Assumptions in copolymerization the rate of the propagation be chain- length-independent only the terminal unit of the polymer radical can affect its reactivity no Side reactions, such as depropagation, monomer partitioning, and various forms of complex formation
11 Assumptions in copolymerization • the rate of the propagation be chain-length-independent. • only the terminal unit of the polymer radical can affect its reactivity • no side reactions, such as depropagation, monomer partitioning, and various forms of complex formation
Reactions in copolymerization k R·+M1 k 2 R·+M Ma. MM1·+M1 Mw MI. MM1·+M MMM2° MM2·+M JMM1· 2 MvM2·+M2 S M. J M. k ·Mu k M1·+·M2MM M·+·Mv 12
12 Reactions in copolymerization M1 + kt,11 M1 M1 + kt,12 M2 M2 + kt,22 M2 R + M1 M1 ki,1 R + M2 M2 ki,2 M1 + M1 M1 k11 M1 + M2 M2 k12 M2 + M1 M1 k21 M2 + M2 M2 k22
2. 1 Copolymer composition equation The overall rates of consumption of monomers [M,, [M2] then follow these expressions 1+R R1 kuM,Mi]+k2I[M2.MII gnore the initiation aM2=R2+R22=k12M,IM、\÷k212 The expression for instantaneous copolymer composition(F /F2 molar fraction of m 1·M]+k2 F2[M2]k2[MM2]+k2[M2M2 molar fraction of m 13
13 The overall rates of consumption of monomers [M1 ],[M2 ] then follow these expressions: 1 1 2 1 1 1 1 1 2 1 2 1 1 R R k M M k M M dt d M − = + = • + • 1 2 2 2 1 2 1 2 2 2 2 2 2 R R k M M k M M dt d M − = + = • + • ignore the initiation The expression for instantaneous copolymer composition (F1 /F2 ) 1 2 1 2 2 2 2 2 1 1 1 1 2 1 2 1 2 1 2 1 k M M k M M k M M k M M d M d M F F • + • • + • = = molar fraction of M1 molar fraction of M2 2.1 Copolymer composition equation
Steady-state assumption dIR. dIma. 0 0 0 dt dt k MvM1·+M MM,. 12 MM1·+M2 M· k JM2·+M MvM1·1 k 2 MM2°+M2 MM2 ck22M, M2]+k2IM2. Mi d,. =-k21[M2lM1]+k2{M1 M1M2]=k2[M2 21ll
Steady-state assumption = 0 • dt d R 0 1 = • dt d M 0 2 = • dt d M M1 + M1 M1 k11 M1 + M2 M2 k12 M2 + M1 M1 k21 M2 + M2 M2 k22 1 2 1 2 2 1 2 1 1 k M M k M M dt d M = − • + • • 2 1 2 1 1 2 1 2 2 k M M k M M dt d M = − • + • • 12 1 2 21 M2 M1 k M • M = k • 12 2 21 1 2 1 k M k M M M = • •
f1+k21M,●M1 [M2]k12[M1M2]+k2M2I F1_k[M1M2M+k2[1] F,k12LMi 刂M2'M2]+k2M2] +k2M1] k1k2[M1]+k12k21[M1M +kaM k12k2[M2]+k12k21[M1M2 12 Mayo-Lewis Equation 11 Ak 2 F2 MiKa M2l+[M,I 2 Mo+M
2 1 2 1 2 2 1 2 1 2 1 1 2 1 2 1 M M k k M M k k M M F F + + = 1 2 1 2 2 2 2 2 1 1 1 1 2 1 2 1 2 1 2 1 k M M k M M k M M k M M d M d M F F • + • • + • = = 1 2 1 2 2 2 2 2 1 1 1 2 1 2 1 1 2 1 / / k M M M k M k M M M k M F F • • + • • + = 1 2 2 1 1 2 2 1 2 2 2 2 1 2 2 1 1 2 2 1 1 2 1 1 2 2 2 1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 1 1 2 1 k k M k k M M k k M k k M M k M k M k M k M k M k M k M k M F F + + = + + = 2 2 1 1 1 2 2 1 2 1 r M M r M M M M F F + + = Mayo-Lewis Equation