Dipole temperature variation

Figure 5. Model spectra of a naked neutron star. The emitted spectrum with electron-phonon damping accounted for and Tsurf = 106 K. Left panel uniform surface temperature right panel meridional temperature variation. The dashed line is the blackbody at Tsurf and the dash-dotted line the blackbody which best-fits the calculated spectrum in the 0.1-2 keV range. The two models shown in each panel are computed for a dipole field Bp = 5 x 1013 G (upper solid curve) and Bp = 3 x 1013 G (lower solid curve). The spectra are at the star surface and no red-shift correction has been applied. From Turolla, Zane and Drake (2004).

One of the important characteristics of ferroelectrics is that the dielectric constant obeys the Curie- Weiss law (equation 6.48), similar to the equation relating magnetic susceptibility with temperature in ferromagnetic materials. In Fig. 6.55 the temperature variation of dielectric constant of a single crystal of BaTiOj is shown to illustrate the behaviour. Above 393 K, BaTiOj becomes paraelectric (dipoles are randomized). Polycrystalline samples show less-marked changes at the transition temperature. 

At the time when P. Debye originated the dipole theory in order to explain the peculiar temperature variations in the dielectric constants of certain substances, most measurements of the alterations in dielectric constants with temperature had been made on liquids. The main point was that the theory should reproduce the behaviour of these liquids, but the agreement with actual measurements was anything but satisfactory. We now know that owing to our ignorance of the constant of the internal field the theory in the strict sense is only capable of explaining the effect of temperature on the dielectric constants of gases and vapours.f... 

Table CXXXVL Temperature Variation of Dipole Moment of dipole...

They then explained (in a descriptive fashion only) the dielectric constant as the result of the reorientation of indefinite liquid crystals in the applied field. Within the crystals the H bonds are more or less regularly oriented in such a manner that the bond dipoles do not cancel. A large dielectric constant results. The temperature variation of is attributed to changes in the relative amount of the three lattice types present. 

Table CXXXVI. Temperature Variation of Dipole Moment of temperature the dipole the Di-substituted Derivatives of Ethane moment must also in-...

The conformation isomerism in a wide range (31 examples) of 1-sub-stituted derivatives of 3,3-dimethylbutane has been examined. In some cases, the temperature variation of the vicinal coupling constants was studied. In 1,1,2-trichloroethane the coupling constants of the gauche and anti isomers are deduced from solvent-dependent changes in the observed coupling constants. In some similar systems (1,1,2-trichloro- and 1,1,2-tribromoethane in carbon tetrachloride and in benzene), a correlation of the dipole moments of the compounds and the vicinal coupling constants was found.Rotational isomerism in the phenylalanine anion and dipolar ion has been studied in deuterium oxide solutions. 

Thus, also a permanent dipole mechanism may be characterized by a transition of the X quantity from a quadratic field strength dependence to a linear one concomitant with the E dependence the temperature variation changes from T to T K Therefore the temperature dependence of equilibrium and rate constants may be used to differentiate between permanent and induced moments. 

The dipole moment of a molecule can be obtained from a measurement of the variation with temperature of the dielectric constant of a pure liquid or gaseous substance. In an electric field, as between the electrostatically charged plates of a capacitor, polar molecules tend to orient themselves, each one pointing its positive end toward the negative plate and its negative end toward the positive plate. This orientation of the molecules partially neutralizes the applied field and thus increases the capacity of the capacitor, an effect described by saying that the substance has a dielectric constant greater than unity (80 for liquid water at 20°C). The dipole moments of some simple molecules can also be determined very accurately by microwave spectroscopy. 

One may wonder whether a purely harmonic model is always realistic in biological systems, since strongly unharmonic motions are expected at room temperature in proteins [30,31,32] and in the solvent. Marcus has demonstrated that it is possible to go beyond the harmonic approximation for the nuclear motions if the temperature is high enough so that they can be treated classically. More specifically, he has examined the situation in which the motions coupled to the electron transfer process include quantum modes, as well as classical modes which describe the reorientations of the medium dipoles. Marcus has shown that the rate expression is then identical to that obtained when these reorientations are represented by harmonic oscillators in the high temperature limit, provided that AU° is replaced by the free energy variation AG [33]. In practice, tractable expressions can be derived only in special cases, and we will summarize below the formulae that are more commonly used in the applications. 

Samples of PVB are prepared, having an isotactic content of 46 %. Dielectric measurements are performed in solutions of both samples in dioxane and 1-methylnaphthalene at several temperatures, and dipole ratios Dx = lxm2 are found to be 0.52 and 0.45, respectively. No noticeable dependence of Dx with molecular weight is found the variation of Dx with temperature is too small to allow an accurate determination of Its temperature coefficient. An RIS model is derived and used to calculate dipole and characteristic (C = 0/o/2) ratios. 

The simplified two-rotational-state scheme previously used for PMA is not able to predict satisfactory values for its dipole moment. A more realistic scheme with four rotational states is introduced which allows for the distinguishing between different interactions for different orientations of the ester group lateral to the chain. Values of dimensions, dipole moments, stereochemical equilibria, and NMR coupling constants calculated using this scheme are in agreement with experimental results. However, this scheme falls to reproduce the experimental variation of dipole moment with temperature. 

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