A simple and general approach for reversible condensation polymerization with cyclization

Abstract

We develop a simple recursive approach to treat reversible condensation polymerization with cyclization. Based upon a minimum set of balance equations, the law of mass action, Gaussian chain statistics, and the assumption of independent reactions, we derive exact analytical solutions for systems without cyclization, for systems containing only smallest loops, or systems that exclusively form loops. Exact numerical solutions are computed for the general case of a homopolymerization of flexible precursor polymers. All solutions were tested with Monte-Carlo simulations. A generalization for good solvent is discussed and it is shown that this generalization agrees with preceding work in the limit of low and high polymer volume fractions. The new aspect of our approach is its flexibility that allows for a rather simple generalization to more complex situations. These include different kinds of reversible linear polymerization, non-linear polymerization, first shell substitution effect, semiflexibility, or a low molecular weight cut-off for cyclization.

References in corpus (9)

• Accurate estimate of the critical exponent $\nu$ for self-avoiding walks via a fast implementation of the pivot algorithm
• Elasticity of Phantom Model Networks with Cyclic Defects
• Effect of Topology on the Conformations of Ring Polymers
• On the Structure of Star-Polymer Networks
• An Analysis of the Gel Point of Polymer Model Networks by Computer Simulations
• On the Elasticity of Polymer Model Networks Containing Finite Loops
• Ring conformations in bidisperse blends of ring polymers
• Short Cyclic Structures in Polymer Model Networks: A Test of Mean Field Approximation by Monte Carlo Simulations
• The Formation and Structure of Olympic Gels

Cited by in corpus (1)

• Reversible stepwise condensation polymerization with cyclization: strictly alternating co-polymerization and homopolymerization based upon two orthogonal reactions