Enhancement-factor

Before the current CIDNP is stated, it is necessary to define the quantities which are generally employed in quantative descriptions of signal enhancements. 

The intensity of an non-degenerate NMR transition between a lower nuclear 2feeman level K and a higher level i of a molecule is proportional to the difference in level populations 

NMR emission corresponds to KL 0 and enhanced absorption to Igi, la,- It is convenient to express the observed deviations from thermal equilibrium by the enhancement factor 

By measuring the intensities in CIDNP patterns and the values KL corresponding to thermal equilibrium of the same system, can be determined experimentally. The usual procedure for the determination of la I volves rapid quenching of the reaction and allowance for thermal equilibration. 

In general, it will be desired to relate the enhancement factors to the rates of product formation in levels K and L. This requires a rather involved procedure since the level populations rig and change with time, not only by the desired rates rg and r, but also by relaxation, and in principle the set of coupled different equations 

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The algebraic form of the expression (9.24) for the enhancement factor is specific to the particular reaction rate expression we have considered, and corresponding results can easily be obtained for other reactions in binary mixtures, for example the irreversible cracking A—2B. ... 

Figure 2.15 Log of viscosity enhancement factor versus parameter measuring branch length for polyisoprene, [Data from W. W. Graessley, T. Masuda, J. E. I. Roovers, and N. Hadjichristidis, Afacromo/ecu/ej 9 127 (1976).]...

The fugacity coefficient of thesolid solute dissolved in the fluid phase (0 ) has been obtained using cubic equations of state (52) and statistical mechanical perturbation theory (53). The enhancement factor, E, shown as the quantity ia brackets ia equation 2, is defined as the real solubiUty divided by the solubihty ia an ideal gas. The solubiUty ia an ideal gas is simply the vapor pressure of the sohd over the pressure. Enhancement factors of 10 are common for supercritical systems. Notable exceptions such as the squalane—carbon dioxide system may have enhancement factors greater than 10. Solubihty data can be reduced to a simple form by plotting the logarithm of the enhancement factor vs density, resulting ia a fairly linear relationship (52). 

In any event the value of iri the presence of a chemical reac tion normally is larger than the value found when only physical absorption occurs, 7c . This has led to the presentation of data on the effects of chemical reaction in terms of the reaction factor or enhancement factor defined as... 

As discussed later, the reaction-enhancement factor ( ) will be large for all extremely fast pseudo-first-order reac tions and will be large tor extremely fast second-order irreversible reaction systems in which there is a sufficiently large excess of liquid-phase reagent. When the rate of an extremely fast second-order irreversible reaction system A -t-VB produc ts is limited by the availabihty of the liquid-phase reagent B, then the reac tion-enhancement factor may be estimated by the formula ( ) = 1 -t- B /VCj. In systems for which this formula is applicable, it can be shown that the interface concentration yj will be equal to zero whenever the ratio k yV/k B is less than or equal to unity. 

To understand the role of solute-solvent interac tions on solubilities and selectivities, it is instructive to define an enhancement factor, E, as the ac tual solubility, y9, divided by the solubility in an ideal gas, so that E = where P is the vapor pressure. This factor is a normahzed... 

FIG. 22-21 Enhancement factor for solids with a variety of polar functionalities in CO9 at 35 C (from bottom to top hexamethylbenzene, 2-naphthol, phthalic anhydride, anthracene, acridine). 

Note that the tower height is inversely proportional to the enhanced mass-transfer coefficient, or to the enhancement factor itself. 

FIG. 23-28 Enhancement factor E and Hatta niimher of first- and second-order gas/liqiiid reactions, numerical solutions hy several hands. 

Clearly there are many permutations of D,b,h,a, etc and Fig. 2.31 shows how the stiffness enhancement factor, q, changes with various values of these parameters. In each case the angle a has been fixed at 85° and the corrugation dimensions have been expressed as a function of the wall thickness, h. 

Nordtest. Electret Filters Determination of the Electrostatic Enhancement Factor of Filter Media. Method NT WS 117. December 1997. 

Fig. 13. Electric-field dependence of the emission current obtained for a carefully aligned MWCNT film [38], Inset Fowler-Nordheim plot, where y is the field-enhancement factor.

