Dynamics near the nematic—smectic-A and nematic—smectic-C phase transitions in liquid crystals

We calculate the contributions to the five viscosities which enter the stress tensor of a liquid crystal in the nematic state and the twist viscosity ${\gamma }_1$ from the order-parameter fluctuations near the nematic—smectic-A, nematic—smectic-C transitions, and the Lifshitz point. Our method is a perturbation theory which involves coupled modes. These contributions are expressed in terms of a viscosity ${\gamma }_3$ which determines the rate of decay of the order-parameter and the static-order-parameter correlation function. We also calculate the parameter which describes the reversible coupling between the shear and the director. These results are compared with those of Jähnig and Brochard near the nematic—smectic-A transition.