Landau Theory of Nematic to Smectic-A Phase Transition
20 Jan 1998-International Journal of Modern Physics B (World Scientific Publishing Company)-Vol. 12, Iss: 2, pp 207-212
TL;DR: In this article, a phenomenological Landau-like theory is presented, which describes the nematic and smectic-A phase transition and the stability of the different phases.
Abstract: A phenomenological Landau-like theory is presented here, which describes the nematic and smectic-A phase. The problem of the first or second order nature of the nematic to smectic-A phase transition is explored and the stability of the different phases are also calculated. On the basis of this work it is argued that the nematic to smectic-A transition is of first order nature.
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TL;DR: The phase diagram and X-ray studies of mixtures of 8OCB (cyanooctyloxybiphenyl) and 4O8 (butyloxybenzilidene octylaniline) as discussed by the authors demonstrate that there is no nematic phase.
Abstract: Phase diagram and X-ray studies of mixtures of 8OCB (cyanooctyloxybiphenyl) and 4O8 (butyloxybenzilidene octylaniline)and 8OCB and 6OCB (cyanohexyloxybiphenyl) demonstrate: 1. 4O8 molecules inhibit the pairing of the 8OCB molecules. One 4O8 molecule is attributed with the breakup of one 8OCB pair. 2. The maximum pressure at which the smectic A phase is stable increases as the number of 8OCB pairs decreases. 3. The temperature at which the smectic A phase is stable is maximum when the mixture is most polar [no 8OCB pairs at all]. For these mixtures, there is no nematic phase. 4. There is no smectic A phase when all of the 8OCB molecules are paired. 5. When the nematic-smectic A transition temperature of the mixture approaches the nematic-isotropic transition temperature of the pure compound, the nematic phase is completely suppressed. Assuming that the smectic A order parameter is coupled to the nematic order parameter and the coupling depends on temperature and composition, a Landau description i...
95 citations
76 citations
TL;DR: In this article, a high-resolution heat-capacity and x-ray study of the nematic-smectic-$A$ transition in the single-layer smectic material butyloxybenzylidene octylaniline (40.8) was performed.
Abstract: We report a high-resolution heat-capacity and x-ray study of the nematic---smectic-$A$ transition in the single-layer smectic material butyloxybenzylidene octylaniline (40.8). We find that the transition is second order to within 3 mK, with critical behavior closely similar to that observed previously in bilayer smectic materials such as octyloxycyanobiphenyl (8OCB). For the critical exponents we measure $\ensuremath{\gamma}=1.31\ifmmode\pm\else\textpm\fi{}0.02$, ${\ensuremath{
u}}_{\ensuremath{\parallel}}=0.70\ifmmode\pm\else\textpm\fi{}0.01$, ${\ensuremath{
u}}_{\ensuremath{\perp}}=0.57\ifmmode\pm\else\textpm\fi{}0.01$, and $\ensuremath{\alpha}={\ensuremath{\alpha}}^{\ensuremath{'}}=0.15\ifmmode\pm\else\textpm\fi{}0.05$. These exponents are consistent with the anisotropic hyperscaling relation ${\ensuremath{
u}}_{\ensuremath{\parallel}}+2{\ensuremath{
u}}_{\ensuremath{\perp}}=2\ensuremath{-}\ensuremath{\alpha}$. In addition, we find that the ratio of the amplitudes of the critical heat capacities in 40.8 and 8OCB is inversely proportional to the ratio of the correlated volumes as measured with x rays. The smectic longitudinal correlation length measured directly with x rays agrees quantitatively with that deduced by von K\"anel and Litster from the director fluctuations. Substantial disagreements with the superconducting analog model remain unexplained.
61 citations
TL;DR: In this paper, high-resolution ac calorimetric, x-ray, and light-scattering measurements have been made on the nematic-smectic-$A$ phase transition.
Abstract: High-resolution ac calorimetric, x-ray, and light-scattering measurements have been made on $\mathrm{N}\ensuremath{-}[4\ensuremath{-}(n\ensuremath{-}\mathrm{butyloxy})\mathrm{benzylidene}]\ensuremath{-}{4}^{\ensuremath{'}}\ensuremath{-}(n\ensuremath{-}\mathrm{heptyl})\mathrm{aniline}$ (4O.7) near the nematic-smectic-$A$ phase transition. This transition is second order, with a variation in ${C}_{p}$ which is well described by a critical exponent $\ensuremath{\alpha}={\ensuremath{\alpha}}^{\ensuremath{'}}=\ensuremath{-}0.026$ corresponding to the three-dimensional $\mathrm{XY}$ model. The longitudinal and transverse correlation lengths exhibit single-power-law divergences over the reduced-temperature range ${10}^{\ensuremath{-}2}$ to 3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ with exponents ${\ensuremath{
u}}_{\ensuremath{\parallel}}=0.78\ifmmode\pm\else\textpm\fi{}0.02$ and ${\ensuremath{
u}}_{\ensuremath{\perp}}=0.65\ifmmode\pm\else\textpm\fi{}0.02$, respectively. The anisotropic hyperscaling relation ${\ensuremath{
u}}_{\ensuremath{\parallel}}+2{\ensuremath{
u}}_{\ensuremath{\perp}}+\ensuremath{\alpha}=2$ is satisfied to within the errors. A dynamical-scaling analysis of light-scattering measurements of the bend-mode director fluctuations with elastic constant ${K}_{3}$ yields values for ${\ensuremath{\xi}}_{\ensuremath{\parallel}}$ which agree absolutely with the x-ray measurements. Thus the data are all internally consistent, and they appear to exclude all current theories of the nematic-smectic-$A$ transition. It is observed that the overall critical behavior in smectic liquid crystals is sensitive to the width of the nematic range; this may offer an explanation for the apparent nonuniversality of the exponents.
59 citations
TL;DR: In this article, it was shown that a tricritical point analogous to that in He 3 -He 4 mixtures should occur in mixtures of liquid crystals with first and second order nematic-smectic transitions.
48 citations