Smectic Order Parameter Research Articles

Formation of smectic phases in binary liquid crystal mixtures with a huge length ratio

A system of two liquid-crystalline phenylpyrimidines differing strongly in molecular length was studied. The phase diagram of these two chemically similar mesogens, with a length ratio of 2, was investigated, and detailed X-ray diffraction and electrooptical measurements were performed. The phase diagram revealed a destabilization of the nematic phase, which is present in the pure short compound, while the smectic state was stabilized. The short compound forms smectic A and smectic C phases, whereas the longer compound forms a broad smectic C phase and a narrow higher-ordered smectic phase. Nevertheless, in the mixtures, the smectic C phase is destabilized and disappears rapidly, whereas smectic A is the only stable phase observed over a broad concentration range. In addition, the smectic translational order parameters as well as the tilt angles of the mixtures are reduced. The higher-ordered smectic phase of the longer mesogen was identified as a smectic F phase.

Rigid probe solutes in a smectic-Aliquid crystal: An unconventional route to the latter's positional order parameters

Biphenylene and pyrene were dissolved in the nematic and smectic-A phases of the liquid crystal 4,4'-di-n-heptyl-azoxybenzene and the orientational order parameters of both solutes and solvent measured via proton and deuteron nuclear-magnetic-resonance spectroscopy. This new data set was then merged with the one previously obtained, formed by 4,4'-di-chloro-benzene and naphthalene as solutes in the same solvent, and the resulting overall data set analyzed with a statistical thermodynamic density-functional theory to provide positional-orientational distribution functions of the various solutes along with the smectic solvent's positional order parameters.

Molecular theory of smectic ordering in liquid crystals with nanoscale segregation of different molecular fragments

A molecular statistical theory of the smectic A phase is developed taking into account specific interactions between different molecular fragments which enables one to describe different microscopic scenario of the transition into the smectic phase. The effects of nanoscale segregation are described using molecular models with different combinations of attractive and repulsive sites. These models have been used to calculate numerically coefficients in the mean filed potential as functions of molecular model parameters and the period of the smectic structure. The same coefficients are calculated also for a conventional smectic with standard Gay-Berne interaction potential which does not promote the segregation. The free energy is minimized numerically to calculate the order parameters of the smectic A phases and to study the nature of the smectic transition in both systems. It has been found that in conventional materials the smectic order can be stabilized only when the orientational order is sufficiently high, In contrast, in materials with nanosegregation the smectic order develops mainly in the form of the orientational-translational wave while the nematic order parameter remains relatively small. Microscopic mechanisms of smectic ordering in both systems are discussed in detail, and the results for smectic order parameters are compared with experimental data for materials of various molecular structure.

Separation of nematic and smectic-A potential effects on solute ordering in a series of binary 6OCB–8OCB mixtures

1H NMR and optical microscopy have been used to study four solutes dissolved in samples of a binary mixture of 4-n-hexyloxy-4′-cyanobiphenyl (6OCB) and 4-n-octyloxy-4′-cyanobiphenyl (8OCB) that are close to the region of the phase diagram where the smectic-A (SmA) and re-entrant nematic (RN) phases exist. Optical microscopy clearly indicates that one of the four studied samples shows the phase sequence of isotropic–nematic–SmA–RN. The derived solute order parameters were interpreted by means of two Maier–Saupe mechanisms in conjunction with the Kobayashi–McMillan theory in the case of the SmA phase. The novel feature of this study is that the nematic potential is extrapolated from the nematic to the SmA phase based on concentrations of the 6OCB–8OCB mixtures. The derived smectic order parameters for each of the studied solutes clearly show a maximum absolute magnitude near the centre of the SmA temperature range. The different partitioning of these solutes in the binary mixture is also discussed.

The SmA phase of a bent-core V-shaped compound: structure and electric-field response

The smectic A (SmA) phase of a V-shaped mesogen with a molecular bending angle of 60° was studied. According to X-ray measurements, the molecules are arranged with the ‘bow-string’ direction parallel to the smectic layer. This point was confirmed by birefringence analysis and the result is compatible with a non-polar structure. A detailed study of the (001) smectic layer reflection versus temperature was also carried out to determine the smectic translational order parameter. The results indicate that the material presents a high degree of translational order. In addition, the electric field response of the material was studied by means of second harmonic generation. This technique turned out to be highly sensitive to small structural distortions due to the V-shape of the constituent molecules.

