CHAIN COPOLYMERIZATION. Chapter 06 Lecture 07

Transcription

1 CHAIN COPOLYMERIZATION Chapte 06 Lectue 07

2 Definition : Homopolyme and Copolyme Homopolyme Copolyme M + M ~M M M M M M M M M M M M M M M M M ~ Mola Ratio Reactivity

3 Impotance of Chain Copolymeization Studying the effect of chemical stuctue on eactivity Tailo-making a polyme poduct with desied popeties Examples: Polystyene bittle, low impact stength, low solvent esistance Poly(styene-acylonitile) impact & solvent esistance Poly(styene-butadiene) elastome Tepolyme impove all popeties mentioned 3

4 Types of Copolymes Random copolyme: -an- Altenating copolyme: -alt- Block copolyme: ex: poly(styene-an-acylonitile) ex: poly(styene-alt-acylonitile) M M Gaft copolyme: M M If the type of copolyme is not specified using -co- 4

5 Copolyme Composition Copolymeization Equation ; Monome Reactivity Ratio Polyme composition (poduct) polyme composition (feeding) Reactivity in homopolymeization Reactivity in copolymeization Maleic anhydide usually Stilbene H H C C O O Fumaic este o O H C C H Copolymeization >> Homopolymeization H HOOC C C H COOH o HOOC H C C COOH H 5

6 Fist-Ode Makov (Teminal Model) of Copolymeization Assume: The chemical eactivity of the popagating chain (feeadical, cabocation, o cabanion) in a copolymeization. Dependent only on the identity of the monome unit at the gowing end. Independent on the chain composition, chain length. M * + M M * M * + M M * M * + M M * M * + M M * (homopopagation ; self-popagation) (coss-popagation ; cossove eaction) 6

7 Fist-Ode Makov (Teminal Model) of Copolymeization Assume: All popagation eaction ae ievesible The ates of disappeaance: -d[m ] dt -d[m ] dt k [M *] [M ] + k [M *][M ] k [M *] [M ] + k [M *][M ] Eq() Eq() Dividing Eq() by Eq(): d[m ] d[m ] k [M *] [M ] + k [M *][M ] k [M *] [M ] + k [M *][M ] Eq(3) Assume:All eaction species (M* and M* ) each a steady-state concentaction. (fo emoving the tems of [M*] & [M*] in eq.) i.e. Both [M*] and [M*] emain constant the ates of inteconvesion ae equal. k [M *][M ] k [M *] [M ] Eq(4) 7

8 Fist-Ode Makov (Teminal Model) of Copolymeization Combine Eq(3), Eq(4) and make a eaangement: k k [M *][M ] + k [M *][M ] d[m ] [M ] d[m ] k [M *][M ] + k [M *][M ] Define: k k k ; (monome eactivity) k When > homopolymeization > coss-eaction < homopolymeization < coss-eaction Then, 0 unable to undego homopolymeization d[m ] d[m ] [M ]( [M ]+[M ]) [M ]([M ]+ [M ]) Copolymeization equation ; Copolyme composition equation 8

9 Fist-Ode Makov (Teminal Model) of Copolymeization Define:The mole faction of monome M in the feed f -f [M ] [M ] [M ] + The mole faction of monome M in the copolyme F -F d[m ] d[m ] d[m ] + Then, the copolyme composition equation can be witten as : F f + f f f + f f + f 9

10 Statistical Deivation of Copolymeization Equation n : the aveage of M monome units that follow each othe consecutively in a sequence uninteupted by M units but bounded on each end of the sequence by M units ex: M M M M M M M M n 6 P : the tansition (conditional) pobability fo foming M M dyad in the copolyme chain P : the tansition (conditional) pobability fo foming M M dyad in the copolyme chain P : the tansition (conditional) pobability fo foming M M dyad in the copolyme chain P : the tansition (conditional) pobability fo foming M M dyad in the copolyme chain 0

11 Statistical Deivation of Copolymeization Equation Theefoe, P P ( * the ate fo M ) adding M ( * The sum of the ates fo M adding M and M ) k k * k[m ][M ] * * [M ][M ] + k [M ][M + ([M ] [M ]) * k[m ][M] * * [M ][M ] + k [M ][M ] ] * [M ][M ] * * [M ][M ] + [M ][M [M] [M ] + [M ] ]

12 Statistical Deivation of Copolymeization Equation The numbe aveage sequence length n of monome M : n X X(N ) X (N ) + (N + 3(N ) + 4(N ) +LL (N ) x : the pobability of foming a sequence of M units with length X M M M M M M P P P ) 3 4 P P P P P P P P P P P P (N ) 5 P 4 P Theefoe: ( ) ( ) ( X ) n N X P ( P 3P 4P ) L P P P P [M ] + [M ( P ) [M ] QP ] <, seies expansion

