A matrix representation of polymer chain size distributions, 1 - Linear polymerization mechanisms at steady-state conditions

The kinetic mechanisms used most often to describe the kinetics of polymeri zation reactions are linear mechanisms at steady state conditions. A genera l kinetic structure is developed to allow the description of different line ar mechanisms at steady state conditions. It is shown that the kinetic stru cture derived is able to represent very different kinetic schemes, such as the typical free-radical, cationic multiple insertion, trigger and depolyme rization mechanisms for computation of both chain size and chain compositio n distributions. Based on the proposed kinetic structure, a mathematical mo del is built. The mathematical model depends on the definition of two matri ces, whose components depend on the particular steps of the kinetic mechani sm analyzed. The first matrix is called the propagation matrix Kp and conta ins information regarding the chain growth. The second matrix is called the consumption matrix (A - Kt) and contains information regarding the chemica l transformations among the possibly many active species present in the sys tem. When Kp is equal to the null matrix, model solutions obtained are comp osition histograms that resemble n-ads distributions. When Kp is non-singul ar model solutions ate generalized Schulz-Flory distributions, whose growth modes are not necessarily real positive numbers, but are guaranteed to hav e moduli smaller than or equal to one. When Kp is not null but is singular, model solutions are similar to the solutions obtained when Kp is non-singu lar. Model solutions are obtained for five different kinetic schemes in ord er to illustrate the application of the technique in different situations.