J. D. Litster

Crossover to tricritical behavior at the nematic to smectic A transition: an X-ray scattering study

AbstractWe have carried out a comprehensive x-ray scattering study of the nematic to smecticA transition in the alkylbenzoate (nCB) and thiosulfate

Order and Fluctuations in Smectic Liquid Crystals

\bar nS5

Light scattering studies of crossover to a liquid crystal tricritical point

series. By changing the aliphatic chain lengthn (CnH2n+1) in these series, crossovers from critical to tricritical behavior are induced. We observe a smooth progression of effective exponents from the set,y≃1.5,v‖≃0.80, andv⊥≃0.67 toy=1.1,v‖=0.6, andv⊥=0.5 for the critical and tricritical regions respectively. In both cases the exponents are close to, but in disagreement with, values expected from current theoretical models. We conclude on an empirical basis that the varied exponents reported in the literature for other systems reflect the critical to tricritical crossover.

Lower Marginal Dimensionality. X-Ray Scattering from the Smectic-A Phase of Iquid Crystals

In this paper, we report results from synchrotron X-ray scattering studies of thefluid/hexactic/solid phases and phase transitions in both very thick and very thin, freely suspended films of tilted hexatic liquid crystals. Contrary to the thick film case, the higher Fourier coefficients describing the bond orientational order are suppressed in very thin films. This suppression is consistent with a two-dimensional bond orientational order parameter,Ψ6, rather than the three-dimensional bond orientational order parameter found in very thick films. For a film containing twently-three (23) smectic layers we find thatΨ6 is two-dimensional whereas the positional order in the crystallineSJ phase is three-dimensional. We present an analysis of the thick film data in terms of the three-dimensionalXY-model and a new mean field theory model which incorporates explicitly the quasi two-dimensional nature of bulk smectic phases.

High Resolution X-Ray and Light Scattering Spectroscopy of Liquid Crystals

Liquid crystals are among the most interesting condensed states of matter; they are interesting in their own right and we also expect that insights into their properties will help to understand other condensed phases that exist in nature. In all condensed phases there are thermally excited fluctuations. Depending on the spatial dimensionality along with the symmetry and range of interparticle interactions, these fluctuations can play a role of varying significance in determining properties of matter. In some materials the fluctuations play an unimportant role and the statistical mechanical calculations to understand which phases occur and their properties can be carried out simply by a mean field approximation. In other materials the fluctuations profoundly alter the material properties in the vicinity of phase transitions, and only recently have we learned how to make approximate calculations with sufficient accuracy to explain the thermodynamic behavior of these materials. This is the class of phase changes known as critical phenomena. Finally, in certain cases, the fluctuations are so important as to prevent the establishment of phases which interactions between the molecules would otherwise favor.

Pretransitional Phenomena in the Isotropic Phase of a Nematic Liquid Crystal

Abstract Although conceptually very simple, the statistical mechanics of surfactant monolayers in solution give rise to the rich phase behavior and novel physical properties of these systems. The fluctuations due to capillary waves of a single saturated monolayer are studied using X-ray reflectivity. The interfacial tension and bending rigidity are found to be very small and account for the disordered structure of bicontinuous microemulsions. Neutron scattering techniques are also used to measure the decay of structural correlations among the surfactant monolayers within a microemulsion phase, and these results are explained using a Ginzburg—Landau theory.

Correlation Between Critical Coefficients and Critical Exponents

We have used light scattering to study nematic elastic constantsK2 andK3 in the alkyl-cyanobiphenyl (n CB) system. As the average alkyl chain lengthn increases, the temperature range of the nematic phase decreases and the system approaches a tricritical point. Our data are analyzed to determine the parallel and perpendicular correlation lengths and critical exponents for smectic short-range order. We find a continuous decrease in the critical exponentsv∥ andv⊥ as the tricritical point, which occurs at ≃9.1 CB, is approached. There is also a significant decrease in the magnitude of the parallel correlation length at a fixed reduced temperature.

Observation of algebraic decay of positional order in a smectic liquid crystal

In the previous chapter we have seen that the critical fluctuations associating a second order phase transition, expressed in terms of a response function X(q) directly measurable by scattering spectroscopy, may be treated in a self-consistent and correct way by simple mean field theory if the dimensionality exceeds a certain marginal dimensionality d*. In particular we stressed that d* depends on the volume in reciprocal space available to the critical fluctuations, and systems with d ≤ d* can indeed be studied experimentally. In this chapter we shall discuss the opposite limit: That the fluctuations are so strong that they prevent the onset of true long range order at all. Let us look upon an example. We postulate an ordered crystalline state in d dimensions and we want to calculate the mean squared fluctuations . If diverges in an infinite sample the postulated long range order cannot take place. First, consider a sinusoidal fluctuation with wavevector \(\vec{q}\) and amplitude \({{\vec{u}}_{q}}\). For simplicity let us assume that the medium is elasrically isotropic.