Elastic constants polar systems

The electronic polarization may be treated by using classical mechanics, where the system is regarded as a simple harmonic oscillator. There are three forces acting on the electron (1) elastic restoring force - Kx, where K is the elastic constant and x is the displacement of the electron from its equilibrium position, (2) viscosity force - ydxfdt, and (3) the electric force - eE e , where Eo and are the amplitude and frequency of the apphed electric field, respectively. The dynamic equation is... 

In this expression only the coefiBcient of the term quadratic in the primary parameter is temperature dependent, whereas the coefficient of the P term is constant this is so because it is not the interaction between the electric polarization that leads to a phase transition. The coefficient is of the form = Aq T - Tqa), where Tqa is the smectic-C-smectic-A transition temperature, Kj is the elastic constant, and A is the coefficient of the so-called Lifshitz term responsible for the helicoidal stmcture. p and C are the coefficients of the flexoelectric and piezoelectric bilinear couplings between the tilt and the polarization. The coefficients A and C are dependent on the chiral character of the molecules. For nonchiral molecules, A and C are zero minimization of the free energy given in Equation (4.94) yields a system where the director axis is homogeneously tilted below the transition temperature T. There is no linear coupling between the tilt and the polarization, and thus, P. For temperatures... 

The absence of slow dynamics in this system can be attributed to the fact that the penta-alanine peptide does not have any polar side-chain atom which can form a strong HB with water. With a higher level of hydration, the rotational dynamics of water approached that of bulk water, again as expected. A QENS study of protein dynamics was also carried out on the picosecond timescale of a protein, lysozyme solvated in glycerol at different water contents, h (g water/g lysozyme). For all h, a well-visible low-frequeney vibrational bump was observed. The quasi-elastic scattering can be decomposed into two Lorentzian components, corresponding to motions with charaeteristic time constants of 15 ps and 0.8 ps. The 15 ps component is the slow component, which is in the same range observed in many other experimental studies. 

In this system of equations the piezoelectric charge constant d indicates the intensity of the piezo effect is the dielectric constant for constant T and is the elastic compliance for constant E eft is the transpose of matrix d. The mentioned parameters are tensors of the first to fourth order. A simplification is possible by using the symmetry properties of tensors. Usually, the Cartesian coordinate system in Fig. 6.12a is used, with axis 3 pointing in the direction of polarization of the piezo substance (see below) [5,6]. 

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