Density functional theory of freezing of a system of conjugated oligomers parameterised via Gay–Berne potential

Density functional theory (DFT) of freezing is used to study the isotropic–nematic, isotropic–smectic A and nematic–smectic A phase transitions in a system of large, semi-flexible conjugated oligomers parameterised within Gay–Berne (GB) potential. The pair correlation functions of the isotropic fluid, used as structural inputs in the DFT, are calculated by solving the Percus–Yevick integral equation theory. Large number of spherical harmonic coefficients of each orientation-dependent functions has been considered to ensure the numerical accuracy at different densities and temperatures for the system of these model GB ellipsoids having large aspect ratio (length-to-breadth ratio). We found that the system of GB ellipsoids parameterised for conjugated oligomers shows stable isotropic, nematic and smectic A phases. At low temperatures, on increasing the density, isotropic fluid makes a direct transition to smectic A phase. Nematic phase get stabilised in between the isotropic and smectic A phases on increasing the temperature. Using the transition parameter obtained through the DFT, we have plotted the temperature–density and pressure–temperature phase diagrams which are found to be qualitatively similar to the one obtained in simulations for the systems with low aspect ratio GB particles.     

Monte Carlo simulation of the self-assembly and phase behavior of semiflexible equilibrium polymers

Grand canonical Monte Carlo simulations of a simple model semiflexible equilibrium polymer system, consisting of hard sphere monomers reversibly self-assembling into chains of arbitrary length, have been performed using a novel sampling method to add or remove multiple monomers during a single MC move. Systems with two different persistence lengths and a range of bond association constants have been studied. We find first-order lyotropic phase transitions between isotropic and nematic phases near the concentrations predicted by a statistical thermodynamic theory, but with significantly narrower coexistence regions. A possible contribution to the discrepancy between theory and simulation is that the length distribution of chains in the nematic phase is bi-exponential, differing from the simple exponential distribution found in the isotropic phase and predicted from a mean-field treatment of the nematic. The additional short length-scale characterizing the distribution appears to arise from the lower orientational order of short chains. The dependence of this length-scale on chemical potential, bond association constant, and total monomer concentration has been examined.     

Fluctuating Interfaces in Liquid Crystals

Summary: We review and compare recent work on the properties of fluctuating interfaces between isotropic and nematic liquid-crystalline phases. Molecular dynamics and Monte Carlo simulations have been carried out for systems of ellipsoids and hard rods with aspect ratio 15:1, and the fluctuation spectrum of interface positions (the capillary wave spectrum) has been analyzed. In addition, the capillary wave spectrum has been calculated analytically within the Landau-de Gennes theory. The theory predicts that the interfacial fluctuations can be described in terms of a wave vector dependent interfacial tension, which is anisotropic at small wavelengths (stiff director regime) and becomes isotropic at large wavelengths (flexible director regime). After determining the elastic constants in the nematic phase, theory and simulation can be compared quantitatively. We obtain good agreement for the stiff director regime. The crossover to the flexible director regime is expected at wavelengths of the order of several thousand particle diameters, which was not accessible to our simulations.     

Induced smectic phases in phase diagrams of binary nematic liquid crystal mixtures

To elucidate induced smectic A and smectic B phases in binary nematic liquid crystal mixtures, a generalized thermodynamic model has been developed in the framework of a combined Flory-Huggins free energy for isotropic mixing, Maier-Saupe free energy for orientational ordering, McMillan free energy for smectic ordering, Chandrasekhar-Clark free energy for hexagonal ordering, and phase field free energy for crystal solidification. Although nematic constituents have no smectic phase, the complexation between these constituent liquid crystal molecules in their mixture resulted in a more stable ordered phase such as smectic A or B phases. Various phase transitions of crystal-smectic, smectic-nematic, and nematic-isotropic phases have been determined by minimizing the above combined free energies with respect to each order parameter of these mesophases. By changing the strengths of anisotropic interaction and hexagonal interaction parameters, the present model captures the induced smectic A or smectic B phases of the binary nematic mixtures. Of particular importance is the fact that the calculated phase diagrams show remarkable agreement with the experimental phase diagrams of binary nematic liquid crystal mixtures involving induced smectic A or induced smectic B phase.     

