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A Matrix Representation of Polymer Chain Size Distributions, 1. Linear Polymerization Mechanisms at Steady‐State Conditions
Author(s) -
Pinto José Carlos
Publication year - 2001
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/1521-3919(20010201)10:2<79::aid-mats79>3.0.co;2-k
Subject(s) - kinetic energy , matrix (chemical analysis) , representation (politics) , statistical physics , thermodynamics , chain (unit) , steady state (chemistry) , mathematics , chemistry , physics , classical mechanics , quantum mechanics , chromatography , politics , political science , law
The kinetic mechanisms used most often to describe the kinetics of polymerization reactions are linear mechanisms at steady state conditions. A general kinetic structure is developed to allow the description of different linear mechanisms at steady state conditions. It is shown that the kinetic structure derived is able to represent very different kinetic schemes, such as the typical free‐radical, cationic, multiple insertion, trigger and depolymerization mechanisms, for computation of both chain size and chain composition distributions. Based on the proposed kinetic structure, a mathematical model is built. The mathematical model depends on the definition of two matrices, whose components depend on the particular steps of the kinetic mechanism analyzed. The first matrix is called the propagation matrix Kp and contains information regarding the chain growth. The second matrix is called the consumption matrix ( A – Kt ) and contains information regarding the chemical transformations among the possibly many active species present in the system. When Kp is equal to the null matrix, model solutions obtained are composition histograms that resemble n‐ads distributions. When Kp is non‐singular model solutions are generalized Schulz‐Flory distributions, whose growth modes are not necessarily real positive numbers, but are guaranteed to have 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‐singular. Model solutions are obtained for five different kinetic schemes in order to illustrate the application of the technique in different situations.