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     

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.     

Nematic ordering in anisotropic elastomers: Effect of frozen anisotropy

Nematic ordering in anisotropic non-Gaussian elastomers is considered theoretically using mean field approximation. We focus on the effect of anisotropy during network cross-linking on the system elasticity and, in particular, on the so-called soft deformation mode. As the main result, we calculate the dependence of the elastomer free energy on the angle between the axis of “frozen” anisotropy and the nematic director. The dependence of the isotropic-nematic transition point on the orientational field acting on the monomers during the cross-linking process is also calculated. Received: 5 November 1997 / Revised and Accepted: 29 June 1998     

Statistical theory of the elastic constants of nematic liquid crystals

A statistical mechanical theory of the Frank elastic constants is formulated. The free energy functional is constructed for the deformed sample and the free energy density is defined for the case of small spatial gradients. The Frank constants are expressed in terms of the direct correlation function c(1, 2) and the orientational single particle distribution function. For the example of Onsager spherocylinders three constants K ₁, K ₂ and K ₃ are calculated. The results of these calculations are similar to those given by Priest and by Straley.     

Free energy of semiflexible polymers and structure of interfaces

The free energy of semiflexible polymers is calculated as a functional of the compositional scalar order parameter and the orientational order parameter of second-rank tensor S_ij on the basis of a microscopic model of wormlike chains with variable segment lengths. We use a density functional theory and a gradient expansion to evaluate the entropic part of the free energy, which is given in a power series of .The interaction term of the free energy is derived with a random phase approximation. For the rigid rod limit, the nematic-isotropic transition point is given by , N and w being the degree of polymerization and the anisotropic interaction parameter, respectively, and the degree of ordering at the transition point is 0.33448. We also find that the contour length of polymer chains becomes larger in a nematic phase than in an isotropic phase. Interface profiles are obtained numerically for some typical cases. In the neighborhood of isotropic-isotropic interfaces, polymer chains tend to align parallel to the interface on the polymer-rich side and perpendicular on the poor side. When an isotropic region and a nematic region coexist, orientational order parallel to the interface is preferred in the nematic region. Received: 28 May 1998 / Revised: 12 August 1998 / Accepted: 8 September 1998     

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.     

Director configuration and dynamics of a nematic liquid crystal around a two-dimensional spherical particle: Numerical analysis using adaptive grids

We study numerically the director and orientational order parameter configurations in a nematic liquid crystal around a two-dimensional spherical particle on the basis of the tensor order parameter formalism. To properly account for the large length scale difference between the particle and the accompanying orientational defect, we devise an adaptive grid scheme in which the lattice spacing is automatically and locally adjusted in response to the spatial gradient of the orientational order parameter. This adaptive grid scheme is useful in studying dynamical as well as static orientational structures. We present a simulation result which shows how a hedgehog defect of topological charge -1 becomes unstable in two dimensions, and splits into a defect pair of topological charge -1/2, located symmetrically around the particle. Received 14 September 2000 and Received in final form 27 December 2000     

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     

Structure and rheology of concentrated wormlike micelles [4]at the shear-induced isotropic-to-nematic transition

We have investigated the simple shear flow behavior of wormlike micelles using small-angle neutron scattering and mechanical measurements. Ternary surfactant solutions made of cetylpyridinium chloride, hexanol and brine (0.2 M NaCl) and hereafter abbreviated as CPCl-Hex were studied in the concentrated regime, . In a preliminary report (Berret et al. [#!ref16!#]), the discontinuity of slope observed in the shear stress versus shear rate curve was interpreted in terms of first-order phase transition between an isotropic state and a shear-induced nematic state ( transition). At the transition rate, , the solution exhibits a macroscopic phase separation into viscous and fluid layers (inhomogeneous shear flow). Above a second characteristic shear rate, the flow becomes homogeneous again, the sheared solution being nematic only. The neutron patterns obtained in the two-state inhomogeneous region have been re-examined. Based on a consistent analysis of both orientational and translational degrees of freedom related to the wormlike micelles, we emphasize new features for the transition. In the present paper, the shear rate variations of the relative proportions of each phase in the two-state region, as well as the viscosity ratio between isotropic and nematic phases are derived. We demonstrate in addition that slightly above the transition rate, the shear induced nematic phase is already strongly oriented, with an order parameter P ₂ = 0.65. The orientational state is that of a nematic flow-oriented monodomain. Finally, from the locations of the neutron scattering maxima for each isotropic and nematic contributions, we evaluate the concentrations for each phase and and derived a dynamical phase diagram of CPCl-Hex, in terms of the stress versus and . According to the classification by Schmitt et al. [#!ref22!#], the transition observed in CPCl-Hex micellar solutions could result from a positive flow-concentration coupling, in agreement with the observed monotonically increasing shear stress in the two-phase region. Received: 16 February 1998 / Revised: 18 February 1998 / Accepted: 24 May 1998     