13 Statistical Deivation of Copolymeization Equation n P (-P ) P [M ] + [M ] [M ] n d[m ] n d[m ] [M ]( [M ]+[M ]) [M ]([M ]+ [M ]) Holds fo both steady-state and nonsteady-state. The eactivity of a popagating species is dependent only on the ultimate unit. No depopagation occu. The fomation of a high MW polyme. 3

14 Range of Applicability of Copolymeization Equation Applicable to adical, cationic, and anionic chain copolymeization. Independent on the diffeences in the ates of initiation and temination. Independent on the absence o pesence of inhibitos o chain tansfe agents. The copolyme must be a high polyme. 4

15 Range of Applicability of Copolymeization Equation The values of monome eactivity atio,, fo any paticula comonome pai can be vey diffeent depending on the mode of initiation Ex: styene methyl methacylate adical cationic 0 0. Fig. 6- anionic

16 Dependence of the instantaneous copolyme composition F and the initial comonome feed composition f fo Styene-MMA 6

17 Types of Copolymeization Behavio ) Ideal copolymeization : ) Altenating copolymeization : 0 3) Block copolymeization : >, > 7

18 Ideal copolymeization ( ) Two types of popagating species M* and M* show the same pefeence fo adding one o the othe of the two monomes. So, the elative ates of incopoation of the two monomes into the copolyme ae independent of the identity of the unit at the end of the popagating species. The copolymeization equation becomes d d [ M ] [ M ] [ ] M [ M ] o F f f + f 8

19 Ideal copolymeization ( ) Most ionic copolymeizations ae chaacteized by the ideal type of behavio when >, < o <, > Random (Benoullian) copolyme The copolyme will contain a lage popotion of the moe eactive monome in andom placement Fig. 6-9

20 Dependence of the instantaneous copolyme composition F and the initial comonome feed composition f fo the indicated values of 0

21 Altenating copolymeization 0 The popagating chain pefeentially eact with the diffeent type of monome as the chain-end altenating copolyme The copolymeization equation is witten as: d d [ M ] [ M ] o F 0.5

22 Dependence of the instantaneous copolyme composition F on the initial comonome feed composition f 0.5

23 Block copolymeization ( >, > ) This type of behavio has been encounteed only in a few copolymeization initiated by coodination catalysts. If >> block copolyme Ex: styene - vinyl acetate monome eactivity atio (by adical polymeization) 3

24 Vaiation of Copolyme Composition with Convesion Instantaneous copolyme composition : at vey low degees of convesion (<5%). Conside: ) A system initially containing a total of M moles of the two monomes. ) F > f (i.e. M is iche in copolyme than in feed) 3) dm moles of monomes have been copolymeization. Then ) Numbe of moles of M in copolyme F dm ) Numbe of moles of M in feed (M-dM)(f -df ) F [( M dm )( f )] dm Mf df # of moles of M befoe eaction Mdf # of moles of M afte eaction 0 + f dm dmdf 4

25 5 Vaiation of Copolyme Composition with Convesion Recalling, fo a given set of and, theefoe, and df f F M dm 0 ln M M M dm M0 M (f ) 0 f ( ) f F df Sub 0 : initial value f f f f f f f F ( ) ( ) ( ) δ δ f f f f f f M M Degee of convesion α β ( )( ) γ δ Fig. 6-4, Fig. 6-5, Fig. 6-6

26 Vaiations in feed and copolyme compositions with convesion fo styene (M ) - methyl methacylate (M ) (f ) , (f ) ,

27 Dependence of the instantaneous copolyme composition F on the initial comonome feed composition f and the pecent convesion of styene (M )--vinylthiophene (M )

28 Distibution of copolyme composition at 00% convesion fo styene--vinylthiophene at the indicated values of mole faction styene in the initial comonome feed 8

29 Micostuctue of Copolyme Sequence-length distibution the distibutions of the vaious lengths of the M and M sequence. The pobability of foming M sequence of length X : (N ) x (P ) (x-) P The pobability of foming M sequence of length X : (N ) x (P ) (x-) P [ M ] P P [ M ] [ M ] + [ M ] [ ] + M Recalling: P [ M ] [ M ] + [ M ] P [ M ] [ M ] + [ M ] High-esolution NMR is a poweful tool fo analysis of copolyme micostuctue. An altenate method fo evaluating the monome eactivity atios. Fig. 6-9, Fig