Computer simulation studies of anisotropic systems. XIX. Mesophases formed by the Gay-Berne model mesogen

We report the results of a molecular dynamics computer simulation of particles interacting via the Gay-Berne potential with parameters selected to approximate those of mesogenic molecules. The system was found to form a variety of mesophases as the temperature was lowered. We have characterized these phases with the aid of computer graphics techniques to visualize the molecular organization within configurations taken from the production stage of the simulations. The phases have been identified, on the basis of such images, as isotropic, nematic, smectic A, smectic B and crystal.     

Dielectric relaxation study of 1-n hexyl-4-(4-isothiocyanatophenyl)bicyclo [2,2,2] octane in the nematic and isotropic phases

Dielectric relaxation investigations on the mesogen 1-n-hexyl-4-(4-isothiocyanato-phenyl)bicyclo[2,2,2]octane in the nematic and isotropic phases have been carried out in the frequency region from about 1 kHz to 1 GHz. Two relaxation processes have been observed in both the isotropic and nematic phases, when the measurements of the electric permittivity versus frequency are made parallel to the orientation axis of the liquid crystal. The possible mechanisms responsible for these two processes are discussed. The height of the potential barrier which hinders the rotation of the liquid crystal molecules around the short axis in the nematic state, and the order parameter of the liquid crystal under investigation have been estimated on the basis of the values for the relaxation times in the nematic and isotropic phases.     

Dielectric study of the liquid crystalline dimer alpha, omega-bis(4'-cyanobiphenyl-4-yloxy)decane

The dielectric properties of a nematogenic dimer alpha,omega-bis(4-cyanobiphenyl-4-yloxy)decane in the nematic and isotropic phases have been investigated in the frequency range between 100 Hz and 13 MHz. It was found that the compound is characterized by a positive dielectric anisotropy. The dielectric constant in the nematic phase is lower than that in the isotropic phase, which suggests variation in the conformational distribution of the dimer after the phase transition. Only one relaxation process, both in the nematic and isotropic phases, has been observed in the frequency range used: the relaxation frequency has been found to take values between 2 and 4 MHz, depending on the temperature.     

Chemical reactivity within a smectic B liquid crystalline phase: A model of enzyme catalysis?

The rearrangement of allyl p-dimethylaminobenzenesulphonate (ASE) to form a zwitterionic product has already been recognized as an effective probe for the study of reactivity within the smectic B phase [4, 5, 19]. We have used deuterium NMR, linear dichroism and X-ray diffraction techniques to investigate the phase diagram of the ASE-OS35 reaction system. The partitioning of the reactant molecules between coexisting smectic, nematic and/or isotropic phases and the structural organization of the smectic catalytic host at different temperatures and reactant guest concentrations have been characterized. On the basis of these measurements, a model of ASE reactivity in smectic solvents has been developed. The reaction takes place provided that coexisting isotropic or nematic phases are present to act as a reservoir for the ASE reactant molecules prior to their entering the smectic phase; they then react and leave the smectic phase as a zwitterionic product. The analogy between this model of reactivity within smectic phases and the Michaelis-Menten enzyme processes is discussed. This relationship opens up the intriguing possibility of designing new experiments with which to investigate further liquid crystalline models of enzyme catalysis.     

Virtual isotropic‐nematic transitions in alkyl cyanobiphenyls

Pretransitional fluctuations in the isotropic phase of liquid crystalline and non‐liquid crystalline alkyl cyanobiphenyls have been investigated using light scattering and magnetic birefringence measurements. We find evidence for a virtual isotropic‐nematic phase transition in short‐chain alkyl cyanobiphenyls with no observable nematic phase. The measured temperature dependence of fluctuations is well‐described by mean‐field theory. Virtual phase transition temperatures extrapolated from separate light scattering and magnetic birefringence experiments are in good agreement. Landau–de Gennes model parameters for the compounds investigated are calculated from the experimental results.     