Elastic properties of nematoid arrangements formed by amoeboid cells

In culture migrating and interacting amoeboid cells can form nematoid arrangements in analogy to a nematic liquid crystal phase. A nematoid arrangement is formed if the interaction has an apolar symmetry. Different cell types like human melanocytes (= pigment cells of the skin), human fibroblasts (= connective tissue cells), human osteoblasts (= bone cells), human adipocytes (= fat cells) etc., form a nematoid structure. Our hypothesis is that elastic properties of these nematoid structures can be described in analogy to that of classical nematic liquid crystals. The orientational elastic energy is derived and the orientational defects (disclination) of nematoid arrangements are investigated. The existence of half-numbered disclinations shows that the nematoid structure has an apolar symmetry. The density- and order parameter dependence of the orientational elastic constants and their absolute values are estimated. From the defect structure, one finds that the splay elastic constant is smaller than the bend elastic constant (melanocytes). The core of a disclination is either a cell free space or occupied by non oriented cells (isotropic state), by a cell with a different symmetry, or by another cell type. Received 3 May 1999 and Received in final form 29 September 1999     

Elastic constants of a nematic liquid crystal: Quadrupole-quadrupole interaction in the ellipsoidal approximation

The elastic constants of a nematic liquid crystal are calculated by means of a pseudo-molecular method that considers the quadrupolar intermolecular interaction with a screening length governing the range of the forces. The bulk as well as the surface-like elastic constants are determined as functions of the eccentricity of the interaction volume of ellipsoidal shape. It is shown that the elastic constants become negative for some values of the eccentricity, and, therefore, that the screened quadrupolar interaction could be the source of instabilities in the nematic phase and should be taken into account to interpret threshold phenomena in these systems.     

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.     

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     

Orientation-dependent depletion interaction in rodlike colloid-polymer mixtures

Depletion interaction in a suspension of rodlike colloids with added non-adsorbing polymer coils is theoretically studied. We calculate an overlap volume of depletion zone between two rodlike colloids, based on the second virial approximation. We examine nematic-isotropic phase transition (NIT) and two-phase coexistence between an isotropic and a nematic phase at low polymer concentrations. We find that the depletion interaction is dependent on the orientational order parameter of rodlike colloids and leads to a decrease in the NIT concentration on the addition of polymer. The coexistence curves have a leaning-chimney shape and are shifted to lower rod concentrations on increasing the polymer concentration. Received 23 May 2001 and Received in final form 18 July 2001     

Effect of high electric fields on the nematic to isotropic transition in a material exhibiting large negative dielectric anisotropy

We report the experimental high electric field phase diagram of a nematic liquid crystal which exhibits a large negative dielectric anisotropy. We measure simultaneously the birefringence (Δn) and the dielectric constant (epsilon_⊥) at various applied fields as functions of the local temperature of an aligned sample. We also measure the higher harmonics of the electrical response of the medium. The following experimental results are noted: (i) enhancement of orientational order parameter S in the nematic phase due to both the Kerr effect and quenching of director fluctuations; (ii) enhancement in the paranematic to nematic transition temperature (T_PN) with field; (iii) divergence of the order parameter susceptibility beyond the tricritical point as measured by third harmonic electrical signal; (iv) a small second harmonic electrical signal which also diverges near T_PN, indicating the presence of polarised domains. Our measurements show that ΔT_PN(= T_PN(E)-T_NI(0)) varies linearly with |E| whereas the Landau de Gennes theory predicts a dependence on E². It is argued that the quenching of director fluctuations by the field makes the dominant contribution to all the observations, including the thermodynamics of the transition.     

