Micellar shape anisotropy and optical indicatrix in reentrant isotropic-nematic phase transitions.

In this work, we will show that the concept of nematic order parameter and a generalization of the concept of optical indicatrix, largely used in optics of anisotropic crystals, can be joined to give a new geometrical representation to the anisotropies found in lyotropic liquid crystals. Our theoretical approach will be illustrated using refractive index data of reentrant isotropic-calamitic (discotic) nematic phase transitions of potassium laurate, decanol, and heavy water mixtures.

Thermal diffusivity and the conformal transformation on nematic liquid crystals.

In this paper, we will study theoretically and experimentally the anisotropy of the thermal diffusivity in nematic liquid crystals. We will show that the Baalss-Hess conformal transformation [D. Baalss and S. Hess, Phys. Rev. Lett. 57, 86 (1986)], can be used to obtain a free of adjustable parameters equation that describes the anisotropy of the heat diffusion in these materials. The results of this theory will be compared with experimental data. This study will partially confirm the widely known experimental evidences that indicate that the thermal diffusivity is larger in the director direction than in the one perpendicular to it. For calamitic nematic phases this is true; for discotic nematic ones the reverse situation would be found; the diffusivity would become larger in the direction perpendicular to the director. We will also present experimental data supporting this theoretical prediction. The data comprehend the calamitic and discotic nematic lyotropic phases and a nematic thermotropic phase.

Reentrant isotropic-nematic phase transition.

This work aims at a geometrical semimicroscopic model to study the reentrant isotropic-nematic phase transition. It will be assumed that the micellar change of shape in lyotropics can be understood as the deformation of an ellipsoid which is assumed to have the idealized form of a micelle. It will be shown that such deformation is characterized by two kinds of quantities. The first one, which is a scalar determined by the ellipsoidal eccentricity, gives the intensity of the ellipsoidal deformation. The second one, which has a tensorial nature, describes the spatial distribution of such deformation and is proportional to the tensorial nematic order parameter. We construct the invariants of such deformation and couple it with the orientational order parameter to study the reentrant isotropic-nematic phase transition. We determine the thermodynamical characteristics of this phase transition and shown that it is a second-order phase transition. By comparing the theory so constructed with the experimental data, the parameters of the model will be determined.

Nonlinear refractive index measurements of discotic and calamitic nematic lyotropic phases.

In this work, through the Z-scan technique, we report on measurements of the nonlinear refractive index (n{2}) in discotic and calamitic nematic phases at room temperature in lyotropic mixtures of potassium laurate, decanol and D(2)O . This technique presents high sensitivity when compared to conventional interferometry. The nonlinear optical birefringence (Deltan{2}) of these nematic phases was also determined. The sign and absolute value of this relevant nonlinear parameter are discussed in terms of structural changes in the micellar configuration which takes place in each nematic lyotropic phase.

Viscosity peaks at the cholesteric-isotropic phase transitions.

In this work, the effective viscosity of the cholesteryl myristate and cholesteryl nonanoate liquid crystals is studied as a function of temperature at the region of their cholesteric-to-isotropic phase transition, where blue phases are found. Using a change of scale it is shown that the viscosity peaks that characterize these phase transitions are shape invariant, which suggests that large-scale fluctuations on the two-point correlation function give an important contribution to the observed viscosity. The consequences of this fact are investigated and, from the experimental data, the critical exponents associated with the diverging two-point correlation function are calculated. The results found for both compounds are essentially the same, being also in good agreement with the known values of the corresponding critical exponents of nematic-isotropic phase transition.

Bend and splay elastic constants at a reentrant isotropic-calamitic-nematic phase transition.

By measuring the ratio between the major and minor axes of closed elliptical loops created by a magnetic field, the ratio between the bend (K33) and splay (K11) elastic constants of a lyotropic mixture of potassium laurate, decanol, and water in the calamitic nematic phase is measured as a function of temperature. Since these systems present two nematic-isotropic phase transitions--the usual one, at high temperatures, and a reentrant one, at low temperatures--such measurements are used to compare the behavior of these elastic constants at the neighborhoods of these two distinct regions, which have in common the vanishing of the order parameter. The experimental data have revealed the existence of two elastic constant branches, characterizing a distinct low- and high-temperature behavior. To explain such asymmetry we support that, because of the lyotropic nature of the compound, the micellar variation, which is mainly responsible for the reentrant phase, plays a distinct role at these two phase transitions.