30 Sequence-length distibution fo an ideal copolymeization with and f f P P P P ad 5% 3ad.5% 4ad 6.5% 5ad 3.3% 30

31 Sequence-length distibution fo an ideal polymeization with 5, 0. and f f P P P P

32 Sequence-length Distibution fo an Altenating Copolymeization 0. and f f P P P P

33 Multicomponent copolymeization Tepolymeization : M, M, M 3 M * + M M * R [M *][M ] M * + M M * R [M *][M ] M * + M 3 M 3 * R 3 3 [M *][M 3 ] M * + M M * R [M *][M ] M * + M M * R [M *][M ] M * + M 3 M 3 * R 3 3 [M *][M 3 ] M 3 * + M M * R 3 3 [M 3 *][M ] M 3 * + M M * R 3 3 [M 3 *][M ] M 3 * + M 3 M 3 * R [M 3 *][M 3 ] Six monome eactivity atios R / R 3 / 3 R / R 3 / 3 R 3 33 / 3 R 3 33 / 3 9 possible eaction outes 33

34 Multicomponent copolymeization The ates of disappeaance of monomes: [ ] d M R + R + R3 dt d[ M ] R + R + R3 dt d[ M 3] R3 + R3 + R33 dt Assume: All eactive adicals each the steady-state concentations. R + R 3 R + R 3 (Disappeaance ategeneation ate) R + R 3 R + R 3 R 3 + R 3 R 3 + R 3 34

35 Multicomponent copolymeization Theefoe, the tepolyme composition equation can be expessed as d[m ] d[m ] d[m 3 ] M 3 [ ] [ ] [ ] [ ] 3 M + + [ M ] : M M 3 M 3 [ ] [ ] [ ] [ ] 3 M + + [ M ] : 3 M 3 M 3 3 M [ M ] [ M 3] [ ] [ ] [ ] [ ] 3 M [ M 3] M 3 M [ M ] [ M 3] [ M ] [ M ]

36 Multicomponent copolymeization Assume: R R ; R 3 R 3 ; R 3 R 3 The equation can be simplified to be: d[m ] d[m ] d[m 3 ] [ M ] [ ] M : [ M ] : + [ M ] [ M ] [ ] M 3 [ M ] [ M ] + [ M ] [ M ] [ M 3] 3 [ ] 3 3 M Table 6-36

37 Pedicted and Expeimental Compositions in Radical Tepolymeization 37

38 Radical Copolymeization Effect of eaction conditions Reaction medium feed composition Homogeneous : bulk, solution Heteogeneous monome eactivity atios Tempeatue effect Pessue effect Reactivity Resonance effects Steic effects Altenation: Pola effects and complex paticipation Rate of Copolymeization Chemical-contolled temination Diffusion-contolled temination 38

39 Reaction medium - feed composition Emulsion polymeization : monome doplets, dispesion medium. Micelles Solubility in micelles Diffusion into micelles f, feed f, micelles MM M M Suspension polymeization: Solubility in dispesing medium 39

40 Reaction medium- monome eactivity atio Poo solubility of the copolyme poduct in the eaction medium Methyl methacylate (MMA) N-vinylcabazole (NVC) H C C CH 3 C O H C CH N OCH 3 (benzene) (MeOH) The popagating copolyme chains ae completely soluble in benzene fom micoheteogeneous in MeOH Adsoption on copolyme chains : NVC > MMA 40

41 Reaction medium- monome eactivity atio Viscosity mobility of monome ph value (especially fo acidic o basic monome) Acylic acid Acylamide H C C H H C CH C O C O OH NH (ph) (ph9) At ph9, H C CH H C CH electostatic epulsion COOH COO 4

42 Reaction medium- monome eactivity atio Polaity of the eaction medium Complexation (eg. pola solvent-pola monome) Ionization The eactivity of pola monome usually deceases in pola solvent. 4

43 Tempeatue Effect E Aexp RT Activation enegy A exp A The activation enegies fo adical popagation ae usually elatively small. Fo most pais of monomes : E -E < 0 J/mole ( E E) RT The monome eactivity atio is usually insensitive to Tempeatue ex : styene,3-butadiene ex : styene MMA (5 ) (60 ) (45 ) (3 ) Howeve, if E -E 0 Temp selectivity of monome 43

44 Pessue Effect The monome eactivity atio vaies with pessue accoding to ln dp ( V V ) d RT V * : The popagation activation volume fo adical M * adding monome M V * : The popagation activation volume fo adical M * adding monome M P popagation ate ( V * - V * ) < V *, V * is insensitive to P P monome selectivity (appoach to ideal copolymeization) 44

45 Pessue Effect Ex: styene acylonitile (atm) 0.06 (000atm) Ex: MMA acylonitile (atm) 0.6 (atm)

46 Reactivity - Resonance effect Resonance Effects: Resonance stabilization monome eactivity Substituents incease the eactivity of a monome towad adical attack in the geneal ode : O O > > CH CH CN C O R C OH C OR O Cl O C R R OR H > > > 46

