Chain transfer constants measurement

This suggests that polymerizations should be conducted at different ratios of [SX]/[M] and the molecular weight measured for each. Equation (6.89) shows that a plot of l/E j. versus [SX]/[M] should be a straight line of slope sx Figure 6.8 shows this type of plot for the polymerization of styrene at 100°C in the presence of four different solvents. The fact that all show a common intercept as required by Eq. (6.89) shows that the rate of initiation is unaffected by the nature of the solvent. The following example examines chain transfer constants evaluated in this situation. 

Five different types of rate constants are of concern in radical chain polymerization—those for initiation, propagation, termination, chain transfer, and inhibition. The use of polymerization data under steady-state conditions allows the evaluation of only the initiation rate constant kd (or kt for thermal initiation). The ratio kp/k J2 or kp/kl can be obtained from Eq. 3-25, since Rp, Rj, and [M] are measurable. Similarly, the chain-transfer constant k /kp and the inhibition constant kz/kp can be obtained by any one of several methods discussed. However, the evaluation of the individual kp, k ktr, and kz values under steady-state conditions requires the accurate determination of the propagating radical concentration. This would allow the determination of kp from Eq. 3-22 followed by the calculation of kt, kIr, and kz from the ratios kp/ltj2, ktr/kp, and kz/kp. 

This article shows how successfully the cascade branching theory works for systems of practical interest. It is a main feature of the Flory-Stockmayer and the cascade theory that all mentioned properties of the branched system are exhaustively described by the probabilities which describe how many links of defined type have been formed on some repeating unit. These link probabilities are very directly related to the extent of reaction which can be obtained either by titration (e.g. of the phenolic OH and the epoxide groups in epoxide resins based on bisphenol A206,207)), or from kinetic quantities (e.g. the chain transfer constant and monomer conversion106,107,116)). The time dependence is fully included in these link probabilities and does not appear explicitly in the final equations for the measurable quantities. 

A few very important points have been neglected by some authors in their evaluation of chain transfer constants by means of kinetic measurements. Frequently, a retardation of the overall rate is to be observed in the presence of chain transfer agents. A correct value of the chain transfer constant can result only if the reactions which lead to this retardation are properly considered in the kinetic scheme. In addition, the equation which one must use to calculate the chain transfer constant depends on the type of molecular weight average which is measured. Failure to... 

From a theoretical point of view, the equations which relate the three different molecular weight averages to the chain transfer constant are equally precise. Practically, however, it is recommended that one uses the viscosity average, because it can be measured most accurately. 

The following sections review the magnitudes of the various chain transfer constants, methods for measuring these parameters, and their significance in free-radical polymerizations. 

Problem 32,5 For polymerization of styrene at 60 , the following chain-transfer constants have been measured. Account for the relative effectiveness of the members of each sequence. 

One of the most striking features of CCT is the exceptionally fast rate at which it takes place. The molecular weight of a polymer can be reduced from tens of thousands to several hundred utilizing concentrations of cobalt catalyst as low as 100—300 ppm or 10 3 mol/L. The efficiency of catalysis can be measured as the ratio between the chain-transfer coefficients of the catalyzed reaction versus the noncatalyzed reaction. The chain-transfer constant to monomer, Cm, in MMA polymerization is believed to be approximately 2 x 10 5.29 The chain-transfer constant to catalyst, Cc, is as high as 103 for porphyrins and 104 for cobaloximes. Hence, improved efficiency of the catalyzed relative to the uncatalyzed reaction, CJCu, is 104/10 5 or 109. This value for the catalyst efficiency is comparable to many enzymatically catalyzed reactions whose efficiencies are in the range of 109—1011.18 The rate of hydrogen atom transfer for cobaloximes, the most active class of CCT catalysts to date, is so high that it is considered to be controlled by diffusion.5-30 32 Indeed, kc in this case is comparable to the termination rate constant.33... 

Problem 9.3 Using the kinetic scheme given above, derive suitable expressions for the rate of polymerization (i ) and average degree of polymerization (DPn). Show how chain transfer constants can be evaluated from measurement of DP . 

Problem 6.22 Weighed amounts of styrene (M) and -butyl mercaptan (S) in sealed glass ampoules were heated at 60° C for different periods of time. The polymers were then precipitated in methanol, dried in oven, and degrees of polymerization evaluated by intrinsic viscosity measurements. From.the data given below calculate the chain transfer constant (Cs) for the st5Tene/dodecyl mercaptan system at 60°C. 

Of the common solvents, tert-butyl alcohol because of its very low chain-transfer constant, may be used to produce polymers of relatively high molecular weight. If we concede that single-point measurements of specific viscosity and inherent viscosity may be considered indications of the general trend of molecular weights, then the effect of various solvents on the molecular weights of the poly(vinyl acetate) produced may be seen in Table XV. 

The efficienqf of a chain transfer catalyst has traditionally been measured by its chain transfer constant (Cs), which is the ratio of the rate constant for chain transfer (feu) to that for propagation (fep). Values of Cs are generally determined from the slope of a plot of 1/DP vs. (CTA)/(M] (the Mayo method. Equation 1.27 [74]), in which DP is the degree of polymerization, CTA is the chain transfer agent, and M is monomer. 

Show that the chain transfer constant cs can also be determined by measuring the average degree of polymerization both in the absence [DP]o and in the presence [DP] of chain transfer agent ... 

Some of the highest chain transfer constants ever measured have been reported for COBF (14), as shown below ... 

A plot of 1/DPn against [S]/[M] should yield a straight line with slope k /kp and intercept l/(DPn)o, where (DPn)o is the average chain length measured in the absence of transfer agent. The form of this equation leads to the definition of a chain-transfer constant C for each species, including monomer, in Eq. (19). 

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. 

The effectiveness of a modifier depends on its chemical structure, concentration, temperature, and pressure. A concentration-independent measure for its effectiveness is the chain transfer constant, defined as the ratio of kinetic coefficients for the transfer reaction to this substance and radical chain propagation reaction. Usually the effectiveness of chain transfer agents is increased with rising temperature and reduced pressure. The chain transfer constant of modifiers falls from aldehydes, which are more effective than ketones or esters, to hydrocarbons. Unsaturated hydrocarbons typically have higher transfer constants than saturated hydrocarbons and a strong effect on polymer density must be considered because of the ability to copolymerize that give a higher frequency of short-chain branches in the polymer. 

As macromonomers act as CTAs when copolymerized with methacrylic monomers, it results in a reduction in the molecular weight of the product. The macro monomer acts as a CTA by an AFCT mechanism (Figure 10), with a measurable chain transfer constant. ... 

Since the radical lifetime provides the final piece of information needed to independently evaluate the three primary kinetic constants-remember, we are still neglecting chain transfer-the next order of business is a consideration of the measurement of r. 

The rate constants for chain transfer and propagation may well have a different dependence on temperature (i.e. the two reactions may have different activation parameters) and, as a consequence, transfer constants are temperature dependent. The temperature dependence of Clr has not been determined for most transfer agents. Care must therefore he taken when using literature values of Clr if the reaction conditions are different from those employed for the measurement of Ctr. For cases where the transfer constant is close to 1.0, it is sometimes possible to choose a reaction temperature such that the transfer constant is 1.0 and thus obtain ideal behavior. 3... 

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