Difference in critical behaviour of the phase transitions nematic-smectic A1 and nematic-smectic Ad

A high resolution X-ray study is presented of the nematic to smectic A₁ phase transition in 8OPCBOB and of the nematic to smectic A_d phase transition in a binary mixture of 7CB and 8CB (7.6CB). The known critical exponents of the heat capacity of both these systems agree with the predictions for the 3D XY model. For 8OPCBOB we find values for the susceptibility g and the parallel correlation length n_|| that also agree with the 3D XY model, thus confirming the predictions of de Gennes. However, the values g and n_|| of 7.6CB are larger than the 3D XY values. This indicates a possible difference in the critical behaviour of the nematic-smectic A₁ and the nematic-smectic A_d phase transition. In all cases n_|| is larger than n_^. Furthermore it is shown how the values for the critical exponents depend on the specific form chosen for the structure factor.