Effect of short and long range forces on the structure of water. II. Orientational ordering and the dielectric constant

The effects of short and long range interactions on the structure of water, both spatial and orientational, has been studied in detail by computing the full pair correlation function, site-site correlation functions, 2-dimensional site-site correlation functions in the (r _OO, r _OH) and (r _OO, r _HH) planes, dipole-dipole correlation function, radial Kirkwood g factor, and the dielectric constant. Two model potentials, the T1P4P and ST2, and their short range versions have been considered at ambient and elevated temperatures and under supercritical conditions. The Ewald summation under different conditions has been used to investigate also their effect on results. An analysis of the results shows that although all site-site correlation functions for the short and long range systems are similar, the orientational ordering in systems of different range may be considerably different, this evidence being provided mainly by the dipole-dipole correlation function and the radial Kirkwood factor. The orientational ordering is only short range in long range systems, whereas in short range systems the hydrogen bonding gives rise to a damped long range regular pattern of alignment. Nonetheless, the resulting dielectric constants for the short and long range systems coincide within the combined error bars. All findings are more pronounced at low temperatures but otherwise they are only marginally temperature and density dependent.     

Shear modulus of polydomain, mono-domain and non-mesomorphic side-chain elastomers: Influence of the nematic order

We investigate the behavior of the complex shear modulus of a series of elastomers including mono-domain and poly-domain liquid crystal samples, and a non-mesomorphic sample. We find that the dynamics of the glass transition are strongly modified by the nematic order. This result explains why the truly elastic response of liquid crystal elastomers can only be observed in the isotropic phase at very high temperatures and at very low frequencies. Between the elastic regime and the glassy state, the elastomers have a visco-elastic regime, which is characterized by a Rouse-like behavior for mono-domain and poly-domain samples, and by a Zimm-like behavior for the non-mesomorphic sample. We also show that the mono-domain sample exhibits marked anisotropy of the shear-modulus G ^′. This anisotropy, which is observed for the first time, is a function of frequency and is inverted between low and high frequencies, due to relaxation effects of the orientational order. Received 28 January 2000 and Received in final form 16 October 2000     

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.     

Temperature dependence of the effective anchoring energy for a nematic-ferroelectric interface

Specific features of the anisotropic interaction between a nematic mixture and a polar surface of a ferroelectric triglycine sulfate crystal have been studied over a wide temperature range including the substrate's Curie point T_c. The mixture was composed of two nematic liquid crystals, 60% of p-methoxybenzylidene-p-n-butylaniline (MBBA) and 40% of p-ethoxybenzylidene-p-n-butylaniline (EBBA), and doped with a small amount of a dichroic dye. The temperature dependence of the polarized components of optical density D_j of the dye absorption band for the nematic and isotropic phases of the MBBA+EBBA mixture has been obtained using polarization optic techniques. The temperature-induced structural changes in the nematic layer near T_c were found to be related to the changes in the orientational part of the tensor order parameter Q_ik. The experimental data have been interpreted using the model, in which the dispersive van der Waals forces of the substrate stabilize the planar orientation of the nematic in the bulk competing with the short-range anchoring forces in the vicinity of T_c. At the same time, the anisotropic part of the surface energy has two terms with the orthogonal easy axes. The nature of the surface electric field and its effect on the director alignment at the interface have been clarified. Taking into account the known relation between anchoring strength and the nematic order parameter, the effective anchoring energy w_eff for the studied system has been determined as a function of temperature.     

Calculation of the dielectric and Kerr constant angular correlation parameters

The angular correlation parameters G _L involved in the dielectric and Kerr constants are written as averages over the angular pair correlation function. A perturbation theory for these parameters is developed, based on the expansion of Gubbins and Gray for the angular pair correlation function. Numerical calculations are presented showing the influence of polar and quadrupolar forces on these parameters.