47 Reactivity - Resonance effect Unsatuated linkages ae most effective in stabilizing the adicals the loosely bonded e - ae available fo esonance stabilization Only the nonbonding e - on halogen o oxygen ae available fo inteaction with a adical Cl > acetoxy > ethe 47

48 Radical Reactivity The ode of substituents in enhancing adical eactivity is the opposite of thei ode in enhancing monome eactivity. The effect of a substituent on adical eactivity is consideably lage than its effect on monome eactivity. Vinyl acetate adical is about 00~000 times moe eactive than styene adical towad a given monome. But, styene monome is only 50~00 times moe eactive than vinyl acetate monome towad a given adical. 48

49 Radical Reactivity Conside a system: R* + M R* R* + M s R s * Stabilized adical R s * + M R* R s * + M s R s * M s : stabilized monome The ode of the eaction ate : R* + M s > R* + M > R s * + M s > R s * + M 49

50 Reaction coodination diagam fo the eaction of a polyme adical with a monome 50

51 Radical Reactivity Theefoe, Monomes without stabilizing substituents (eg. vinyl chloide, vinyl acetate.) will self-popagate faste than those with stabilizing substituents (eg. styene). Copolymeization will occu pimaily between two monomes with stabilizing substituents o between two monomes w/o stabilizing substituents. The copolymeization of styene-vinyl acetate is not efficient. H C CH COOCH 3 5

52 Reactivity - Steic effect Rate constant ( ) fo adical-monome eactions monome H H C C H Cl Vinyl chloide H H C C Cl Cl Vinylidene chloide Cl Cl H H C CH O O C Polyme Radical CH 3 H C C Vinyl acetate styene acylonitile 0,000 3, ,50 H CN H C C Cis-.-dichlooethylene Cl H C C H H Cl Tans-.-dichlooethylene H Cl 365,30 x Cl C C Cl tichlooethylene Cl Cl 3, Cl C C Cl tetachlooethylene

53 Reactivity Polaity Effect and Complex Paticipation - Altenation Polaity diffeence between two monomes Tendency towad altenation copolymeization Values of in Radical Copolymeization 53

54 Reactivity Polaity Effect and Complex Paticipation - Altenation Two possible mechanisms : ) The patial e-tansfe between the e-dono and e-accepto species stabilizes the tansition state. O HC C H C. O C O maleic anhydide adical H C H CH O HC C H C O C O HC CH H CH C HC CH CH CH HC CH H O C O C O C C -O O O 54

55 Reactivity Polaity Effect and Complex Paticipation - Altenation ) Fomation of a : complex between dono and accepto monomes polymeization of these complexes. M + M M M complex MM + M M M M M M 55

56 Reactivity Polaity Effect and Complex Paticipation - Altenation a) Spectoscopic (UV and NMR) evidence fo the fomation of chage tansfe complexes. b) Altenation copolymeization occus ove a wide ange of feed compositions and a high eaction ate was obseved at o nea the equimola feed composition, which coesponds to the max. conc. of complex. c) Small effect on mola weight fo adding chain-tansfe agents. d) Some altenating copolymeization poceed spontaneously w/o adding fee-adical initiato. e-tansfe between monomes leads to adical fomation 56

57 Reactivity Polaity Effect and Complex Paticipation - Altenation To some comonome pais, the addition of a Lewis acid (ZnCl, dialkyl aluminum chloide, alkylaluminum sesquichloide [AlR -5 Cl -5 ]) inceases the tendency to fom altenating copolyme. Possible mechanisms: Lewis acid /e-accepto complex Coss-popagation [LA/e-accepto] e-donno Tenay complex homopopagation Tempeatue Altenation tendency Total monome conc. Altenation tendency 57

58 Rate of copolymeization Two appoaches: A. chemical-contolled temination Assume: the temination eaction to poceed by chemical contol Fo popagation eactions: M M M M M M M M M M + M M 58

59 Rate of copolymeization Thee temination eactions: M M M M M M The oveall ate of copolymeization the sum of the 4 popagation ates R p -(d[m ]+d[m ]) dt [M *][M ]+ [M *][M ]+ [M *][M ]+ [M *][M ] 59

60 Rate of copolymeization Assume: each type of adical eaches its own steady-state concentation (i.e. inte convesion ates ae equal) Assume : the total concentation of adicals is also on steady-state. Theefoe, [M *][M ] [M *][M ] R t t [M *] + t [M *][M *]+ t [M *] R p ( [M ] +[M ][M ]+ [M ] )R t / { [M ] + [M ][M ]+ [M ] } / 60

61 Rate of copolymeization Whee, t / t / t ( t t ) / The coss-temination is statistically favoed ove like-adical-temination by a facto of Coss-temination ate constant Geometic mean of the ate constants fo self-temination of like adicals > coss-temination is favoed < self-temination is favoed 0 (i.e. towad altenation), (i.e. coss-temination) pola effect leads to the tendency towad coss-temination 6

