Influence of pressure on the electric-field-induced phase transitions in liquid crystals

Within the framework of Landau-de-Gennes formulation, we analyse the effect of pressure on electric-field-induced phase transitions in a liquid crystal which shows spontaneously an isotropic-smectic A transition. Inferring from the experimental pressure dependences on the layer spacing in smectic A phase, as well as the nematic-smectic A metastable temperature T^*_AN, we incorporated the pressure dependence in the free energy through (the surface energy term) and the coupling between the quadrupolar nematic ordering Q_ij and the smectic order parameter ψ. From the S-T phase diagram, we found that the stability of field-induced nematic phase increases with pressure, whereas the discontinuity of the transition decreases. Also, the region where paranematic phase transits directly to smectic A phase increases with pressure.     

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     

A molecular theory of smectic C liquid crystals made of rod-like molecules

Organic compounds exhibiting the smectic C phase are made of rod-like molecules that have dipolar groups with lateral components. We argue that the off-axis character of the lateral dipolar groups can account for tilt in layered smectics (SmC, SmC*, SmI etc.). We develop a mean-field theory of the smectic C phase based on a single-particle potential of the form U _C ∝ sin(2θ)cosφ, consistent with the biaxial nature of the phase, where θ and φ are the polar and azimuthal angles, respectively. The hard-rod interactions that favour the smectic A phase with zero tilt angle are also included. The theoretical phase diagrams compare favourably with experimental trends. Our theory also leads to the following results: i) a first-order smectic C to smectic A transition above some value of the McMillan parameter α, leading to a tricritical point on the smectic C to smectic A transition line and ii) a first-order smectic C to smectic C transition over a very small range of values of the model parameters. We have also extended the theory to include the next higher-order term in the tilting potential and to include the effect of different tilt angles for the molecular core and the chain in the SmC phase. Received 3 August 2002 RID="a" ID="a"Present address: Department of Physics, Vijaya College, R. V. Road, Bangalore - 560 004, India. RID="b" ID="b"e-mail: nvmadhu@rri.res.in     

Field-induced realignment of a smectic nanodroplet in an external magnetic field: A numerical investigation

The field-induced realignment of a smectic-A phase is in principle a complicated process involving the director rotation via the interaction with the field and the layer rotation via the molecular interactions. Time-resolved X-ray scattering experiments have revealed major phenomena concerning the maintenance of the integrity of the smectic-A layer structure during the alignment process. In order to obtain a deeper insight into this process, we have carried out a dissipative particle dynamics study of the realignment kinetics of a nanodroplet of a smectic-A liquid crystal suspended in an isotropic fluid following a switch in the direction of an applied magnetic field. The strength of the mesogen-field interaction is small compared to the inter-molecular interactions. The reaction of the smectic configuration to the field switch was found to depend on the balance between the inter-molecular interactions stabilising the formation of the smectic layering and the interaction of the mesogens with the external field. It is found that the rotational behaviour of the smectic layers under the influence of an external magnetic field arises from a combination of stochastic translational displacements and rotational motions of the centres of mass of the mesogens in the nanodroplets. The simulations indicate that X-ray scattering and NMR experiments monitoring the orientational order are sensitive to different aspects of the realignment process.     

Effect of aerosil dispersions on the nematic-to-isotropic interface

The effect of silica aerosils on the kinetics of the first-order nematic-isotropic (NI) phase transition is phenomenologically described in the framework of the time-dependent Landau-Ginzburg equation. A steady-state solution to the equation is presented such that the NI interface may propagate with a solitary-like wave profile under constant quenching. The results provide a plausible basis for the interpretation of the dynamical effects of quenched disorder in the liquid-crystal systems, caused by randomly interconnected porous media, such as aerosils. In the low silica aerosil ρ_s ( ≤0.1 g/cm^3) regime, the calculated values of the interface velocity v(T,ρ_s), the interface thickness κ(T,ρ_s), and the critical radius of a spherical nucleus of new nematic phase in a bulk isotropic environment, composed of polar molecules, such as 4-n-octyl- 4^′- cyanobiphenyl and 4-n-heptyl- 4^′- cyanobiphenyl shows that the effect of silica aerosils on the kinetics is reflected in a shifting of the set of temperature-dependent curves to lower temperature values.-1     

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.     

First order phase change during isotropic-nematic and nematic-smectic a transitions of NPOB

The temperature variation of the magnetic susceptibility (χ) of NPOB are reported in isotropic, nematic and smectic A phases, χ and Δχ undergo sudden changes at the phase transitions. The isotropic-nematic and nematic-smectic A transitions are assigned to be first order phase transition.     

