Propagation rate coefficients

Here Ceq is the ethylene concentration equilibrium to the concentration in a gaseous phase, Kp the propagation rate constant, N the concentration of the propagation centers on the catalyst surface, Dpe the diffusion coefficient of ethylene through the polymer film, G the yield of polymer weight unit per unit of the catalyst and y0at, ype are the specific gravity of the catalyst and polyethylene. 

These equations identify the dominant source and loss processes for HO and H02 when NMHC reactions are unimportant. Imprecisions inherent in the laboratory measured rate coefficients used in atmospheric mechanisms (for instance, the rate constants in Equation E6) can, themselves, add considerable uncertainty to computed concentrations of atmospheric constituents. A Monte-Carlo technique was used to propagate rate coefficient uncertainties to calculated concentrations (179,180). For hydroxyl radical, uncertainties in published rate constants propagate to modelled [HO ] uncertainties that range from 25% under low-latitude marine conditions to 72% under urban mid-latitude conditions. A large part of this uncertainty is due to the uncertainty (la=40%) in the photolysis rate of 0(3) to form O D, /j. 

In the present discussion we will confine attention to the propagation rate-constant kp. Once kp is known, the other rate-constants can usually be calculated from the chainbreaking coefficients obtained from, e.g., Mayo plots. For some non-stationary polymerisations kt and/or kt (initiation and termination) can be measured independently (see Section 4.1). 

If aU propagation rate coefficients are equal and all termination rate coefficients are equal, we can obtain a simple expression for the chain length distribution, called the Schultz Flory distribution... 

For the conditions shown in Fig. 8, it was estimated that the electron density was 8x 10 cm" . This means that kj = 2.5 x 10" cm /s, a value in good agreement with measured rate coefficients for dissociation of small molecules by electron impact . The gas phase propagation rate coefficient kp was also found to be in very good agreement with values determined for conventional butadiene polymerization. The agreement of the adjusted parameter values with those measured independently lends further support to the validity of the proposed model of plasma polymerization. 

The information available up to 1965 on the polymerization kinetics of vinyl acetate has been reviewed by Lindemann 184% who collected data on the transfer coefficients with monomer and polymer, which may be denoted as Clm and Clp respectively. These are the ratios of rate constants for attack on monomer or polymer (per monomer unit) to the propagation rate constant they are the... 

The same authors used photoDSC to obtain time- or conversion-dependent ratios of the termination and propagation rate coefficients 2kt/kp for the polymerization of VA. The starting point of this approach is the classical equation derived from formal kinetics ... 

On reviewing and reinvestigating the polymerization of MMA in the presence of halogenated benzenes and other aromatic solvents, Barn-ford and Brumby (3) have shown that the dependence of the rate of polymerization on the nature of the solvent arises partly from the viscosity dependence of the termination coefficient and partly from the dependence of the propagation rate constant on the nature of the solvent, and that the rate of initiation is not influenced by the nature of the solvent. Their results are compatible with the hypothesis of Henrici-Olive and Olive, but they contradict the suggested mechanism of Burnett et al. (I, 10) which considers solvent participation in the initiation step. 

Use of triphenylmethyl and cycloheptatrienyl cations as initiators for cationic polymerization provides a convenient method for estimating the absolute reactivity of free ions and ion pairs as propagating intermediates. Mechanisms for the polymerization of vinyl alkyl ethers, N-vinylcarbazole, and tetrahydrofuran, initiated by these reagents, are discussed in detail. Free ions are shown to be much more reactive than ion pairs in most cases, but for hydride abstraction from THF, triphenylmethyl cation is less reactive than its ion pair with hexachlorantimonate ion. Propagation rate coefficients (kP/) for free ion polymerization of isobutyl vinyl ether and N-vinylcarbazole have been determined in CH2Cl2, and for the latter monomer the value of kp is 10s times greater than that for the corresponding free radical polymerization. 

If the bulk process is dominating, in the electrical experiment the total conductivity (ionic and electronic) is measured, the second gives information on the tracer diffusion coefficient (D ) which is directly related to the ionic conductivity (or DQ). In the third experiment one measures the chemical diffusion coefficient (D5), which is a measure of the propagation rate of stoichiometric changes (at given chemical gradient) it is evidently a combination of ionic and electronic conductivities and concentrations.3,4,173 175... 

For most monomers, the propagation rate coefficient, kp, is somewhat higher for the first one or two propagation steps than for later addition to longer polymer radicals [53], This is of concern only in oligomerization, not if polymerization is carried to high molecular weight, as is the more common practice. 

The simple copolymer model is a first-order Markov chain in which the probability of reaction of a given monomer and a macroradical depends only on the terminal unit in the radical. This involves consideration of four propagation rate constants in binary copolymerizations, Eqs. (7-2)-(7-4). The mechanism can be extended by including a penultimate unit effect in the macroradical. This involves eight rate constants. A third-order case includes antepenultimate units and 16 rate coefficients. A true test of this model is not provided by fitting experimental and predicted copolymer compositions, since a match must be obtained sooner or later if the number of data points is not saturated by the adjustable reactivity ratios. 

Table 11. Rate coefficients and rate constants of propagation (kp) and activation parameters in the polymerization of cyclic ethers (except THF) at 0 °C... 

One other system has been studied in which there is evidence of lack of association of active centres at high dilutions [76] the propagation rate of polybutadienyl potassium in cumene at —30°C. At concentrations about 10" M the rate appears to be first order in potassium compound with a rate coefficient of about 7 x 10 1 mole" see . ... 

Figure 14 illustrates the effect of solvent on the propagation rate of polystyrylsodium at 25—30°C. The ordinate represents the apparent propagation coefficient (feapp J p/[monomer] [active centres]) i.e. assuming a simple bimolecular reaction... 

As indicated earlier, the concentration of free anions even in tetrahydrofuran is only 1 % of the total at millimolar concentration so they must be of very high reactivity to influence the propagation rate. The increase in k pp with D at moderately low concentrations of active centres is largely caused by the increased concentration of free anions. Only in dioxane is the observed rate coefficient that of the ion-pair since... 

As far as the prop ation reaction is concerned, the rate of propagation, Rp, can be regarded, for simplicity, as being composed of a free ion and a single ion pair contribution, the latter combining the effect of the various types of ion pair present. The observed propagation rate coefficient, fep o b s given by... 

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