Free-Radical Copolymerization VII. Reinterpretation of Velocity-of-Copolymerization Data

Abstract

ABSTRACT:Velocity-of-copolymerization data available in the literature were reinterpreted on the basis of the current notions that the penultimate-unit effect with respect to absolute values of propagation rate constant (but not with respect to the monomer reactivity ratios) is a general rule, and that the termination step is diffusion-controlled, i.e., normal. By making a few simplifying approximations, a new velocity equation was derived, which was found to describe experimental data generally better than the classical equation based on the terminal propagation model with a single adjustable parameter </>, the cross-termination factor. The single adjustable parameter s included in the new equation, which measures the penultimate-unit effect, was found to have a strong correlation with the monomer reactivity ratios such that the smaller r1r2 , the smaller is s, i.e., the more significant is the penulimate-unit effect. This result is in support of the relation r1r2 =s1s2 suggested by the phenomenological theory (T. Fukuda et al., Makromol. Chem., Rapid Commun., 8, 495 (1987) In former times, experimental data on copolymerization velocities were analyzed, in almost all cases, by assuming that the terminalmodel propagation scheme 1 was correct.Among the classical velocity equations along this line, the following one commonly termed Walling's equation 2 has been most widely used:where kP and k1 are the rate constants of propagation and termination, respectively, with the subscripts 1 and 2 referring to thehomopolymerizations, r/s are the monomer reactivity ratios, andf/s are the feed monomer compositions. This equation allows the determination of the cross-termination factor <p without knowing k 11 and k12 • This factor should be close to 1:1nity unless 1 ~2 crossterminations are chemically favored over 1-1 and 2-2 homo-terminations. Values of¢ experimentally determined via eq 1 were often * Present address:

A kinetic study of free radical copolymerization of styrene/butyl acrylate

“…As it can be observed, the best agreement between theoretical curve and experimental data, as well as the lowest standard deviation, is obtained when the Case III is applied. Notwithstanding, in our case r 2 /w 2 is smaller than r 1 /w 1 by a factor of about 400, and therefore, as Fukuda et al 40) stated, it is virtually impossible to determine s 2 with meaningful accuracy. Furthermore, if we assume changes in the value of w 2 of the order of l35%, the relation r 1 /w 1 is from 300 to 600 times higher than r 2 /w 2 but no significant influence in the radical reactivity ratio values is noted, which, in agreement with Hutchinson et al 18) , indicates that the uncertainty in the absolute value of w 2 has no effect on the parameter estimation.…”

“…Following the treatment of Fukuda et al 13) , and assuming that termination in copolymerization can be expressed by the chemical factor b = 1, the penultimate model expression for w k p ak 1a2 t reads 40) w r 1 f In these relationships, the k ijm are propagation rate constants with i, j and m representing the penultimate, the terminal and the monomer units, respectively, and the k ti are termination rate coefficients referring to the homopolymerizations.…”

“…Taking into account the stabilization energy model 19) , in which it is proposed that the penultimate unit affects only the stability of the reacting radical but is too far away to interact with the reacting monomer, and that, as Fukuda et al 19,40) suggested, the relationship between the monomer and radical reactivity ratios is given by In the entropic model, Heuts et al 20) proposed that the penultimate unit affects the frequency factor of the propagation reaction, but, provided the two monomers are not too dissimilar in size, the effect cancels from the monomer reactivity ratios and only appears in the radical reactivity ratios. Then a radical reactivity ratio may be approximated by the ratio of two frequency factors, and we must consider another case:…”

“…The standard deviations, as defined by Fukuda et al 40) , were taken as a measure of agreement between theory and experiment.…”

A Comparative Study of Methyl Methacrylate/Butyl Acrylate Copolymerization Kinetics by Atom-Transfer and Conventional Radical Polymerization

“…In addition, it has been proved in conventional copolymerization that the approximation [34] s = (r M N s B ) 1/2 does not always explain the variation of copolymerization rate with monomer feed composition.…”