Analysis of Disproporationate Termination Effects in Free Radical Polymerization and Damped Oscillatory Kinetics of Simple Reactions in Circle

摘要

A system of reactions in circle is modeled using the methods of Laplace transforms and the method of Jacobian matrix. The conditions of reaction rate constants when the damped oscillatory kinetics may be observed are derived for the cases of three reactants, of four reactants, eight reactants and general case. For the case of Reactions in Circle with 3 reactants the kinetics will exhibit damped oscillatory behavior when k_3 < k_2 + k_1 + 2sqrt(k_2 k_1) or when in any one of the rate constants is less than the square of the sum of the square root of the other two rate constants respectively. For the case of Reactions in Circle with 4 reactants the kinetics will exhibit damped oscillatory behavior when B~3/27 + C~2/4>0 where B = (β - α ~2/3) and C = x + 2α ~3/27 - αβ/3 . In terms of the rate constants α is given by the sum of all the four reaction rate constants and β represents the sum of all the possible binary products of rate constants and x is the sum of all the possible triple products of rate constants in the system in circle. For the general case the characteristic equation is written whose solution will determine the exact solution of the system. The cases where complex roots result will represent the conditions of the rate constants where damped oscillatory behavior can be expected.