Isotropic-nematic Research Articles

Phase equilibria in systems of hard disks with thickness polydispersity.

We study isotropic-nematic (I-N) phase equilibria in the Onsager (-Parsons) model for systems of hard colloidal disks allowing for arbitrary polydispersity in thickness. The phase behavior is investigated by analyzing the exact phase equilibrium equations for Gaussian orientational distribution functions. We observe a strong fractionation effect, with the thicker disks found preferentially in the isotropic phase. Due to this effect, the system may undergo an I-N density inversion indicating that the mass density of the isotropic phase becomes higher than that of the coexisting nematic phase. This phenomenon has been observed explicitly in experiment. We also encounter a divergence of the I-N coexistence region for Schulz-distributed parents with polydispersities larger than 46%. An implication of this phenomenon is that the system cannot become fully nematic at high densities but will continue to split off a small fraction of a dilute isotropic phase predominantly containing very thick species.

Side Chain Polymer Liquid Crystals in High Magnetic Fields

We report an optical study of Side Chain Polymer Liquid Crystals (SCPLCs) in magnetic fields up to 20T. A novel sensitive set-up, which allows simultaneous birefringence and static light scattering measurements, was used to study polynorborene and polyacrylate based SCPLCs. We find that only magnetic fields bigger than a threshold value B min are able to induce orientation effects and this only at the crossing of the Isotropic-Nematic (IN) transition when cooling from the melt. The existence of a minimum field B min proves to be general, while its value is strongly dependent on the polymeric backbone elasticity, polymerization degree and spacer length. We have produced bulk and thin film aligned samples, stable at room temperature, characterized by an optical uniaxial anisotropy, with a director order parameter S D ∼0.9999.

Isotropic−Nematic Density Inversion in a Binary Mixture of Thin and Thick Hard Platelets

We study the phase behavior of a binary mixture of thin and thick hard platelets, using Onsager’s second virial theory for binary mixtures in the Gaussian approximation. Higher virial terms are included by rescaling the excluded volume part of the Onsager free energy using a modified form of the Carnahan-Starling free energy for hard spheres (Parsons’ approach). Our calculations provide a simple explanation for the isotropicnematic (I-N) density inversion, as experimentally observed in systems of polydisperse gibbsite platelets by Van der Kooij et al. (J. Phys. Chem. B 2001, 105, 1696). In these systems, a nematic upper phase was found to coexist with an isotropic bottom phase. We confirm the original conjecture of the authors, which states that the phenomenon originates from a pronounced fractionation in thickness between the phases, such that the thick platelets are largely expelled from the nematic phase and preferentially occupy the isotropic phase. Our calculations show that the inverted state is found in a major part of the I-N coexistence region. In addition, a nematic-nematic demixing transition is located at sufficiently high osmotic pressures for any thickness ratio L2/L1 > 1. The N-N coexistence region is bounded by a lower critical point which shifts toward lower values as the thickness ratio is increased. At high thickness ratios (L2/L1 > 3.3), a triphasic coexistence is found at which two nematic phases coexist with an isotropic phase. We show that the demixing transition is driven by a small Φ(L/D) contribution to the excluded volume entropy.

Small quartz silica spheres induced disorder in octylcyanobiphenyl (8CB) liquid crystals: a thermal study.

A photopyroelectric technique has been applied to the study of specific heat and thermal conductivity of homeotropically aligned mixtures of small quartz spheres (aerosil) and octylcyanobiphenyl (8CB) with concentration 0</=rho(s)</=0.04 g/cm(3). Thermal conductivity data show that, even at these very low concentrations, an annealing of the disorder introduced by the aerosil takes place on cooling at the smectic-A-nematic (Sm-A-N) phase transition and not only at the nematic-isotropic (N-I) one. This means that there is some elastic strain in the nematic phase of the sample which is not quenched. Accordingly the suppression of the N-I transition temperature as a function of rho(s) does not fit a random field with a random dilution model that accounts for random quenched disorder only. High resolution specific heat measurements at the A-N and N-I transition show the effect of the aerosil is not the same. While in the first case its peak is suppressed with increasing concentration, in the second case there are some indications that outside the two-phase coexistence region it is enhanced. The effect of surface-induced alignment is also discussed to explain some discrepancies between our data and the ones reported in literature. It is concluded that the amount of disorder in the sample does not depend on rho(s) only, but also on other variables such as external fields. Finally, a relaxation phenomenon in the aerosil network that partially compensate the disordering effect of the particles is suggested to explain the concentration dependence of the transition temperatures.

