Growth instantaneous

It can be seen that Eqs. (7.9) and (7.10) represent the same type of current-time transient, iocl. Thus, to distinguish between 2D growth (progressive nucleation) and 3D growth (instantaneous nucleation), it is necessary to perform additional optical microscopic or electron microscopic experiments. These experiments can provide information enabling one to distinguish between progressive nucleation [Eq. (7.9)] and instantaneous nucleation [Eq. (7.10)]. 

With Overlap. For two-dimensional cylindrical growth, instantaneous nucleation... 

The rate of formation of radicals will depend on a number of features, including the concentration of initiator, temperature and the presence of other agents. Since subsequent stages of polymer growth occur almost instantaneously it is the relative slowness of this stage which causes the overall conversion times in most polymerisations to be at least 30 minutes and sometimes much longer. 

MeCabe s (1929a,b) AL law states that erystals of the same substanee growing under the same eonditions should grow at the same rate. Experimental evidenee has shown that this law is frequently violated. The growth rate of a erystal faee, for example, and the instantaneous veloeity of steps spreading aeross the surfaee of a erystal have been shown to fluetuate with time, even though external eonditions, e.g. temperature, supersaturation and hydrodynam-ies, remain eonstant. 

Bubbles are formed instantaneously. This conclusion made in [33] is based on estimates taken from earlier works [37]. As seen from the above cited works by S. E. Sosin et al., this is not always true viscoelastic liquids under triaxial stretching stress are not destroyed instantly. The existence of an induction period may produce a considerable effect on foam growth kinetics upon free foaming, when pressure is lowered instantaneously from P > Pcr to P < Pcr in a melt with dissolved gas. However, it would appear that microfaults in polymer melts, which are caused by factors... 

Kinetic expressions for appropriate models of nucleation and diffusion-controlled growth processes can be developed by the methods described in Sect. 3.1, with the necessary modification that, here, interface advance obeys the parabolic law [i.e. is proportional to (Dt),/2]. (This contrasts with the linear rate of interface advance characteristic of decomposition reactions.) Such an analysis has been provided by Hulbert [77], who considers the possibilities that nucleation is (i) instantaneous (0 = 0), (ii) constant (0 = 1) and (iii) deceleratory (0 < 0 < 1), for nuclei which grow in one, two or three dimensions (X = 1, 2 or 3, respectively). All expressions found are of the general form... 

The kinetic observations reported by Young [721] for the same reaction show points of difference, though the mechanistic implications of these are not developed. The initial limited ( 2%) deceleratory process, which fitted the first-order equation with E = 121 kJ mole-1, is (again) attributed to the breakdown of superficial impurities and this precedes, indeed defers, the onset of the main reaction. The subsequent acceleratory process is well described by the cubic law [eqn. (2), n = 3], with E = 233 kJ mole-1, attributed to the initial formation of a constant number of lead nuclei (i.e. instantaneous nucleation) followed by three-dimensional growth (P = 0, X = 3). Deviations from strict obedience to the power law (n = 3) are attributed to an increase in the effective number of nuclei with reaction temperature, so that the magnitude of E for the interface process was 209 kJ mole-1. 

The amount of growth occurring when rainfall is limited depends on the ratio of assimilation rate to transpiration rate. In a leaf the instantaneous transpiration efficiency, A E, is given approximately by... 

By virtue of the conditions xi+X2 = 1>Xi+X2 = 1, only one of two equations (Eq. 98) (e.g. the first one) is independent. Analytical integration of this equation results in explicit expression connecting monomer composition jc with conversion p. This expression in conjunction with formula (Eq. 99) describes the dependence of the instantaneous copolymer composition X on conversion. The analysis of the results achieved revealed [74] that the mode of the drift with conversion of compositions x and X differs from that occurring in the processes of homophase copolymerization. It was found that at any values of parameters p, p2 and initial monomer composition x° both vectors, x and X, will tend with the growth of p to common limit x = X. In traditional copolymerization, systems also exist in which the instantaneous composition of a copolymer coincides with that of the monomer mixture. Such a composition, x =X, is known as the azeotrop . Its values, controlled by parameters of the model, are defined for homophase (a) [1,86] and interphase (b) copolymerization as follows... 

The thermodynamic drives cited are the energy released instantaneously by the metabolic reaction, at the moment reaction commences. The drives tell whether the reaction can proceed, and whether it can supply enough energy for a cell to conserve energy by synthesizing ATP, as discussed in Section 7.4. The values, however, do not describe how much energy microbes can extract from a fluid, and hence how much microbial growth the fluid can sustain. 

Fig. 9.5. Schematic of decline of D and growth of 7Li and oxygen abundances in the Simple or homogeneous outflow model, assuming instantaneous recycling with a = 0.67 and yields p(O) = 0.8 Zq(O) p(7Li) = 0.7 Z0(7Li) Zo(7Li) =...

The transients given in Figure 3b are asymmetric. The area under the curves is almost two times higher than the product of imax and traax. In ttle initial segment of the curves, the current varies linearly with time. These features are consistent with the process controlled by the instantaneous nucleation and growth of a fixed number of oxide islands % in the CO monolayer. The transients are well described by the expression [16, 17] ... 

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