Temperature-dependent polarization

Asymmetric two-site model. If the two sites are not equivalent they may be unequally populated in equilibrium under no field. This will in general give rise to a temperature-dependent polarization in zero field, that is, to a variety of pyroelectricity. A set of pyroelectric elements can be arrayed in a material so that the behaviour cancels, whereas they all contribute to the polarization response to an electric field. 

In non-dipolar dielectrics sufiSciently dense for molecular interaction, the temperature-dependent polarization (241) is generally non-zero. Such interaction will lead to an effect consisting in the induction, in any given molecule immersed in the dense medium, of a dipole moment M by the fluctuating electric field of the permanent quadrupoles, > octu-poles, >hexadecapoles, and in general multipoles" of its nei bours. 

F., and Stirling, C. J. M., Pyroelectric molecular baskets temperature-dependent polarization from substituted calix(8)arene Langmuir-Blodgett films, Langmuir, 11, 4623, 1995. 

The gradient model has been combined with two equations of state to successfully model the temperature dependence of the surface tension of polar and nonpolar fluids [54]. Widom and Tavan have modeled the surface tension of liquid He near the X transition with a modified van der Waals theory [55]. 

It seems that structural irregularities that cause spontaneous polarization are a relatively common property of niobium and tantalum oxyfluoride crystals. Fig. 100 shows the temperature dependence of SHG signals for several compounds that form island-type and chain-type structures. 

Four studies suggest that k /kK has a significant temperature dependence (Table 5.5). Although not agreeing on the precise value of ktJkte, all four studies indicate that the proportion of disproportionation increases with increasing temperature. These results are at variance with model studies that suggest that kJkK is independent of temperature. It was also proposed that the preferred termination mechanism is solvent dependent and that disproportionation is favored in more polar media.161... 

Fig. 14. Temperature dependences of the layer spacing in the smectic Ad and Cd phases for terminally polar polyphilic compounds F4H11OCB (squares), FsHnOCB (circles), FgHioOCB (triangles) and FioHnOCB (diamonds). The arrows indicate the smectic Ad - smectic Cd phase transition points (Ostrovskii et al. [45])...

In accordance with observed data, this model shows that water flux increases linearly with applied pressure AP, decreases with higher salt concentration through its impact on osmotic pressure Jt, increases with a smaller membrane thickness I, and increases with temperature through the temperature dependence of the water permeability P . The model also demonstrates that the solute or salt flux J, increases linearly with applied pressure AP, increases with higher salt concentration c , increases with a smaller membrane thickness I, and increases with temperature through the temperature dependence of the solute permeability Pj. Polarization, as described early in this section, causes the wall concentration c to exceed the bulk concentration ci,. 

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