Phase transitions from THE isotropic liquid to liquid crystalline mesophases studied by linear and nonlinear static dielectric permittivity

Results of studies of static dielectric permittivity (epsilon) and nonlinear dielectric effect (NDE) in the isotropic phase of 4-n-4'-isothiocyanatobiphenyl (nBT) homologous series from n = 2 to n = 10 exhibiting the isotropic-smectic E (I-SmE) transition, are presented. They are compared with results of similar studies in 4-cyano-4-n-alkylbiphenyls (nCB) from n = 4 to n = 12. In this homologous series isotropic-nematic (I-N) and isotropic-smectic-A (I-Sm-A) transitions take place. Despite significant differences between N, Sm-A, and Sm-E phases the same pretransitional behavior of epsilon and NDE in the isotropic phase, described by critical exponents gamma = 1 and alpha = 0.5, was found. It has been shown that when the length of the alkyl chain of a compound increases the discontinuity of the transition drops in nBT and rises in nCB. The influence of pressure on the discontinuity is also discussed.

Effects of fluctuations in the orientational order parameter in the cyanobiphenyl (nCB) homologous series

Photopyroelectric measurements of the anisotropy in the thermal conductivity Deltak vs temperature in the nCB (n=5,ellipsis,9) series are reported. The data have been used to deduce the behavior of the orientational order parameter Q close to the nematic-isotropic (N-I) and smectic A-nematic (A-N) phase transitions, respectively. It has been shown that near the N-I transition the data for 5CB and 6CB are consistent with the so-called "tricritical hypothesis," which predicts beta=0.25. This is not true for 7CB and 8CB in which the order parameter exhibits a behavior that could be caused by the presence of fluctuations that become increasingly important when the transition temperature is approached. A very simple model, which takes into account the contribution of fluctuations to the orientational order, has been developed close to the A-N transition and it has been shown that it is in good agreement with the experimental results. A semiquantitative explanation for the observed behavior in compounds with different nematic range has been also given.

Disorder effects in low concentration dispersions of small quartz spheres in cyanobiphenyl liquid crystals

A photopyroelectric study of the specific heat and the thermal conductivity of small quartz sphere (aerosil) dispersions in heptylcyanobiphenyl (7CB) and octylcyanobiphenyl (8CB) liquid crystals with a concentration rho(s)=0.005 g cm(-3) is reported. The thermal conductivity data show that, even at this low concentration, the elastic strain introduced in the liquid crystal by the aerosil particle is not completely annealed at the nematic-isotropic (NI) phase transition. In 8CB, annealing has been found at the smectic-nematic phase transition, while in the case of 7CB it occurs in the nematic phase also. Moreover, the depression of the NI transition temperature has been found to be much smaller than the one predicted by a random field model in which quenched disorder simply affects the average order of the sample and no effects of the elastic strain are considered.

Universality in the fast orientational relaxation near isotropic–nematic transition

Detailed molecular dynamics simulations of Lennard-Jones ellipsoids have been carried out to investigate the emergence of criticality in the single-particle orientational relaxation near the isotropic–nematic (IN) phase transition. The simulations show a sudden appearance of a power-law behavior in the decay of the second-rank orientational relaxation as the IN transition is approached. The simulated value of the power-law exponent is 0.56, which is larger than the mean-field value (0.5) but less than the observed value (0.63) and may be due to the finite size of the simulated system. The decay of the first-rank orientational time correlation function, on the other hand, is nearly exponential but its decay becomes very slow near the isotropic–nematic transition. The zero-frequency rotational friction, calculated from the simulated angular velocity correlation function, shows a marked increase near the IN transition.

Polymer Dispersed Liquid Crystals Based on Epoxy Networks: Transformations and Phase Separation Phenomena During Polycondensation

