Smectic-C–smectic-Icritical point in a liquid crystal mixture: Static and dynamic thermal behavior

The theoretically predicted smectic-C (Sm-C)--smectic-I (Sm-I, a tilted hexatic phase) critical point has been discovered in a racemic mixture of methylbutyl phenyl octylbiphenyl-carboxylate (8SI) and the octyloxybiphenyl analog (8OSI). High-resolution ac calorimetry and nonadiabatic scanning calorimetry show an evolution from a first-order Sm-C--Sm-I transition in 8SI to continuous supercritical behavior in 8OSI (no thermodynamic transition). The critical composition is Xc{}75, where X is the weight percent 8OSI. The static critical heat capacity Cₚ(T,X=75) is characterized by a critical exponent x=1.06±{}0.08 that corresponds to the exponent {γ} due to the path of approach to the critical point. This is a mean-field value of {γ} rather than the value associated with the new universality class that includes Sm-C--Sm-I, Sm-C*--Sm-C*, and Sm-Ad--Sm-A₂ (partial bilayer--bilayer smectic) critical points. It is proposed that mean-field behavior is observed due to long bare correlation lengths (Ginzburg criterion). Note that Cₚ(T,X) measured along the path X=Xc is effectively a susceptibility, like Cₚ for a pure fluid near its liquid-gas critical point. Data obtained close to Tc show a systematic frequency dependence, and these Cₚ(T,{ω}) data are discussed in terms of critical slowing down and dynamic scaling behavior.