Accumulation curve

The kinetic curve of the accumulation and consumption of o-DNB anion-radicals is S-shaped and that of the accumulation of o-nitrophenolate is parabolic. The anion-radical accumulation curve starts to go down when the o-nitrophenolate accumulation curve reaches its maximum (Abe and Ikegame 1978). 

In addition, at very low water contents, ampicillin accumulation curves do not exhibit a clear-cut maximum, inherent in the enzymatic acyl transfer reactions in aqueous medium (including quite concentrated heterogeneous aqueous solution-precipitate systems), because of the secondary hydrolysis of the target product by penicillin acylase (Figure 12.6) [84]. 

It should be stressed once more that the accumulation curve n(t) (or U(t)), especially at high doses, cannot be described by a simple equation (7.1.53) which is often used for interpreting the real experimental data (e.g., [19, 20]). Despite there is the only recombination mechanism, the A + B —> 0 accumulation kinetics at long t due to many-particle effects is no longer exponential function of time (dose). Therefore, successful expansion of the experimental accumulation curve U = U(t) in several exponentials (stages) does not mean that several different mechanisms of defect creation are necessarily involved (as sometimes they suggest, e.g., [39, 40]). 

In the review article [15] numerous analytical expressions have been presented to describe experimental accumulation curves n(t) - see Section 7.4. Note here that such kinetics are studied widely in all kinds of solids, from alkali halides [5, 9, 10, 42] to metals [43-46]. 

It is important to note that it was K. Dettmann [34] who first created the solid basis of a rigourous theory of the kinetics of accumulation of the Frenkel defects in crystals. He showed that in the absence of diffusion the accumulation curve, n = n(t), is determined by the infinite sum of the correlation functions pm o> m — 2,... oo that describe the spatial correlations of all orders of similar defects only. 

The dependence of the low-temperature accumulation curve on the intensity p of irradiation is a characteristic feature of the tunnelling recombination It has been observed in the most varied solid matrices alkali-halide crystals [17], glasses [121, 123] etc. 

Some analytic expressions are collected in Table 7.6 that have been used in literature to describe the experimental accumulation kinetics, n(t), or dn/dt, the rate of concentration accumulation. Experimentally such kinetics have been studied, both in the alkali-halide crystals [13, 17] and in many metals [43-45] in a wide temperature interval, starting with low (liquid-helium, 4 K) temperatures. Since often a succesful approximation of the accumulation curve is associated with better understanding of a micromechanism of defect formation (see, e.g., [40]) and with other important physical conclu-... 

Finally, the simple empirical equation (13) was presented in [107, 112], which describes well the computer simulation results. It was shown that the efficiency of recombination depends on the accumulation time and on the number of lattice sites within the recombination sphere, vp. Therefore, this equation could serve as a solid basis for analyzing the actual experimental data. However, in this case, first of all, we must convince ourselves by comparison of the experimental and theoretical accumulation curves of then-qualitative resemblance. For example, we easily note that convex relationships of the type of Fig. 1 in [43, 44] require the use of more complex models than those discussed above, where the rate of accumulation declines monotonically. 

An approximate analysis using equation (13) for description of the accumulation curve for defects in Cu (Fig. 7 in [45]) yields the value Uq = uqvq m 1.2, which clearly indicates an aggregation effect [35], This result was obtained on the basis of estimates of values of p and vp obtained in the same paper with the assumption of the absence of the correlation in genetic pairs. (Evidently taking account of correlation would have led to an even larger value of the Uq parameter.)... 

The Richards model reduces the unexplained statistical variation in the accumulation of PCBs by phytoplankton, but it does not provide any information about the mechanisms responsible for the observed pattern. Numerous causes are possible for deviation from the classical pattern of accumulation. However, violations of assumptions associated with the classical model (i.e., constant uptake rate, instantaneous mixing within a single compartment, and a time-independent probability of depuration) are most likely the cause. With phytoplankton, several physiological mechanisms can potentially contribute to a sigmoidal accumulation curve. 