Modeling and Understanding Smectic-Phase Formation in Binary Mixtures of Rodlike Polysilanes: Comparison of Onsager Theory and Experiment

We study a binary mixture of short and long parallel hard rods in the smectic A phase to understand the role of length ratio (weight ratio) in the formation of three different types of ordering which were observed in binary mixtures of helical polysilanes. Using Onsager’s second virial theory of parallel hard rods, and modeling the short and long polymers as hard cylinders of different lengths (L1 ≠ L2) and same diameters (D), we show that the normal smectic A phase (S1) forms for length ratios (l = L2/L1) between 0.58 and 1, the microsegregated smectic structure (S2) takes place for 0.32 < l < 0.56 and 0 < l < 0.39 in short-rod-rich and long-rod-rich phases, respectively, and the two-in-one ordering (S3) is stable only in mixtures rich in long rods for 0.33 < l < 0.58. These results are in very good agreement with the available experimental data of binary mixtures of polysilanes [Okoshi et al. Macromolecules 2009, 42, 3443]. In addition, the theory predicts the existence of a partially microsegregated smectic structure (S4), in long-rod-rich mixtures, for 0.3 < l < 0.39. Our theoretical results show that two or even three smectic order parameters should be measured, for all types of smectic phases, in order to obtain the correct positional distribution functions from the X-ray diffraction pattern.

The smectic effect on solute order parameters rationalized by double Maier–Saupe Kobayashi–McMillan theory

From the dipolar couplings obtained by NMR spectroscopy we have calculated the order parameters of a wide variety of solutes in the nematic and smectic A phases of the liquid crystals 8CB and 8OCB. These measurements are then rationalized with the previously tested two Maier-Saupe Kobayashi-McMillan interaction potential from which smectic order parameters are calculated.

Solute order parameters in liquid crystals from NMR spectra solved with evolutionary algorithms: Application of double Maier–Saupe Kobayashi–McMillan theory

We obtain dipolar couplings via a novel application of evolutionary algorithms solving for multiple spin-systems simultaneously and automatically from the NMR spectra of several solutes in several nematic and smectic liquid crystal solvents. The order parameters obtained from the dipolar couplings are used to test a novel Hamiltonian that includes two Maier–Saupe nematic terms plus Kobayashi–McMillan smectic A terms. It is shown that this Hamiltonian can rationalize the NMR experiments with physically reasonable smectic order parameters and Hamiltonian prefactors.

Simple experimental assessment of smectic translational order parameters

A procedure to obtain the smectic translational order parameter Sigma from the temperature-dependent intensity I of the fundamental (001) smectic layer peak, observed in small-angle x-ray scattering experiments, is presented. We report results obtained with this procedure on the smectic-A or chiral smectic-A phases of six different liquid crystals, among them a "de Vries"-type 2-{4'-[1'',1''-dihydro-2''-(2''-perfluorobutoxyperfluoroethoxy)- perfluoroethoxy]}phenyl-5'-octylpyrimidine(3M8422) and the antiferroelectric R-4-(1-methylheptyloxycarbonyl)phenyl-4'-octloxybiphenyl-4-carboxylate (MHPOBC) materials. The smectic order parameters obtained are in the range between 0.5 and 0.9. For the "de Vries"-type 3M 8422 we found remarkably high values of Sigma in the order of approximately 0.9.

Pretransitional anomalies in the orientational dynamics induced by temperature gradient in nematic hybrid-oriented cells

We have carried out a numerical study of the system of hydrodynamic equations including director reorientation, fluid flow, and temperature redistribution across a hybrid-oriented liquid crystal cell (HOLCC), where the nematic sample is confined by two parallel horizontal surfaces, a temperature gradient is applied and directed normal to the boundaries, and the temperature on the lower cooler boundary is reduced towards T(NA). Calculations show that the temperature gradient causes the investigated system to settle down to a stationary flow regime in the horizontal direction. Presmectic anomalies in the vicinity of the lower boundary have been investigated as well, taking into account the fluctuations of the local smectic order parameter above T(NA). It has been shown that these fluctuations influence both magnitude and direction of the hydrodynamic flow, produced by the temperature gradient. We have also investigated the role of hydrodynamic flow in the resulting relaxation processes, for a number of dynamic regimes in a HOLCC containing 4-cyano-4'-octylbiphenyl.