62 Rate of copolymeization B. diffusion-contolled temination It is well established that temination in adical polymeization is geneally diffusion-contolled. Conside the temination as the eactions: M *+M * M *+M * M *+M * t() Dead polyme The temination ate constant t() is a function of the copolyme composition. 6

63 Rate of copolymeization Assume: the total concentation of adicals is on the steady-state. R t t() ([M *]+[M *]) Assume : each type of adical eaches a steady-state concentation. [M *][M ] [M *][M ] Combining these equations with the popagation ate equation, R p ( [M ] +[M ][M ]+ [M] )R t / / [M ] [M ] t() + 63

64 Ionic Copolymeization Ionic Copolymeization v.s. Radical Copolymeization: Ionic copolymeization ae much moe selective. Cationic copolymeization is limited to monomes with e-donating substituents. Anionic copolymeization is limited to monomes with e-withdawing substituents. The monome eactivity atio fo ionic copolymeization is sensitive to the changes in the initiato, eaction medium, o tempeatue. 64

65 Cationic Copolymeization Reactivity is often influenced to a lage degee by the eaction conditions (solvent, counteion, tempeatue) than by the stuctue of the monome. Not as well defined as adical copolymeization The effect of a substituent on the eactivity of a monome: ex: the extent to incease the electon density on the double bond. the ability to esonance stabilize the cabocation CH CH R > > > > > Cl NO ex: H C OCH 3 CH 3 Cl H CH 3 C > H C C > OR CH 3, H C H C C H 3 C CH 65

66 Cationic Copolymeization Oxygen is a stongly electonegative goup. H H H C H C O CH 3 C C O CH 3 H Resonance stabilization Resonance-donating OCH 3 OCH 3 CH 3 NO Distance field effect Field effect 66

67 Effect of solvent and counteion Solvent and counteion changes alteations in the elative amounts of the diffeent types of popagating cente. BA B + A - B + + A - covalent Ion pai Fee ion Each is affected diffeently Complex and difficult to pedict 67

68 Effect of solvent on values C isobutylene P-chloostyene solvent initiato.0.0 n-hexane AlB nitobenzene AlB 3 isobutylene Cl P-chloostyene The popagating centes in the nonpola medium (n-hexane) ae pefeentially solvated by the moe pola monome (pchloostyene). the cone. of p-chloostyene at the eaction site. In the pola nitobenzene, the popagating centes ae completely solvated by the solvent. moe eactive isobutylene exhibits its geate eactivity 68

69 Effects of solvent and counteion on copolyme composition in styene-p-methylstyene copolymeization (Feed :) % styene in copolyme initiation effectiveness initiato SbCl 5 AlX 3 TiCl 4, SnCl 4 Cl 3 CCOOH I toluene,-dichlooethane nitobenzene Initiato : SbCl 5 (stongest) ; I (weakest) polymeization by I and tichlooacetic acid poceed pedominantly though colvalent species. Fo high polaity solvents (,-dichlooethane, nitobenzene), the copolyme composition is insensitive to the initiato. The copolyme composition is insensitive to the solvent polaity fo any initiato except SbCl 5 (stongest). 69

70 Effect of solvent and counteion SbCl 5 system : solvent polaity styene content in copolyme Low polaity solvent (toluene) system : initiato stength styene content Polaity, eactivity : p-methylstyene > styene In poo solvent (toluene) : pefeence on the solvation of the popagating ion pais : p-methylstyene > styene Initiation ability selectivity styene content In good solvent : ability to complex with popagating centes : solvent > monome the influence of the counteions in the eaction copolyme composition is detemined pimaily by the chemical eactivity of the monomes. 70

71 Effect of tempeatue Ionic copolymeization have a geate spead of popagating activation enegies than adical copolymeization T has a geate influence on monome eactivity atios T deviates fom No geneal tend 7

72 Anionic Copolymeization Monome eactivity: Anionic copolymeization cationic copolymeization Enhanced by e-withdawing substituents and esonance stabilization Geneal ode : CN Tend to be ideal behavio altenative copolymeization styene-p-methylstyene styene- -methylstyene Steic effects O C OR opposite > > >, C CH H 5.3, 0.8, 35, 0.003, 0.95 (ideal) CH 3 0. ( altenation) 7

73 Effect of Solvent and Counteion Effect of Solvent and Counteion on Copolyme Composition in Styene-Isopene Copolymeization Solvent None Benzene Tiethylamine Ethyl ethe Tetahydofuan % Styene in Copolyme fo Counteion Na + Li , Initiato: n-buli Relative ate of homopolymezation: styene isopene In poo solvent: Isopene is pefeentially complexed by Li + ich in copolyme In good solvent: The influence of monome solvation is much less impotant The quantitative effect of solvent on copolyme composition is less fo moe loosely bound Na+ counteion. 73