A diepoxy-diamine/liquid crystal mixture (50/50 wt%) is studied in the course of the crosslinking step-polymerization at different isothermal reaction temperatures or with a two temperature cure cycle. Depending on the reaction temperature, the systems undergoe phase separation either isothermally, when the reaction temperature is far below the nematic-isotropic (N-I) temperature of the neat LC, or on cooling partially reacted systems when the reaction temperature is above the N-I temperature of the neat LC. Phase separation is characterized simultaneously by two glass transition temperatures (Tg ), one nematic-isotropic transition (T N-1) and the appearance of nematic droplets as determined by differential scanning calorimetry (DSC) or polarized optical microscopy (POM). Thus, temperature-polymerization conversion phase diagrams are presented in the form of the evolution of Tg 's and of T N-1 of the LC-rich phase. Furthermore, we attempted to use the calorimetric data to calculate the mass fraction of the LC-rich phase and the mass fraction of separated LC. The gel point conversions of the epoxy-amine network are determined. For example, T N-1 of the LC phase markedly increases near the gel point during an isothermal crosslinking at 30°C. The observation of the PDLC samples confined between two glass plates showed that final morphology (at full conversion) depends strongly on the thermal cycles of crosslinking. Finally, for a cure at 100°C, in bulk samples, evidence is given for a macrosyneresis of the LC in the fully crosslinked network. However, this phenomenon occurs very slowly with time. This means that depending on the cure cycles, on the LC content and on the confinement of the LC, the resulting PDLC may be prepared in off equilibrium conditions.

Phase properties of nematics confined by competing walls

The consequences of confinement on the isotropic-nematic (IN) transition are investigated for a slab geometry with walls that compete in molecular alignment. We employ the Landau-de Gennes free energy with symmetrically opposing wall fields that favor random parallel and homeotropic orientations, respectively, at each wall, and describe the phase diagram with the use of the associated nonlinear dynamical-system phase portraits. The differences in phase behavior with respect to the bulk, or with the system confined by identical walls, are important: Depending on the wall separation L and the strength of the walls' field μ s , the IN transition is either unaffected and its temperature T IN remains fixed, or, the transition disappears altogether. We find: (i) when μ s < μ s w (where μ s w is the wall field value for the wetting transition of the semi-infinite system) the transition occurs for all wall separations, and (ii) when μ s > μ s w there is no transition for all wall separations above a given value L qw ( μ s ). The boundary L qw ( μ s ) between these two regions is identified as a shifted wetting transition in which IN phase coexistence is transformed into an interface-like state, and it is of the 1st order, tricritical and critical when μ s w < μ s < μ s tc , μ s = μ s tc and μ s > μ s tc , respectively. For temperatures in the neighborhood of T IN , L qw ( μ s ) is continued as a locus of shifted prewetting transitions. This behavior is equivalent, but manifests differently, to that already known for a magnetic slab under symmetrically opposing surface fields and vanishing surface coupling enhancement.

Rheo-Optical Evidence of a Flow-Induced Isotropic−Nematic Transition in a Thermotropic Liquid-Crystalline Polymer

A direct rheo-optical characterization of the flow-induced isotropic-nematic (I-N) transition in a semiflexible thermotropic liquid-crystalline polymer (TLCP) was investigated, using a specially constructed apparatus enabling in-situ optical microscopic observations at elevated temperatures, along with cone-and-plate rheometry. For the investigation, an aromatic polyester, poly((phenylenesulfonyl)- p-phenylene 1,10-decamethylenebis(4-oxybenzoate)) (PSHQ10), was synthesized via solution polymeri- zation. Above the equilibrium isotropic-nematic transition temperature for this polymer, T ) 170.5 °C, application of steady-state shear flow above a certain critical value of shear rate, A o c, produces a first- order I-N transition, with A o c increasing with temperature. This transition is evidenced by the formation of elongated nematic (birefringent) domains in the isotropic matrix, accompanied by a drastic decrease in shear viscosity ( ). Remarkably, the nematic domains that form for A o> A o care optically uniform under cross-polarized optical microscopy; i.e., they are apparently free of disclinations (defects), typical of textured TLCPs. The flow-induced I-N transition in PSHQ10 is found to be reversible; i.e., upon cessation of shear flow, the domains melt to the original isotropic phase and the dynamic moduli rise toward the pretransition values. The observed flow-induced I-N transition may find important applications, such as envisaging new routes for processing TLCPs with better mechanical properties and helping to understand bioprocesses such as silk thread spinning.

Nematic Isotropic Phase Transition: An Alternative Formulation

Nematic-Isotropic (N-I) phase transition is discussed in an alternative way by using Landau–de Gennes phenomenological theory. The temperature difference of T NI -T* is obtained near the tricritical point. We also obtained the value of the ratio (Q*-Q NI )/Q NI , where Q* is the order parameter at the temperature T* of the absolute stability limit of the isotropic phase and Q NI is the order parameter at the nematic-isotropic transition temperature T NI .

