Temperature parameters

Figure A2.5.27. The effective coexistence curve exponent P jj = d In v/d In i for a simple mixture N= 1) as a fimction of the temperature parameter i = t / (1 - t) calculated from crossover theory and compared with the corresponding curve from mean-field theory (i.e. from figure A2.5.15). Reproduced from [30], Povodyrev A A, Anisimov M A and Sengers J V 1999 Crossover Flory model for phase separation in polymer solutions Physica A 264 358, figure 3, by pennission of Elsevier Science.

Although the viscosity index is useful for characterizing petroleum oils, other viscosity—temperature parameters are employed periodically. Viscosity temperature coefficients (VTCs) give the fractional drop in viscosity as temperature increases from 40 to 100°C and is useful in characterizing behavior of siHcones and some other synthetics. With petroleum base stocks, VTC tends to remain constant as increasing amounts of VI improvers are added. Constant B in equation 9, the slope of the line on the ASTM viscosity—temperature chart, also describes viscosity variation with temperature. 

We characterize the reduction process by defining the reduction temperature as the point where the C03O4 concentration has dropped to 50% and the delta reduction temperature as the temperature difference between the points at which 50% C03O4 and 50% Co were reached. These definitions are arbitrary and their values will change with experimental conditions, but they are useful for comparing samples examined at the same conditions. Both of these temperature parameters must be considered when assessing the reduction properties of the samples. 

Fig. 5.17. Number average (Rg)n of the gyration radius of PE with Mn = 20 effective bonds plotted vs. temperature. Parameters of the symbols show the values of d. From [184].

Abb. 27. Leitfahigkeit von Pb —Te-Schichten als Funktion der Temperatur. Parameter Anzahl der angewendeten. Sauerstoffimpulse (nach Levinstein und Bode). 

The melting point Tm is computed by solving this equation iteratively. It is often convenient to use Ec/(kBTm) as our unit of (inverse) temperature. The phase diagram of the polymer solution then depends on the molecular parameters r, q, B/Ec, and Ep/Ec, the composition parameters n and 2, and on the temperature parameter Ec/(kBTm). 

Time of flight (TOF), 75 660-661 Time-of-flight (ToF) mass analyzers, 24 109 Time of flight diffraction (TOFD), 79 486 Time-of-flight instrumentation, in particle counting, 78 150—151 Time-of-flight-SIMS technique, 24 109 Time-resolved fluorimetry, 74 148-149 Time-resolved spectra, analysis of, 74 613 Time standards, 75 749—750 Time-temperature parameters (TTP), 73 471, 478, 479 creep properties and, 73 480 Time-temperature superposition, 27 746-747... 

When analyzing a chemical reaction process, especially in the scale-up and design stages, the review team must keep in mind some significant differences between the behavior of a chemical system in the laboratory or pilot operation and in a full-scale facility. Reaction rate and process temperature parameters, for example, do not generally scale up directly from the laboratory scale due to reasons such as ... 

Generally, most non-aqueous solvents possess greater coeffcients of expansion as compared to water, which is why small differences in temperature may afford significant and appreciable errors that can be eliminated by the application of appropriate correction factors. Hence, it is always advisable to carry out standardization and titration preferably at the same temperature. In a situation where these temperature parameters cannot be achieved, the volume of titrant may be corrected by the application of the following formula ... 

Manipulation of mobile phase and temperature parameters can have some unusual effects on chiral separations. Variation of temperature and mobile phase composition has been reported to reverse the elution order on protein phases and polysaccharide phases (Persson and Andersson, 2001). 

In principle, as the y models do not have an internal temperature dependence, the extrapolations in temperature must be carried out with great care. When extrapolating in temperature, the parameters in the y models should be made temperature dependent by fitting to experimental data at different temperatures. Parameter estimation is obtained by minimizing an object function such as ... 

The second letter in the Greek alphabet hence, used to denote the second item in a series (for example, the second methylene carbon from the carboxyl group of a fatty acid). 2. Symbol for the coefficient of [B] in the denominator of a generalized rate expression. 3. Symbol for reciprocal temperature parameter, p = llkT. 4. Symbol for pressure coefficient, p = (dpldT)y. 5. Symbol for depth of penetration of light (Napierian). 6. p, Symbol for electron. 7. /3+, Symbol for positron. 

