Probability of propagation

In Chap. 5, p was defined as the fraction (or probability) of functional groups that had reacted at a certain point in the polymerization. According to the current definition provided by Eq. (6.66), p is the fraction (or probability) of propagation steps among the combined total of propagation and termination steps. The quantity 1 - p is therefore the fraction (or... 

Thus, Equation 27 is in this case a possible distribution function. It is of the type of the Schulz-Flory (25) distribution function. The expressions p and alternating polymerization (chain termination). The validity of the Schulz-Flory distribution function in this example of a polymerization with reversible propagation steps is evident. This type of distribution is always present if the distribution of the chain lengths... 

Doubt has been cast on the initiating ability of this type of diradical. In would tend rather to cyclization the probability of propagation is negligible [3], However, it appears again in more recent theories. 

Figure 12. Relationship between probability of propagation and number of tests for a given confidence level...

Now that we can determine the monomer concentration as a function of time, we will focus on determining the distribution of dead polymer, E,. The concentrations of dead poisoner and the molecular weight distribution can be derived in the following manner. The probability of propagation is... 

Such chains might have a small probability of propagating by dissociation of the complex, but could also lead to the cyclic ketone above in a true termination reaction, or in the reaction with tritiated acetic acid. In the... 

Here r is the rate of polymerization, a is the probability of propagation, DP)nst is the instantaneous degree of polymerization, i.e., the number of monomer units on the dead polymer, and/is the initiation efficiency. Compare r in Eq. (7-144) with the simpler Eq. (7-68). When chain transfer is the primary termination mechanism, such as in anionic polymerization, then the polydispersity is 2. 

Fraction of initial catalyst activity, probability of propagation for chain polymerization, confidence level... 

Another effect of decreasing the reaction rate should be to make the probability of propagating any one channel more nearly equal. In the transport-controlled case, branching of channels may occur, but one of the channels will quickly dominate at the expense of the other because of the efficiency of reactive flow capture. In the kinetic rate-con trolled case, any one channel will be less able to capture flow from another. Therefore, in a porous medium with a random distribution of permeability, we expect that the degree of branching should be greater in the kinetic rate-controlled case. 

Zip length = Probability of propagation Probability of (transfer + termination)... 

Considerable simplification of the mathematical treatment is achieved by noting that Equation 6.48 is linear on the Pi, i = I, c (probabilities of propagating chain types). Out of the c equations in Equation 6.48, only c-1 are linearly independent, and so, to solve for thePi, i = 1, c, in terms of the/ , i = 1, c, an additional consistency equation, which can be seen as a dimensionless expression of the mass balance of the propagating chain types directly arising from the definition 6.47, is necessary ... 

Fig. 1, Schematic of the photoemission three-step model. A photon of energy hv is incident onto a sample and excites a photoelectron a distance z below the surface. The photoelectron has a finite probability of propagating to the surface and escaping into vacuum where it is detected. (The motion of the photoeleotron need not be in the same plane as the photon propagation.) The inset below shows the photoelectron final state wave vector inside (kf) and outside (k ) the surface.

A generic polymer chain of length i is produced through i -1 propagation reactions, after which the chain becomes inactive by termination (by disproportionation) or transfer. One can start by defining the probability of propagation, q, as shown in Equation 1.46 ... 

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