Linear region in the

An Arrhenius plot of the cation self-diffusivity will then possess two linear regions. In the high-temperature intrinsic regime, the slope will be — Hg/3 + Hm)/k in the low-temperature extrinsic regime, the slope will be simply Hm/k, where Hm is the migration enthalpy of a cation vacancy. 

Fig. 2 shows typical dependences of I(q) q vs. q for the investigated silica gels and, for comparison, the scattering curve for pure silica sample Si-200. From the short linear regions in the curves it is possible to define the exponents of the power low scattering. These exponents were a = 3.6, 3.8 and 4.5 for RP-2, RP-8 and RP-18, respectively. The a =3 was obtained for two-phase system of silica gel Si-200. 

Therefore, we have established once again that the linear dependence of the adsorption on concentration corresponds to the initial linear region in the surface tension - concentration dependence (see Fig. (II-7)). Since b is constant within the homologous series, it is the value of constant A that determines the steepness of the adsorption increase with increasing concentration. For this reason constant A is referred to as the adsorption activity. By comparing eqs. (II. 19) and (11.20) one establishes that A is related to the work of adsorption, p0 - p(0s), as... 

We find two linear regions in the Eyring diagram for almost all the systems studied. The characteristic point where a change is observed in the slopes is called the inversion point, and the corresponding temperature is the inversion temperature (7] ,). From the two linear correlations determined for each aminoalcohol, two different sets of discrimination parameters can be observed AAHf and AASf) and defined for T> 7] v when AAH and AAS are obtained for T < ] . The two regions correspond to the dominance of enthalpy or entropy factors in the selection [46] (see Table 4). 

As shown in Fig. 17.5, differences between the equilibrium-simulated and step strain-simulated Gs t) curves occur mainly in the cases of = 2 and 5 and virtually no differences can be observed for A = 10 and 20 even though A = 0.2 and 0.5 are not really in the linear region. In the N = 2 case, while the whole shapes of the Gs(t) curves are very similar, differences can be observed in different regions. In the N = 5 case, the difference becomes obvious in the early part of the slow mode, where an effect related to the coupling between S t) and bx t)by t) — a subject discussed in the... 

The evaluation of a was also made in the /-direction, i.e. perpendiculary to the scanning direction. In this case, two linear regions in the log log Ls plot can also be observed with a crossing point at log and... 

In order to get a linear calibration curve it is also very inportant to select sipport volumes to obtain equal pore volumes from the different stpports (108). nils is equivalent to procuring calibration curves with parallel linear regions in the plot of log M versus VpX A recent r x>rt described the p )earance of artificial peaks vdien oolums oonteLining supports of different pore sizes are oonbined (114). However, the noticed effect nay be due to that no ocnpensatlon of support volumes was made for the differences in pore volumes of the two supports. 

This time is smaller than for a linear chain of Aymonomers but much larger than rd. Since D is very small, it is difficult to measure in a simulation and has not been done. The rotational diffusion time, which should be comparable to td, can be analyzed by studying the time autocorrelation function of the center-to-end vector R or the autocorrelation of the squares of the second-order spherical harmonics of the angles at which the principal axes of the ellipsoid are oriented with respect to a fixed-coordinate system. However even for small there was no linear region in the semilog plots of C t) for the times that can presently be simulated, making it impossible at present to test eq. (9.23). 

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