Elastic constants electrostatic contribution

The observed elastic shear constant C44 of aluminum is 2,8 x 10" crg/cm, whereas the electrostatic contribution is 14.8 x 10" erg/cm (Harrison, 1966a, p, 179 the value there was based upon an effective charge 7.9 percent larger tlian the 3,0 appropriate here). The band-structure energy is an estimate of the difference, —12.0 x 10" crg/cm. Even if we sum all terms, the result is approximate because of the neglect ofterms of higher order than two and the use of an approximate pscudopoteiitial. We obtain the effect of the nearest lattice wave numbers here. 

The electrostatic contribution to the elastic constant for SrTiOj is estimated by considering point charges of 2c at Sr sites, 4c at Ti sites, and —2c at oxygen sites. We will find that this approach leads to a contribution to C44 of 24.7 x 10 erg/cm for SrTiO, and 26.2 x 10" erg/cm for KTaO (also 27.8 and 34.7 for KM0O3 and ReOj, respectively, in the. same units). These values are con-... 

Since the flexoelectric effect is associated with curvature distortions of the director field it seems natural to expect that the splay and bend elastic constants themselves may have contributions from flexoelectricity. The shape polarity of the molecules invoked by Meyer will have a direct mechanical influence independently of flexoelectricity and can be expected to lower the relevant elastic constants.The flexoelectric polarization will generate an electrostatic self-energy and hence make an independent contribution to the elastic constants. In the absence of any external field, the electric displacement D = 0 and the flexoelectric polarization generates an internal field E = —P/eo, where eq is the vacuum dielectric constant. Considering only a director deformation confined to a plane, and described by a polar angle 9 z), and in the absence of ionic screening, the energy density due to a splay-bend deformation reads as ... 

The confinement of water in nanometer-size pores between the walls of the polymer material affects the structure of water. The observed freezing-point suppression [49,50] and reduced dielectric constant of water [115-117], are macroscopic manifestations of this effect. The interfacial area between polymer and water provides a complex environment for proton transport. The complications for the theoretical description are caused by the flexibiHty of the sidechains, their random distributions and their partial penetration into the bulk of water-filled pores. The charged polymer sidechains contribute elastic ( entropic ) and electrostatic terms to the free energy [54,55]. Distribution and mobilities of protons depend strongly on the resulting sidechain-water interactions [54,56,118]. 

This brings us to the structure of the micelle in the strongly charged limit. As usual, the micellar structure in equilibrium reflects the interplay of and corona- In thc present case, with R/b Na and h /Na 1, the elastic term in corona IS a constant while the electrostatic term is negligible. The dominant contribution is due to the mixing entropy of the condensed counterions Fcorona/ kT kTNA In pNa and thus... 

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