematic phase which ends at a tricritical point. In the limit of infinite field strength, the orientations of the particles are confined in a plane perpendicular to the field and continuous isotropic–nematic phase transition takes place.     

Theoretical model of the transition between C1 and C2 chevron structures in smectic liquid crystals

We present a study of the effect of weak anchoring on the transition between C1 and C2 chevron structures in smectic-C liquid crystals. The coexistence of C1 and C2 chevron structures within a single cell causes zigzag defects to occur and may affect the optical characteristics of the cell. By standard Euler-Lagrange minimisation of the total energy of the system, we obtain analytical expressions for the equilibrium director cone angle in the two chevron states. These in turn allow us to compare the total energies of the states and determine the globally stable chevron profile. We show that analytical predictions for the critical transition temperature, which depends on anchoring strength and pretilt angle, are in good agreement with those obtained numerically.     

Oscillating viscosity in a lyotropic lamellar phase under shear flow

We report some time-dependent behavior of lyotropic lamellar phase under shear flow. At fixed stress, near a layering instability, the system presents an oscillating shear rate. We build up a new stress versus shear rate diagram that includes temporal behavior. This diagram is made of two distinct branches of stationary states which correspond, respectively, to disordered and ordered multilamellar vesicle phases. When increasing the shear stress, prior to the transition to the ordered structural state, sustained oscillations of the viscosity are recorded. They correspond to periodic structural change of the entire sample between a disordered and a ordered state of multilamellar vesicles.     

Breaking of periodicity at positive temperatures

We discuss a classical lattice gas model without periodic or quasiperiodic ground states. The only ground state configurations of our model are nonperiodic Thue-Morse sequences. We show that low temperature phases of such models can be ordered. In fact, we prove the existence of an ordered (nonmixing) low temperature translation invariant equilibrium state which has nonperiodic Gibbs states in its extremal decomposition.     

A non-equilibrium Ising model of turbulence

We introduce a model of interacting lattices at different resolutions driven by the two-dimensional Ising dynamics with a nearest-neighbor interaction. We study this model both with tools borrowed from equilibrium statistical mechanics as well as non-equilibrium thermodynamics. Our findings show that this model keeps the signature of the equilibrium phase transition. The critical temperature of the equilibrium models corresponds to the state maximizing the entropy and delimits two out-of-equilibrium regimes, one satisfying the Onsager relations for systems close to equilibrium and one resembling convective turbulent states. Since the model preserves the entropy and energy fluxes in the scale space, it seems a good candidate for parametric studies of out-of-equilibrium turbulent systems.     

Metastable molecular fluid hydrogen at high pressures

Warm dense hydrogen is studied in the region of fluid–fluid phase transition within the framework of the density functional theory. We report a procedure of obtaining metastable states and calculate the equation of state. Metastable states are diagnosed by pair correlation functions and values of conductivity. We obtain a strong overlapping through the density of metastable and equilibrium branches of pressure isotherms. This indicates the plasma nature of the phase transition.     

强迫耗散系统的有序结构和系统的发展(Ⅰ)，最小熵产生原理和有序结构

一个系统的发展总是由不可逆热力过程和非线性动力过程所驱动.将大气动力学方程组同考虑了动能变化的Gibbs关系结合起来构建的熵平衡方程，才能更好地描述大气系统的不可逆热力过程和非线性动力过程.至今非平衡态热力学仅利用Onsager线性唯象关系证明了最小熵产生原理.利用新建立的熵平衡方程和大气动力学方程的性质证明，最小熵产生原理在热力学线性区和非线性区都是普遍成立的.且当热量输送平衡、水汽输送平衡和动量输送平衡时，系统达到不可逆过程最弱的最小熵产生热力学状态.当系统又是动力平衡且无平流时，这种最小熵产生态就是 关键词： 非线性热力学 熵产生 最小熵产生原理 有序结构     

Localized bifurcations and defect instabilities in the convection of a nematic liquid crystal

The stationary and the time-dependent homogeneous ordered states in convection may both become unstable against localized perturbations. Defects are then created and they may contribute to the disorganization of the homogeneous state. We present an experimental study of defects in some homogeneous stationary structures as well as in the traveling-wave states of convection of a nematic liquid crystal. We show that the core of the defects is a germ of the unstable state and it can become unstable under the external stress. Then, either fully homogeneous states with the symmetry of the core, or complex disordered states can develop from the local instability of defects in processes quite similar to displacive transitions in solids. Some of the main features are qualitatively similar to numerical simulations of an appropriate Landau-Ginzburg equation.     

