Ch ical chemistr Reaction Kinetic Free-Radical polymerizations Chain polymerization Results in the rapid growth of an individual polymer chain for each activated monomer, and often occurs by a radical chain process Let and m stand for the initiator and monomer (a)Initiation ki 72I R● R●+M一 ka>RM· (b)Propagation M+M1 ● M+Mn-1 ● (c) Termination·Mn+·M mm m+n
6 Free-Radical Polymerizations Physical Chemistry Let I and M stand for the initiator and monomer I ⎯⎯→ R• i k 2 R•+M ⎯⎯→RM • a k 1 2 1 M M M p k + • ⎯⎯→• m n k Mn Mm ⎯⎯t→M + • +• m = 0,1,2, , n = 0,1,2, Chain polymerization Results in the rapid growth of an individual polymer chain for each activated monomer, and often occurs by a radical chain process. (a) Initiation (b) Propagation (c) Termination 2 3 2 M M M p k + • ⎯ ⎯→• n k M Mn M p n + • ⎯⎯⎯→• − − , 1 1 Reaction Kinetics
Ch ical chemistr Reaction Kinetic Free-Radical polymerizations (a)Initiation k 2R● kill] R●+M knRM· ( fast) The rate-determining step is the formation of the radicals R (b) Propagation M+M,.-pl >oM M+M2·-2>M3 M+Mn_1·-·M The chain of reactions propagates quickly, 2k[ (1799 f is the yield of the initiation step, the fraction of radicals that R successfully initiate a chain 0.3<f<0.8
7 Free-Radical Polymerizations Physical Chemistry I ⎯⎯→ R• i k 2 R•+M ⎯⎯→RM • a k (a) Initiation (b) Propagation r k [I] = i (fast) 1 2 1 M M M p k + • ⎯⎯→• 2 3 2 M M M p k + • ⎯ ⎯→• n k M Mn M p n + • ⎯⎯⎯→• − − , 1 1 r k [M][ M] p = • The rate-determining step is the formation of the radicals R•. The chain of reactions propagates quickly, f is the yield of the initiation step, the fraction of radicals that R• successfully initiate a chain. 0.3 f 0.8 2 [ ] [ ] fk I dt d M = i • (17.99) Reaction Kinetics
choical Chemistry Reaction Kinetic Free-Radical polymerizations c)ermination k m=0,1,2, n=0.12 m+n Assume that the rate of termination is independent of the length of the chain, the rate of change of radical concentration by this process is ● -2k,[M (17.101 The total radical concentration is approximately constant throughout the main part of the polymerization the rate at which radicals are formed by initiation the rate at which they are removed by termination)
8 Free-Radical Polymerizations Physical Chemistry m n k Mn Mm ⎯⎯t→M + (c) Termination • +• m = 0,1,2, , n = 0,1,2, 2 r k [ M ] t = • Assume that the rate of termination is independent of the length of the chain, the rate of change of radical concentration by this process is The total radical concentration is approximately constant throughout the main part of the polymerization. (the rate at which radicals are formed by initiation the rate at which they are removed by termination) 2 2 [ ] [ ] k M dt d M t = − • • (17.101) Reaction Kinetics
choical Chemistry Reaction Kinetic Free-Radical polymerizations Applying the steady-state approximation d°M=2/M|1-2kM=0 dt The steady-state concentration of radical chains =/)2 k (17102) The rate of propagation of the chains (the monomer is consumed) plmM 1/2 1/2 k (17103) Central the rate of polymerization is proportional to ature the sql uare root of the initiator concentration
9 Free-Radical Polymerizations Physical Chemistry 2 [ ] 2 [ ] 0 [ ] 2 = − • = • fk I k M dt d M i t Applying the steady-state approximation The steady-state concentration of radical chains The rate of propagation of the chains (the monomer is consumed) [ ][ ] [ ] k M M dt d M p = − • 1/ 2 1/ 2 [ ] [I] k fk M t i • = (17.102) [ ] [ ] [ ] 1/ 2 1/ 2 I M k fk k dt d M t i p = − (17.103) The rate of polymerization is proportional to the square root of the initiator concentration. Central feature Reaction Kinetics