Orientational ordering in hard rectangles: The role of three-body correlations

We investigate the effect of three-body correlations on the phase behavior of hard rectangle two-dimensional fluids. The third virial coefficient B3 is incorporated via an equation of state that recovers scaled particle theory for parallel hard rectangles. This coefficient, a functional of the orientational distribution function, is calculated by Monte Carlo integration, using an accurate parametrized distribution function, for various particle aspect ratios in the range of 1-25. A bifurcation analysis of the free energy calculated from the obtained equation of state is applied to find the isotropic (I)-uniaxial nematic (N(u)) and isotropic-tetratic nematic (N(t)) spinodals and to study the order of these phase transitions. We find that the relative stability of the N(t) phase with respect to the isotropic phase is enhanced by the introduction of B3. Finally, we have calculated the complete phase diagram using a variational procedure and compared the results with those obtained from scaled particle theory and with Monte Carlo simulations carried out for hard rectangles with various aspect ratios. The predictions of our proposed equation of state as regards the transition densities between the isotropic and orientationally ordered phases for small aspect ratios are in fair agreement with simulations. Also, the critical aspect ratio below which the N(t) phase becomes stable is predicted to increase due to three-body correlations, although the corresponding value is underestimated with respect to simulation.     

A density-functional theory study of the confined soft ellipsoid fluid

A system of soft ellipsoid molecules confined between two planar walls is studied using classical density-functional theory. Both the isotropic and nematic phases are considered. The excess free energy is evaluated using two different Ans?tze and the intermolecular interaction is incorporated using two different direct correlation functions (DCF's). The first is a numerical DCF obtained from simulations of bulk soft ellipsoid fluids and the second is taken from the Parsons-Lee theory. In both the isotropic and nematic phases the numerical DCF gives density and order parameter profiles in reasonable agreement with simulation. The Parsons-Lee DCF also gives reasonable agreement in the isotropic phase but poor agreement in the nematic phase.     

Phase equilibrium of poly(n-butyl acrylate) and E7

The experimental equilibrium phase diagram of mixtures of linear poly(n-butyl acrylate) of molecular mass M_w = 112000 g mol^-1 and the low molecular mass LC mixture E7 has been established using polarized optical microscopy and light scattering techniques. The diagram is found to be reminiscent of an upper critical solution temperature system. Two independent series of samples with the same composition were studied, yielding consistent results. A region of nematic and isotropic coexisting phases and a region of a single isotropic phase were identified in the composition-temperature phase diagram. The results were analysed within a theoretical model combining the Flory-Huggins lattice theory for isotropic mixing and the Maier-Saupe theory for nematic ordering. Interestingly, no region of isotropic coexisting phases was observed in our experiments. This is probably due to the fact that the nematic interaction overwhelms the isotropic interaction in the region where (I + I) coexisting phases could appear. A preferential solubility of certain constituents of the LC mixture in the polymer could possibly be a reason for this behaviour.     

Simulation of the rheological properties of liquid media containing solid anisometric particles

Theoretical simulation of the rheological properties of liquid media containing solid anisometric particles is performed. Procedures for the calculation of the degree of ordering in the nematic systems under equilibrium conditions and their rheological characteristics are proposed. Earlier developed notions of the calculation procedures for the properties of systems considered are analyzed and corrections to the theory are substantiated. Based on developed model notions, equilibrium and transport equations are derived and a program for their numerical solution is proposed. Model calculations of the lines of phase transition and the ordering of systems containing isotropic and nematic phases, as well as anisotropic (in orienting field) and effective dynamic viscosities under the conditions of free flow of such systems, are carried out at various concentrations and geometry of anisometric particles. A comparison of calculated and experimental data for the solutions of polymer-salt compositions with induced chain rigidity demonstrates the adequacy of the model proposed.     

Nematic ordering of rigid rod polyelectrolytes induced by electrostatic interactions: effect of discrete charge distribution along the chain

Similar to the Debye-Hu?ckel plasma, charged groups in solutions of rigid rod polyelectrolytes attract each other. We derive expression for the correlation free energy of electrostatic attraction of the rods within the random phase approximation. In this theory, we explicitly take into account positions of charged groups on the chains and examine both charge and polymer concentration fluctuations. The correlation free energies and the osmotic pressures are calculated for isotropic and completely ordered nematic phase. The results of the discrete model are compared with results of a continuous model. The discrete model gives rise to a stronger attraction between the charged groups both in the isotropic and nematic phases and to a stronger orienting action of the electrostatic forces.     

