Critical behavior of the layer-compressional elastic modulus at a smectic-smectic isolated critical point

We report on the compressional-elastic-modulus critical behavior in the vicinity of the smectic-${\mathit{A}}_2$–smectic-${\mathit{A}}_{\mathit{d}}$ 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-field (0.67) and Ising (0.79) predictions. This favors the idea that the smectic-${\mathit{A}}_2$–smectic-${\mathit{A}}_{\mathit{d}}$ critical point belongs to a new universality class, as recently predicted.