Molecular Weight and Chain Transfer

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1 1 Molecular Weight and Chain Transfer Kinetic Chain Length ( ): 動力學鏈長 Average number of monomer polymerized per radical, which initiates a polymer chain. = R p /R i = R p /R t = k p [M][M.]/2k t [M.] 2 = k p [M]/2k t [M.] = k p 2 [M] 2 /2k t R p = k p [M]/2(fk d k t [I]) 1/2 The at constant polymerization rate is a characteristic of the particular monomer and independent of the method of initiation. Mode of Termination X n = average no. of monomer molecules contained in a polymer. = 2 for coupling X n = for disproportionation M n = M o X n (M o : MW of the monomer) 2017/2/21 Yun Chen 1 Initiation: I k d 2R. R. k + M i M. Propagation: M n. + M k p M n+1. (k p = 10 2 ~10 4 l/mole-s) Termination: M n. + Mm. k t dead polymer (k t = 10 6 ~10 8 l/mole-s) Coupling ( 偶合 ) or Disproportionation ( 岐化 ) k t = ak tc + (1-a)k td a: fraction by coupling Coupling: Disproportionation: 2017/2/21 Yun Chen 2

2 2 Mode of termination: determined from the number of initiator fragments per polymer molecule (b). a: fraction of propagating chains undergo coupling (1 - a): fraction of propagating chains undergo disproportionation b: average no. of initiator fragments per polymer n: propagating chains initiator fragments: an + (1-a)n an + (1-a)n b = an/2 + (1-a)n polymer molecules: an/2 + (1-a)n X n = b = 2 /(2-a) = 2R p /(2-a)R t = R p /(2-a)(R t /2) a = (2b-2)/b = 2/(2-a) 1-a = (2-b)/b *Predominately coupling for most polymer radicals. *Disproportionation increases when propagating radical is sterically hindered (or has many -H available for transfer), high temperature, or highly reactive (vinyl acetate, ethylene). MMA undergoes termination by a combination of coupling & disproportionation. 2017/2/21 Yun Chen 3 Chain Transfer( 鏈轉移 ): Chain-breaking reaction X n is decreased. Premature termination of a growing polymer by the transfer of a H or atom or species to it from some compound present in the system. k tr M n. + XA M n -X + A. R tr = k tr [M. ][XA] k a A. + M M. (Re-initiation: 再起始 ) XA: monomer, initiator, solvent, chain transfer agent,. ( 調聚反應 ) ( 降解性鏈轉移 ) 2017/2/21 4

3 3 X n : polymerization rate divided by the sum of the rates of all chain-breaking reactions (normal termination + all chain-transfer reactions) X n = R p /{(2-a)(R t /2) + k tr,m [M. ][M] + k tr,s [M. ][S] + k tr,i [M. ][I]} X n = R p /{(R t /2) + k tr,m [M. ][M] + k tr,s [M. ][S] + k tr,i [M. ][I]} (coupling: a = 1) R p = k p [M. ][M] 代入 Chain transfer constants: C M = k tr,m /k p, C S = k tr,s /k p, C I = k tr,i /k p Mayo equation: 1/X n = (R i /2R p ) + C M + C S [S]/[M] + C I [I]/[M]...(3-108a) 1/X n = (k t R p /k p2 [M] 2 )+ C M + C S [S]/[M] + C I k t R p2 /k p2 fk d [M] 3...(3-108b) When disproportionation is important: 1/X n = [(2-a)R i /2R p )] + C M + C S [S]/[M] + C I [I]/[M]. (3-108c) 2017/2/21 Yun Chen 5 Intercept = C M Slope = k t /k p2 [M] 2 Or C I [I]/[M} 1/X n = (k t R p /k p2 [M] 2 )+ C M +C I k t R p2 /k p2 fk d [M] /2/21 Yun Chen 6

4 4 [1/X n -C M ]/R p = (k t /k p2 [M] 2 ) + C I k t R p /k p2 fk d [M] 3... (3-110) Slope = C I k t /k p2 fk d [M] 3 可求 C I when chain transfer to monomer is negligible: (1/X n ) - (k t R p /k p2 [M] 2 ) = C I [I]/[M] Styrene by initiated BPO: C M = C I = /X n = (k t R p /k p2 [M] 2 )+ C M + C I [I]/[M] 2017/2/21 Yun Chen 7 Reactive radicals Chain transfer to monomer (usually small: C M = 10-5 ~ 10-4 ) places the upper limit to the MW that can be obtained (assuming no other transfer reactions). For VCl: 1/X n = 10 x 10-4 X n = 1000 M n = X n M o = /2/21 Yun Chen 8

