Layer undulations in a smectic C liquid crystal with weak anchoring

The free energy for a sample of smectic~C liquid crystal bounded between two semi-infinite plates with weak surface anchoring on the boundaries is considered. A magnetic field is applied across the sample and the ensuing layer undulations are studied. The free energy is minimised to give relations involving the elastic energies, magnetic field strength and wave numbers which govern the layer undulations. Forms for the critical field strength and critical wave numbers are derived and compared to analogous results in a system with strong surface anchoring. An expression for the layer undulation amplitude is derived for weak anchoring which can be compared with the classical Helfrich--Hurault theory for strong anchoring and recent experimental results for cholesteric liquid crystals.