10.569 Synthesis of Polymers Prof. Paula Hammond Lecture 21: Living Anionic Polymerization, Effects of Initiator and Solvent Living Polymerization Rp = −[]= kp [−]Md M M []dt [M −]≅[]I (assumes all initiator is active and available)o M [ ] []o −] I t ⇒ Rp = kp []Io ⇒ ln MM = kp [M t = kp [][] constant log [M]o [M] slope = kp[I] loglo[M]o[M]g[M]o[M]slope = kp[I]timti eme[] π[]oMM pn = = []I []pppI nnnnnnpolymer grows at exactly p linear with timepp linear with timethe same rate (monomer [M][M]⇒⇒initiated at exactly the [I][I]same time) ---------------00timetime[M ]o∴ for complete conversion pn = []I M νPDI: w = 1 + (not real PDI, but for statistical purposes)Mn (ν+1)2 Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date.Where ν = kinetic chain length Mw⇒ as ν↑, → 1 Mn ⇒ predicts PDI ∼ 1.01 → 1.001 Poisson distribution instead of Gaussian distribution Solvent Characteristics Most common solvents pentane hexane cyclohexane benzene dioxane increasing polarityO O 1,2 dimethoxyethane CH3OCH2CH2OCH3 tetrahydrofuran O dimethyl formamide O H3CN C H CH3 • solvent must solvate monomer + polymer ⇒ function of polarity • important solvent effects in anionic polymerization - rate of polymerization highly dependent on accessibility (propagating anion) - association effects - degree of counterion/ion dissociation 1. Association Effects: Low dielectric (nonpolar) solvents are poor environments for ions: Possible to form micelle-like aggregates: of ---------++++ nonpolar solvent ------------++++++++nonpolarsolventnononpnpoollaarrchchaaiinnssaggregation probabilities ↑ as polarity of solvent ↓ and as counterion size ↓ dependency on concentration: as conc ↑, agg ↑ 10.569, Synthesis of Polymers, Fall 2006 Lecture 21 Prof. Paula Hammond Page 2 of 5 Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date.+ ------+++ + dynamic equilibrium -Li “unimer” this species can ++------++++------------++++++++dynamicequilibrium--Li“unimer”this species canstructure propagatestructurepropagate− Ke −{ }n ←⎯ let n = # of chains per aggregateM ⎯→ nM bracket denotes (assume all aggregates have same number of chains) aggregate −n[M ]K =[{ n equilibrium constante −M ] [M −] 1/ n [M − 1/ n = K { }]en [] pM [− n 1/ nRp = −d M = k Ke 1/ n []{M ]dt see 1/n dependency in rate of propagation with respect to [M-] [{ }][M ]=[]M − n ∝− I can assume [I] ∼[{M −}]n ⇒Rp ≅ k pKe 1/ n []M [ ]1/ nI If aggregation number is 2, (n=2) 1/ 2 − 1/ 2R []{ M ]= k K M [p p e 2 ≅ k pKe 1/ 2 [][]1/ 2 aggregate formM I 2. Degrees of dissociation of counterion and chain (happens much more frequently) different degrees of dissociation: Free ions: + -Na --10.569, Synthesis of Polymers, Fall 2006 Lecture 21 Prof. Paula Hammond Page 3 of 5 Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date.-+-+Na Na + Na [+ SSS S SSS++SSSSSSSions are fully dissociated from negative charge ⇒ assume full availability of charge to react with monomer Versus … 2 types of ion pairs a) unsolvated ion pairs (tight pairs) + -++--“contact ion pairs” b) solvent separated ion pairs (loose ion-ion connections) ---solvent molecules separate ions thin layer of solvent that separates counterion from + charge reaction rates of species are going to be different kp-⇒ rate constant for free ions kpI ⇒ rate constant for all ion pairs and kpI = ykpll + (1-y)kpc parallel sign kpll = solvent separated pair y = fraction of solvent separated pair Equilibrium between free and dissociated ion pairs: + -Na KD + -Na kp-kpI +-Na++--NaKD++--Nakp-kpIpopolylymemerriizzeepopolylymemerriizzeeDissociated rate constant KKDD==[[[[[[----NaNaNa]]][[[ ]]]NaNaNa ]]]⇒ assume (no addition of NaCl that drives up [Na+]) [[NaNa ]][[ ]]]==-----+++++++----++++10.569, Synthesis of Polymers, Fall 2006 Lecture 21 Prof. Paula Hammond Page 4 of 5 Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date.[[-]2---]2KDK = D=[ [[ ]]]--Na---NaNa+Na++++Given that [M-] = concentration of all ionic sites (free and associated) α≡# of dissociated (free) ions all ions 2 −22 −α[M ] α[M ] −KD=(1 −α)[M ]= 1 −α solve for α: 1/ 2 α≅⎝⎜⎛[ KD ]⎠⎟⎞ assuming that α = small⎜M −⎟→ neglect 1-α term in denominator kp =αkp−+(1 −α)k pI d M D ⎞ )−]M⇒ RP = − []=⎢⎡ k pI +⎜⎛⎜K −⎟⎟1/ 2(kp−− k pI ⎥⎤[M []dt ⎢⎣ ⎝[M ]⎠ ⎥⎦ [I] 10.569, Synthesis of Polymers, Fall 2006 Lecture 21 Prof. Paula Hammond Page 5 of 5 Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology,