Crossover value

Povodyrev et aJ [30] have applied crossover theory to the Flory equation ( section A2.5.4.1) for polymer solutions for various values of N, the number of monomer units in the polymer chain, obtaining the coexistence curve and values of the coefficient p jj-from the slope of that curve. Figure A2.5.27 shows their comparison between classical and crossover values of p j-j for A = 1, which is of course just the simple mixture. As seen in this figure, the crossover to classical behaviour is not complete until far below the critical temperature. 

Another important detail on the Sugano-Tanabe diagram shown in Figure 6.8 is the vertical line at the value DqlB = 2.2, at which the states T2g and E are equal in energy. This value of DqlB is usually referred to as the crossover value. Materials (crystal - - ion) for which Dq/B is less than the crossover value are usually called low crystal field materials. Eor these materials, the lowest energy level is the " T2g and so they present a characteristic broad and intense emission band associated with the spin-allowed T2g A2g transition (which is usually a vibronic transition). On the other hand, the materials on the right-hand side of the crossover line are called high crystal field materials. These materials (such as the ruby crystal) present a narrow-line emission related to the spin-forbidden Eg A2g transition, usually called R-line emission. 

Crossover value The crossover value is a characteristic quantity of an already cold refrigerator cryopump. It is of significance when the pump is connected to a vacuum chamber via an HV / UHV valve. The crossover value is that quantity of gas with respect to T =293 K which the vacuum chamber may maximally contain so that the temperature of the cryopanels does not increase above 20 K due to the gas burst when opening the valve. The crossover value is usually slated as a pV value in in mbar I. 

The crossover value and the chamber volume V result in the crossover pressure p to which the vacuum chamber must be evacuated first before opening the valve leading to the cryopump. The following may serve as a guide ... 

The measurement of T c is important to probe the three-dimensional regime at low fields and to compute tx. In fact, according to the field dependence of g(we) there exists a crossover value of the field (given through u) ) at uyi 1 between the high-field one-dimensional regime, for which expression (39), applies (i.e., Tf1 Hq m) and a low-field three-dimensional regime that is field independent. 

The methanol crossover rates of operating direct methanol fuel cells possessing PSSA-PVDF membranes has been measured at different temperatures and is shown in Fig. 1.83. This was accomplished by measuring the CO2 content of the cathodic exit stream with an on-line CO2 analyzer. The methanol crossover values obtained with this technique correlated well with results obtained with a chemical analytical method involving the reaction of CO2 with Ba(OH)2 to produce BaCOs. The methanol crossover rates observed with a MEA fabricated with a PSSA-PVDF membrane (MEA 2) and using a 1 x 1 ... 

Table 1.7 Methanol crossover values under open circuit conditions of a DMFC containing a PSSA-PVDF membrane ( MEA 3) at 60 °C. 

Temperature can propagate with the speed of sound. When the critical point is approached more closely than a crossover value given by asymptote analysis, the characteristic time of the piston effect does not monotonicaUy decrease to zero, but tends to reach a constant value, which is the characteristic acoustic time. For CO2 contained in a 10 mm long container set at 1 K above its critical temperature, the crossover value is some mK. At these conditions, the... 

A fully close-packed brush, with the whole area of the interface taken up by the grafting sites, would have a value of a of unity and thus a volume fraction inside the brush of unity. However, this invalidates our assumption that the concentration inside the brush is in the semi-dilute regime recall that, for volume fractions of polymer greater than a crossover value 0 v/a, where V is the excluded volume parameter, we have a concentrated solution, for which... 

After the dominant defect process was identified, the energetics of the defect formation was determined through static calculations, in order to obtain reliable estimates of defect processes at low temperatures. Fig. 4 plots the formation energies of a (5-7-7-S) defect in an armchair (5,5) tube, as obtained in ab initio calculations. Calculations for other armchair tubes show that the crossover value is only weakly dependent on their diameters and always falls in the range of 5-6%. 

Suppose we find the value of n for which the natural abundances of the Cjj and C jjCi isotopologs (i.e., those with k = 0 and k = 1) are equal the corresponding molecular mass is sometimes referred to as the crossover value. All we have to do is equate the first two terms... 

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