Orientational order parameter of two cyano nematogens by optical spectroscopy

Refractive index and density measurements of two cyano nematogens, namely p-hexyloxybenzylidene p-aminobenzonitrile and p-octyloxybenzylidene p-aminobenzonitrile have been carried out. From these data, orientational order parameter S has been estimated using different methods. Principal polarizabilities have been calculated using the well-known Vuks isotropic and Neugebauer anisotropic models. Polarizability anisotropy has been estimated using Lippincott δ-function, molecular vibration, Haller's extrapolation and Vuks scaling methods. Using these values, the orientational order parameter S has been estimated at different temperatures in their nematic phases. The values obtained have been compared and discussed. Further, using the experimental refractive index data, the nematic crossover temperatures have also been estimated for these compounds.     

Orientational order parameter studies in two symmetric dimeric liquid crystals – an optical study

The optical technique developed by [W. Kuczynski, B. Zywucki, and J. Malecki, Determination of orientational order parameter in various liquid-crystalline phases, Mol. Cryst. Liq. Cryst. 381 (2002), pp. 1–19; B.J. Zywucki and W. Kuczynski, IEEE transactions on optical phenomena – The orientational order in nematic liquid crystals from birefringence measurements, Dielectr. Electr. Insul. 8 (2001), pp. 512–515] is fabricated and used to determine the orientational order parameter in two dimeric liquid crystalline compounds nematic and SmA phases of α,ω-bis(4-alkylanilinebenzylidene-4′-oxy)alkane (m.OnO.m) homologous series. The compounds studied are 5.O8O.5 and 5.O10O.5 which exhibit nematic and SmA, and nematic phases, respectively. The orientational order parameter in both the phases of nematic and SmA phases of the compound one and the nematic phase of the compound two are obtained using the principle of Newton's rings which gives directly the birefringence, δn of the liquid crystal dimer. The merits of the technique used are presented over the conventional techniques for the determination of orientational order parameter. The results for the two compounds are compared with those values estimated from n _e, n _o and density using the two internal field models due to Vuks and Neugebauer applicable to nematic phase.     

Refractive index and orientational order parameter of a polar–polar binary system showing induced smectic Ad and re-entrant nematic phases

Refractive index measurements have been done on a polar–polar binary system, 4-cyanophenyl [4′(4″-n-heptylphenyl)] benzoate (7CPB)?+?4-cyanophenyl-4-nonylbenzoate (9.CN), exhibiting nematic–smectic A_d–re-entrant nematic phase sequence using thin prism technique. From refractive index as well as density data, the polarizability anisotropy in the mesomorphic state has been calculated from the standard Vuks model and the orientational order parameter (?P ₂?) values have been determined. By measuring the refractive indices and density in the solid phase, the validity of the Haller's extrapolation method for systems having higher order phases has been verified. The temperature variation of the density, birefringence, and ?P ₂? values at the nematic–smectic A_d and smectic A_d–re-entrant nematic transitions for all the mixtures are found to be continuous. The experimental ?P ₂? values have been compared with our previous X-ray data and also those calculated from the Luckhurst and Timimi model.     

Orientational order and distribution function in nematic 1-(4-trans hexylcyclohexyl)-4-[(2-4-isothiocyanato phenyl)ethyl] benzene

The refractive indices (n _e,?n _o) and density have been measured as a function of temperature in the liquid-crystalline and liquid phases of nematic 1-(4-trans hexylcyclohexyl)-4-[(2-4-isothiocyanato phenyl)ethyl] benzene. The molecular polarizability and orientational order parameter have been computed using the Neugebauer anisotropic local field model. The distribution function f(β), and hence the higher order parameter ?P ₄?, and nematic pair-potential have been computed at different temperatures in the nematic phase.     

Orientational order parameter estimated from molecular polarizabilities – an optical study

An optical study of N-(p-n-alkyloxybenzylidene)-p-n-butyloxyanilines, nO.O4 compounds with the alkoxy chain number n?=?1, 3, 6, 7, and 10 has been carried out by measuring the refractive indices using modified spectrometer and direct measurement of birefringence employing the Newton's rings method. Further, the molecular polarizability anisotropies are evaluated using Lippincott δ-function model, the molecular vibration method, Haller's extrapolation method, and scaling factor method. The molecular polarizabilities α _e and α ₀ are calculated using Vuk's isotropic and Neugebauer anisotropic local field models. The order parameter S is estimated by employing the molecular polarizability values determined from experimental refractive indices and density data and the polarizability anisotropy values. Further, the order parameter S is also obtained directly from the birefringence data. A comparison has been carried out among the order parameter obtained from different ways and the results are compared with the body of the data available in the literature.     