The isotropic–nematic phase transition in uniaxial hard ellipsoid fluids: Coexistence data and the approach to the Onsager limit

The isotropic–nematic (I-N) phase transition in hard ellipsoid fluids has been studied by computer simulation, using the Gibbs–Duhem integration technique introduced by Kofke; and theoretically, using Onsager theory and the Parsons–Lee improvement. In the simulations, the I-N coexistence line is mapped out in the P–x plane, where P is the pressure and x is the elongation, by numerically integrating a Clapeyron-like first-order differential equation, using constant-pressure simulation data for the two coexisting phases. The elongation range 5≤x≤20 has been studied, using independent starting points provided by chemical potential calculations and thermodynamic integration of the equation of state at x=5,20, plus a direct Gibbs ensemble simulation at x=20. The Onsager–Parsons–Lee theory has been applied to the I-N phase transition for aspect ratios up to x=1000, affording an accurate investigation of the approach to the Onsager limit for this model. This involved the numerical computation of the orientation-dependent second virial coefficient in a way that avoids expansions in Legendre polynomials, so as to be accurate at high elongation. Over the elongation range studied here, agreement between simulation and the Parsons–Lee theory is good.

Studies of nematic-isotropic transition for a Gay-Berne fluid using the second virial approximation

Abstract In this paper we use the second virial approximation to study the nematic-isotropic (N-I) transition for a Gay-Berne liquid for a broad range of parameters. For Gay-Berne hard Gaussian overlap (HGO) fluid particles we found that a N-I transition exists as a function of density for all length to breadth ratios k > 4, in reasonable agreement with other theoretical studies and results of Monte Carlo simulations. For the full Gay-Berne potential (GB) the location of the N-I transition as a function of density for different temperatures was studied for several values of shape and energy anisotropy parameters k and k′. It was shown that the transition temperature increases or the transition density decreases with increasing k and/or decreasing k′. Wherever the molecular dynamics (MD) or Monte Carlo (MC) data were available, comparison was made. For each system, coexistence density and pressure were calculated, and, wherever possible, also compared with MC or MD data to show qualitative agreement. The r...

Orientational ordering in the nematic phase of a thermotropic liquid crystal: A small angle neutron scattering study

The long range orientational order in the nematic phase of 4,4′-dimethoxyazoxybenzene (PAA) has been studied using small angle neutron scattering (SANS) from mixtures of protonated and perdeuterated molecules. Unlike spectroscopic methods, the determination of the complete set of orientational order parameters is, in principle, possible using this technique. The orientational order parameters were extracted from the anisotropic single molecule scattering isolated at small scattering angles. These order parameters were compared to those extracted from previous neutron scattering measurements, to second rank order parameters extracted from NMR, and to those predicted from the Maier–Saupe theory of nematic ordering. It was found that only the second and fourth rank terms in the expansion of the single molecule scattering in a basis of Legendre functions are statistically significant, which means that the order parameters P2̄ and P4̄ only could be obtained. For the semirigid nematogen PAA, the Maier–Saupe theory is found to underestimate P2̄ and its dependence on the reduced temperature T/TNI where TNI is the nematic–isotropic (NI) transition temperature. The theoretical values of P4̄ are, however, in remarkably good agreement with the measured values. Order parameters extracted from NMR are found to be slightly lower than those determined from the SANS experiment, and we also make comparisons with earlier neutron scattering results. Singlet orientational distribution functions are reconstructed from the measured order parameters using the maximum entropy method.

Phase equilibria of a polymer-smectic-liquid-crystal mixture.

Phase diagrams of nematic--liquid-crystal mixtures have been extensively studied theoretically and experimentally to improve the basic understanding of miscibility and phase separation behavior of polymer-dispersed liquid crystals (PDLC's). To the best of our knowledge, the phase behavior of a PDLC composed of a polymer and a smectic liquid crystal is largely an unexplored area. We have developed a theoretical model for predicting phase diagrams of a polymer/smectic--liquid-crystal mixture by combining the Flory-Huggins (FH) theory for isotropic mixing and the Maier-Saupe-McMillan (MSM) theory for anisotropic ordering of liquid crystals (LC's). Our combined FH-MSM model is capable of predicting the phase diagrams of PDLC systems in which the LC component has either a smectic-A--nematic (Sm-A--N) transition and a nematic-isotropic (N-I) transition or a smectic-A--isotropic (Sm-A--I) transition. \textcopyright{} 1996 The American Physical Society.

