| The critical dynamics near two liquid crystal phase transitions are studied theoretically using a mode coupling formalism. At the smectic A - smectic C phase transition, a mode coupling theory due to Andereck and Swift accounts successfully for the properties of attenuation and speed of ultrasound, but scaling relations suggest that the specific heat should diverge, contrary to the observed mean field behavior. The contributions to the specific heat made by the couplings considered in the Andereck-Swift theory are calculated both for the static and dynamic cases. In neither case is it found that the contribution to the specific heat from these couplings is large enough to account for the discrepancy.; Next, the behavior of the thermal diffusivity at the smectic A - smectic C phase transition is studied. The thermal diffusivity measured for the compound A7 shows unusual behavior near the transition, as it first shows a dip followed by a divergence as the critical temperature is approached from above. Model C, a standard dynamical model which has been suggested as appropriate to describe the thermal behavior for this transition, is studied and found to not describe the thermal diffusivity. After this, the theory of Andereck and Swift is applied and does show a divergence which gives reasonable numerical values when evaluated with parameters known for TBBA. The fact that the same theory is used to explain both thermal and acoustic properties at the smectic A - smectic C transition allows the possibility for a number of qualitative predictions for specific compounds.; Finally, a theory of the attenuation and speed of ultrasound near the cholesteric - twisted-grain-boundary-A phase transition is presented. The chiral Chen-Lubensky free energy is employed to calculate the behavior of the elastic constants and the viscosities near the transition. An isotropic dip in the speed of sound is predicted, and a divergence in the attenuation coefficient is predicted which has an anisotropic prefactor, but isotropic critical exponents. |