Orientational order parameter studies on 3.Om and 3O.Om liquid crystals

Orientational order parameter S is evaluated in the nematic phase of six liquid crystal compounds, N-(p-n-propyl benzylidene)-p-n-alkoxy anilines, 3.Om and N-(p-n-propyloxy benzylidene)-p-n-alkoxy anilines, 3O.Om compounds with m = 6, 7 and 8, using different methods. The techniques employed are S from birefringence δn, Haller's approximation from (1?T/T_c) ^β, effective geometry parameter α_g and Vuks’ scaling factor S_C. The values of S obtained using the above methods are compared with one another and with the results on a number of liquid crystals; the liquid crystals favor isotropic Vuks’ method.     

Order parameter and its critical exponent for some binary mixtures showing induced nematic phase

Refractive index measurements as a function of temperature have been performed for an induced nematic binary system by means of thin prism technique. The temperature dependence of the birefringence (Δn) has been assessed from the measured refractive index data. A direct extrapolation method has been employed to determine the orientational order parameter for the investigated mixtures and the order parameter so obtained has also been compared with the mean field values. The Haller type fitting expression results in a relatively lower value of the order parameter critical exponent (β) compared to the theoretically predicted values. Therefore, a four-parameter power law expression, consistent with the mean field theory as well as the first-order character of the nematic–isotropic (N-I) phase transition have been used to explore the critical behavior of the order parameter near the N-I transition.     

Study of optical parameters of two fluorinated isothiocyanato nematic liquid crystals exhibiting high birefringence

Optical studies have been carried out on two fluorinated isothiocyanato nematic liquid crystal (LC) compounds 4′-butylcyclohexyl-3, 5-difluoro-4-isothiocyanatobiphenyl and 4′-pentylcyclohexyl-3, 5-difluoro-4-isothiocynatobiphenyl. Transition temperatures of the two samples were confirmed using a polarizing microscope. The two LC compounds were found to exhibit fairly high clearing temperatures. Measurements of refractive indices of the two compounds were done by using thin prism method with He-Ne laser beam of wavelength 630 nm. Birefringence of the two LC compounds was calculated from the measured refractive indices. Both the compounds are found to display fairly high values of birefringence. Validation of a modified four-parameter model, based on Vuks equation describing the temperature dependence of refractive indices of the two liquid crystals, is also presented in this paper. The model is validated by fitting the experimentally measured values of refractive indices, birefringence and average refractive indices of the two nematic LCs with the theoretical values. In this paper, the calculation of order parameters of the LCs is presented by using two methods: direct extrapolation method based solely on the birefringence data and by using modified Vuks method based on Haller’s extrapolation. As observed from the obtained results, this procedure of calculating order parameter gives very reasonable results.     

The McMillan parameter as an effective field variable for the nematic–smectic tricritical point in NO.M compounds

The dependence of the coupling of orientational and translational order parameters on the nematic-smectic A tricritical point (TCP), observed through birefringence experiments in the pure compounds and in the binary mixtures in the homologous series of N(p-n-alkyloxybenzylidene)p-n-alkylanilines, results in a mean field tricritical exponent. The McMillan parameter, M = T _NA/T _NI (where T _NA and T _NI are the smectic A—nematic (AN) and the nematic—isotropic (NI) phase transition temperatures respectively), is used as an effective and relevant field variable in analysing the TCP. The observed linear dependence of the jump in the orientational order parameter with new density variables in the tricritical region is found to be consistent with the results obtained from both the Landau mean field and the decoupled mean field models. The width of the mean field tricritical region is discussed in terms of the McMillan parameter. Further, the McMillan parameter is observed to be characteristic of chemical composition at the NA tricritical point.     

