M. Simões

Global behaviour of the order parameter in nematic phase

In this paper we study the behaviour of the order parameter of the nematic phase for all temperatures of the phase: from the neighbourhoods of the nematic crystalline phase transition region to the neighbourhoods of the nematic isotropic phase transition region. To do this, we use experimental birefringence data and thermal anisotropy conductivity data in a recursive process that makes an independent and local calculation of the order parameter exponent β(T) for each temperature value T. With these data, and with this procedure, we construct the profile of β(T) and reveal that it remains constant along the entire range of the phase.

Universal Nature of the Nematic Phase

In this paper, we synthesize and resume some previous results found on the universality of the nematic phases anisotropic behavior. Throughout a linear transformation on the experimental data of some anisotropic macroscopic properties, we show that the corresponding points become distributed along universal lines that extend along the entire range of the nematic phase, from the nematic-isotropic phase-transition region until the nematic-crystalline phase-transition region. We also show that the universal curve of the order parameter is characterized by a singular power law behavior, with a single exponent that encompasses the entire range of the nematic phase.

Global Order Parameter Critical Exponent: A Different Calculation Approach

In this paper we present an approach that permits to study the behavior of the nematic phases order parameter exponent (β) for all temperatures of the phase; our method makes an independent calculation of β for each temperature value T. Here use hypothetical data to analyze the consistence of the results, the limitation of the experimental data usability and the influences of the experimental errors on the β(T) curves. After that, we use experimental data to show that the order parameter critical-like exponent presents a constant behavior along the entire domain of the nematic phase.

Smectic A – Cholesteric Phase Transition: A Viscosity Study

Viscosity measurements of the cholesteryl myristate as a function of temperature and shear rate are presented. Ranging from the smectic A phase to the isotropic phase the data cover every liquid crystalline interval of the compound. It is shown that the viscosity values of the sample, originated from the non-fixed director alignment, can be reduced to a unique temperature dependent curve. That is, using a simple scaling hypothesis, it is shown that curves corresponding to the different shear rates coalesce into a single viscosity curve characterizing each different phase of the compound.

An image processing study of a reentrant discotic cholesteric – biaxial cholesteric phase transition

ABSTRACT In this work, we study and characterize the cholesteric sequence of phases (ChDr − ChB − ChD), where the first ChDr is the reentrant cholesteric discotic phase, ChB is the cholesteric biaxial phase and the second ChD is the cholesteric discotic phase. This sequence of phases is studied through polarized light microscopy and image processing technique, where, for the first time, the domains and borders of these transitions are established and characterized. They are also investigated and optically characterized throughout their textures.

Anomalies and analytic torsion on hyperbolic manifolds

The global additive and multiplicative properties of the Laplacian on j-forms and related zeta functions are analyzed. The explicit form of zeta functions on a product of closed oriented hyperbolic manifolds Γ\Hd and of the multiplicative anomaly are derived. We also calculate in an explicit form the analytic torsion associated with a connected sum of such manifolds.

Refractive index measurements in a reentrant discotic nematic–biaxial nematic phase transition

ABSTRACT The optical characterization of uniaxial (reentrant discotic – and discotic – ) and biaxial nematic ( phases requires the measurements of two and three refractive indices, respectively. These optical parameters were determined near the reentrant isotropic -isotropic (I) phase transitions in a lyotropic mixture of potassium laurate, decanol and . Biaxial positive ( nematic phase is optically characterized between two uniaxial discotic nematic phases from refractive index data and confirmed via conoscopic images. The micellar configuration of uniaxial and biaxial nematic phases is discussed as a consequence of our experimental data.

Conoscopic image of a biaxial nematic phase in a sodium decyl sulfate – decanol – D2O mixture

ABSTRACT The nematic phases of a lyotropic system NadS/ decanol/ heavy water are investigated using optical conoscopy and image processing. The phase diagram obtained from these lyotropic materials predicts the occurrence of a direct phase transition, which does not present the biaxial nematic phase, between the discotic (ND) and calamitic (NC) nematic phases. A biaxial nematic (NB) phase is optically characterized and confirmed through conoscopic image, inside the biaxial range, between the two uniaxial nematic phases. Also, their respective transition points are determined by means of image processing. The NB phase observed here is discussed as part of the nature of the micellar configuration of lyotropic materials which exhibit uniaxial nematic phases.

A Geometrical Approach to the Miesowicz's Coefficients

Here we will show how the use of a geometrical approach leads to a reduction of the number of the viscosity coefficients of the nematic liquid crystals. Usually they are described by five free parameters; we will show that a geometrical approach can reduce this number to three. This result will follow from the modified version of the Hess-Baalss approach. As a consequence of the application of the Onsager relation, these three viscosity terms become related by the effective eccentricity of the nematic grain, leading to a connection between the Miesowiczs coefficients.

A geometrical relation between the Miesowicz's coefficients

In this work, it will be shown that the Miesowiczs viscosity coefficients of the nematic liquid crystals are not independent, but connected by the effective geometry that the nematic molecules/micelles acquire under random oscillatory vibration. This result follows from a straightforward application of the Onsager reciprocal relation to a recent proposed generalisation of the conformal transformation approach of the nematic rheology [1], where it had been assumed that the nematic dissipative process is not driven by a unique initial isotropic viscosity term, but by two; a rotational term has been added. As a consequence of the application of the Onsager relation, these two viscosity terms become related by the effective eccentricity of the nematic grain, leading to a connection between the Miesowiczs coefficients. Known experimental data of nematic compounds are used to test this prediction, resulting in its confirmation, which gives to the conformal transformation approach a predictive vigour that is not found in any other nematic viscosity theory.