74 Deviations fom Teminal Copolymeization Model Two impotant assumptions fo Teminal Copolymeization Model : inetic natue: The eactivity of the popagating species depend only on the type of monome at the teminal of the popagating chain. Themodynamic natue: All popagation eactions ae ievesible. Not always tue fo some systems! 74

75 inetic Penultimate Behavio (Second-Ode Makov Behavio) The eactivity of the popagating species is affected by the next-to-last (penultimate) monome unit. Obseved in many adical copolymeization with monomes containing highly bulky o pola substituents. Example: styene + fumaonitile ( C C ) NC (M ) (M ) H H CN H H CN H C C C C. C C H CN CN H H H CN low eactivity Steic and pola epulsions between the penultimate fumaonitile unit in the popagating chain and the incoming fumaonitile monome. 75

76 Mathematical Teatment of Penultimate Effect Eight popagating eactions: MM + M MM + M M M + Fou eactivity atios: M + M + M M M M M MM + M MM + M + M M M ' M M M M M M M M M M M M M M M M M M M M M M M M ' 76

77 d Mathematical Teatment of Penultimate Effect [ M ] dt [ M M *][ M ] + [ M M *][ M ] + [ M M *][ M ] + [ M M *][ M ] d [ M ] dt [ M M *][ M ] + [ M M *][ M ] + [ M M *][ M ] + [ M M *][ M ] d d [ M] [ M ] [ MM *][ M] + [ M M *][ M] + [ MM *][ M] + [ M M *][ M] [ M M *][ M ] + [ M M *][ M ] + [ M M *][ M ] + [ M M *][ M ] Assume: Steady-state concentation fo all eactive species (elimination geneation) [ M M *][ M ] + [ M M *][ M ] [ M M *][ M ] [ M M *][ ] + M 77

78 78 [ ] [ ] ( ) ' ' M M + + x x x d d Define: Copolyme composition equation with kinetic penultimate effect If 0 ( in capable of self-popagation) The copolyme composition equation can be simplified to Mathematical Teatment of Penultimate Effect [ ] [ ] M M x [ ] [ ] ( ) ( ) ( ) ( ) x x x x x x d d ' ' ' ' M M

79 inetic Penultimate Effect in the adical copolyme of Styene (M ) Fumaonitile (M ) Copolyme composition [ M] [ M ] Solid line: theoetical plot calculated fom with 0.07,.0 vs. comonome feed composition X dashed line: calculated fom the copolyme composition equation based on st-ode Makov model Open cicle: expeimental data d d d d [ M] [ M ] ' x ( x + ) ' x + 79

80 Penultimate Effect Ex: Anionic copolymeization of styene and 4-vinylpyidine (styene)-(4-vinylpyidine) + 4-vinylpyidine (faste) (4-vinylpyidine)-(4-vinylpyidine) + 4-vinylpyidine The 4-vinylpyidine penultimate unit acts as e- sink and hindes bond fomation with the appoaching monome. Detections on the penultimate effects: Expeimentally detemine copolyme compositions pecisely and accuately. Easily detected in expeiments caied out at vey low o vey high f values. 80

81 Depopagation duing Copolymeization (Themodynamic appoach) The altenation of copolyme compositions in copolymeization pocesses is accounted fo the tendency of one of the monomes to depopagate in cetain conditions. Monome concentation dependence. Tempeatue dependence. Conside a monome pai (M -M ) system: Case Assume:. M has absolutely no tendency to depopagate iespective of the poceeding units in the chain.. M has no tendency to depopagate if it is attached to an M units. ( M M *) 3. M tends to depopagate if it is attached to anothe M unit. ( M M *) MM M M M M + 8

82 8 The copolyme composition equation in this case is: Whee, : equilibium constant Case Assume: () and () ae the same as case. (3) M tends to depopagate only when it is attached to a sequence of two o moe M units (M M M *) Depopagation duing Copolymeization (Themodynamic appoach) [ ] [ ] [ ] [ ] ( )( ) [ ] M M M M M α + d d [ ] [ ] [ ] [ ] [ ] M 4 M M M M α M M M M M M M M +

83 Depopagation duing Copolymeization (Themodynamic appoach) The copolyme composition equation in this case is: [ M ] α [ M ] [ M ] + α + M d α [ M ] + d[ M ] α + Whee, : equilibium constant Example: Anionic copolymeization of vinylmesitylene- -methylstyene T -78 depopagation is negligible T 0 α [ ] [ M ] α (M ) vinyl mesitylene (M ) -methystyene [M ] > [M ] C (0.75 moles/l ) depopagation is not impotant. [M ] < [M ] C at constant [ M] [ M ] depopagation is significant and the content of M in copolyme 83

