Quantifying competition between

The likelihood of the medium being frozen by the electric field is given by the Lan-gevin function resulting from statistical theories which quantify competition between the orienting effect of electric field and disorienting effects resulting from... 

From SCRP spectra one can always identify the sign of the exchange or dipolar interaction by direct exammation of the phase of the polarization. Often it is possible to quantify the absolute magnitude of D or J by computer simulation. The shape of SCRP spectra are very sensitive to dynamics, so temperature and viscosity dependencies are infonnative when knowledge of relaxation rates of competition between RPM and SCRP mechanisms is desired. Much use of SCRP theory has been made in the field of photosynthesis, where stnicture/fiinction relationships in reaction centres have been connected to their spin physics in considerable detail [, Mj. 

The competition between ortholithiation and alternative reactivity—a- or lateral lithi-ation for example, or halogen-metal exchange—has been quantified in only a few cases, and where such issues of chemoselectivity arise they are mentioned in the sections on these topics. 

The most straightforward way to quantify the competition between the transferase reaction and hydrolysis is to measure the initial ratio of these two reactions. Intuitively, one would assume the transferase/hydrolysis ratio to decrease with increasing water activity because of the effect of water as a reactant This is often the case when lipases are used as catalysts [34—36]. However, in reactions catalyzed by glycosidases and proteases the transferase/hydrolysis ratio can either increase or decrease with increasing water activity [37, 38]. 

The competition between transferase and hydrolysis reactions can be described in terms of nucleophile (acceptor) selectivities of the enzymes, and selectivity constants can be defined. These constants are meant to quantify the intrinsic selectivity of the enzymes. Selectivity constants in combination with the concentrations (or thermodynamic activities) of the competing nucleophiles give the transferase/hydrolysis ratio. The selectivity constants are defined as follows [38, 39] ... 

Non-activated double bonds, e.g. in the allylic disulfide 1 (Fig. 10.2) in which there are no substituents in conjugation with the double bond, require high initiator concentrations in order to achieve reasonable polymerisation rates. This indicates that competition between addition of initiator radicals (R = 2-cyanoisopropyl from AIBN) to the double bond of 1 and bimolecular side reactions (e.g. bimolecular initiator radical-initiator radical reactions outside the solvent cage with rate = 2A t[R ]2 where k, is the second-order rate constant) cannot be neglected. To quantify this effect, [R ] was evaluated using the quadratic Equation 10.5 describing the steady-state approximation for R (i.e. the balance between the radical production and reaction). In Equation 10.5, [M]0 is the initial monomer concentration, k is as in Equation 10.4 (and approximately equal to the value for the addition of the cyanoisopropyl radical to 1-butene) [3] and k, = 109 dm3 mol 1 s l / is assumed to be 0.5, which is typical for azo-initiators (Section 10.2). The value of 11, for the cyanoisopropyl radicals and 1 was estimated to be less than Rpr (Equation 10.3) by factors of 0.59, 0.79 and 0.96 at 50, 60 and 70°C, respectively, at the monomer and initiator concentrations used in benzene [5] ... 

Observation (i) above can be understood in terms of droplet nucleation and the lack of competition between nucleation and growth. A mechanistic understanding of observation (ii) above was provided by Samer and Schork [64]. Nomura and Harada [136] quantified the differences in particle nucleation behavior for macroemulsion polymerization between a CSTR and a batch reactor. They started with the rate of particle formation in a CSTR and included an expression for the rate of particle nucleation based on Smith Ewart theory. In macroemulsion, a surfactant balance is used to constrain the micelle concentration, given the surfactant concentration and surface area of existing particles. Therefore, they found a relation between the number of polymer particles and the residence time (reactor volume divided by volumetric flowrate). They compared this relation to a similar equation for particle formation in a batch reactor, and concluded that a CSTR will produce no more than 57% of the number of particles produced in a batch reactor. This is due mainly to the fact that particle formation and growth occur simultaneously in a CSTR, as suggested earlier. 

The competition between and flow-induced and boundary-induced orientation is quantified by an Ericksen number, defined by... 

Nucleophilicities relative to a standard solvent can be quantified by the Swain-Scott equation (12)66, in which k and k0 are the second-order rate constants for reactions of the nucleophile and solvent respectively, and s is a measure of the sensitivity of the substrate to nucleophilicity n. By this definition, the nucleophilicity of the solvent is zero. For all reactions examined, there will be competition between attack by solvent (present in large excess) and reaction with added anionic nucleophiles. Hence, only n values well above zero can be obtained with satisfactory reliability. In the original work66, the solvent was water and all but one of the substrates were neutral s was defined as 1.0 for methyl bromide and was calculated to be 0.66 for ethyl tosylate the lowest reliable n value reported was 1.9 for picrate anion, but a value of < 1 for p-tosylate anion was reported66 in a footnote. 

Perhaps the single word that best characterizes the acid deposition phenomenon is competition. The nature of acid deposition depends on competition between gas-phase and liquid-phase chemistry, competition between airborne transport and removal, and competition between dry and wet deposition. The key questions in acid deposition are related to identifying the essential processes involved and then understanding their interactions and quantifying their contributions. In this section we summarize our current understanding of the answers to these questions. 

This notion of faradic yield is most often used for quantifying the competition between several reactions occurring simultaneously at a given interface. It represents the fraction of the actual current used for the half-reaction in question. The faradic yield (either anodic or cathodic) of a particular half-reaction is therefore inferior to 100%. 

To summarize, VSEPR model has been remarkably successful in predicting the structures of main-group compounds, but the predictions remain qualitative. All attempts to quantify them were so far unsuccessfiil, as well as attempts to extend this approach to transition metals ( extended VSEPR model ) taking into account such factors as ligand-ligand repulsion and polarization of the core electron shells of the central atom [158-160], In the latter case, many other factors must be considered, such as rf-electron configuration of the central atom, competition between a and n bonding, etc. (see discussion in [154]). 

We note from this expression a clean separation into various rate-limiting processes. The first term on the rhs of Eqn. 55 quantifies the process of electron percolation through the layer. The second term describes competition between the surface reaction represented by the rate constant k and the layer reaction represented by the second-order rate constant k. The larger of these two terms dominates. Equation 55 therefore quantifies the transport and kinetics of mediation in the W 1 limit provided we can neglect the direct electrode reaction. The reciprocal form of this expression for k ME nwans that the slower term, whether transport or kinetic, determines the modified electrode rate constant k E-The LIXe ratio determines the location of the reaction zone in the layer. If Xe L, corresponding to a thick film, then tanh (LIXe) = 1, and substrate S penetrates only a distance Xe into the layer. In this case the layer term for the mediation kinetics reduces to kboxXE. On the other hand when L Xe, tanh (LIXe) J-, Xe, and the mediation kinetics are so slow that the layer term reduces to kboKL and the entire layer is used in the mediation reaction. 

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