Intramolecular Reactions in Randomly End-Linked Polymer Networks and Linear (Co)polymerizations

• Published in: Macromolecules 2005-03, Vol.38 (6), p.2515-2523
• Main Authors: Lang, Michael, Göritz, Dietmar, Kreitmeier, Stefan
• Format: Article
• Language: English
• Subjects: Applied sciences; Exact sciences and technology; Organic polymers; Physicochemistry of polymers; Polymerization; Preparation, kinetics, thermodynamics, mechanism and catalysts
• ISSN: 0024-9297; 1520-5835
• DOI: 10.1021/ma049025z

This work studies intramolecular reactions in irreversible linear and nonlinear random (co)polymerizations with computer simulations. We find a relative rate for the formation of rings of i chains proportional to i -3/2 in agreement with predictions of rate theory based on Gaussian chain statistics. This result is used to develop a general ansatz for ring formation in irreversible random polymerizations or in cyclization equilibria. Using the approximation c ext ≫ c int for the concentrations of reactive groups on the external molecules c ext and on the selected molecule c int, this ansatz reduces to a result previously found by Suematsu. In this special case we find that the ring size distribution R i is proportional i -5/2[(f − 1)(g − 1)p A p B] i -1, where f and g denote the functionality of two different types of molecules A and B, and p A and p B are the conversions of the reactive groups on the molecules, respectively. Our findings explain preceding experiments, simulations, and all results within this work as well as we can discuss the limitations of previous theoretical approaches.