Uncoupling rate constant

The effect of media viscosity on polymerization rates and polymer properties is well known. Analysis of kinetic rate data generally is constrained to propagation rate constant invarient of media viscosity. The current research developes an experimental design that allows for the evaluation of viscosity dependence on uncoupled rate constants including initiation, propagation and macromolecular association. The system styrene, toluene n-butyllithium is utilized. 

Uncoupled Rate Constants. An initial evaluation of polymerization kinetics is presented in Figure (2), constrained by viscosity invariant rate constants K. The slopes of these straight lines give initial estimates of Rgg/Kp according to Equation (14). Figure 3 presents graphically a power law relationship between K g/Kp and viscosity at 21°C and at 16.6 C. More scatter In Yu s data may be attributed to the use of an older GPC instrument of relatively low resolution. The ratio Kgq/Kp is temperature-sensitive a change of the order or five times is observed if the temperature is reduced by 4.4°C and viscosity is kept constant. 

To obtain the overall uncoupling rate constant, ku, we can again make use of the capture probability y [see Eq. (35)], such that kc = yk+. Recall that y quantifies the extent to which receptor/ligand association is rate-limited by the reaction step. As y approaches 0, association is severely reaction-limited, while as y nears 1, binding is almost purely diffusion-limited. ku is thus given by... 

Hence, the overall uncoupling rate constant is the product of the intrinsic dissociation rate constant and the escape probability (equal to 1 - y). 

The deactivation kinetics were determined through a series of seven separate parameter estimation problems. As with the start-of-cycle case, separate estimating problems resulted from uncoupling the reactions of each carbon number by properly selecting the charge stock. This allowed the independent determination of submatrices in the rate constant matrix Dp [Eq. (37)]. 

The system described is highly coupled, and although it can be solved analytically by conventional methods, such a solution requires substantial data to ensure reliable evaluation of the rate constants. Therefore, this system is transformed into an uncoupled system wherein... 

The partition functions can be factorized into contributions corresponding to the various forms of motion when they are uncoupled (see Appendix A.l), and it is advantageous to rewrite the expression for the rate constant in terms of partition function ratios for the translational, rotational, vibrational, and electronic motion ... 

Elements of classical dynamics of unimolecular reactions in particular, the Slater theory for indirect reactions, where the molecule is modeled as a set of uncoupled harmonic oscillators. Reaction is defined to occur when a particular bond length attains a critical value, and the rate constant is given as the frequency with which this occurs. 

This is an approach for the calculation of the microcanonical rate constant k(E) for indirect unimolecular reactions that is based on several approximations. The molecule is represented by a collection of s uncoupled harmonic oscillators. According to Appendix E, such a representation is exact close to a stationary point on the potential energy surface. Furthermore, the dynamics is described by classical mechanics. 

When a reaction system has an equivalent rate constant matrix in the canonical form N, the general form of the rate equations and their solutions may be inferred from those of an n-component system with m-fold degeneracy in one characteristic direction and p-fold degeneracy in another. For this system there are n — m p) = q characteristic directions with rate equations corresponding to complete uncoupling... 

The connection between the Porter-Thomas nonexponential N(r, E) distribution and RRKM theory is made through the parameters k and v. The average of the statistical state-specific rate constants k is expected to be similar to the RRKM rate constant k(E). This can be illustrated (Waite and Miller, 1980) by considering a separable (uncoupled) two-dimensional Hamilton H = + Hy whose decomposition path is... 

The derivations presented on p. 145 show that the interpretation of records of reactions involving more than two reversible steps requires the use of excessively cumbersome equations with three or more roots. One can often adjust the conditions of an experiment so that two of the steps of a complex reaction sequence are isolated from each other and/or the rest. Such uncoupling of part of a reaction occurs when all prior steps are much faster and the subsequent step is much slower. A numerical example can be used to demonstrate the reaction profile of different intermediates. The time course of a three state reversible reaction (see figure 4.4) is equivalent to three states of an enzyme, and this is illustrated with different effects of the two time constants on the three progress curves. The elucidation of the mechanism and evaluation of the individual rate constants depends on a number of factors. The problem of assigning the two time constants to the... 

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