Molecular Weight Distribution of Living Polymerization Involving Chain-Transfer Agents: Computational Results, Analytical Solutions, and Experimental Investigations Using Ring-Opening Metathesis Polymerization

Abstract

The number-average degree of polymerization and polydispersity index of living polymerization in the presence of chain-transfer agents are calculated numerically and analytically to determine how the molecular weight of the polymer can be regulated. The solutions reveal that un-steady-state polymerization exists in certain cases. The Mayo plot is nearly linear, but (as opposed to a nonliving system) its slope is not equal to k tr /k p in general (where k i , k p , and k tr are the specific rate constants of initiation, propagation, and chain transfer, respectively), the former differing from the latter by about 0.5-1 order of magnitude when k tr k p = 0.01-1.0. Plots of the slopes of Mayo plot versus k tr k p for different values of k p /k i reveal that only when k tr is equal to or greater than k p by an order of magnitude can the molecular weight be effectively controlled by addition of chain-transfer agent. A sufficient amount of chain-transfer agent is a necessary but not a sufficient condition to ensure monomodal molecular weight distribution. An analytical expression for the number-average degree of polymerization of the dead chains when k tr < k p has been derived and shows excellent agreement with numerical results. An analytical expression relating the slope of the Mayo plot to k tr /k p has also been obtained. These equations hold exactly when the concentration of the catalyst is much less than that of the chain-transfer agent. An experimental investigation of the kinetics of ring-opening metathesis polymerization (ROMP) of norbornene by Mo(=CHCMe 2 Ph)(NAr)(OCMe 3 ) 2 (Ar = 2,6-diisopropylphenyl) (1) in the presence of neohexene suggests that this ROMP system is adequately described by a relatively simple polymerization scheme. As measured from NMR spectroscopy, the specific rate constants of initiation, propagation, and chain transfer at 22° C are 0.57, 17, and 0.00003 M -1 s -1 , respectively.