Time-temperature index plots

In Chapter 8 we will see that programmed temperature GC results in a regular, linear relationship between retention time and carbon number. Under those circumstances logs should not be used in Eq. (8) and in the retention index plot. The increase in temperature decreases the partition coefficients and effectively removes the logarithmic dependence of I. 

Arrhenius plot A linear Arrhenius plot is extrapolated from the Arrhenius equation to predict the temperature at which failure is to be expected at an arbitrary time that depends on the plastic s heat aging behavior. It is usually 11,000 hours, with a minimum of 5,000 hours. This is the relative thermal index (RTI). 

Fermentation Curves. Fermentation curves are an index of the general well being of the fermentation processes taking place in the fermentation room. Abnormal yeast populations or improper temperature control often can be seen first in the plotted data of sugar content vs. time during fermentation. 

As mentioned in the introduction, hydroperoxides can be measured by recording the area under the CL curve in an inert atmosphere i.e. the total luminous intensity (TLI). Kron et al. found that when measuring CL in inert atmosphere together with peroxide concentration, as measured by iodome-try, for oxidised polypropylene, proportional relationships were obtained when the TLI was plotted versus peroxide concentration (see Fig. 3) [60]. In addition, changes in melting temperature and polydispersity index with aging time have also been found to correlate with changes in the TLI [59]. 

The rotational temperature obtained from a linear relation in the Boltzmann plot of the rotational energy distribution is an index of the lifetime in the intermediate excited state and decreases with decreasing lifetime. The rotational temperature of CO desorbed from Pt(l 1 1) is very low as compared with that of NO desorption, i.e. the lifetime of the excited CO is supposed to be much shorter than that of NO. In the case of CO desorption from Pt(l 11), however, the lifetime is not obtained from the rotational energy distribution, since desorbed molecules are detected by the (2 + 1 )REMPI method in the experiment [ 12] and then the single rotational states are not resolved. On the other hand, the rotational temperature of NO desorbed from Pt(l 1 1)-Ge surface alloy is lower than that from Pt(l 1 1). Then, it is speculated that the lifetime of the excited CO on the alloy is shorter than that on Pt( 111) and the residence time of the excited CO on the alloy is too short to be desorbed. As a consequence, the excited CO molecules are recaptured in the relaxation without desorption. However, it has not been understood why the lifetime of the excited CO molecule (or the excited CO-Pt complex) on Pt( 1 1 1) is shorter than that of the excited NO molecule (complex) on Pt(l 11), and further on the Pt-Ge alloy as compared with Pt(l 1 1). 

Figure 4.19 Memory effect in B2 O3. The Active temperature (here calculated from the refractive index) is plotted versus time t—12 after a second temperature step. The first temperature step was from equilibrium at 583.2 K to Ti = 498.7 K, and the second step at time t2 was from T to T2 = 543.4 K. The solid curve is calculated from Eqs. (4-22), (4-27), and (4-28) using C = 5.6 x 10 sec, AH 92 kcal/mol, fi — 0.82, and x = 0.50. In Kovacs original experiments, the memory effect was monitored by careful measurement of an increase, followed by a decrease, in the sample s volume after the second temperature step. (From Moynihan et al. 1976, with permission from the New York Academy of Sciences.)...

Fig. 12 Tensile elongation (%) of PBD as a fimction of ageing time (days) at different temperatures (between 50 and 125 °C). Permission for reproduction from Elsevier [98] (p 1873). Inset Arrhenius plot of PP-toc ( ), and PP-Irgl076 ( ) as a fimction of carbonyl index induction times. owned by first author...

Figure 3.25 shows a plot of crystalline index versus elapsed time in the spin line for H-0660. As may be seen, crystallization rates generally increase with an increase in take-up speed or stress. However, included in these results are effects due to cooling rate, which also increases with take-up speed. Henson and Spruiell [193] gave a plot of crystallization start temperature versus spin-line stress at several cooling rates (Figure 3.26). As seen, stress increases the start temperatures and increase in cooling rates depresses the start temperatures.

In Fig. 24c, log k[ values calculated from retention times with the use of Equation (6) at a constant density of 0.44 g cm (same density as in Fig. 24a) are plotted as a function of the reciprocal absolute temperature, and in Fig. 24b at a constant temperature of 395 K against the density of the mobile phase. Within the ranges of the experiments, both plots give nice straight lines. These findings are, for example, of interest for the estimation and correlation of capacity ratios (and by this of retention times) and consequently for the development of index systems similar to those used in gas chromatography. 

The data in Figure 2.9 demonstrate the marked influence of density on the creep behavior of polyethylene. The curves in Figure 2.9 are relevant to a total strain of 1%, but similar plots for other permissible strains can be readily derived from the isochronous stress-strain curves. The linear relationship between creep and density for polyethylene at room temperature, irrespective of the melt index over the range investigated (i.e., 0.2-5.5), has enabled the stress-time curve of Figure 2.10 to be interpolated for the complete range of polyethylene. In this case, the data have been based on a permissible strain of 2%, but as previously explained, data for other permissible strains can be similarly interpolated from the creep curves. 

It has long been known that within a homologous series, a plot of the logarithm of adjusted retention time (carbon atoms is linear, provided the lowest member of the series is excluded. Such a plot for C4 to C9 normal alkane standards is shown in Figure 27-18. Also indicated on the ordinate are log adjusted retention times for three compounds on the same column and at the same temperature. Their retention indexes are then obtained by multiplying the corresponding abscissa values by 100. Thus, the retention index for toluene is 749, and for benzene it is 644. 

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