No abstract

The twist-bend nematic phase, N_{TB}, may be viewed as a heliconical molecular arrangement in which the director n precesses uniformly about an extra director field, t. It corresponds to a nematic ground state exhibiting nanoscale periodic modulation. To demonstrate the stability of this phase from the elastic point of view, a natural extension of the Frank elastic energy density is proposed. The elastic energy density is built in terms of the elements of symmetry of the new phase in which intervene the components of these director fields together with the usual Cartesian tensors. It is shown that the ground state corresponds to a deformed state for which K_{22}>K_{33}. In the framework of the model, the phase transition between the usual and the twist-bend nematic phase is of second order with a finite wave vector. The model does not require a negative K_{33} in agreement with recent experimental data that yield K_{33}>0. A threshold is predicted for the molecular twist power below which no transition to a twist-bend nematic may occur.

We argue that the impedance spectroscopy of an electrolytic cell in the low-frequency range can give information on the ambipolar diffusion. Our analysis is based on a theoretical investigation of the real part of the electrical impedance of an electrolytic cell. When the mobility of the positive ions differs from that of the negative ions, a second plateau of the resistance of the cell, in series representation, is expected close to the dc limit of the applied voltage. The effective diffusion coefficient, related to the measured resistance of the cell, in the dc limit, coincides with the ambipolar diffusion coefficient. The associated relaxation time corresponds to the ambipolar diffusion, and it is proportional to the square of the thickness of the sample. In the high-frequency range, the relaxation time coincides with the Debye relaxation time, connected to the free diffusion coefficient, and it is independent of the thickness of the sample. Finally, we propose a method to calculate the diffusion coefficients of the individual ions from the impedance spectrum and we discuss the implications of ambipolar diffusion in impedance measurements and interpretation of experimental quantities.