Although the Richards model does not provide mechanistic information, it does point out a need for further study and understanding of the uptake mechanisms. Brisbin et al. (30) reported that one consequence of sigmoidal accumulation is that there must be a period of accelerated or enhanced accumulation after the lag period in order to attain equilibrium levels similar to the classical model. In contrast to reports that cellular processes play no role in the accumulation of contaminants by phytoplankton (23, 25, 34-36), a sigmoidal accumulation curve may indicate that cellular processes such as the cycling of materials within the cell may enhance the rate of accumulation or depuration to a level above that which is attainable by diffusion alone. 

Comparison of the pressure-dependent molecular oxygen accumulation and CH4 consumption (or CH3OH accumulation) curves in Figure 4.14 shows a correspondence of the 02 accumulation minimum to the maximum of CH4 conversion to CH3OH. 

The curve of 02 accumulation shows that short contact times, at which the methane oxidation rate is low, are enough for complete H202 dissociation. However, as observed from shapes of 02 and CH3OH accumulation curves, methanol yield increases synchronously with 02 yield decrease, and from the moment r = 10.2 s both curves stabilize. Such stabilization and synchronization of catalase and monooxygenase reaction product yields is the experimental proof of their interaction, displayed by chemical conjugation. The existence of the stabilization zone of 02 and CH3OH yields is associated with full H202 dissociation. 

Ethylene and carbon dioxide are produced by the plant cells in the culture and their respective headspace concentrations increase in the stoppered flasks. As expected, oxygen consumption by the cells results in reduction of the head-space composition. Specific 02 consumption rate and biomass accumulation curves as a function of time are presented in Fig. 2. The biomass accumulated at a rate of approximately 0.05 gdw 1 1 h the average specific 02 consumption rate calculated as 0.05 mmol gih v h The same data plotted as specific 02 con-... 

The question of which cumulative mantle degassing curve D is realty relevant in this context is difficult to answer and depends on the relative rates of drawdown by photosynthesis and silicate weathering-carbonate formation in Archaean time. From the carbon isotope record, these are mainly considered to have remained constant (Schidlowski 1988), in which case the stippled lower curve D would be more appropriate. However, for the timing of drawdown derived from Figure 7 the choice of mantle accumulation curve is unimportant, given the tentative character of this whole consideration. 

Figure 15. Accumulation curves for different levels of mercurv in daily intake (After Bunce, 1994).

Figure 3. Graphical definition of the metabolic transition time, x. The concentration of some metabolic product, P, is plotted as a function of time after the pathway is switched on (e.g., by addition of the initial substrate), with the system being devoid of metabolic intermediates initially. The extrapolation to the time axis, of the linear portion of the product accumulation curve is denoted as the transition time (see Welch and Easterby, 1994).

Fig. 5. Product accumulation curves measured as a function of reaction time at 573 K for n-hexane aromatization catalyzed over platinum single-crystal surfaces. ( ), Pt( 10,8,7) (O), Pt(lll) (A), Pt(100) (A), Pt(l3,l,l). H2/HC = 10. P1M = 220 torr. From Ref. 54.

The treatment of data acquired in sedimentation analysis usually involves graphical differentiating of the sediment accumulation curve. This method of obtaining particle size distribution is based on the Svedberg - Oden equation ... 

Enrichment factors may also be illustrated in a graphical manner as accumulation curves that show how the fraction of actives recovered varies with the percent of the database screened (Figure 8). While the diagonal shows results expected by chance, the dark line indicates the results obtained by use of a structure-based screening protocol. An enrichment factor of 3.5 is yielded when 20% of the database are screened (i.e., 69% actives are recovered). If 50% of the database are assayed, the enrichment factor is decreased to 1.8. 

Fig.2. Accumulation curves for (A) biopterin and (B) xanthopterin under a stirring rate of 3000 rpm. Biopterin was accumulated at —0.3 V and xanthopterin was accumulated in open circuit. Other conditions as in Fig.l.

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