Nematic liquid crystals exhibiting high birefringence

Two fluorinated isothiocyanato nematic liquid crystalline compounds, 4′-butylcyclohexyl-3, 5-difluoro-4-isothiocyanatobiphenyl and 4′-pentylcyclohexyl-3, 5-difluoro-4-isothiocynatobiphenyl are studied in detail to obtain their different physical parameters. Optical polarizing microscopy, differential scanning calorimetry, density and dielectric studies have been carried out for the two samples. Both the samples were found to have high clearing temperature (>100 °C) and exhibit small enthalpy of transition. The two samples exhibit high optical birefringence (Δn > 0.2). The values of order parameters for the two samples were obtained using different approaches, namely, Vuks’, Neugebauer’s, modified Vuks’ and direct extrapolation method from birefringence data. Experimentally obtained values of order parameters have also been compared with theoretical Maier–Saupe values. The parallel and perpendicular components of dielectric permittivity values of the two compounds were also calculated and their anisotropy values were found to be small. The effect of temperature on the molecular dipole moment μ and the angle of inclination β of the dipole axis with the director have also been investigated in this work.     

Molecular orientation of lyotropic nematic phase in a mixture of two non-mesogenic compounds

We report the results of our studies on the optical and thermal properties of the mixture of two non-mesogenic compounds, namely, sodium dodecyl sulfate (SDS) and glacial acetic acid (GAA). The mixture exhibits very interesting schlieren texture of lyotropic micellar nematic (N_D) phase, SmA and SmB phases, respectively, at different concentrations of SDS in GAA sequentially when the specimen is cooled from its isotropic phase. The order parameter (S) of the lyotropic micellar nematic (N_D) phase is estimated with the help of temperature dependence of optical anisotropy from the measured values of refractive index and density data. The experimental curve showing the temperature variation of order parameter is very well fitted with the Mayer–Saupe theoretical curve. X-ray studies have also been discussed. The formation of the above phases has been confirmed by optical and differential scanning calorimetry studies.     

Phase transition and some physical properties of binary mixtures of two nematogenic compounds showing induced smectic phase

The binary mixtures of nematogenic compounds 4-n-pentyl phenyl 4-n′-hexyloxy benzoate (ME6O.5) and 4-cyanophenyl 4-pentyl benzoate (CPPB) show the presence of induced smectic phase. In this article, we report the phase diagram and the results of refractive index, density, static dielectric permittivity and X-ray diffraction measurements of different binary mixtures of (ME6O.5?+?CPPB) throughout the entire composition range. The density and refractive index values have been analysed to obtain orientational order parameters. The various physical properties of the system have been discussed on the basis of the phase diagram.     

Optical properties of a liquid crystal with small ordinary and extraordinary refractive indices and small optical anisotropy

Optical properties of a nematic liquid crystal with small refractive index and small birefringence were studied. The ordinary and extraordinary refractive indices and birefringence were measured as functions of temperature by using an Abbe refractometer and wedge nematic cells. From values of these indices the nematic orientational order parameter was calculated by using several methods and corresponding mathematical models. Kuczyński et al. method was found to be suitable for determining the order parameter also for materials featuring small ordinary refractive index, with unknown density.     

DSC,density and refractive index studies on two nematogenic p-alkylphenyl-2-chloro-4-(p-alkylbenzoyloxy)-benzoates and their mixtures

The compounds p-pentylphenyl-2-chloro-4-(p-pentylbenzoyloxy)-benzoate [PCPB] and p-octylphenyl-2-chloro-4-(p-heptylbenzoyloxy)-benzoate [OCHB], and mixtures of different mole fractions of them, show a nematic phase with a supercooling effect. From DSC studies both ΔH and ΔS at T _NI are found to have minimum values for the equimolar mixture, which happens to be an eutectic mixture (Mix-II). However the density of this mixture is found to be less than that of the pure compounds. Refractive indices (n _o, n_e) are measured by thin prism method at different temperatures for pure components and the eutectic mixture. The birefringence values of the eutectic mixture are less than those of the individual components at higher temperature region, and are in-between at lower temperatures. The principal polarizibilities (α _o, α _e) of all the compounds have been calculated using both Vuks’ and Neugebauer's methods. These values have been compared with those calculated from additivity rules of bond polarizability. The average polarizability α increases with chain length. The orientational order parameter (P ₂) at different temperatures has been calculated using Haller's extrapolation procedure. (P ₂) values of OCHB are found to be greater than those of PCPB and Mix-II at higher temperatures, and are consistent with those determined from our X-ray studies. The temperature dependence of (P ₂) of all the compounds has been compared with Maier-Saupe theoretical values.     

