A mathematical model for describing the bulk free‐radical polymerization of methyl‐methacrylate was developed. This model includes a novel methodology for describing the diffusive step of the kinetic rate coefficients, which is based on geometric considerations and application of the Einstein diffusion Equation. The effect of polymer content and temperature on the Rp behavior is discussed in terms of the evolution of the interdependent parameters defining the Rp. The applicability of Smoluchowski equation and the importance of the translational diffusion of short radicals in the rate of termination reaction are questioned in this context. Similitudes and differences between the model results and experimental data are discussed including minima in the Rp curves at low conversions.
The model and methodology for estimating diffusion‐controlled rate coefficients for the methyl methacrylate (MMA) polymerization system is extended to the vinyl acetate (VAc) case. Comparison of the kinetic behavior and termination rate coefficients (kt) of both monomers suggests that at low conversions the termination reaction is controlled by the chemical step, whereas at moderate and high conversions it is controlled by the diffusive step which in turn is determined by the segmental diffusion of the long radicals and not by the center of mass diffusion of short radicals. It is found that, for most of the conversion range, diffusion coefficient for VAc is lower than the one for MMA notwithstanding that ktVAc > ktMMA. An explanation of this apparent inconsistency on the base of the model results and in terms of segmental mobility is proposed.
The model and methodology for estimating diffusion‐controlled rate coefficients for the methyl methacrylate polymerization system reported in Parts I and II of this series is extended to include the chain transfer reaction to an agent (CTA). Theoretical and experimental results exhibit minima in the rate of polymerization curves at low conversions as it is observed in the absence of CTA. Such minima are proposed to be the onset of the autoacceleration effect where the termination reaction undergoes a transition from chemically controlled to diffusion controlled where the segmental mobility of the chain ends plays a key role. As the CTA concentration increases, the conversion at which the minimum is presented is higher and the autoacceleration is less pronounced. This behavior is explained in terms of the effect of polymer chain entanglements and segmental mobility of the chain ends on the termination rate coefficient k
t.
The kinetics of bulk free‐radical polymerizations of n‐butyl methacrylate (n‐BMA), iso‐butyl methacrylate (i‐BMA), and tert‐butyl methacrylate (t‐BMA) are studied by differential scanning calorimetry and with the aid of a mathematical model previously reported by the authors. In all the cases, the rate of polymerization (Rp) evolution curve exhibits a minimum at low conversions and the characteristic maximum of the autoacceleration effect. It is found that the monomer conversion xmin at which the minimum is observed, follows the order n‐BMA > i‐BMA > t‐BMA and that for monomer conversions (x) smaller than xmin, the termination rate coefficient (kt) shows a plateau. According to the model results it is obtained that for x > xmin, the termination reaction is chemically controlled whereas for x > xmin, it is diffusion‐controlled and that the xmin values are related to the value of the termination rate coefficient of the chemical step (kt0) of every isomer, which is highly influenced by the steric hindrance of the alkyl substituent group.
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