Phase diagram, fluctuations, and phase transitions near the liquid-crystal nematic–smectic-A–smectic-Cmulticritical point

We have performed high-resolution x-ray scattering studies of the binary liquid-crystal system of octyloxycyanobiphenyl and heptyloxypentylphenylthiolbenzoate (80CB+7¯S5) near the nematic–smectic-A–smectic-C (NAC) multicritical point. We find that the phase diagram and smectic-order fluctuations are well described by a Lifshitz-point model. Above the nematic–smectic-C(N-SmC) phase boundary, we find a line along which the fluctuations change from being SmA-like to SmC-like; this is signaled by the vanishing of the transverse quadratic term in the expression for the x-ray scattering intensity; that is, the transverse fluctuations scale like $q_{\perp }^{\mathrm{-}4}$. The geometry of this Lifshitz line appears to mirror that of the SmA-SmC boundary. A much more extended SmC fluctuation region is observed for lower concentrations of 80CB. Thus the N-SmC pretransitional area is divided into two regions: a pure N-SmC region and a multicritical region. The tilt angle exhibits a first-order transition at the N-SmC boundary. Along the SmA-SmC phase boundary, the tilt is well described either by a power law with an average exponent β=0.43±0.03 or by mean-field theory including a sixth-order correction. No crossover to critical or tricritical behavior is observed as the NAC point is approached. Along the N-SmA phase boundary, we observe second-order N-SmA transitions with average values of the exponents in this region of ${\nu }_{?}$=0.90, ${\nu }_{\perp }$=0.75, and γ=1.55 for the parallel and perpendicular correlation lengths and susceptibility, respectively. Very near the NAC concentration, we observe multicritical behavior, with the above exponents renormalized by the crossover exponent of the N-SmA phase boundary.