Self-consistent-phonon-approximation study of a double Morse hydrogen-bonded chain

Thermodynamic properties of a quasi-harmonic model for ferroelectric transitions

Within a framework of a quasi-harmonic model for quantum particles in a local potential of the double Morse type and within the mean-field approximation for interactions between particles, we investigate the thermodynamic properties of ferroelectric materials. A quantum thermodynamic treatment gives analytic expressions for the internal energy, the entropy, the specific heat, and the static susceptibility. The calculated thermodynamic characteristics are studied as a function of temperature and energy barrier, where it is shown that at the proper choice of the theory parameters, particularly the energy barrier, the model system exhibits characteristic features of either second-order tricritical or first-order phase transitions. Our results indicate that the barrier energy seems to be an important criterion for the character of the structural phase transition. The influence of quantum fluctuations manifested on zero-point energy on the phase transition and thermodynamic properties is analyzed and discussed. This leads to several quantum effects, including the existence of a saturation regime at low temperatures, where the order parameter saturates giving thermodynamic saturation of the calculated thermodynamic quantities. It is found that both quantum effects and energy barrier magnitude have an important influence on the thermodynamic properties of the ferroelectric materials and on driving the phase transition at low temperatures. Also, the analytical parameters' effect on the transition temperature is discussed, which seems to give a general insight into the structural phase transition and its nature.

Symmetry-breaking defect in coupled dipole-proton system of hydrogen-bonded ferroelectric

We consider the coupled dipole-proton system of hydrogen-bonded ferroelectric crystal with one defect dipole that is coupled more strongly with the protons than the original dipole. This defect dipole simulates the symmetry-breaking defects that are often introduced in the crystals as probes in the electron paramagnetic resonance (EPR) experiments. A particular attention is paid to the explanation of strong isotope effects that have been detected in the measurements of static and dynamic properties of the pure crystals and the symmetry-breaking defects. We suppose that the isotope effects are caused by the isotope-dependent tunneling energy and we analyze behavior of the system with and without the defect in two adiabatic approximations that correspond to the case when the protons tunnel faster than the dipoles oscillate and to the opposite case. These two approximations lead to the two models which predict different properties the pure crystals and the symmetry-breaking defects.

Discrete kink dynamics in hydrogen-bonded chains: the two-component model

We study discrete topological solitary waves (kinks and antikinks) in two nonlinear diatomic chain models that describe the collective dynamics of proton transfers in one-dimensional hydrogen-bonded networks. The essential ingredients of the models are (i) a realistic (anharmonic) ion-proton interaction in the hydrogen bond, (ii) a harmonic coupling between the protons in adjacent hydrogen bonds, and (iii) a harmonic coupling between the nearest-neighbor heavy ions (an isolated diatomic chain with the lowest acoustic band) or instead a harmonic on-site potential for the heavy ions (a diatomic chain subject to a substrate with two optical bands), both providing a bistability of the hydrogen-bonded proton. Exact two-component (kink and antikink) discrete solutions for these models are found numerically. We compare the soliton solutions and their properties in both the one- (when the heavy ions are fixed) and two-component models. The effect of stability switchings, discovered previously for a class of one-component kink-bearing models, is shown to exist in these two-component models as well. However, the presence of the second component, i.e., the softness of the heavy-ion sublattice, brings principal differences, like a significant difference in the stability switchings behavior for the kinks and the antikinks. Water-filled carbon nanotubes are briefly discussed as possible realistic systems, where topological discrete (anti)kink states might exist.

Collective proton transport with weak proton-proton coupling

A mechanism based on the peculiar dynamical properties of the hydrogen bond is suggested to describe fast proton transfers in hydrogen-bonded chains with realistic (weak) intersite proton-proton interactions. For this purpose, a two-sublattice model is suggested and studied analytically that admits an exact soliton solution. The solitons, which are topological objects (kinks and antikinks) on the one hand, but dynamical entities (like Boussinesq solitons) on the other hand, are shown to have a sufficiently large width to allow free propagation along the chain.