84 Effect of depopagation on copolyme composition in the anionic copolymeization of vinylmesitylene(m ) -methystyene(m ) T0 f 0.9 Solid-line and open-cicle: expeimental data Boken-lines: pedictions fom models ( 0.0, 0.7) is obtained fom the polymeization-depolymeization equilibium data fo the homopolymeization of M Case is bette than Case in the expeiment. 84

85 Copolymeization with Complex Paticipation The comonome complexes (e.g.m M ) paticipate in the popagation eaction and compete with each of the individual monomes. Eight popagation steps: Six eactivity atios: M M M M M M M M + M + M + M + M + MM + M M + MM + M M M M M M M M M M ' '' ' '' 85

86 Copolymeization with Complex Paticipation The copolyme composition obtained by the statistical appoach is: d d [ M] [ M ] ( ( )( P Define: the tansition pobabilities [ M ] [ M ] P P R P P P [ M ] R '' [ M M ] R ' '' R [ M M ] R P P P P P [ M ] ' '' '' )( P [ M M ] R [ M M ] R R + + P P R R ) ) + ( P + ( P (the sum of )( P )( P + + P P [ M ] + [ M ] + ''[ M M ]( + ') [ M ] + [ M ] + ''[ M M ]( + ') ) ) the xn ates of * M ) 86

87 Copolymeization with Complex Paticipation The complex paticipation model pedicts a vaiation of the copolyme composition with tempeatue monome concentation T monome complex monome at fixed f monome complex 87

88 Copolymeizations Involving Dienes - Cosslinking Diene: a monome contains two double bonds. often used to obtain a cosslinked stuctue. Reaction time (ealy o late): the elative eactivities of the two double bonds of the diene. Extent of cosslinking: the amount diene elative to the othe monome. 88

89 Cosslinking Case - Copolymeization of monome A with diene BB Assume: All double bonds have the same eactivity (i.e. the A double bonds and both B double bonds), F f P: the faction of all (A and B) double bonds eacted. P A : the numbe of type-a double bond eacted. P B : the numbe of type-b double bond eacted. P B : the numbe of BB monome having both double bonds eacted. A : the conc. of type-a double bond. B : the conc. of type-b double bond. BB : the conc. of BB B BB 89

90 Cosslinking The numbe of cosslinks the numbe of BB monome molecules in which both B double bonds ae eacted P BB The numbe of polyme chains ( the total numbe of A and B double bonds eacted) (the degee of polymeization) ([ A ] + [ B] ) X w P degee of polymeization The citical extent of eaction at the gel point P c : The numbe of cosslinks pe polyme chain/ P [ BB] [ A] + [ B] {([ A] + [ B] ) P} X w [ BB] X w [ A] [ B] [ B] X w + P c 90

91 Cosslinking in the copolymeization of Styene-Divinylbenzene Mole Faction of DVB Gel Point (P c ) Calculation Obsevation Mole faction of DVB P c The calculation fom model: good in low conc. egime If DVB is too high intamolecula cyclization Calculated P c Obseved P c 9

92 Cosslinking in the copolymeization of Styene-Divinylbenzene An altenate expession fo P c : q : ξ : f a : : P c af(f q - )( q + ξ ) (the popagation ate)/ (popagation ate + temination ate + tansfe ate) (the temination ate)/(temination ate + tansfe ate) functionality of diene (4 ; each double bond is bifunctional) the faction of all functional goups in the eaction mixtue belonging to the diene. 9

93 Cosslinking Case : A+BB The eactivities of the two goups ae not equal. The citical extent of eaction at gelation is: P c ( X w [ A] + [ A][ B] + [ B] ) [ B ][ ( A] + [ B ])( [ B] + [ A] If [A] >> [B] (geneal case), then When > (the double bonds of the diene ae moe eactive than that of the othe monome) cosslinking occus in the ealy stages. P c [ A] [ B] x w When > cosslinking occus in late stages. 93

94 Cosslinking Case : Monome A+ Diene BC Goups A and B have equal eactivity, but goup C has a much lowe CH eactivity. 3 CH 3 B CH C C O O H C CH CH A C alkyl methacylate CH Cosslinking does not occu until elatively late in the eaction The eactivity atio: AC AC BC BC AA AB BA BB Then, the citical extent of eaction at gelation is given by P c exp qx w q: the mole faction of the diene in the initial comonome feed. C C O O methyl methacylate CH 3 94