Geometry of nematic liquid crystals under shearing flow

In this work, an extended version of the Hess-Baalss conformal approach is used to propose a relation connecting the viscosity coefficients of the nematic liquid crystals. Starting from the well-known fact that, in its usual form, the conformal transformation leads to results which are not observed experimentally, it is shown that, when the director field of an ordered nematic phase under sheared motion is taken as a three-dimensional surface with torsion, the resulting theory describes the observed experimental data efficiently. Moreover, this model predicts that the five viscosity coefficients of the Leslie ah hoc model are not independent, but connected. A comparison of the deduced relationship with experimental data is performed and an excellent agreement is obtained.     

SRB States and Nonequilibrium Statistical Mechanics Close to Equilibrium

Nonequilibrium statistical mechanics close to equilibrium is studied using SRB states and a formula [10] for their derivatives with respect to parameters. We write general expressions for the thermodynamic fluxes (or currents) and the transport coefficients, generalizing the results of [4, 5]. In this framework we give a general proof of the Onsager reciprocity relations. Received: 2 December 1996 / Accepted: 13 March 1997     

Fokker-Planck equation approach to fluctuations about nonequilibrium steady states

We examine the properties of steady states in systems which interact at the boundary with a nonequilibrium environment. The examination is based on a nonlinear Fokker-Planck equation, the structure of which is determined by the fact that it also governs the time evolution of the equilibrium fluctuations of the system. The nonlinearities in the Fokker-Planck equation may have two origins: thermodynamic nonlinearities which arise if the thermodynamic potential is not a bilinear function of the state variables, and nonlinear mode coupling which arises if the transport coefficients depend on the state. While these nonlinearities have only a small effect on the equilibrium fluctuations of a system away from critical points, they are shown to be important for the determination of fluctuations about nonequilibrium steady states. In particular the state dependence of the transport coefficients may lead to deviations from local equilibrium and to a breakdown of detail balance. An explicit formula for the time correlations of fluctuations about the nonequilibrium steady state is obtained. The formula leads to long-range correlations in fluids in the presence of a temperature gradient. The result is compared with earlier approaches to the same problem. Finally, we study the linear response to external forces and obtain a generalization of the fluctuation-dissipation formula relating the response functions with the nonequilibrium correlation functions.     

On spatial variations of nematic ordering

We present a theory of orientational order in nematic liquid crystals which interpolates between several distinct approaches based on the director field (Oseen and Frank), order parameter tensor (Landau and de Gennes), and orientation probability density function (Onsager). As in density-functional theories, the suggested free energy is a functional of spatially-dependent orientation distribution, however, the nonlocal effects are taken into account via phenomenological elastic terms rather than by means of a direct pair-correlation function. In illustration of this approach we consider a simplified model with orientation parameter on a circle and reveal its relation to the complex Ginzburg-Landau theory.     

On the Onsager Variation Principle and its Generalization for Nonlinear Irreversible Thermodynamics

The Onsager variation principle is examined from the viewpoint of the thermodynamic analogue of the D'Alembert principle in mechanics when the irreversible processes are linear and thus the system is near equilibrium. The thermodynamic D'Alembert principle is shown to be a precursor to the Onsager variation principle. The thermodynamic D'Alembert principle is then generalised to the cases of nonlinear irreversible processes occurring removed from equilibrium and a generalised form of the Onsager variation principle is obtained under some restricting conditions. The restricted variation principle so deduced has an accompanying exact differential form generalising the Clausius entropy differential (equilibrium Gibbs relations) and contains in it the essence of the thermodynamics of irreversible processes in systems where non-linear transport processes occur. An example is given for the nonlinear dissipation function in the variation functional. The evolution equations for fluxes are shown to yield those known in the literature.     

Kubo formulas for relativistic fluids in strong magnetic fields

Magnetohydrodynamics of strongly magnetized relativistic fluids is derived in the ideal and dissipative cases, taking into account the breaking of spatial symmetries by a quantizing magnetic field. A complete set of transport coefficients, consistent with the Curie and Onsager principles, is derived for thermal conduction, as well as shear and bulk viscosities. It is shown that in the most general case the dissipative function contains five shear viscosities, two bulk viscosities, and three thermal conductivity coefficients. We use Zubarev’s non-equilibrium statistical operator method to relate these transport coefficients to correlation functions of the equilibrium theory. The desired relations emerge at linear order in the expansion of the non-equilibrium statistical operator with respect to the gradients of relevant statistical parameters (temperature, chemical potential, and velocity.) The transport coefficients are cast in a form that can be conveniently computed using equilibrium (imaginary-time) infrared Green’s functions defined with respect to the equilibrium statistical operator.