Reduced-time kinetic plots

There have been few discussions of the specific problems inherent in the application of methods of curve matching to solid state reactions. It is probable that a degree of subjectivity frequently enters many decisions concerning identification of a best fit . It is not known, for example, (i) the accuracy with which data must be measured to enable a clear distinction to be made between obedience to alternative rate equations, (ii) the range of a within which results provide the most sensitive tests of possible equations, (iii) the form of test, i.e. f(a)—time, reduced time, etc. plots, which is most appropriate for confirmation of probable kinetic obediences and (iv) the minimum time intervals at which measurements must be made for use in kinetic analyses, the number of (a, t) values required. It is also important to know the influence of experimental errors in oto, t0, particle size distributions, temperature variations, etc., on kinetic analyses and distinguishability. A critical survey of quantitative aspects of curve fitting, concerned particularly with the reactions of solids, has not yet been provided [490]. 

Kinetic plots have been obtained for the polymerization of several monomers. Time vs. conversion and conversion vs. reduced viscosity curves of p-PDA Et at various temperatures are shown in Figs. 4 and 5. 

By analogy with the use of plots of a against reduced time in isothermal kinetic analysis to determine the appropriate conversion function, Meindl et al. [50] have... 

Jones et al. (122) used the reduced-time method oF Sharp et al. (123) in which the experimental kinetics data are plotted against the master data in such a way as to produce a linear plot. The experimental data are first expressed in the form sce as a function of(t/t05)c, where e refers to the experimental data Three equivalent plotting procedures are then possible ... 

Figure 12 Kinetics of decomposition of calcium oxalate. (A) Reduced time plot and (B) Arrhenius plot...

Fig. 8.9 Log-log plot of the relative error in kinetic temperature left) and configurational temperature (right) against stepsize by using various numerical methods. The system was simulated for 1,000 reduced time units but only a trajectory s tail of time length 800 was used to calculate the static quantity to make sure the system was well equilibrated. The stepsizes tested begtm at h = 0.05 and were increased incrementally by 15 % until all methods either were above 100% relative error or became unstable...

As it is seen from given data, with increasing of the oxidation tempeiatuie amount of gaseous products increases and period of their evolvement reduces. On the basis of these facts dependences between pressure change in the lowest point of kinetic curve and temperature AP =f(T) and between time of evolvement and time were plotted. 

Similarly ki was determined on systems where 82=0, i.e. on single polysiloxane networks formed from PSIa, PSIb and PSIc precursors. The corresponding kinetic plots Ln ([C]/[Co]) versus time are shown in Figure 5. In this case ai=0.6 and the reduced equation is ... 

In addition to the elimination rate constant, the half-life (T/i) another important parameter that characterizes the time-course of chemical compounds in the body. The elimination half-life (t-1/2) is the time to reduce the concentration of a chemical in plasma to half of its original level. The relationship of half-life to the elimination rate constant is ti/2 = 0.693/ki,i and, therefore, the half-life of a chemical compound can be determined after the determination of k j from the slope of the line. The half-life can also be determined through visual inspection from the log C versus time plot (Fig. 5.40). For compounds that are eliminated through first-order kinetics, the time required for the plasma concentration to be decreased by one half is constant. It is impottant to understand that the half-life of chemicals that are eliminated by first-order kinetics is independent of dose. ... 

The reduction of Co(III) by Ag(I) in perchlorate solutions has been studied by Sutcliffe et al. Since the initial product of reaction is the very reactive Ag(Il) species, all solutions were subject to preliminary ozonolysis to remove traces of reducible impurities. The final products of reaction are Co(II) and Ag(l). Kinetic data were obtained spectrophotometrically by following the disappearance of Co(III) at 605 m/i, a small correction being applied for the absorbance of Co(ll). With Ag(I) in excess, the disappearance of Co(III) is second order, i.e., plots of the reciprocal of the corrected absorbance versus time are linear. The rate is directly proportional to the concentration of Ag(I), and inversely proportional to the square of the concentration of Co(II). These results can be understood in terms of the mechanism... 

For a classical diffusion process, Fickian is often the term used to describe the kinetics of transport. In polymer-penetrant systems where the diffusion is concentration-dependent, the term Fickian warrants clarification. The result of a sorption experiment is usually presented on a normalized time scale, i.e., by plotting M,/M versus tll2/L. This is called the reduced sorption curve. The features of the Fickian sorption process, based on Crank s extensive mathematical analysis of Eq. (3) with various functional dependencies of D(c0, are discussed in detail by Crank [5], The major characteristics are... 

These results could be complemented well with the curve slopes in the double logarithmic coordinates as plotted in Fig. 6.33(a) using idea of the intermediate critical exponent a(t), equation (4.1.68). In the traditional chemical kinetics its asymptotic limit ao = a(oo) = 1 is achieved already during the presented dimensionless time interval, t 104. For non-interacting particles and if one of two kinds is immobile, Da = 0, it was earlier calculated analytically [11] that the critical exponent is additionally reduced down to ao = 0-5. However, for a weak interaction (curve 1) it is observed that in the time interval t 104 amax 0.8 is achieved only for a given n(0) = 0.1, i.e., the... 

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