Thermal rigidity factor

One may go one step further and determine thermal rigidity factors for capture of dipoles in individual rovibrational states i, that is, derive /rigid,/(T). 

Comparison of Eqs. (20) and (16) leads to a low-temperature limiting thermal rigidity factor of... 

In this approximation, hence, the thermal rigidity factor is given by... 

The final result for cap also allows for a rigorous determination of the thermal rigidity factors /ngjd(T). This is particularly illuminating when approximate models such as the pure oscillator model of Eqs. (22)-(24) are compared with the complete result. The charge-permanent dipole capture (i.e., a — -0), for 2, using Eqs. (25) and (26), would be characterized... 

One might suspect that the discrepancy between the thermal rigidity factors of Eqs. (24) and (36) is due to inadequacies of the SACM treatment in general or of the pure harmonic oscillator model. However, after having corrected the analytical representation of the trajectory results through Eqs. (28)—(31), for x 11, Eq. (28) leads to... 

Processes in which solids play a rate-determining role have as their principal kinetic factors the existence of chemical potential gradients, and diffusive mass and heat transfer in materials with rigid structures. The atomic structures of the phases involved in any process and their thermodynamic stabilities have important effects on drese properties, since they result from tire distribution of electrons and ions during tire process. In metallic phases it is the diffusive and thermal capacities of the ion cores which are prevalent, the electrons determining the thermal conduction, whereas it is the ionic charge and the valencies of tire species involved in iron-metallic systems which are important in the diffusive and the electronic behaviour of these solids, especially in the case of variable valency ions, while the ions determine the rate of heat conduction. 

HDPE same properties as LDPE but more rigid better thermal and creep behaviour lower coefficient of friction and higher pressure strength, allowing antifriction applications with higher PV (pressure velocity) factor more transparent. 

The introduction of standard aspherical-atom scattering factors leads to a very significant improvement in Hirshfeld s rigid bond test. The results are a beautiful confirmation of Hirshfeld s (1992) statement that an accurate set of nuclear coordinates (and thermal parameters ) and a detailed map of the electron density can be obtained, via X-ray diffraction, only jointly and simultaneously, never separately or independently . 

Extrinsic stabilization from low-molecular-mass "thermoprotectants." The intrinsic stability of a protein reflects selection for an amino acid sequence that confers on the protein the appropriate balance between rigidity and flexibility that is required for physiological function under the thermal conditions facing the organism. This being said, the stability of the protein in vivo may be modulated by extrinsic factors, including pH, which varies with temperature, and low-molecular-mass organic osmolytes, whose concentrations may be tern-... 

Although the effects of thermal motion might be considered undesirable in crystallography, they provide, in fact, important information about the properties of the molecules under study (see, for example, Finzel et al., 1984). In terms of refining a crystal structure, the stmcture factors calculated assuming the atoms to be rigidly fixed on the lattice will be too large compared to the observed structure factors. The thermal factors for each atom reduce the sizes of the calculated structure factors by an amount appropriate for the thermal motion present. 

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