Nonlinear scission/recombination kinetics of living polymerization
Abstract
Living polymers are formed by reversible association of primary units (unimers). Generally the chain statistical weight involves a factor σ < 1 suppressing short chains in comparison with free unimers. Living polymerization is a sharp thermodynamic transition for σ ≪ 1 which is typically the case. We show that this sharpness has an important effect on the kinetics of living polymerization (onedimensional association). The kinetic model involves i) the unimer activation step (a transition to an assemblycompetent state); ii) the scission/recombination processes providing growth of polymer chains and relaxation of their length distribution. Analyzing the polymerization with no chains but unimers at t = 0 , with initial concentration of unimers M ≳ M^{*} (M^{*} is the critical polymerization concentration), we determine the time evolution of the chain length distribution and find that: 1) for M^{*} ≪ M ≪ M^{*}/σ the kinetics is characterized by 5 distinct time stages demarcated by 4 characteristic times t_{1}, t_{2}, t_{3} and t^{*}; 2) there are transient regimes (t_{1} ≲ t ≲ t_{3}) when the molecularweight distribution is strongly nonexponential; 3) the chain scissions are negligible at times shorter than t_{2}. The chain growth is autoaccelerated for t_{1} ≲ t ≲ t_{2} : the cutoff chain length (= polymerization degree <n>_{w} N_{1} ∝ t^{2} in this regime. 4) For t_{2} < t < t_{3} the length distribution is characterized by essentially 2 nonlinear modes; the shorter cutoff length N_{1} is decreasing with time in this regime, while the length scale N_{2} of the second mode is increasing. (5) The terminal relaxation time of the polymer length distribution, t^{*}, shows a sharp maximum in the vicinity of M^{*}; the effective exponent {frac{{partialln1/t^{*}}}{{partialln M}}} is as high as ∼ σ^{1/3} just above M^{*}.
 Publication:

European Physical Journal E
 Pub Date:
 October 2007
 DOI:
 10.1140/epje/i200710227y
 Bibcode:
 2007EPJE...24..167N
 Keywords:

 82.35.x;
 82.20.w;
 82.20.Bc;
 82.20.Db;
 Polymers: properties;
 reactions;
 polymerization;
 Chemical kinetics and dynamics;
 State selected dynamics and product distribution;
 Transition state theory and statistical theories of rate constants