Energetics of 2D colloids in free-standing smectic-C films

The formation of regular colloid patterns in free-standing smectic films at the transition from the smectic-C to the isotropic or nematic phase is well known experimentally. The self-organization of isotropic or nematic droplets is caused by their mutual interaction, mediated by elastic distortions of the local director in the surrounding liquid crystal. These distortions are related to the anchoring conditions of the director at the droplet border. We describe analytically the energetics of the liquid crystal environment of a single droplet in one-constant approximation. A method of complex analysis, Conformal Mapping, is employed. Following a suggestion of Dolganov et al. (Phys. Rev. E. 73, 041706 (2006)), energetics of chain and grid patterns built from the colloids are investigated numerically in order to explain experimentally observed formations and their director fields.     

Stability of the director profile of a nematic liquid crystal around a spherical particle under an external field

We study numerically the effect of an external magnetic or electric field on the director profiles of a nematic liquid crystal around a spherical particle. We pay particular attention to the stability of a hyperbolic hedgehog defect accompanying the particle, which transforms into a Saturn-ring defect encircling the particle under a sufficiently strong external field. We focus on the particle size dependence of the two important threshold field strengths: the “thermodynamic-transition” field strength H₁ at which the hedgehog and the Saturn-ring configurations have the equal free energy, and the critical field strength H₂ at which the hedgehog loses its (meta)stability. Our numerical results demonstrate that while H₁ is non-monotonically dependent on the particle radius R₀, H₂ monotonically increases with R₀ and the dependence of H₂ is weak for large R₀. The non-monotonic dependence of H₁ on R₀ can be explained by comparing the energies of the two configurations and assuming the dependence of those energies on a rescaled field. A crude argument of the energetics of a hyperbolic hedgehog defect under an external field shows that for an asymptotically large R₀ the critical field strength is independent of R₀, which agrees with our numerical finding.     

Molecular-statistical approach to a behavior of ferroelectric,antiferroelectric and ferrielectric smectic phases in the electric field

The fundamental theoretical approach derived in A.V. Emelyanenko et al., Phys. Rev. E 74, 011705 (2006) is complemented by a consideration of the influence of the homogeneous electric field on Sm- C _A ^* , biaxial intermediate phases, and Sm-C ^* . The crucial role of the induced polarization is investigated for the first time. The evolution of any tilted smectic phase in the electric field is found to meet the two thresholds. The first threshold corresponds to the unwinding process, and the second one corresponds to the phase transition into the bi-domain structure of Sm-C ^* , where the tilt plane has some contribution either along or against the electric field, while the average direction may still be perpendicular to the electric field. The tilt plane in the monodomain (conventional) structure preceding the second threshold is the same in every unwound phase, and is perpendicular to the electric field. No 3D distortion in Sm- C _A ^* is predicted on application of the electric field. The entire electric-field-temperature phase diagrams including the possibility of existence of the maximal number of tilted smectic phases are plotted and compared with the experimental ones. The numerical calculations in the framework of this fundamental study are done with help of AFLC Phase Diagram Plotter software developed by the author and available at his web page.     

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     

Tilted smectic layers of a liquid crystal between homeotropically treated plates

We investigated SmC^* films sandwiched between silane coated glass plates and observed formation of textures exhibiting a uniform tilt of the smectic layers with respect to the boundary plates. The layer tilt angle increases from zero to as the sample is cooled from the smectic A phase to room temperature. These films show linear electro-optical effects because the permanent polarization can be aligned so that it has a component parallel to the applied field without changing the layer structure. Our analysis indicates that mainly two effects determine the layer tilt. On the one hand, the surface tension tends to minimise the layer tilt. On the other hand, the surface energy promotes the director to be normal to the boundary plates. Received 17 July 1998     

Induced ferrielectricity in antiferroelectric liquid crystals

The behaviour of the antiferroelectric SmC_A liquid crystal phase under applied electric field is discussed theoretically. The phase diagram involving the SmA, SmC_A and SmC _A ^* phases is worked out and shown to exhibit a Lifshitz critical point. The deformation of the bilayer structures induced by the field transforms the SmC_A phases into a ferrielectric phase whose specific configuration is described. Received: 23 October 1997 / Revised: 8 April 1998 / Accepted: 14 July 1998     