Presmectic wetting and supercritical-like phase behavior of octylcyanobiphenyl liquid crystal confined to controlled-pore glass matrices

The influence of controlled-pore glass (CPG) confinement on the phase behavior of octylcyanobiphenyl liquid crystal (LC) is studied by means of x-ray scattering and high precision calorimetry. For CPG samples with pore diameter 2R>24 nm, the smectic order parameter temperature dependence eta(T) reveals apparent presmectic ordering far above the bulk smectic A-nematic (SmA-N) phase transition for both nontreated and silane-treated CPG matrices. The behavior of eta(T) is qualitatively similar in all samples, well obeying the mean field approach (MFA) in which the surface wetting tendency plays the dominant role. In contrast, the critical fluctuations remain important in the specific heat data, which cannot be described within the MFA. We show experimentally that randomness and surface wetting become dominant over finite-size effects for 2R approximately<10 nm, in agreement with theoretical analysis. In nontreated samples, the noncritical character of the static disorder and the interfacial LC-CPG coupling almost completely suppress the quasi-SmA-N and nematic-isotropic phase transitions at 2R approximately 15.1 and approximately 7.5 nm, respectively.

Landau–de Gennes theory of isotropic-nematic-smectic liquid crystal transitions

We propose a Landau-de Gennes variational theory fit to simultaneously describe isotropic, nematic, smectic- A , and smectic- C phases of a liquid crystal. The unified description allows us to deal with systems in which one, or all, of the order parameters develop because of the influence of defects, external fields and/or boundary conditions. We derive the complete phase diagram of the system, that is, we characterize how the homogeneous minimizers depend on the value of the constitutive parameters. The coupling between the nematic order tensor and the complex smectic order parameter generates an elastic potential which is a nonconvex function of the gradient of the smectic order parameter. This lack of convexity yields in turn a loss of regularity of the free-energy minimizers. We then consider the effect on an infinitesimal second-order regularization term in the free-energy functional, which fixes the optimal number of defects in the singular configurations.

The smectic potential in a liquid crystal with a reentrant nematic phase: NMR of solutes

We test the application of Kobayashi–McMillan theory for the solutes ortho-, meta- and para-dichlorobenzene in a binary mixture of 6OCB/8OCB in which both high temperature nematic and low temperature reentrant nematic phases exist. Proton NMR spectra of these solutes are analyzed to give two independent order parameters from which the solute smectic potential can be parametrized. The derived smectic order parameters for the solutes in this binary mixture are discussed and compared with those previously found in pure 8OCB solvent.

Critical behaviour at the isotropic–nematic and nematic–smectic A phase transitions of 4‐butyloxyphenyl 4′‐decyloxybenzoate liquid crystal from refractive index data

We present new high‐resolution experimental data on the temperature dependence of the refractive index in the isotropic (I), nematic (N) and smectic A (SmA) phases of the 4‐butyloxyphenyl 4′‐decyloxybenzoate () liquid crystal. From an analysis of the data, using both the Vuks and Neugebauer models for the internal electric field, information on the orientational order parameter S(T) was derived. From a fitting procedure consistent with mean‐field theory and the first‐order character of the N–I transition, we obtain a value of 0.246±0.06 for the exponent β describing the critical behaviour of S(T) at the N–I transition, which is in good agreement with the tricritical value β = 0.25. In a temperature range of about 4 K above and below the N–SmA transition temperature, pre‐transitional evidence for the coupling between the nematic and smectic order parameters was observed. We show, for the first time, that the temperature derivative of the S(T) curve below and above the N–SmA transition has the same power law behaviour as the specific heat capacity with an effective critical exponent of 0.23±0.01.

Surface ordering at the air–nematic interface. Part 1. A neutron reflection study of translational order

Neutron reflection was used to measure the build‐up of layers at the air surface as the smectic phase was approached from higher temperatures in a nematic liquid crystal. The liquid crystal was 4‐octyl‐4′‐cyanobiphenyl with a deuterated core and hydrogenous tails. The development of surface smectic layers in the nematic phase was followed by measuring specular reflectivity and monitoring the pseudo‐Bragg peak from the layers. The pseudo‐Bragg peak therefore corresponded to the formation of long‐range smectic layers at the surface as the transition temperature is approached. The results were consistent with the continuous growth of smectic layers at the surface and the amplitude of the smectic density wave decayed with increasing distance from the surface. The depth over which the smectic layering occurred at the interface was found to be ∼450 Å at a quarter of a degree above the nematic to smectic A bulk transition. The smectic order parameter at the surface was ∼0.1 which is much less that found for typical homeotropic alignment agents.

