Enhancement exponent

Figure 12. The effective coordination numbers /r, and enhancement exponents 7, versus 9 for —10 < 9 < 10 of SAW configurations on the backbone of the critical percolation cluster in d = 2 (adapted from Ref. [74]). The values for fi and 7 on regular square lattice are marked by arrows, clearly showing that lim, joo % is larger than 7 on regular square lattice. The inset shows p, versus 9 for —2 < g < 2 in d = 2, in good agreement with the theoretical result p, = no(l + qa IT) (continuous line), suggested for jqj 0, with Ho = 1.456 and cto = 0-45 [75].

In Eq. (49), the limiting case ngg - 1 corresponds to the limit 9 —t 0, while the usual average (cf. Eq. (1)) is recovered when rieff = ritot- A dependence of the coordination numbers ju< ,neff md the enhancement exponents 7,neir en indicates that the given ensemble is too small to obtain the asymptotic values. If, on the contrary, the ensemble of substrate configurations is sufficiently large, then Hq,n,g and 7,n,(r no longer depend on neB-... 

Equations (22-86) and (22-89) are the turbulent- and laminar-flow flux equations for the pressure-independent portion of the ultrafiltra-tion operating curve. They assume complete retention of solute. Appropriate values of diffusivity and kinematic viscosity are rarely known, so an a priori solution of the equations isn t usually possible. Interpolation, extrapolation, even precuction of an operating cui ve may be done from limited data. For turbulent flow over an unfouled membrane of a solution containing no particulates, the exponent on Q is usually 0.8. Fouhng reduces the exponent and particulates can increase the exponent to a value as high as 2. These equations also apply to some cases of reverse osmosis and microfiltration. In the former, the constancy of may not be assumed, and in the latter, D is usually enhanced very significantly by the action of materials not in true solution. 

A reaction with a high activation energy tends to have a weaker interaction with the surface and hence will have enhanced mobihty that is reflected in a larger activation entropy. For this reason, the pre-exponents of surface desorption rate constants are lO — lO larger than the pre-exponents of surface reaction rates. 

The rate-enhancing effect of cationic detergents was analyzed by using Hill s equation. The observed exponent (n = 3 — 4) suggests that polymer-bound detergents facilitate the subsequent binding acceleratively hence the sigmoidshaped dissociation behavior of hydroxamic acid. 

From Eq. (c) it may observed that as the temperature T is enhanced then the rate of reaction also enhances simultaneously because a higher value of T offers a smaller negative exponent of e or a larger number. Therefore, in actual experimental operations temperature is increased by the aid of a heat-bath so as to accelerate the reaction which in turn allows the reaction to attain equilibrium state as rapidly as possible. 

Intcrmolecular Contributions. Increasing concentration reduces the effects of excluded volume and intramolecular, hydrodynamic on viscoelastic properties (Section 5). Internal viscosity and finite extensibilty have already been eliminated as primary causes of shear rate dependence in the viscosity. Thus, none of the intramolecular mechanisms, even abetted by an increased effective viscosity in the molecular environment, can account for the increase in shear rate dependence with concentration, e.g., the dependence of power-law exponent on coil overlap c[r/] (Fig. 8.9). Changes in intermolecular interaction with increased shear rate seems to be the only reasonable source of enhanced shear rate dependence, at least with respect to the early deviations from Newtonian behavior and through a substantial portion of the power law regime. 

Due to approximations in the derivation, (18) ceases to hold as AE - 0.) The energy e refers to the depth of the minimum of the interaction potential, and may be considered either as an acceleration effect, or as an enhancement of the collision frequency. Inclusion of the term usually increases the transition probability by a factor of about two fold for weak van der Waals interaction. The first term in the exponent of equation (18), -%A, is generally the dominant term, and it should be noted that the theory therefore predicts a linear dependence of log P0, i on T. ... 

Butyrylcholinesterase (BuChE EC 3.1.1.8) from either horse or mice serum displayed different profiles. A steady state was not developed, although the rate constants of inhibition decreased with time. Since the presence of multiforms of serum BuChE has been established, it is likely that the first-order plot represents more than one exponent. The inhibited enzyme did not regenerate as fast as AChE-TDPI conjugate. However, 2-PAM enhanced the reactivation of horse-serum BuChE after inhibition with TDPI. The various rate constants were computed from the initial slopes of the inhibition and reactivation of... 

Again the argument of the exponent here must always be more negative than that of equation (12) for the stationary state indicating an enhanced removal of labeled metabolites due to the oscillations. For the case of very large oscillations in X(t) such that x-j - X, equation (14) shows that complete removal of R occurs with one period of oscillation. This can also be shown to be true for large oscillations of undefined waveform ( ). 

The second-order hyperpolarizabilities in oligothiophenes measured by THG showed an exponent a=2.8 [78]. DFWM and EFISH data revealed an exponent a= 4.05 [79] and a=4.6 [80],respectively, for these oligomers. These larger exponents, however, can be explained by a two-photon resonance enhancement in the DFWM and EFISH experiments. 

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