Rotation characteristic temperature

The values of p and T can now be used for the statistical mechanical calculations. In order to calculate the rotational characteristic temperature t with Eq. (20), use the literature value for the rotational constant Bo = 0.037315 cm [or calculate Bo from the internuclear distance in the molecule, rg = 0.2667 nm, with Eqs. (17) to (19)]. From the literature value of the molecular vibrational frequency in the gas phase, Tg = 213.3 cm , calculate the vibrational characteristic temperature vu, with Eq. (22). From the phonon dispersion data in Table 1, calculate the 12 vibrational characteristic temperatures , -. 

To determine the moment of inertia and the rotational characteristic temperature of HCl from its rotation spectrum in the far infra-red. 

The rotational characteristic temperature r is related to the principal moments of inertia 7i, Jj, I3 by... 

The molar mass M. of nitrogen is 28.02 gmole-i. The rotational characteristic temperature 0, is 2.87 deg and the vibrational characteristic temperature 0 is 3.35 x 10 deg (calculated from data in Herzberg, Molecular spectra of diatomic molecules , Prentice-Hall, 1939). 

The rotational characteristic temperature 0, of water is 22.2 deg. It is defined by (Guggenheim, Thermodjiiamics, North Holland Publishing Company, 1949, equation 4.32.2)... 

The phase transition of bilayer lipids is related to the highly ordered arrangement of the lipids inside the vesicle. In the ordered gel state below a characteristic temperature, the lipid hydrocarbon chains are in an all-trans configuration. When the temperature is increased, an endothermic phase transition occurs, during which there is a trans-gauche rotational isomerization along the chains which results in a lateral expansion and decrease in thickness of the bilayer. This so-called gel to liquid-crystalline transition has been demonstrated in many different lipid systems and the relationship of the transition to molecular structure and environmental conditions has been studied extensively. 

A surprising disappearance of the thermomechanical inversion of heat at elevated temperatures has been observed by Kilian 9,88). At 90 °C, the thermomechanical inversion in SBR and NR is found to disappeare in spite of the constant value of the thermal expansion coefficient. This means that the temperature dependence of elastic force should be negative from the initial deformations, which is in contradiction with experiment. This very unusual phenomenon was supposed to be closely related to rotational freedom which will continuously be activated above some characteristic temperature 9,88). 

A number of characteristic temperatures are important in LC polymer work. The glass transition temperature, Tg, is that temperature below which segmental motion of the main chain of the polymer does not occur, although motions (e.g., rotation) of side-groups may occur. The isotropization or clearing temperature, 7j, is the temperature at which the polymer enters the isotropic melt from one of its mesophases and the birefringence of the mesophase disappears. Temperatures are often quoted more specifically defining where phase transitions occur. For example, 7, would be the temperature where the nematic phase enters the isotropic melt. In this case, of course, TNI is the same as Tr... 

The more exoergic reaction Ba + NzO has a smaller reaction cross section ( 90 A2 or 27 A2) [347, 351] and crossed-molecular beams studies [349] show that the BaO product is backward-scattered with a large amount of internal excitation ((Fr) < 0.20). Laser-fluorescence measurements [348] of the BaO(X Z+) product for the reaction in the presence of an argon buffer gas, find population of vibrational states up to v = 32. The relative populations have a characteristic temperature of 600 K for v = 0—4 and 3600 K for v = 5—32 with evidence of non-thermal population of v — 13—16. This study also observes population of A n and a 3II states of BaO with v = 0—4. A molecular beam study of Ba + N20 with laser-induced fluorescence detection indicates that the BaO( X) product is formed with a very high rotational temperature. 

Table IX-2.—Characteristic Temperature for Rotation, Diatomic Molecules...

Particular characteristic temperatures are denoted with subscripts, e.g. rotational <9r = hcB/k, vibrational <9v = hcv/k, Debye 0D = hcvD/k, Einstein <9E = hcvE/k. 

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