Time plots

Figure A3.14.16. Spatiotemporal complexity in a Couette reactor space-time plots showing the variation of...

In Fig. 8.3(a) a distance-time plot is shown to illustrate the progression of... 

Figure 8.3. Wave interactions in planar tensile fracture experiment, (a) Shows the distance-time plot of interacting compression C , rarefaction R , and tension T , waves (b) Shows the corresponding particle-velocity profiles including the initial compressive shock wave (tj, tj), the pull-back signal (tj, tj), and subsequent reflection >h).

Figure 4-82. Speed versus time plot during coupling failure.

Fig ure 12-27. Temperature versus time plot from a semi-batoh heat flow experiment. (Source Hazard Evaluation Laboratory Ltd.)... 

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. ... 

Figure 3-14. Absorbance-time plots for the reaction of carbon suboxide and triethylamine in ether solution in the presence of acetic anhydride. The initial C3O2 concentration was 2.03 X I0 - M the amine concentrations were 3 X lO " M, 5 x 10 M, and 7 X lO " M.

Ribbed belts Toothed or timing" plot link bell... 

Actual time-domain vibration signatures are commonly referred to as time traces or time plots (see Figure 43.17). Theoretical vibration data are generally referred to as waveforms (see Figure 43.18). 

Fig. 3.6 Space-time plots of the same legal rules appearing in figure 3.5 but starting from an initial state with nonzero sites occupying only a small central region.

Pig. 3.7 Space-time plots r = 2 totalistic rules. The lattice consists of 256 sites and each rule is iterated 64 times. The initial condition, in each case, is a single non-zero site at the center. 

Plate 1. A space-time plot of a Wolfram class-4 one-dimensional fc = 10 (i.e. 10 state), radius r = 6 totalistic CA rule. 

As we have already observed in section 3.1.4.5,CA evolution may conserve locally defined quantities. Moreover, local conservation laws often cause walls to appear that prohibit sites sitting on opposite sides of those walls from exchanging any information. Figure 8.3, which shows the space-time plots of ERCA 18, 73r, and 129/j, provides three such examples. 

They varied only the values of the adsorption and desorption rate constants of the reaction intermediate B, and by using the simplest Langmuir kinetics, they calculated time-concentration curves of compounds A, B, and C shown in Fig. 5. Also from this example, which does not consider any step as clearly rate determining, it is evident how very different concentration versus time plots can be obtained for the same sequence of surface reactions if adsorption and desorption of the intermediate B proceed by different rates, which are, however, comparable with the rate of surface reactions. In particular, the curves in the first and second columns of Fig. 5 simulate the parallel formation of substances B and C, at least... 

Two alternative methods have been used in kinetic investigations of thermal decomposition and, indeed, other reactions of solids in one, yield—time measurements are made while the reactant is maintained at a constant (known) temperature [28] while, in the second, the sample is subjected to a controlled rising temperature [76]. Measurements using both techniques have been widely and variously exploited in the determination of kinetic characteristics and parameters. In the more traditional approach, isothermal studies, the maintenance of a precisely constant temperature throughout the reaction period represents an ideal which cannot be achieved in practice, since a finite time is required to heat the material to reaction temperature. Consequently, the initial segment of the a (fractional decomposition)—time plot cannot refer to isothermal conditions, though the effect of such deviation can be minimized by careful design of equipment. 

Characteristic features of a—time curves for reactions of solids are discussed with reference to Fig. 1, a generalized reduced-time plot in which time values have been scaled to t0.s = 1.00 when a = 0.5. A is an initial reaction, sometimes associated with the decomposition of impurities or unstable superficial material. B is the induction period, usually regarded as being terminated by the development of stable nuclei (often completed at a low value of a). C is the acceleratory period of growth of such nuclei, perhaps accompanied by further nucleation, and which extends to the... 

Fig. 1. Generalized a—time plot summarizing characteristic kinetic behaviour observed for isothermal decompositions of solids. There are wide variations in the relative significance of the various stages (distinguished by letter in the diagram). Some stages may be negligible or absent, many reactions of solids are deceleratory throughout. A, initial reaction (often deceleratory) B, induction period C, acceleratory period D, point of inflection at maximum rate (in some reactions there is an appreciable period of constant rate) E, deceleratory (or decay) period and F, completion of reaction.

Fig. 2. Reduced time plots for the Avrami—Erofe ev equation [eqn. (6)] with n = 2, 3 and 4 and tT = (t/ta.g) the Prout—Tompkins expression [eqn. (9)] is included as the broken line.

Fig. 3. Reduced time plots, tr = (t/t0.9), for the contracting area and contracting volume equations [eqn. (7), n = 2 and 3], diffusion-controlled reactions proceedings in one [eqn. (10)], two [eqn. (13)] and three [eqn. (14)] dimensions, the Ginstling— Brounshtein equation [eqn. (11)] and first-, second- and third-order reactions [eqns. (15)—(17)]. Diffusion control is shown as a full line, interface advance as a broken line and reaction orders are dotted. Rate processes become more strongly deceleratory as the number of dimensions in which interface advance occurs is increased. The numbers on the curves indicate the equation numbers.

The magnitude of t0 can be measured from the intercept of a f(a)—time plot. The existence of the induction period can introduce uncertainty into a reduced time analysis if the temperature coefficient of t0 differs from that later applicable, and it is necessary to plot (t — t0)/(tb — t0) against a where tb is the time at which the selected common value of a is attained. The occurrence of a slow initial process can be reflected in deviations from linearity in the f(a) time plot, though in favourable systems the contribution may be subtracted before analysis [40]. 

From microscopic measurements of the rates of nucleation and of growth of particles of barium metal product, Wischin [201] observed that the number of nuclei present increased as the third power (—2.5—3.5) of time and that the isothermal rate of radial growth of visible nuclei was constant. During the early stages of reaction, the acceleratory region of the a—time plot obeyed the power law [eqn. (2)] with 6 temperature coefficients of these processes were used by Wischin [201]... 

Exp lam and demonstrate clearly how spectroelectrochemistry can provide useful information about a reaction mechanism involving a redox process followed by a chemical reaction (EC mechanism), involving decomposition of the reaction product. Draw an absorbance-time plot for different rate constants of the decomposition reaction. 

The "add-to-memory" signal averaging method currently available to us distorts fluorescence intensity versus time plots when the fluorescence intensity is a non-linear function of incident laser energy and the laser energy varies from shot to shot. For this reason we have not attempted detailed kinetic modelling of the observed fluorescence intensity decay curves recorded at high 532 nm laser fluence. 

For each data set examined, the onset of the gel effect (which is the initial value for the integration of the differential equations) was taken at the point where there is a departure from linearity in the conversion-time plot. While a good argument can be made ( ) for using another definition of the onset of the gel effect, the data available did not allow for a more detailed approach. 

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