Reverse transfer constant

For very active transfer agents, the transfer agent-derived radical (T ) may partition between adding to monomer and reacting with the polymeric transfer agent (Pn 1) even at low conversions. The transfer constant measured according to the Mayo or related methods will appear to be dependent on the transfer agent concentration (and on the monomer conversion).40 2 A reverse transfer constant can be defined as follows (eq. 20) ... 

VAc polymerization 294 retarders 264 7 definition 264 reverse transfer constant... 

Chain transfer constant, Ca° Reversible transfer constant, Ca Intrinsic molecular weight, Mn° Formula weight of monomer, Fwm Monomer/precatalyst ratio, Meq CTA/precatalyst ratio, Aeq Monomer conversion, X,... 

The relative importance of the disproportionation process (SET between two anion radicals) depends principally on the thermodynamic constant (K). It can be easily determined more or less accurately from the potential difference existing between the first cathodic peak and the second one. (An exact calculation would be possible from the thermodynamic potentials of the two reversible transfers in the absence of proton sources and at reasonable sweep rates so as to inhibit any undesirable chemical reaction.)... 

To derive an expression for the change in entropy when a system is heated, we first note that Eq. 1 applies only when the temperature remains constant as heat is supplied to a system. Except in special cases, that can be true only for infinitesimal transfers of heat so we have to break down the calculation into an infinite number of infinitesimal steps, with each step taking place at a constant but slightly different temperature, and then add together the infinitesimal entropy changes for all the steps. To do this is we use calculus. For an infinitesimal reversible transfer dgrev at the temperature T, the increase in entropy is also infinitesimal and, instead of Eq. 1, we write... 

Forward rate constant for reversible surface reaction Exam. 10.2 Reverse rate constant for reversible surface reaction Exam. 10.2 Mass transfer coefficient for a catalyst particle 10.2... 

FIG. 28 Normalized steady-state diffusion-limited current vs. UME-interface separation for the reduction of oxygen at an UME approaching an air-water interface with 1-octadecanol monolayer coverage (O)- From top to bottom, the curves correspond to an uncompressed monolayer and surface pressures of 5, 10, 20, 30, 40, and 50 mN m . The solid lines represent the theoretical behavior for reversible transfer in an aerated atmosphere, with zero-order rate constants for oxygen transfer from air to water, h / Q mol cm s of 6.7, 3.7, 3.3, 2.5, 1.8, 1.7, and 1.3. (Reprinted from Ref. 19. Copyright 1998 American Chemical Society.)... 

The situation becomes more complex for semi-reversible chain transfer, where kcl and /cRT are both positive, but kCT > kRT As demonstrated in Fig. 7, MJMn can be greater than, less than, or equal to 2.0, depending on the conversion and the magnitudes of the chain transfer constants. The Mn of the polymer is simply a function of C ° the value of C has no effect on M up to C = C °. However, M is dramatically affected by lower values of Ct. If C° Ca > 0, then the initial increase in M IM is dramatic, and M IM does not dip below 2 until high conver-sion. However, as C approaches C 0, the initial increase in MJMn is negligible, and MJMn drops below 2.0 at low conversion. In any case, if Ca > 0, then MJMn asymptotically approaches two from the low side. 

The forward and reverse rate constants are thus equal at zero standard free energy. However, this will be difficult to check in practice, for both reactions are very slow, since a bond-breaking/bond-forming process endowed with a quite large internal reorganization is involved. The result is that dissociative electron transfer reactions are usually carried out with electron donors that have a standard potential largely negative to the dissociative standard potential. The reoxidation of the R, X- system is thus possible only with electron acceptors, D +, that are different from the D,+ produced in the reduction process (they are more powerful oxidants). There is no reason then that the oxidation mechanism be the reverse of the... 

Kinetic techniques (72B4779) require the determination of the forward and reverse rate constants corresponding to the ionization equilibrium in the excited state. This information is obtained by analysis of the fluorescence decay of the species involved in the proton-transfer equilibria in the excited state as a function of the pH. 

Now attach T to the P reservoir and reversibly transfer the aliquot of n moles of gas at constant P (with no work) into the reservoir to reach the final equilibrium state B of the reservoirs. 

An explanation for this difference in selectivity of the Ni catalysts is suggested by the studies of Okamoto et al. who correlated the difference in the X-ray photoelectron spectra of various nickel catalysts with their activity and selectivity in hydrogenations (ref. 28,29). They find that in individual as well as competitive hydrogenations of cyclohexene and cyclooctene on Ni-B, cyclooctene is the more reactive while the reverse situation occurs on nickel prepared by the decomposition of nickel formate (D-Ni). On all the nickel catalysts the kinetically derived relative association constant favors cyclooctene (ref. 29). The boron of Brown s P-2 nickel donates electrons to the nickel metal relative to the metal in D-Ni. The association of the alkene with the metal is diminished which indicates that, in these hydrocarbons, the electron donation from the HOMO of the alkene to an empty orbital of the metal is more important than the reverse transfer of electron density from an occupied d-orbital of the metal into the alkene s pi orbital. 

Hydrogen atom transfer from anthracene, excited into its lowest excited singlet state, to anthraquinone impurity molecules creates a radical pair that strongly quenches the fluorescence from anthracene crystals. The reverse transfer rate constant, found from measurements of fluorescence intensity and its characteristic lifetime at different moments after the creation of the radical pair, varies from 106 to 10s s 1 in the range 110-65 K, kc = 4 x 104 s 1, TC = 60K. The kc values drops to 102 s 1 in the deuteroanthracene crystal [Lavrushko and Benderskii, 1978]. 

For the above study the usual value of the transfer coefficient a = 0.5 has been considered. With small a values, DDPV peaks are found to show a special shape under certain conditions. As can be seen in Fig. 4.17a, fora < 0.3 the DDPV curves corresponding to quasireversible processes with k° 10-3 cm s-1 present a striking splitting of the peak, with a sharper peak appearing at more anodic potentials. This phenomenon is promoted by small transfer constants and is more obvious for positive pulse heights (AE > 0, reverse mode, where the anodic peak is even greater than the cathodic one) and at planar electrodes, since it becomes less apparent as the electrode size is reduced (see Fig. 4.17b). The description of this phenomenon is of great interest since this could lead to erroneous interpretation of... 

The kinetic law, regarding the reverse of average degree of telomerisation, DPn, depends upon the transfer constant of the telogen (CT), the telogen [XY] and monomer [M] molar concentrations, as follows [21 -24] ... 

The high pA"a for HNO would normally not be expected to entirely preclude reactivity of NO- at neutral pH. However, the HNO/NO pair is unique in that proton transfer requires a spin change and that both species are consumed by rapid self-dimerization [(168) 8 x 106M 1 s 1 for Eq. 3 (106)]. The intersystem crossing barrier slows proton transfer by as much as seven orders of magnitude (169) thus allowing dimerization (and other reactions) to not only become competitive with, but to exceed, the rate of proton transfer. Thus for the HNO/ NO pair, an acid-base equilibrium has little relevance the chemistry is instead dependent on the forward and reverse rate constants for proton transfer relative to consumption pathways. 

Since the quantum yield of reversible quenching was found in Ref. 53 using Markovian chemical kinetics, the nonstationary quenching and the concentration dependence of the Stern-Volmer constant were lost. As a result, the linear Stern-Volmer law (3.63) was reproduced but with constant depending on both forward and reverse transfer rates ... 

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