Phase Diagrams and Phase Separation Dynamics in Mixtures of Side-Chain Liquid Crystalline Polymers and Low Molar Mass Liquid Crystals

Miscibility phase diagrams and phase separation dynamics in mixtures of side-chain liquid crystalline polymers (SCLCP) and monomeric liquid crystals have been investigated experimentally in order to test with theoretical predictions. The theoretical calculation on equilibrium phase diagrams of binary nematic mixtures involves a combination of the Flory−Huggins (FH) free energy for isotropic mixing in conjunction with the Maier−Saupe (MS) free energy for nematic ordering of the mesogenic units. Two orientational order parameters and two nematic−isotropic (NI) transitions of the constituent mesogens are taken into consideration in the calculation. This combined FH−MS theory predicts a variety of phase diagrams depending on the relative strength of the cross-interaction between two dissimilar mesogens as compared to that in the same species. A series of epoxy resins [ethylene glycol glycidyl ether (EGDE)] grafted with mesogenic amines 4-(ω-aminoalkoxy)-4‘-cyanobiphenyl were synthesized. The temperature−composition phase diagrams of these SCLCP mixtures and the eutectic low molar mass liquid crystal (E7) have been established by a cloud point method. The calculated phase diagrams are found to accord well with the experimental phase diagrams. The dynamics of phase separation has been investigated by means of time-resolved light scattering and optical microscopy. The time evolution of the structure factor following various temperature quenches into the nematic−liquid and/or nematic−nematic coexistence regions has been analyzed in terms of a power law scheme.

Electric dipoles and phase stability in nematic liquid crystals

A theory for the nematic-isotropic (N-I) phase transition of prolate uniaxial molecules with longitudinal dipole moments is presented. The theory is based on the variational cluster expansion, truncated after the two-molecule term, and is implemented for polar hard spherocylinders with and without attractions, and for polar linear arrays of Lennard-Jones interactions centre. We find that the dipole interactions substantially shift the N-I transition temperature and strongly promote antiparallel molecular association, but have a weak effect on the order parameters, the pressure, and the N-I coexistence densities. The effect of dipoles on phase stability is very sensitive to their position within the molecular frame. Off-centre dipoles are shown to give rise to phase re-entrance according to the sequence N-I-N on heating at constant density. The theory does not predict a stable ferroelectric nematic phase.

Deuteron NMR study of liquid crystals confined in aerogel matrices.

The temperature dependence of the deuteron NMR line shape was studied in pentylcyanobiphenyl (5CB) and octylcyanobiphenyl (8CB) liquid crystals confined in porous silica aerogel matrices with two different pore size distributions. The average pore sizes 〈${\mathit{R}}_{\mathit{c}}$〉 of the two aerogel matrices were 0.8 and 0.2 \ensuremath{\mu}m, respectively. The deuteron NMR lines of 5CB and 8CB confined liquid crystals are in the isotropic regime broader than in the corresponding bulk phases. This observation shows that the interaction with the aerogel internal surface induces nematic order far above the bulk isotropic-nematic transition temperature. The nematic-isotropic (N-I) transition for both confined liquid crystals is continuous. No hysteresis was observed. A simple Landau-type model is used to describe these observations.

Heat-capacity study of nematic-isotropic and nematic-smectic-A transitions for octylcyanobiphenyl in silica aerogels.

Quenched randomness and finite size can both have substantial effects on critical behavior at phase transitions. A high-resolution ac calorimeter study has been carried out on octylcyanobiphenyl (8CB) in four silica aerogels of different porosities (mass densities \ensuremath{\rho}=0.08--0.60 g ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$). The weakly-first-order nematic-isotropic (N-I) and second-order nematic--smectic-A (N--Sm-A) transitions in bulk liquid crystals belong to different universality classes and have been very well characterized in bulk 8CB. The excess heat capacity peaks \ensuremath{\Delta}${\mathit{C}}_{\mathit{p}}$(N-I) and \ensuremath{\Delta}${\mathit{C}}_{\mathit{p}}$(N--Sm-A) are observed to undergo distinctly different changes as a function of aerogel density. The changes in peak height h\ensuremath{\equiv}\ensuremath{\Delta}${\mathit{C}}_{\mathit{p}}$(max) and peak position ${\mathit{T}}_{\mathrm{peak}}$ relative to the bulk values are not well represented by finite-size scaling for either transition, and the underlying influence of quenched randomness is discussed as the major cause of the observed effects.