Lattice Model of Living Polymerization I. Basic Thermodynamic Properties
J Dudowicz, Karl Freed, Jack F. Douglas
A Flory-Huggins type model of living polymerization is formulated, incorporating chain stiffness, variable initiator concentration and polymer-polymer interactions. Basic equilibrium properties [average chain length L, average fraction of associated monomers diameter}, specific heat Cp, entropy S, and the chain length distribution p(N)] are calculated within mean-field theory. Our illustrative calculations are restricted to systems that polymerize upon cooling [e.g., poly(α-methylstyrene)], but the formalism also applies to polymerization upon heating (e.g., sulfur, actin). Emphasis is given to living solutions having a finite initiator concentration r in order to compare theory with recent experiments by Greer and coworkers, whereas previous primary focus on the r-> 0+ limit where the polymerization transition has been described as a second order phase transition. The general phenomena are analyzed in terms of three characteristic temperatures: a crossover temperature demarking the onset of polymerization, a polymerization temperature where Cp has a maximum, and a saturation temperature at which the extent of polymerization is almost complete. Paper 2 considers the interplay between polymerization and phase separation in living polymer solutions. Many of the properties of living polymers are representative of self-assembling systems (thermally reversible polymer gels, colloidal gels, micelles), and comparisons with other self-assembling systems are briefly indicated.
associating polymer, gelation, glasses, living polymers, micelles
, Freed, K.
and Douglas, J.
Lattice Model of Living Polymerization I. Basic Thermodynamic Properties, Journal of Chemical Physics, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=851616
(Accessed May 29, 2023)