Propagator principal

Kinetics. Details of the kinetics of polymerization of THF have been reviewed (6,148). There are five main conclusions. (/) Macroions are the principal propagating species in all systems. (2) With stable complex anions, such as PF , SbF , and AsF , the polymerization is living under normal polymerization conditions. When initia tion is fast, kinetics of polymerizations in bulk can be closely approximated by equation 2, where/ is the specific rate constant of propagation /is time [I q is the initiator concentration at t = 0 and [M q, [M and [M are the monomer concentrations at t = 0, at equiHbrium, and at time /, respectively. 

Since the dimension of the principal propagator matrix may be large, it is impractical to calculate the inverse matrix in eq. (10.115) directly. In practice the propagator is therefore calculated in two steps, by first solving for an intermediate vector X (corresponding to U in eq. (10.50)). 

There are four principal propagation reactions, of which the first two are most common ... 

The order of reactivity of the halogens can be explained by energy considerations. For the substrate methane, AH values for the two principal propagation steps are... 

Here Uj and Uj are Cartesian unit vectors, a) and j3) are localized orbitals that are doubly occupied in the HF ground state, jm) and n) are virtual orbitals. Rq is the position vector of the local gauge origin assigned to orbital a) and = (r — R ) x p is the angular momentum relative to Re- Superscript 1 denotes terms to first order in the fluctuation potential, and = [A — is the principal propagator at the zero energy... 

The question whether this reaction is monoeidic or enieidic was not discussed by that author, but in view of the low polarity of bulk THF it seems likely that the principal propagating species is ion-pairs but since there is no definite evidence we will denote the rate constant by kp, but write the equations in terms of x rather than Exr. For this equilibrium polymerisation therefore... 

However, I feel acutely that as soon as I attempt to venture beyond this safe position, I am attacked by severe doubts and misgivings as to the appropriate choice of model, as far as solvent and solvation effects are concerned. A complicating factor is that the three principal propagating species are affected differently [6] by changes in the nature of the solvent. 

The following reactions have been offered as a modified description of the radiation-induced polymerization of several vinyl monomers. The symbolism and nomenclature is that used by Williams et al. (36), wherein, after eliminating the contribution of anionic initiation and/or propagation, the principal propagating species is considered to be a carbonium ion. Thus,... 

As discussed in Sections 1.6 and 1.7, the initiation reaction and principal propagation reactions are... 

In order to evaluate the principal propagator, Tj 1 ( ), through third order it is not necessary to use the complete 0 > wavefunction. Jorgensen and Simons (1975) have shown that only the singly excited part of enters in A3 and none of the other matrices involve 0 >. 

It should be noted that the strict order analysis applies to the inverse principal propagator. That means, as has always been carefully stated, that T11 itself is computed through a given order. There are several terms which are summed to infinite order. This can for instance be seen from iterating on Eq. (79) ... 

Splitting the h2 operator into an excitation and deexcitation part, h2 = e,d, allows the propagator to be written as two property vectors times an inverse matrix, often called the principal propagator. 

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