In practice, the probability distribution often includes static disorders in the crystal. The temperature parameter B in such cases is more properly described as a mean-square displacement parameter. 

Comparison with Eq. (2.23) shows that the classical OPP model predicts the elements of the anisotropic harmonic temperature parameter to be proportional to the absolute temperature. 

It is not possible to determine k for a hydrogen atom directly from experimental X-ray data, because its value correlates strongly with the temperature parameter due to the absence of unperturbed inner-shell electrons. The use of neutron temperature parameters provides an alternative. Combined analysis of X-ray and neutron data on glycylglycine and sulfamic acid suggests that for X—H (X = C, N) groups, the H atom is more contracted than for the H2 molecule, with a k value as large as 1.4 for both C—H and N—H bonds (Coppens et al. 1979). 

That the positive bias in the scale factors correlates with an increase in thermal parameters is evident from comparison of X-ray and neutron results (Coppens 1968). The apparent increase in thermal parameters of some of the atoms may be interpreted as the response of the spherical-atom model to the existence of overlap density. Because of the positive correlation between the temperature parameters and k, this increase is accompanied by a positive bias in k. 

Such effects will contribute to the discrepancies between X-ray (X) and neutron (N) temperature parameters, which have been found to exist even room-temperature studies, for which temperature ambiguities are minimal (Craven and McMullan 1979). The effect of TDS can be especially pronounced in room-temperature studies of often soft molecular crystals, and, if not recognized, can lead to an artificial enhancement of features in difference maps based on a combination of the two techniques (Scheringer et al. 1978) (see chapter 5). 

To account for temperature factor differences, a temperature scale factor kT multiplying the neutron temperature parameters may be introduced, as defined by the expression (Coppens et al. 1981)... 

The X-N technique is sensitive to systematic errors in either data set. As discussed in chapter 4, thermal parameters from X-ray and neutron diffraction frequently differ by more than can be accounted for by inadequacies in the X-ray scattering model. In particular, in room-temperature studies of molecular crystals, differences in thermal diffuse scattering can lead to artificial discrepancies between the X-ray and neutron temperature parameters. Since the neutron parameters tend to be systematically lower, lack of correction for the effect leads to sharper atoms being subtracted, and therefore to larger holes at the atoms, but increases in peak height elsewhere in the X-N deformation maps (Scheringer et al. 1978). 

A final refinement of the static data with both sets of parameters gave a further small decrease in the R factor to 3.98%, and, reassuringly, temperature parameters smaller than three times their estimated standard deviations. At least for static data, the refinement properly attributes the asphericity to the multipole functions. 

J Anharmonic in this table refers to the Fe atom only harmonic temperature parameters of the other atoms are fixed at values from refinement I. 

As noted below, the temperature parameters for zeolites are often considerably larger than those for simple silicates. Disorder may contribute to this difference. 

Symmetry restrictions for third- and fourth-order anharmonic temperature parameters are Used in the International Tables for X-ray Crystallography Vol. IV (1974). A more complete list for elements up to rank eight has been derived by Kuhs (1984). 

Aniszewski, T., Drozdov, S. N., Kholoptseva, E. S., Kurets, V. K., Obshatko, L. A., Popov, E. G. and Talanov, A. V. 2001. Effects of light and temperature parameters on net photosynthetic carbondioxide fixation by whole plants of five lupin species Lupinus albus L., Lupinus angustifolius L., Lupinus luteus L., Lupinus mutabilis Sweet, and Lupinus polyphyllus Lindl.). Acta Agriculturae Scandinavica, 51 17-27. 

According to the vendor, biofilters require little or no maintenance. Microbial productivity is primarily limited by moisture and temperature levels. Input gases must be maintained within certain moisture and temperature parameters for the effective oxidation of contaminants. 

The generic shape of the desorption peak for TPD, second order kinetics. The peak is not symmetric around the peak temperature. (Parameters A=10 s, E = 100 kJ/mol, initial... 

Record the results of the transition measurements using the temperature parameters (Tm, etc.). 

If absolute minimum time and minimal temperature parameters are not used during the componentry challenge mns, manufacturing order parameter limits must reflect the parameters used during these runs. 

Figure 17 shows generalized relationships of the temperature parameter <+ to the position parameter y+ for the various values of the molecular Prandtl number. 

This expression is analogous to Eq. (30) for the temperature parameter. Under such circumstances, as in the case of the temperature distribution, it follows that... 

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