Thermodynamic parameters of N-(p-n-alkoxybenzylidene)-p-n-(butyloxyanilines), (nO.O4) liquid crystal compounds — A dilatometric study

Different thermodynamic parameters are estimated from volume expansion coefficient, α for a number of N-(p-n-alkoxybenzylidene)-p-n-butyloxyanilines, nO.O4 compounds in isotropic phase (at T_IN + 5 °C) and in liquid crystalline phases. The variation of different thermodynamic parameters with the alkoxy chain length in nO.O4 series and their variation with the temperature in individual liquid crystal compounds are discussed. The parameters like available volume (V_a), inter molecular free length (L_f) and molecular radius (M_r) are also computed from density, and refractive index for these nO.O4 compounds and the nature of molecular free length and molecular radius are analyzed and discussed.     

Orientational order parameters of nematogenic trans-4-propyl cyclohexyl-4 (trans-4-alkyl cyclohexyl) benzoates

The refractive indices and densities of three members of trans-4-propyl cyclohexyl-4 (trans-4-alkyl cyclohexyl) benzoates are reported as functions of temperature in the nematic and isotropic phases. The principal molecular polarizabilities and order parameters (S) have been evaluated using the anisotropic internal field model (Neugebauer’s approach). Also order parameters have been estimated by studying the dipole-dipole splittings in the wide line proton magnetic resonance (PMR) spectra. The results obtained are in close agreement with those obtained from refractive index measurements.     

Phase transition studies in N(p-n-pentyloxy benzylidene) p-n-decyl aniline

The temperature dependences of the molar volume, the ultrasonic velocity and the refractive index in N(p-n-pentyloxy benzylidene) p-n-decyl aniline, which exhibits nematic, smectic-A and smectic-B, phases, are presented. The isotropic-nematic and smectic-A-smectic-B phase transitions are found to be of first order while the nematic-smectic-A transition is of second order. The thermal expansion coefficient (a) computed from the molar volume data agrees with a second-order N-S_A transition. The computed adiabatic compressibility β_ad, molar sound velocity (or Rao number R_n ) and molar compressibility (or Wada constant A) are presented.     

Optical birefringence and order parameter of three nematogens

Results of the measurement of refractive indices and densities of three nematic liquid crystals at different temperatures are reported. The molecular polarizabilities have been calculated from refractive indices using both the Vuks’ and the Neugebauer’s relations. The orientational order parameters are determined from the polarizability values. The variation of order parameter with temperature for these compounds shows a reasonably good agreement with Maier and Saupe theory except near the clearing points where the experimental values are less than those obtained from the theory. The possible reasons for this have been discussed.     

Orientational order parameter and rotational viscosity in C60 doped E7 nematic liquid crystal

The reorientational order parameter dependent complex linear susceptibilities are derived based on the angular averaged linear response theory of the molecular polarizability, which includes the Vuks type equations of anisotropic refractive indices and absorbances. The polar angular absorbance at 633 nm wavelength is measured as a function of the concentration of fullerene C₆₀ in E7 nematic liquid crystals (NLCs), from which the order parameter is deduced. It is shown that the order parameter has a linear dependence of dopant concentration. We also present a simple optical transmission method by adopting the closed-aperture Z-scan geometry under the influence of switching on and off the dc electric field to determine the optical relaxation time and the rotational viscosity coefficient of C₆₀ doped E7 NLC. The experimental results are pretty well explained by using the Osipov-Terentjev theory of the rotational viscosity with the measured order parameter.     

Birefringence study on lyotropic micellar nematic phase in a binary mixture

We report the results of our studies on optical and thermal properties of two non-mesogenic compounds, namely, didodecyl dimethyl ammonium bromide (DDAB) and glacial acetic acid. The mixture exhibits schlieren texture of lyotropic micellar nematic (N_D), SmA, SmB, and SmG phases, respectively, at different concentrations of DDAB sequentially when the specimen is cooled from isotropic phase. The order parameter (S) of lyotropic micellar nematic (N_D) phase is estimated with the help of temperature dependence of optical anisotropy from the measured values of refractive index and density data. The temperature variation of order parameter of the experimental curve is in agreement with the Mayer–Saupe theoretical curve. The formation of the above phases has been confirmed by optical studies.