Phase equilibrium of poly(n-butyl acrylate) and E7

The experimental equilibrium phase diagram of mixtures of linear poly(n-butyl acrylate) of molecular mass M_w = 112000 g mol^-1 and the low molecular mass LC mixture E7 has been established using polarized optical microscopy and light scattering techniques. The diagram is found to be reminiscent of an upper critical solution temperature system. Two independent series of samples with the same composition were studied, yielding consistent results. A region of nematic and isotropic coexisting phases and a region of a single isotropic phase were identified in the composition-temperature phase diagram. The results were analysed within a theoretical model combining the Flory-Huggins lattice theory for isotropic mixing and the Maier-Saupe theory for nematic ordering. Interestingly, no region of isotropic coexisting phases was observed in our experiments. This is probably due to the fact that the nematic interaction overwhelms the isotropic interaction in the region where (I + I) coexisting phases could appear. A preferential solubility of certain constituents of the LC mixture in the polymer could possibly be a reason for this behaviour.     

Forces between cylindrical nanoparticles in a liquid crystal

Using classical density functional theory, the forces between two cylindrical nanoparticles in a liquid crystal solvent are calculated. Both the nematic and isotropic phases of the solvent are considered. In the nematic phase, the interaction is highly anisotropic. At short range, changes in the defect structure around the cylinders leads to a complex interaction between them. In the isotropic phase, an attractive interaction arises due to overlap between halos of ordered fluid adsorbed on the surfaces of the cylinders.     

Broadband dielectric relaxation study of 6CB and 6CB-aerosil dispersions in the nematic and isotropic phases

Experimental studies of dielectric relaxation in the nematic and isotropic phases of 6CB (4-hexyl-4′-cyanobiphenyl) and two mixtures of 6CB perturbed by 160 Å hydrophobic silica aerosil are presented. The measurements have been made from 1 MHz to 1 GHz in the temperature range from 19 to 40°C. For bulk 6CB, the dynamic aspect in the isotropic phase as well as the principal dielectric permittivities ε ∥ * (ω) and ε ┴ * (ω) in the nematic phase have been fully explored. For the mixtures, measurements on the isotropic phase and also on homeotropically aligned samples in the nematic phase have been made, and these results are systematically compared with those for the bulk. The possible molecular reorientational movements corresponding to the different absorption domains in the dielectric spectrum are discussed and compared with the previously proposed interpretations.     

Complete phase diagrams of mixtures of a nematic liquid crystal with n-alkanes

The full experimental phase diagrams of mixtures of the nematic liquid crystal 4.4'-azoxyanisole, (PAA), and n-tetracosane and of PAA and n-octadecane are given. Equilibria of a nematic phase with an isotropic phase, of two isotropic phases, and a reentrant isotropic phase could be observed directly. The experimental phase diagram is in qualitative agreement with the result derived from the Flory lattice model adopted for thermotropic systems.     

Dielectric spectroscopy of liquid crystalline dispersions

We describe dielectric spectroscopy measurements on dispersions of two thermotropic liquid crystals (5CB and 8CB) in a poly(dimethylsiloxane) matrix. 5CB exhibits nematic and isotropic phases, while 8CB exhibits smectic, nematic, and isotropic phases. The spectra of the dispersions exhibit a temperature-dependent dielectric relaxation in the interval from 100 to 1000 Hz, with relaxation times that depend strongly on whether the dispersed phase is isotropic, nematic, or smectic. The dielectric relaxation times also depend on the viscosity of the matrix fluid. These results suggest a coupling between the electric field and the mechanics of the interface that affects the spectrum of the dispersed phase and shifts the Maxwell-Wagner interfacial polarization peak.     

Liquid Crystalline Organisation and Reaction Rate in the Formation of Liquid Crystal Thermoset Networks from Diepoxides and Dicyanates

Summary: The influence of the type of mesophase on the rate of reaction in amine curing or anionic polymerisation of mesogenic diepoxides, and in the cyclotrimerisation of mesogenic dicyanates has been investigated by isothermal DSC and IR-spectroscopy. Epoxide/amine systems were found to react faster in the nematic than in the isotropic phase. Anionic polymerisation of epoxides is an example where increase of the reaction rate occurs with the transition from a mesophase of higher order (smectic) to phases with lower order (nematic, isotropic). For triaromatic dicyanates with one or three methyl groups at the central ring cyclotrimerisation is faster in the isotropic than in the nematic phase showing an increase of activation energy in the nematic phase with the number of methyl groups. A pronounced rate increase has been observed in the smectic phase as compared to the nematic phase for the unsubstituted triaromatic dicyanate. In this case activation energies in the two phases are comparable with those of non liquid crystalline dicyanates.