两式相除 (5-10) d[m-d[M,dt KuMM+k2IM,[MI dm,l-d[m, ydt kMIM,I+k,,,IM, 对M1、M2作稳态假定 d[mi dt=o, d[M,)dt=0
两式相除: k [M ][M ] k [M ][M ] k [M ][M ] k [M ][M ] d[M ]/dt d[M ]/dt d[M ] d[M ] 2 * 2 2 2 2 * 1 2 1 1 * 1 2 1 2 * 1 1 1 2 1 2 1 + + = − − = 对M1 * 、M2 *作稳态假定 d[M ]/dt 0, d[M ]/dt 0 * 2 * 1 = = ( 5－10 )
稳态假定:Mlt=0,d2dt=0 d[M, R1+k2[M2]M1]-k12M1]M2] dt ku[M1]-k12[M]M2]=0 dm, R12+k12[M1]M2]-k2M2IM1] 2CM2]-k2M2[M]=0
稳态假定: k [ ] [ ][ ] 0 R k [M ][M ] k [M ][M ]- dt d[M ] 1 2 1 2 2 t11 1 2 * 1 1 2 1 * i 1 2 1 2 * 1 − = = + − • • • M kt M M k [ ] [ ][ ] 0 R k [M ][M ] k [M ][M ]- dt d[M ] 2 1 2 1 2 t22 2 1 * 2 2 1 2 * i 2 1 2 1 * 2 − = = + − • • • M kt M M
d[M,] R1+k2M2I[M1]-k12M1M2] dt kuM]2-k12[M'I[M2】=0 稳态假定 ①M1和M2*的引发速率分别等于各自的终止速率: R1-k1M]2-k2MM2]=0 R2-k2M2]2-ka2M2]M]=0 ②M1和M2的互换速率相等: k2IM2JM=k12MIIIM2I (5-13)
稳态假定： ①M1 * 和 M2 * 的引发速率分别等于各自的终止速率: k [ ] [ ][ ] 0 R k [M ][M ] k [M ][M ]- dt d[M ] 1 2 1 2 2 t11 1 2 * 1 1 2 1 * i 1 2 1 2 * 1 − = = + − • • • M kt M M R k [M ] k [M ][M ] 0 * 2 * t12 1 * 2 i 1 − t11 1 − = ② M1 * 和 M2 * 的互换速率相等: R k [M ] k [M ][M ] 0 * 1 * t21 2 * 2 i 2 − t22 2 − = k [M ][M ] k [M ][M ] 2 * 1 12 1 * 21 2 = (5-13)
M]_k1M1M1]+k12M1IM2] KLm +k,2 12 k1M1]+k2M2] 2M2]+k k2M2] 22 21 同除k12k21并令 [M。kk2M+k2k2M2 M2]k2k21M1]+k2k12M2] II 22 12 21 [M1],rM1]+[M2] IM2][M]+rM2]Mayo- Lewis方程
[M ] [ ] k [ ][ ] k [M ][M ] k k [M ][M ] k [M ][M ] d[M ] d[M ] 2 2 1 1 2 * 1 2 1 2 2 2 * 1 2 1 2 * 1 1 2 1 * 1 1 1 2 1 k M M M + + = [ ] k [ ] k [M ] k k [M ] k [M ] 21 1 2 12 2 12 2 22 11 1 12 2 k M M + + = k k [M ] k k [M ] k k [M ] k k [M ] [ ] [ ] 1 2 2 1 1 2 2 1 2 2 1 1 2 1 1 1 2 2 1 2 2 1 + + = • M M 同除k12k21并令 12 11 1 k k r = 21 22 2 k k r = [M ] [M ] r [M ] [M ] [ ] [ ] 1 2 2 1 1 2 2 1 M r M + + = • Mayo-Lewis方程
dIM1][M1]r1M1]+[M2 Mayo- lewis方程dM]M2]M+2M2 式中各项意义: 1.dIM1l/dIM2l:瞬时形成的聚合物组成 2.[MM2:瞬时单体组成 3.r1、r2竞聚率 117112 ~M1+M1→kn自增长速率常数(均聚 ~M1+M2→k12交叉增长速率常数(共聚)
Mayo-lewis方程 ◼ 式中各项意义： 1. d[M1 ]/d[M2 ]: 瞬时形成的聚合物组成 2. [M1 ]/[M2 ]：瞬时单体组成 3. r1、 r2 竞聚率： ~~M1 * + M1→ k11 ~~M1 * + M2 → k12 [M ] r [M ] r [M ] [M ] [M ] [M ] d[M ] d[M ] 1 2 2 1 1 2 2 1 2 1 + + = r1 = k11/k12 = 自增长速率常数(均聚)/ 交叉增长速率常数(共聚)