Molecular models of the smectic-C phase and magnetic resonance experiments

Abstract

In recent molecular models of the smectic-C phase the tilt angle χ is related to a characteristic biaxial order parameter μc; χ=const. ×μc, for small χ. We derive the effective nuclear spin Hamiltonian taking into account the orientational order parameter μc, and apply this Hamiltonian to a consideration of published nuclear magnetic resonance experiments. The order parameter μc may be defined as the Z, Y component of the order matrix 〈ν3ν2+ν2ν3〉, where ν3 and ν2 denote the directions of the long molecular axis and a given transverse axis, respectively, Z is the preferred orientation of ν3 (i.e., ? is the nematic director), and the plane ZY is the tilting plane. It is expected that μc may reach values of order 10−1. Experimentally, the orientational order in the smectic-C phase of terephtal bis(butylaniline) (TBBA) has been investigated by Luz, Hewitt, and Meiboom, using the technique of deuterium magnetic resonance. It is shown here that the outward movement of the edges of the spectra, which should occur for small sample rotations, is smaller than 1% of the maximum quadrupole splitting, if μc≲10−1. The accuracy of the experiment is not sufficient to detect this effect. On the other hand, some peculiar features of the experimental spectra, not explained by the uniaxial model, are pointed out and interpreted qualitatively in terms of μc. Such features are also present in proton resonance spectra of neat TBBA and DHAB (diheptyloxyazoxybenzene) obtained by Luz and Meiboom. We conclude that more experiments and more detailed numerical studies of the spectra, including the effect of the order parameter μc, are required to determine whether the biaxial picture of the smectic-C phase is valid.