High-resolution x-ray and light-scattering study of critical behavior associated with the nematic-smectic-A transition in 4-cyano-4′-octylbiphenyl

We have carried out a high-resolution x-ray study of the mass-density fluctuations and a light-scattering study of the bend-mode-director fluctuations associated with the nematic-smectic-A phase transition in 4-cyano-4′-octylbiphenyl (8CB). This phase transition is found to be nearly second order with a first-order temperature jump of less than 10 mK. The peak scattering intensity, σ(q→0), with q→0=(0, 0, 2πd), where d is the layer spacing, and the longitudinal correlation length, ξ, exhibit single power-law divergences for 5×10-5<|1-TTc|<2×10-2 with critical exponents of γ=1.26±0.06 and ν=0.67±0.02, respectively. These exponents agree within the errors with the predicted d=3, n=2 values appropriate to de Gennes' superconductor analogue model. The ratio of the longitudinal to transverse correlation lengths, ξξ, increases gradually with decreasing reduced temperature, changing by a factor of 2.6 over the above temperature range. This corresponds to an effective exponent difference †=0.16. The bend mode elastic constant K3, which is predicted to have a divergent contribution (kBTqo224π)2ξ, exhibits single power law behavior for 10-4≤1-TTc<10-2, with ν=0.62±0.03 in reasonable agreement with the x-ray results. The predicted amplitude is, however, wrong by a factor of four. Measurements of B, the layer compressibility coefficient in the smectic-A phase, yield BK1∼(Tc-T)φ with φ=0.26±0.06, in agreement with previous experiments in N-p-cyanobenzylidene-p-octyloxyanilene (CBOOA) and octyloxycyanobenzylidene (80CB), but in marked disagreement with the superconducting analogue model which predicts φ=ν1=0.67.