Investigation on the critical behaviour in the vicinity of the smectic-A to re-entrant nematic-phase transition.

The study focused on the binary system 6OCB and 8OCB, which is well-suited for investigating stable re-entrant nematic-phase transitions. High-resolution measurements of heat capacity and birefringence are used to analyse critical behaviours near the nematic – smectic-A (N-SmA) and the smectic-A – re-entrant nematic (SmA- ${{\rm{N}}_{\rm{R}}}$ N R ) phase transitions. The critical behaviour of these transitions has been explored with the aid of a differential quotient extracted from the birefringence $\left({\rm \Delta {{n}}} \right)$ Δ n values. Simultaneously, critical exponents extracted from the specific heat capacity anomaly are also used to analyse the critical behaviour of the phase transition. The results indicate that the SmA to ${{\rm{N}}_{\rm{R}}}$ N R phase transition exhibits non-universal behaviour, with effective exponents falling between the tricritical (TCP) and 3D-XY values, similar to the N-SmA phase transition. The study reveals the existence of two tricritical points: one associated with the N-SmA transition and the other corresponding to the SmA- ${{\rm{N}}_{\rm{R}}}$ N R transition. This is supported by plotting the McMillan ratio against the critical exponents obtained from both birefringence and specific heat capacity anomaly. Again, with an increase in the SmA range, the SmA- ${{\rm{N}}_{\rm{R}}}$ N R transition tends towards the tricritical point (TCP), suggesting a relationship between the SmA range and the transitional behaviour. [ABSTRACT FROM AUTHOR]