Non‐uniqueness in determination of terminal and penultimate model reactivity ratios in the styrene‐methyl methacrylate free‐radical copolymerization system

Abstract

SUMMARY:The terminal and penultimate model reactivity ratios in the free-radical copolymerization of styrene and methyl methacrylate in bulk at 40 "C were calculated by means of the simplex and scanning methods. Calculations showed that for the terminal model rl and r2 vary in comparatively narrow ranges of 0.548 -0.552 and 0.480-0.483, respectively. For the penultimate model, the most accurate reactivity ratios calculated by the simplex method, which were rI1 = 0.727, r22 = 0.490, r2, = 2.890, r12 = 4.583, are surrounded with sets of reactivity ratio values of equal accuracy. The ranges of variation were found to be 0.711 -0.746, 0.487-0.492, 2.810-2.970 and 4.213-5.049, respectively. Numerical values of the penultimate r-parameters calculated with the simplex method depend, due to the structure of the multidimensional space (rT1, r22, r2,, rI2, CT), on the initial guess for the r-parameters. Use of the covariance matrix for the estimation of the indetermination ranges is discussed.

Application of the monomer reactivity ratios to the kinetic-model discrimination and the solvent-effect determination for the styrene/acrylonitrile monomer system

“…Similar results were obtained for both the STY-MMA and STY-AN monomer systems. 3,4,12 Contrary to the STY-MMA system, for which the penultimate model did not yield any significant improvement in the fit to experimental data when compared to the terminal model, implications of the nonuniqueness in determining the penultimate-model reactivity ratios can be quite different for the system displaying a pronounced penultimate unit effect (e.g., the STY-AN system). This is quite obvious, because for examining solvent effects formulated in terms of the relation between the copolymer composition and the monomer-feed composition (the so-called "bootstrap effect" by Harwood 13 ), an adequate kinetic model and well-fitted reactivity ratios are required.…”

“…This method enables to estimate reactivity ratios and related standard deviations with optional precision. With a scanning procedure based on the simplex method, it has been demonstrated 4,12 that the equivalent representation of the copolymer composition in terms of the monomer-feed composition can be achieved with multiple penultimate-model reactivity ratios. These multiple penultimate-model reactivity ratios belong to two different sets of parameters, Set I and Set II, resulting from two different initial guesses for r 11 , r 22 , r 21 , and r 12 (Guess I: r 11 ϭ r 21 ϭ r 1 , r 22 ϭ r 12 ϭ r 22 ; Guess II: r 11 ϭ r 1 , r 21 ϭ 1/r 2 , r 22 ϭ r 2 , r 12 ϭ 1/r 1 ) used for the nlls approach.…”

Statistical approach to model discrimination for the radical copolymerization of methyl methacrylate and styrene from a posteriori data of composition

“…The MML method in principle can be used also for the penultimate (or any other suitable) model. However, its use has been excluded due to the non-uniqueness in determination of the penultimate model parameters for the styrene -methyl methacrylate copolymerization system in bulk discussed in one of our previous papers [9].…”

“…For the penultimate model, additionally non-uniqueness in the determination of the reactivity ratio parameters should be taken into account as discussed previously in ref. [9].…”

“…Experimental data sets on radical copolymerization in bulk were those published by Fukuda et al [1] and Maxwell et al [7]. The first data set has already been proven to be accurate [8][9], with a sufficient number of experimental points and reliable estimates of error. The data of Maxwell have a small number of points and, as it will be shown below, the error estimates are probably inaccurate.…”