Induction of orientational order in the isotropic phase of a nematic liquid crystal.

The orientational properties of an isotropic dense liquid composed by anisotropic molecules, such as a liquid crystal in an isotropic phase, is studied. Using a Langevin-like equation it will be shown that the rotational motion of each molecule can be divided in two elements describing two kinds of physical motion. The first describes the Brownian rotational motion and another the coherent rotation induced by the external fields. It will be shown that, even at the isotropic phase, an order parameter describing the mean degree of alignment of the molecules around a given point can be defined. This order parameter also separates the order coming from the coherent motion from the order generated by the anisotropy in the thermal fluctuations. At the end the proposed model is compared with an experiment and it is shown that the coherent motion is enough to explain the experimental results.

Refractive index measurements in a reentrant isotropic-calamitic nematic phase transition.

In this work the temperature dependence of the extraordinary/ordinary refractive indices and optical birefringence are determined near the reentrant isotropic (I(RE))-calamitic nematic (N(C)) and N(C)-isotropic (I) phase transitions in a lyotropic mixture of potassium laurate, decanol, and water. This reentrant isotropic phase is verified by our experimental data and discussed in terms of thermal variation of the micellar shape anisotropy. The results showed also, with basis in the Vuks's equation, that near the maximum optical birefringence in the range of N(C) phase the extraordinary coefficient of electronic polarizability (phi(parallel)) is equal to the ordinary coefficient (phi( perpendicular)).

Arising of magnetic walls in the vicinities of the Frèedericksz transition.

In this paper, the dynamical formation of twist-bend periodic walls at the neighborhoods of the Frèedericksz critical point of a nematic sample of liquid crystals is studied. The theory that describes the arising of these periodic structures affirms that the mode with the fastest initial growth will fix the observed properties of these patterns. But, just above the Frèedericksz threshold there is a region where this leading mode becomes null and, therefore, a homogeneous bending of the director may be detected. This prediction was not confirmed by the experiment, and walls with very well defined wavelength were found. We will show here that the fastest growing mode cannot be defined around the Frèedericksz threshold and, therefore, a new way to compute the observed periodicity must be formulated. We assume that the observed wall results from a sum of a continuum and nonsharp distribution of modes in which the null mode is at the center.

Periodic structures in a biaxial nematic phase.

In this work experimental and theoretical results will be used to show that under convenient conditions; appropriated geometry, well chosen boundary conditions, and suitable external fields, the elastic and dynamic behavior of a sample of a biaxial nematic liquid crystal can become similar to the one observed on usual uniaxial nematic liquid crystals. It is shown that this result can be used to determine the values of some combinations of the rheologic parameters of the biaxial phase.

Temperature dependence of the refractive index near the reentrant-isotropic--calamitic-nematic phase transition.

The laser-induced nonlinear optical response of a lyotropic liquid crystal system in the reentrant-isotropic and calamitic-nematic phases is investigated by the use of the thermal lens technique. The occurrence of an inversion in the temperature coefficient of the ordinary refractive index, dn(radially)/dT, near the reentrant-isotropic-calamitic-nematic phase transition, is discussed. This effect is attributed to the behavior of the electronic polarizability due to the change in micelle shape near the isotropic-nematic transition, and correlated with the results obtained near the nematic-isotropic transition, previously reported.

Temperature dependence of the coefficient of electronic polarizability in calamitic nematic liquid crystals.

In this report the temperature dependence of the coefficient of electronic polarizability (straight phi(i)) is determined by means of the thermal expansion coefficient (beta) and ordinary/extraordinary refractive indexes measurements near the calamitic nematic-isotropic phase transition in a lyotropic mixture of sodium decylsulphonate, decanol, and water. These parameters (straight phi(i) and beta) were related to the extraordinary and ordinary refractive indexes via the temperature derivative of the Vuks's equation. The results showed that near the nematic-isotropic phase transition, the measured value of straight phi(i) was found to be about two orders of magnitude smaller than that obtained for thermotropic, showing a remarkable difference in the molecular electronic polarizability strength between lyotropic and thermotropic liquid crystals.