Tricritical point induced by smectic ordering of a nematic gel

The authors study volume phase transitions of a nematic gel immersed in a liquid crystal (LC) solvent, which shows a second-order nematic-smectic A phase transition (NST). Combining Flory's elastic energy [Principles of Polymer Chemistry (Cornell University Press, Ithaca, 1953)] for a swelling of the gel with the McMillan model [Phys. Rev. A 4, 1238 (1971)] for smectic ordering, the authors calculate the equilibrium swelling of the gel and smectic order parameters as a function of temperature. The authors take into account an attractive interaction parameter c between the gel and LC solvents. On increasing the value of the coupling constant c, a second-order NST of the gel is changed to a first-order one and a continuous volume phase transition of the gel is changed to a discontinuous one. The authors find a tricritical point of the gel induced by smectic ordering.

Smectic order parameters from diffusion data

Microcanonical molecular dynamics simulations have been performed in the smectic A phase of an elementary liquid-crystal model. Smectic order parameters and diffusion coefficients along directions parallel and perpendicular to the director have been calculated during the same trajectory for a number of state points. This has permitted the satisfactory testing of a procedure, adopted in the analysis of experimental self-diffusion coefficients, leading to an estimate of the temperature dependence of the smectic order parameters. This methodology has been then confidently applied to two smectogenic thermotropic liquid crystals belonging to the 4,4(')-di-n-alkyl-azoxybenzene series. The derived smectic order parameters are larger for the homologue compound with the longest alkyl chains. This is consistent with the well-established increased tendency, for members of a homologue series, to form a smectic phase as their alkyl chains become longer.

Anisotropic translational diffusion in the nematic phase: Dynamical signature of the coupling between orientational and translational order in the energy landscape

We find in a model system of thermotropic liquid crystals that the translational diffusion coefficient parallel to the director D(parallel) first increases and then decreases as temperature drops through the nematic phase, and this reversal occurs where the smectic order parameter of the underlying inherent structures becomes significant. We argue, based on an energy landscape analysis, that the coupling between orientational and translational order can play a role in inducing the nonmonotonic temperature behavior of D(parallel). Such a view is likely to form the foundation of a theoretical framework to explain the anisotropic translation diffusion.

Two-dimensional chiral model for liquid crystals, bent hard needles: A Monte Carlo simulation

The liquid crystalline behavior of a two dimensional (2D) model of hard needles bent into a "zigzag shape" is studied. This model, originally designed to study two dimensional chiral segregation, also shows liquid crystalline behavior and has some anomalous features which are contrasted in relation to the following: (i) Most of the microscopical models used to study liquid crystals have a symmetry axis that coincides with a molecular axis; (ii) in three-dimensions, chiral molecules can form cholesteric instead of nematic phases; (iii) the smectic phase is usually found when attractions are present or at least when the molecules have finite volume. Despite the fact that the present 2D model does not have any of these characteristics, numerical evidence is found for the occurrence of nematic and smectic phases. Since these molecules are athermal, infinitely repulsive, and infinitesimally thin, the liquid crystalline characteristics are attributed to excluded volume effects. To determine the mesophases of the model, both nematic and smectic order parameters as well as distribution functions are computed.

Smectic order induced at homeotropically aligned nematic surfaces: A neutron reflection study

Neutron reflection was used to measure the buildup of layers at a solid surface as the smectic phase is approached from higher temperatures in a nematic liquid crystal. The liquid crystal was 4-octyl-4'-cyanobiphenyl (8CB), and the solid was silicon with one of five different surface treatments that induce homeotropic alignment: (i) silicon oxide; (ii) a cetyltrimethylammonium bromide coating; (iii) an octadecyltrichlorosilane monolayer; (iv) an n-n-dimethyl-n-octadecyl-3- aminopropyltrimethyloxysilyl chloride monolayer; and (v) a lecithin coating. The development of surface smectic layers in the nematic phase of 8CB was followed by measuring specular reflectivity and monitoring the pseudo-Bragg peak from the layers. The scattering data were processed to remove the scattering from short-ranged smecticlike fluctuations in the bulk nematic phase from the specular reflection. The pseudo-Bragg peak at scattering vector Q approximately 0.2 A(-1) therefore corresponded to the formation of long-range smectic layers at the surface. The amplitude of the smectic density wave decayed with increasing distance from the surface, and the characteristic thickness of this smectic region diverged as the transition temperature was approached. It was found that the characteristic thickness for some of the surface treatments was greater than the correlation length in the bulk nematic. The different surfaces gave different values of the smectic order parameter at the surface. This suggests that the interaction with the surface is significantly different from a "hard wall" which would give the same values of the smectic order parameter and penetration depths similar to the bulk correlation length. Comparison of the different surfaces also suggested that the strength and range of the surface smectic ordering may be varied independently.