Chain transfer constants prediction

Chain transfer is kinetically equivalent to copolymerization. The Q-e and Patterns of Reactivity schemes used to predict reactivity ratios in copolymerization (Section 7.3.4) can also be used to predict reactivities (chain transfer constants) in chain transfer and the same limitations apply. Tabulations of the appropriate parameters can be found in the Polymer Handbook 3 ... 

Chain transfer agents (CTA) are added to a latex formulation to help regulate (i.e., decrease) the molar mass and molar mass distribution of the latex polymer. The extent of chain transfer can be predicted, if the chain transfer constants (Cs) are known for a given monomer system. Riddle [114] presents a table summarizing some of the chain transfer constants for methyl methacrylate with a wide variety... 

In other words, n means that a branch exists in every n monomer units on an average. In equation (1), a = 2 means that all the nitro groups reacted with growing polymer radicals have two branches, and when a equals unity, all the nitro groups reacted have one branch. If the value of a is known, the value of n may be predicted from the chain transfer constant and the extent of monomer conversion a for a given monomer-nitro group containing trunk polymer system. 

Recently, the occurrence of the MAH process, eq 12, has been probed by two methods (i) Buchholz and Kirchner (22) and Pryor and Patsiga (6a,20) used the uv absorptioh of AH to follow its rate of appearance and measure its steady state concentration. Buchholz and Kirchner obtain a steady state concentration for AH of about 0.6 X 10" M at 64°. (ii) We had previously published a computer simulation (23) of the thermal polymerization of styrene in which we assumed that eqs 11-12 were the only initiation mechanism this simulation predicts the steady state concentration of AH to be 5 X 10 M at 60°. This certainly is in acceptable agreement with the later experimental measurement by Buchholz and Kirchner. In addition, our simulation gives the chain transfer constant for AH, i.e., kia/ki5, to be about 1. Thus, AH is a remarkably reactive hydrocarbon toward radicals. 

Figure 6.3 Predicted dependence of (a) degree of polymerization and (b) dispersity on conversion in pol5merizations involving reversible chain transfer as a function of the chain transfer constant (Ctr). Predictions are based on equations proposed by Muller et with a = 10 (the concentration...

Transfer constants of the macromonomers arc typically low (-0.5, Section 6.2.3.4) and it is necessary to use starved feed conditions to achieve low dispersities and to make block copolymers. Best results have been achieved using emulsion polymerization380 395 where rates of termination are lowered by compartmentalization effects. A one-pot process where macromonomers were made by catalytic chain transfer was developed.380" 95 Molecular weights up to 28000 that increase linearly with conversion as predicted by eq. 16, dispersities that decrease with conversion down to MJM< 1.3 and block purities >90% can be achieved.311 1 395 Surfactant-frcc emulsion polymerizations were made possible by use of a MAA macromonomer as the initial RAFT agent to create self-stabilizing lattices . 

The inlet monomer concentration was varied sinusoidally to determine the effect of these changes on Dp, the time-averaged polydispersity, when compared with the steady-state case. For the unsteady state CSTR, the pseudo steady-state assumption for active centres was used to simplify computations. In both of the mechanisms considered, D increases with respect to the steady-state value (for constant conversion and number average chain length y ) as the frequency of the oscillation in the monomer feed concentration is decreased. The maximum deviation in D thus occurs as lo 0. However, it was predicted that the value of D could only be increased by 10-325S with respect to the steady state depending on reaction mechanism and the amplitude of the oscillating feed. Laurence and Vasudevan (12) considered a reaction with combination termination and no chain transfer. 

The general equation for the gel effect index, equation (la) which incorporates chain transfer, was used in those cases where there was not a good agreement between model predictions and experimental data. The same values of and (derived from the values of and C2 found at high rates) were used in the integration of equation (1) and the value of the constant of chain transfer to monomer, C, was taken as an adjustable parameter and used to minimize tfie error of fitting the time-conversion data by the model. 

Solvent polarity and temperature also influence ihe results. The dielectric constant and polarizability, however, are of little predictive value for the selection of solvents relative to polymerization rates and behavior. Evidently evety system has to he examined independently. In cationic polymerization of vinyl monomers, chain transfer is the most significant chain-breaking process. The activation energy of chain transfer is higher than that of propagation consequently, the molecular weight of the polymer increases with decreasing temperature. 

The "ideal" concept of emulsion polymerization was built on the assumption that the monomer was water insoluble and that in the absence of chain transfer, the number average degree of polymerization, Xj can be related to the rate processes of initiation and propagation by the steady-state relationship Xjj = 2 Rp/Rj. Since Ri and Rp are both constant and termination is assumed to be Instantaneous during the constant rate period described by Smith-Ewart kinetics, the above equation predicts the generation of constant molecular weight polymer. Data has been obtained which agrees with Smith-Ewart but there is... 

This expression for contains two unknown rate constants, k and ks. The Arrhenius coefficients for these rate constants were determined using the 140 °C conversion data from Figure 7.6. The parameters were estimated for both the case of chain transfer to monomer, and again for chain transfer to DH. Given that the two chain transfer models differ only in their predictions of Mw and that the fit was against conversion data, the optimum Arrhenius constants for both cases were the same ... 

During the parameter estimation, it was noted that the model is relatively insensitive to changes in k, and therefore it should not be taken as a reliable prediction of the Diels-Alder reaction rate constant. Effectively, the rate R is very large compared with the rates of initiation and chain transfer, and therefore the DH ratio calculation could be simplified without significantly changing the model results ... 

Therefore, at steady-state, the complete CLD or MWD of polyolefins can be predicted using Equation 2.84 and the value of x calculated for the concentrations of monomer, cocatalyst, and chain transfer agent in the reactor, as well as the several required polymerization kinetic constants calculated at a given polymerization temperature. This is a rather straightforward procedure. 

The chain length of the polymer formed is proportional to the transfer constant which is the ratio of the specific rate of radical transfer to the specific rate of chain propagation . Wall and Brown measured the isotope effect fet(H)/ t(D) of (he chain transfer step in the butanethiol-S-dj mediated polymerization of styrene. A value of 4, somewhat less than the predicted value of about 6, was obtained. The low kinetic isotope effect indicated that either the loss of zero point energy of the S—H bond had been compensated by the formation of unusually strong bonds or that the reaction was complicated by the abstraction of butyl hydrogens as well as thiol hydrogen. Data such as these can often aid in the search for more efficient transfer agents. 

A Smith-Ewart case 1 behavior in 1) can be observed during emulsion polymerization of monomers with a high chain-transfer rate constant such as vinyl chloride because the monomer radicals have a high tendency to escape from the particles. Especially for vinyl chloride emulsion polsunerization, Ugelstad and Hansen (113) derived the following equation 18 to calculate n, which predicts dependence, h a... 

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