The effects of the molecular symmetry on macroscopic properties of conventional and unconventional nematic phases are investigated theoretically. These effects concern: (1) the form of the molecular orientation fluctuations, (2) the thermodynamic behavior and the list of stable ordered phases, (3) the effective symmetry of the molecules in the ordered phases. The order-parameter consists of tensors forming the main harmonics of the fluctuation distribution. In conventional models (valid for uniaxial molecules) a single tensor is sufficient while unconventional models (valid for less symmetric molecules) need several tensors with the same rank. We analyze the qualitative differences arising when the number of equivalent tensors varies. We show how to work out complete models in the general case, and to calculate the sequences of stable phases and the corresponding effective molecular symmetries. This yields, for each molecular group and each tensor rank, a complete classification and a deep insight into the structure of thermotropic nematics. This work generalizes the approach we have applied to polar nematics recently observed in polyester compounds and to unconventional uniaxial and biaxial phases of bent-core materials.

The ferroelectric order and magnetic field induced effects observed in the spiral phase of MnWO4 are described theoretically. It is demonstrated explicitly that the Dzyaloshinskii-Moriya antisymmetric interactions contribute to the correlation between spins and electric dipoles in the incommensurate and commensurate ferroelectric phases of magnetic multiferroics. However, other single-site symmetric interactions are shown to be involved in the magnetoelectric process, suggesting the possible existence of an electric polarization originating from purely symmetric effects.

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The theory of unconventional one-dimensional periodic mesophases forming in a liquid of achiral bent-core molecules is presented. The order parameter is a polarization wave. Three distinct phases which can be stabilized directly from the isotropic liquid phase are associated with linear, circular, and elliptic polarizations of the wave. The elliptic polarization leads to the structure of the commonly studied B2 "bent-core" mesophase whereas the recently discovered C(p) phase may be assigned to the linear polarization. We present the molecular configurations and macroscopic properties of the stable states. Their behavior under chiral doping and electric field application are investigated and the corresponding phase diagrams are calculated.

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