Pressure variation of reentrant transition temperature in liquid crystals

High pressure experimental studies show that in certain mesogenic materials, the nematic-smectic A (N-Sm A) transition temperature T_AN exhibits nonlinear pressure dependence. As a consequence, the material shows reentrant phenomena that is a phase sequence nematic — smectic A — reentrant nematic appears. The characteristic features of this phenomenon have been addressed here within the framework of Landau-de-Gennes theory, where the coupling between nematic and smectic A order parameters (γ, λ_eff) plays an important role. The cubic coupling γ is chosen to be negative in order to form Sm A phase whereas the biquadratic coupling λ_eff is made large and positive to obtain reentrant behaviour. In the present work, we incorporate the pressure dependence in the theory through γ and λ_eff which justifies the experimental pressure dependence in the reentrant transition temperature . The pressure dependence of γ and λ_eff are employed in the calculation of excess specific heat capacity near the reentrant transition. The computed heat capacity shows strong pressure dependence near the reentrant transition which can be confirmed from high pressure measurement.     

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.     

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     

Density studies across the smectic G-nematic and nematic-lsotropic transitions

The densities of N(p-n-pentyloxy benzylidene) p-ethylaniline and N(p-n-hexyloxy benzylidene) p-ethylaniline are measured as a function of temperature from the isotropic liquid to the smectic G phase. Both the compounds exhibit enantiotropic smectic G and nematic liquid crystalline phases. The changes in density across the phase transformations and the thermal expansion coefficient confirm the order of the transitions as of first order. The particular importance of the smectic G to nematic transformation is apparent from the density jump across the transition. An estimate of the pressure dependence of the isotropic-nematic transition temperature is found to be in reasonable accord with the literature data.     

Universal non-monotonic smectic fluctuations of liquid crystal films in a magnetic field

Free-standing liquid crystal films with positive diamagnetic susceptibility can have the smectic ordering enhanced by an external field applied perpendicular to the plane layers. Within a quadratic functional integral approach, we investigate the interplay between the smectic order induced by an external field H and that due to the surface tension γ between the film and the surrounding gas. We find that the average smectic fluctuation is a non-monotonic function of film thickness, with a characteristic thickness scale ξ _H delimiting the predominance of surface tension and magnetic field effects. This characteristic thickness obeys simple asymptotic power-law relations as a function of the ordering terms which allows us to represent the average smectic fluctuations in a universal scaling form. Received 7 January 2003 Published online 1st April 2003 RID="a" ID="a"e-mail: marcelo@ising.fis.ufal.br     

Smectic-A edge dislocations in a very thin cell

We study stable “bookshelf” smectic-A structures within a very thin plane-parallel cell of thickness L in which the mismatch between surface preferred (d _s) and intrinsic (d₀) smectic layer thicknesses occurs. The Landau-Ginzburg approach based on a complex smectic order parameter is used. For a weak enough smectic positional anchoring strength W smectic layers adopt the modified bookshelf profile. In a thick enough cell with increasing W a lattice of edge dislocations is continuously formed at the confining surfaces and then depinned from them. The structure with dislocations is formed when the condition d ₀/( d ₀/d _s - 1) ∼ 2 is fulfilled, where is the positional surface anchoring extrapolation length. If the cell is thin enough the dislocations formed at opposite cell plates annihilate and consequently the smectic layers adopt a locked bookshelf structure. This transition is discontinuous and takes place when d ₀/(L d ₀/d _s - 1) ∼ 5 is realized. To observe these transitions in a cell of thickness L∼ 1μm the conditions W∼ 10^-6 J/m ² and d ₀/d _s - 1∼ 5 ^. 10^-4 have to be fulfilled. All the three qualitatively different structures coexist at the triple point. Received 21 February 2002     

A dissipative particle dynamics study of the realignment of a nanodroplet of a nematic in a weak external magnetic field

We present a dissipative particle dynamics (DPD) approach for simulating the realignment of a nematic nanodroplet suspended in an isotropic fluid following a switch in the direction of an applied external magnetic field. The interaction of the mesogens with the external field is weak relative to the inter-molecular interactions. The simulations were used to investigate the way orientational equilibrium is re-established. The results reveal that the realignment process of the nanodroplet is consistent with its fluid structure. The reorientation of the nanodroplet as a whole is found to be caused by an internal structural rearrangement rather than a coherent rotation of the centres of mass of the mesogens about the centre of the nanodroplet. The switch in the field direction furthermore is found to induce a transient spatial variation in the orientational order of the long axes of the mesogens: the orientational order parameters decreases on moving from the core of the nanodroplet to the surface in contact with the isotropic environment. The results highlight differences between the time evolution of the orientation of the long molecular axes in the field and the rotations of the centres of mass of the mesogens about the centre of the nanodroplet.