Calculation of the nematic entropy using digital images.

In this work we will use digital images to compute the entropy dependence on temperature of a nematic lyotropic sample. The set of images comprehend the entire temperature range between a reentrant nematic isotropic phase transition, at a low temperature, and a usual nematic isotropic phase transition at a higher temperature. We will show that, inside the nematic phase, the image entropy profile agrees accurately with the entropy given by the Maier-Saupe model. As far as we know, this is the first time that the entropy of a lyotropic nematic phase is evaluated by this method, which introduces a way to measure their macroscopic variables. Namely, being that the entropy is a thermodynamical potential, this result implies that digital images can be used to compute mean values of nematic random variables.

Rotational dissipation and the Miesowicz coefficients.

In this work, we will study the relative contribution of each of the two dissipative channels of the Eriksen, Leslie, and Parodi (ELP) approach to the observed values of the Miesowicz viscosity coefficients of the nematic liquid crystals. According to the fundamental equation of the liquid crystal's viscosity dissipative process, TS=-integral d3r(sigma)ijA(ij)+hxN , there are two channels by which the nematic viscous dissipation can occur: or it occurs by means of a shear flow configuration, where A(ij) is the characterizing term, or it occurs by means of a rotational configuration, where N is the characterizing term (these parameters will be defined in the paper). It will be also shown that this relative contribution can be measured by a simple relationship connecting the Miesowicz coefficients, which exhibits a quasitemperature independent behavior, suggesting that it is nearly constant through the entire domain of the nematic phase.

Reentrant isotropic-calamitic nematic phase transition in potassium laurate-decanol- D2O mixtures.

The phase diagram is an interesting field of research, particularly in lyotropic liquid crystals (LLC). In this way, one of the most important phase diagrams of this LLC system was reported by Yu and Saupe. Two uniaxial (calamitic--N(C) and discotic--N(D)) and one biaxial nematic (N(B)) phases were determined by these authors. Furthermore, in this phase diagram the classical isotropic phase (I was observed at high temperature as well as a reentrant isotropic phase (I(RE)) which takes place at lower temperature. Later, this phase diagram was also studied by several authors and in all cases the I(RE)-N(C)-I phase transitions were not observed. In this work, we present a study of this phase diagram through digital image processing and refractometry optical techniques. The occurrence of these phase transitions is investigated and characterized. In addition, the order parameter is obtained based on the Vuks hypothesis from a particular point, in the range of the N(C) phase, where the absolute value of the optical birefringence (Deltan is maximum.

Forbidden walls.

In this paper the presence of periodic twist-bend walls in the upper vicinity of the Frèedericksz critical point of a nematic calamitic sample is reported. According to the existing theory, the formation of these structures could not happen in this region of the magnetic field. The length of the periodicity of these walls as well as the time spent with their formation have been measured, and it was demonstrated that the coherent motion of the nematic material cannot drive their construction. We assume that the mechanism responsible for their appearance results from the magnification of some selected random fluctuations occurring at the neighborhood of the Frèedericksz critical point.

Micellar shape anisotropy and elastic constants in discotic lyotropic liquid crystals.

The elastic constants of a discotic lyotropic nematic liquid crystal are calculated by means of a pseudomolecular approach as functions of the micellar shape anisotropy. By assuming that the temperature dependence of the ratio of the elastic constants comes from the temperature dependence of the micellar shape anisotropy, the theoretical predictions are connected with experimental measurements for the ratio K(33)/K(11). This procedure permits one to determine, in a phenomenological way, the temperature dependence for the ratio of elastic constants and for the micellar shape anisotropy near the nematic-isotropic transition in agreement with the experimental data.

Inversion in the change of the refractive index and memory effect near the nematic-isotropic phase transition in a lyotropic liquid crystal.

This work demonstrates the occurrence of dn/dT inversion from negative to positive near the nematic-isotropic phase transition in a lyotropic liquid crystal. It is suggested that this effect can be attributed to a sudden increase of the electronic polarizability due to a change in the micelle shape near this phase transition. Formation of a long lasting lenslike element within the sample when it is irradiated at moderately high laser powers is also reported. This permanent lens is erasable by increasing the temperature above the nematic-isotropic transition temperature.