ZEBRA 567 energy efficiency 15 enhancement factor, lithium alloys 367 enhancing cation mobility 518 enthalpy 9... 

Glucose uptake T Myocyte enhancer factor-2 f GLUT4 expression Muscle... 

A sequence stretch 300 base pairs upstream of the transcriptional start site suffices for most of the transcriptional regulation of the IL-6 gene (Fig. 1). Within this sequence stretch several transcription factors find their specific recognition sites. In 5 to 3 direction, AP-1, CREB, C/EBP 3/NF-IL6, SP-1 and NF-kB can bind to the promoter followed by TATA and its TATA binding protein TBP. Most enhancer factors become active in response to one or several different stimuli and the active factors can trigger transcription individually or in concert. For example, AP-1 is active upon cellular stress, or upon stimuli that tell cells to proliferate CREB becomes also active if cells experience growth signals, but also upon elevation of intracellular levels of cyclic adenosine monophosphate (cAMP), which occurs upon stimulation if so called hormone-activated G protein-coupled receptors. 

The exchange current I0 is an important parameter for the quantitative description of NEMCA. As subsequently analyzed in this chapter it has been found both theoretically and experimentally1,4 19 that the order of magnitude of the absolute value A of the NEMCA enhancement factor A defined from ... 

As already noted, the enhancement factor or faradaic efficiency, A, is defined from ... 

Figure 4.23. Comparison of predicted and measured enhancement factor A values for some of the early studies of catalytic reactions found to exhibit the NEMCA effect.1,19 Reprinted with permission from Elsevier Science.1...

A qualitatively similar behaviour was obtained during C3H6 epoxidation on Ag 43 Enhancement factor A values of the order of 150 were measured.43 Both the rates of epoxidation and oxidation to C02 increase with I>0 and decrease with I<0. The intrinsic selectivity to propylene oxide was very low, typically 0.03 and could be increased only up to 0.04 by using positive currents. This was again an exploratory study, as no reference electrode was used, thus T and UWr could not be measured 43... 

This causes a 380% increase in rn2co and a 413% increase in rCo- The corresponding enhancement factors are AH2co=-17.5, ACo=-3. There is also a 190% increase in r< H4 with an enhancement factor ACh4= 0.3, but this rate increase has been shown56 to be Faradaic and due to the electrocatalytic reaction ... 

A qualitatively similar behaviour has been observed during CH3OH dehydrogenation on Pt at temperatures between 400° and 500°C, where enhancement factors A of the order of -10 were measured.58... 

The hydrogenation of CO and C02 on transition metal surfaces is a promising area for using NEMCA to affect rates and selectivities. In a recent study of C02 hydrogenation on Rh,59 where the products were mainly CH and CO, under atmospheric pressure and at temperatures 300 to 500°C it was found that CH4 formation is electrophobic (Fig. 8.54a) while CO formation is electrophilic (Fig. 8.54b). Enhancement factor A values up to 220 were... 

The reaction was investigated under atmospheric pressure and at temperatures 500°C to 600°C, where the only product was CO, as Pd, contrary to Rh, does not adsorb C02 dissociatively.59 This difference in reaction pathway is also reflected in the NEMCA behaviour of the system, since in the present case CO formation is enhanced (by up to 600%) not only with decreasing catalyst potential and work function, but also enhanced, although to a minor extent, via catalyst potential increase (Fig. 8.56). Enhancement factor A values up to 150 were measured. The reaction exhibits typical inverted volcano behaviour, which is characteristic of the weak adsorption of the reactants at the elevated temperature of this investigation, and thus of promotional rule G4. 

It was found that both the catalytic rates and the selectivity to the various products can be altered significantly (rate changes up to 250% were observed) and reversibly under NEMCA conditions. Depending on the product, electrophobic or electrophilic behaviour is observed as shown in Fig. 8.57. In addition to the selectivity modification due to the different effect on the rate of formation of each product, acetaldehyde, which is not produced under open circuit conditions is formed at negative overpotentials (Fig. 8.58). Enhancement factor A values up to 10 were observed in this complex system.59... 

Figure 8.69. Effect of applied current on the change in the rate of C2H4 oxidation on Pt/Ti02 for high oxygen to ethylene ratios. Dashed lines are constant enhancement factor (faradaic efficiency) lines.24 Reprinted with permission from Academic Press.

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