5 5 Chain transfer to initiator: M n. + RN=NR M n -R + N 2 + R. M n. + RO-OR M n -OR + RO. M n. + RO-OH M n -H + ROO. Initiator chain-transfer constant (C I ) varies with the reactivity of propagating radical. MMA radical is more reactive than styrene radical. 2017/2/21 Yun Chen 9 Chain transfer to chain transfer agent: 1/X n = (k t R p /k p2 [M] 2 )+ C M + C S [S]/[M] + C I [I]/[M] 1) Low [I] or low C I (AIBN). 2) Keep R p /[M] 2 constant by appropriately adjusting [I]. 1/X n = 1/(X no ) + C S [S]/[M] 2017/2/21 Yun Chen 10

6 轉移反應性6 Structure & Reactivity Benzylic hydrogen M n. + XA k tr M n -X + A. C S =k tr /k p Chain transfer agent Weak bonds 2017/2/21 Yun Chen 11 Chain transfer constant: increases in the order of increasing radical reactivity, i.e. vinyl chloride > vinyl acetate > acrylonitrile > methyl acrylate > methyl methacrylate > styrene> 1,3-butadiene Polar effect: the reactivity of an electron-donor radical with an electronacceptor substrate is greater than with electron-donor one. 對Hydrocarbon 鏈2017/2/21 Yun Chen 12

7 7 Stabilization of transition state from polar structure: Practical Utility of Mayo Equation: Control MW * MW lower than needed: adjust [I] or less reactive solvent. * MW too high: add chain transfer agent S (regulators or modifiers: C S >> 1). Ex. 1-dodecanethiol in emulsion polymerization of styrene (SM) and 1,4- butadiene (BD), telomerization. 2017/2/21 Yun Chen 13 Catalytic Chain Transfer (CCT) Two-step mechanism Cobaloxime (II) Cobaloxime boron fluoride Characteristics of CCT: 10 2 ~10 4 as compared to C S = 10~20 for 1-butanethiol. CCT involves transfer of an H atom in the opposite direction. Polymer with unsaturated end group (macromonomer: 巨單體 ). 1/X n = 1/(X no ) + C S [S]/[M] Low MW polymers can be produced without using large amounts of conventional chain-transfer agents or high [I]/[M] ratio or high temperature. 2017/2/21 Yun Chen 14

8 8 Chain Transfer to Polymer Cannot be neglected at high conversion Branching decreased crystallinity M n. + CH 2 C M n H + CH 2 * Transfer constant C p = k tr,p /k p is not easily obtained. C p ~ 10-4 or higher. * It doesn t necessarily lead to a decrease in the overall X n. Y H CH 2 Y C. m M Y C M m Branching density: = - C p [1 + (1/p)ln(1-p)] (by Flory) : no. of branches per monomer polymerized. For C p = 1x 10-4, = , , at 80, 90, and 95% conversion. Reactive radicals result in greater branching such as PE, PVAc, PVC. 2017/2/21 Yun Chen 15 Backbiting intramolecular transfer 2017/2/21 Yun Chen 16

9 9 Short branches (C < 7): formed by backbiting intramolecular transfer, exhibit significant effect on the polymer crystallinity (maximum: 60~70%). The number of short branches are 20~30 times of long branches. n-butyl branches are the most abundant: 5 ~15/1000 C (1~2/1000 C for ethyl, amyl, and n-hexyl branches). Long branches: formed by normal chain transfer to polymer. Affect melt flow (viscosity) properties (influence processing characteristics). HDPE: High density PE [degree of crystallinity (D): 70~80%] Ziegler-Natta catalysts, low pressure, density > 0.95 g/cm 3. LDPE: Low density PE (D: 45~55%) Free radicals, high pressure (1000~3000 atm), density < 0.93 g/cm 3. LLDPE: Linear LDPE Ziegler-Natta catalysts, low pressure, add 1-hexene as comonomer. 2017/2/21 Yun Chen 17

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