Sudipta Kumar Sarkar

Critical behaviour of optical birefringence in the vicinity of nematic–isotropic and smectic A–isotropic phase transitions of the eight members of alkyloxy-cyanobiphenyls

ABSTRACT We report the measurements of birefringence (Δn) as a function of the temperature of a homologous series of alkyloxy-cyanobiphenyls (nOCB) liquid crystalline compounds by means of high-resolution optical transmission method. The temperature dependence of the birefringence has been determined from the transmitted intensity data for two different wavelengths. The order parameter critical exponent β, obtained by using a four-parameter fitting procedure consistent with the mean-field theory for a weakly first order transition, is found to be in good agreement with the theoretically predicted tricritical value. A weak birefringence has been found to develop on approaching the clearing temperature, which is tentatively attributed to the formation of a small mesophase domain within the isotropic phase. This striking behaviour leads to a further quantification of the critical fluctuation close to the transition. Finally, the order character of the nematic–isotropic (N–I) and smectic A–isotropic (SmA–I) phase transitions have been assessed by using the birefringence data. The critical exponent α (usually assigned to the heat capacity) extracted from Δn data describes the critical nature of N–I and SmA–I transitions and strongly supports the tricritical nature of the same. GRAPHICAL ABSTRACT

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.

Critical behaviour at the nematic–smectic A phase transition in a binary mixture showing induced nematic phase

High resolution optical birefringence (Δn) measurements have been performed on thirteen mixtures of two smectogenic compounds, 5-trans-n-pentyl-2-(4-isothiocyanatophenyl)-1,3-dioxane (5DBT) and 4-cyano-4′-n-decyloxy-biphenyl (10OCB), showing an induced nematic phase from the optical transmission method for two different wavelengths. The values of the birefringence have also been compared with those determined from the thin prism method. The critical behaviour of the nematic–smectic A (N–SmA) phase transition has been studied from the birefringence measurements and the nature of the transition in these mixtures has been discussed. The critical exponent values for these mixtures show a definite pattern when plotted both against molar concentration as well as McMillan ratio (TSN/TNI). On both sides of the phase diagram, a uniform crossover trend from second order to first order N–SmA phase transition is observed as the tricritical point (TCP) is approached. For both the TCPs there exists a common value of the McMillan ratio = 0.992. In addition, the 3D-XY model is reached almost exactly at x5DBT = 0.696 for which the McMillan ratio is 0.912.

Critical behaviour of a polar-polar binary system from optical birefringence measurements

ABSTRACT High resolution measurements of optical birefringence (Δn) have been carried out to study the critical behaviour at the nematic-isotropic (N–I) and smectic A-nematic (SmA–N) phase transitions in a binary system composed of nonyloxycyanobiphenyl (9OCB) and heptylcyanobiphenyl (7CB). From a fitting procedure compatible with the weakly first order nature of the N–I transition, the order parameter critical exponent β at the N–I transition has been found to be in well agreement with the tricritical hypothesis. The pretransitional behaviour at the SmA–N transition has been investigated with the aid of a differential parameter extracted from Δn data and the yielded critical exponent α has been found to be non-universal in nature. A weak birefringence have been found to develop on approaching the N–I transition temperature, which is tentatively attributed to surface induced ordering. In this case, a treatment identical to that for the SmA–N transition yields a tricritical nature for the N–I transition in the investigated mixtures. Such an outcome has also appeared to be in well agreement with those obtained from the direct analysis of the Δn data (i.e. in parameterisation of β). Graphical Abstract

Dielectric studies and critical behaviour in the vicinity of nematic–isotropic phase transition of a smectogenic binary mixture showing induced nematic phase

The phase diagram of a binary mixture composed of compounds, one having NCS terminal group (4DBT, showing smectic A1 phase) and the other with CN terminal group (11OCB, showing smectic Ad phase), exhibiting induced nematic phase in a certain concentration range (0.100 < x4DBT < 0.951) is reported here. Results of the static dielectric parameters measurement on this binary system within the entire mesomorphic range are presented. Evidence of strong pretransitional behaviour near the nematic–isotropic (N–I) phase transition, indicating the influence of tricritical behaviour, is observed. Precise determination of discontinuity (ΔT) and the critical exponent (α) of N–I phase transition have been carried out. Moreover, the order parameter critical exponent β is correctly predicted by the tricritical hypothesis through the dielectric anisotropy data for all the investigated mixtures.

Critical behavior in the vicinity of nematic to smectic A (N–SmA) phase transition of two polar–polar binary liquid crystalline systems

ABSTRACT Phase diagram, critical behavior and order of the nematic (N)–smectic A (SmA) phase transition of two polar–polar binary systems (i) 4-n-heptyloxy-4′-cyanobiphenyl (7OCB) and 4-n-octyloxy-4′-cyanobiphenyl (8OCB); (ii) 4-n-octyloxy-4′-cyanobiphenyl (8OCB) and 4-n-nonyloxy-4′-cyanobiphenyl (9OCB) by means of a high-resolution temperature scanning measurement of birefringence have been reported in this work. A simple power law analysis has been adopted to extract the specific heat critical exponent (α′) at N–SmA transition from birefringence data. The α′ for N–SmA transition indicates a uniform crossover behavior and has appeared to be non-universal in nature. With increasing concentration of the higher homologues for both the binary systems, the N–SmA transition reveals a strong tendency to be driven towards the tricritical nature. The 3D-XY limit (i.e. α′ = −0.007) for N–SmA transition reaches at the concentration x8OCB = 0.28 corresponding to the McMillan ratio 0.914, whereas the tricritical point has been found to appear near x9OCB = 1.0 corresponding to McMillan ratio 0.992.

Measurement of splay elastic constant and rotational viscosity of an induced nematic binary system

ABSTRACT We investigated the temperature dependence of the splay elastic constant (K11) and rotational viscosity (γ1) of a binary liquid crystal system comprising 5-trans-n-butyl-2-(4-isothiocyanatophenyl)-1,3-dioxane (4DBT) and 4-cyano-4′-n-undecyloxy-biphenyl (11OCB), exhibiting induced nematic phase. Both the splay elastic constant and rotational viscosity increased following lowering of the temperature. In the vicinity of smectic A-nematic (SmA-N) transition, both the relaxation time and rotational viscosity exhibited a strong pretransitional behaviour. The critical exponent (ν) presented here led to valuable qualitative information about the pre-transitional behaviour of the rotational viscosity data near the SmA-N phase transition. The extracted ν values ranging between 0.336 and 0.352 are in fair agreement with those predicted in the de Gennes model as compared to that by the mean-field model. GRAPHICAL ABSTRACT