95 Cosslinking In geneal, the gelation point can be delayed by educing the amount of the diene adding chain-tansfe agent choosing a diene monome in which one of the double is much less eactive to the othes. Sometimes, the eaction of one of the double bonds of the diene esults in a decease in the eactivity of the emaining double bond Simila to the assumption of Case Ex:,4-polymeization C C C C n,3-diene,3-double bond with loweed eactivity 95

96 Cyclopolymeization: Altenating Inta-Inte molecula polymeization CH CH CH CH CH Z CH CH CH Z B CH. A homopolymeization CH CH Z CH Linea polyme Z CH CH CH CH. A intamolecula cyclization B Z CH CH CH may futhe cosslinked via pendant double bonds. CH. Z CH CH CH CH n Z CH CH CH CH n 96

97 Cyclopolymeization: Altenating Inta-Inte molecula polymeization Example: Radical polymeization of diallyl quatenay ammonium salt Soluble, uncosslinked polymes with little o no esidual unsatuation CH CH CH CH CH CH CH CH CH CH CH CH R N + N + R R B - B - R CH CH CH CH CH CH n N + R R 97

98 Cyclopolymeization: Altenating Inta-Inte molecula polymeization The extent of cyclization geneally inceases in the following ode: 5 and 6-membeed ings 7 o longe-membeed ings Usually,.5-dienes 5-membeed ing Ex:.5-hexadiene. C H. Howeve, polymeization of o-divinynyl benzene 7- membeed ing. H C. H C 98 n

99 Cyclopolymeization: Altenating Inta-Inte molecula polymeization Intemolecula popagation R p Intamolecula cyclization R c The faction of cyclized units: f c R competition c R + c R p whee, theefoe, R R f c p c c c p [ M *][ M] [ M *] M conc. of diene monome (Not double bonds) c [ M *] c [ M *] + p[ M *][ M] + p[ M] c o f c + p [ M] c M the extent of cyclization M the extent of cyclization 99

100 Cyclopolymeization: Altenating Inta-Inte molecula polymeization f c vs. M : [ M] the cyclization atio ( c / p ): obtained fom the slope of the plot Fo most symmetical,6-dienes, f c + c p : Activation enegy: cyclization intemolecula popagation T Tendency to cyclization Solvent polaity Cyclization (Not undestood yet!) p c ~0 moles/l 00

101 Cyclopolymeization: Altenating Inta-Inte molecula polymeization Ring sizes 7 o lage cyclization (shaply) Some exceptions: diallyl este 5~0% of cyclization ing stuctue containing up to 7 atoms. o-dially phthalate 40% cyclization 0

102 Cyclopolymeization: Altenating Inta-Inte molecula polymeization Some copolymeizations vey complex ing stuctues Example: polymeization of divinyl ethe uncosslinked polymes with little unsatuation. O CH O CH O CH. O O Inte molecula popagation CH CH O O. O cyclization CH O. cyclization CH O O CH Inte molecula O popagation CH O CH. 0

103 Intepenetating Polyme Netwoks (IPN) Combination of the popeties of two diffeent cosslinked polymes Example: Swollen PU MMA, BPO timethyl popane timethacylate PU/PMMA IPN 03

104 CH CH OTHER COPOLYMERIZATIONS Radical Copolymeization of Alkenes O O. CHR CHR + SO + CO CH CHR+ : S CH. CHR + O : C O CH CHR polymeic sulfones O CH CHR S O ketones C n n R' CH CHR + R NO CH CHR+ N O. CH CHR R' N O n CH CHR + O. CH CHR + : O O CH CHR O O n peoxide 04

105 Radical Copolymeization of Alkenes Reactions with sulfu dioxide: Only fo alkenes w/o stong e- withdawing substituents (fom eactive adicals). such as : -olefins, vinyl chloide, vinyl acetate Yielding : altenating copolymes ( pola effect between the electopositive SO and electonegative alkene) Stable adical less SO content in copolyme Monomes with stong e- withdawing goups (e.g. - CN) copolymes Pola epulsions of electophilic sulfu dioxide Substituents: bulky o electopositive Reactions with oxygen and quinones: depopagation Vey slow copolymeization ates Usually classified as etadation o inhibition eactions 05

106 Copolymeization of Cabonyl Monomes H H H H R C O + R' C O C R O C R' O n Not common The geneal tendency of the copolymeization is ideal behavio. But, bulky substituent tend to fom altenation 06

107 Applications of Copolymeization : Styene SBR ubbe: styene-,3-butadiene Styene(5%) +,3-butadiene(75%) poduced by emulsion polymeization (some by anionic polymeization) tensile stength: simila to natual ubbe uses: tie, belting, hose.. Styene(50-70%)-,3-butadiene(30-50%) latex paint Caboxylated SBR Copolymeized with small amount of caboxyl goups Backing mateial fo capets can be used fo futhe cosslinking Styene-divinyl benzene Packing mateials of GPC and ion-exchange 07