The temperature dependence of the layer compressional elastic constant B has been studied in four diferent compounds.Two of them, 4-cyano-4'-{n-octyl}biphenyl and 4-cyano-4'-{noctyloxy)biphenyl, are polar and give partially bilayered smectic-Ad phases while the remaining two are nonpolar and present monolayered smectic-A phases. In all cases, the smectic-Ato nematic phase transition was found to be second order. A second-sound resonance technique has been used to measure 4, the critical exponent of 8 on approaching the nematic phase. The values found lie in between 0.39 and 0.42, while the uncertainty is about 0.03. Although the nematic-smectic-A transition does not belong to a single universality class the 4 exponents are much less scattered than previously reported, with a mean exponent of 0.41 being consistent with the four reported values. When available, in the case of polar compounds, the set of critical exponents measured by calorimetry or x-ray scattering together with 4, seems to be accounted for by the anisotropic model of the smectic-A -nematic phase transition.

In four different compounds of the alkyl(oxy)cyanobiphenyl series, the elastic modulus B is found not to vanish at the nematic-smectic-^ {Sm-A) phase transition, contrary to most theoretical expectations. The phase transition is marginal, as the Sm-A phase is a one-dimensional solid in three-dimensional space, and it seems that B cannot decrease below a limiting value (about 10 7 dyncm ~2 here) where the fluctuations of the layers due to the Landau-Peierls instability, which scale as B ~° 2 \ would destroy the Sm-A ordering. PACS numbers: 64.70.Md The nematic-smectio/1 (N-Sm-A) phase transition remains an open problem in the field of condensed matter physics. Although the nematic phase is quite well understood in terms of anisotropic fluid, the peculiarity of the smectic-/* phase is that it consists of a one-dimensional solid in three-dimensional space [l]. In analogy with two-dimensional crystals, as shown by Landau [2] and Peierls [3], such a system should not exist at finite temperature [4], the mean square of the layer fluctuation u diverging logarithmically with the sample size L. iu 2 (r)) = ksT L %n{BK s V n d (1)In practice, putting into Eq. (1) the usual parameter values Z? = 10 8 dyncm" 2 , K\ (the splay elastic constant) = 10~6 dyn, £*r=4xl0" 14 cgs, and d (the molecular length) =30 A, one should achieve a sample thickness of several meters in order to get an amplitude of the layer fluctuation comparable to the layer thickness. This allows for the existence in the real world of a multitude of Sm-/4 phases with a rather rich polymorphism in the case of polar molecules. The main consequence of the Landau-Peierls instability, evidenced early by the highresolution x-ray-scattering technique, is that the profiles of quasi Bragg peaks are described by power laws in the reciprocal space, with exponents linked to the Caille parameter [5,6] 77c: l(q ± =0)^\/(q z -qo)" Kq==qo)~~\/q± 4-2nc

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We report on the compressional-elastic-modulus critical behavior in the vicinity of the smectic-A2-smectic-Ad liquid-crystal critical point in mixtures of undecyloxyphenyl cyanobenzyloxy benzoate and nonyloxybiphenyl cyanobenzoate. Our results show a critical vanishing of the elastic modulus with an exponent about 0.4+0. 1, which appears to disagree with both mean-Geld (0.67) and Ising (0.79) predictions. This favors the idea that the smectic-A2smectic-Ad critical point belongs to a new universality class, as recently predicted. 422521

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