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Step-growth kinetics

� As a result of their macromolecular nature, polymers would be expected to have retardedmobility.

� It was therefore predicted, purely on theoretical arguments, that the chemical reactivity of polymers should be low.

� Flory states that “the intrinsic reactivity of allfunctional groups is constant, independent of the molecular size.”

� A pair of neighboring functional groups may collide repeatedly before they either diffuse apart or react. The lower the diffusion rate, the longer these groups remain in the same vicinity.

Kinetics of polyesterification

� The kinetics of most other common SG polym. follows an analogous pathway (Carraher’s book).

� catalyzed systems

� Rate of polymerization = −� �

��= �[�][]

� for [A]=[B] −� �

��= �[�]�

� −� �

[�] ��= �� integrate=> kt=

�

��−

�

��

� kt= �

��−

�

��(p is franction of reacted groups) ��=��(1 − �)

� kt=�

��(���)−

�

��=> XN=A0kt + 1 XN= A0/At= 1/(1 − �)

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� XN=A0kt + 1

� predicts a linear relationship of XN=A0/At with reaction time.

The number-average degree of Polymerization, Xn

� Ifpisthefractionoffunctionalgroupsthathavereacted

� ,- =-./0123432565-78/3819.81:

-./01234/3819.81:7�7:�195459�5/1=

;�

;=

��

��=

��

��(���)

� Useful high molecular weight linear polymers are not obtained unless the value for the fractional conversion p is at least 0.990, i.e., a DP greater than 100.

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Step-Chain growth

C-G Polymerizations

� Chain growth polym. is usually rapid.� Unlike the case of SG polym.

�Very long macromolecules can be formed just after induction of the reaction.

� A chain reaction usually consist of at least three steps� Initiation – Propagation - Termination.

�they can occur simultaneously.

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A � P* (initiation 1st phase)

P* + M � PM* (initiation 2nd phase)

PM*n + M � PM*(n+1) (propagation)

PM*n � PMn (termination)

PM*n + T � PM + T* (chain transfer)

T* + M � TM*

Main Reactions used in C-G Polym.

� Free radical: whose propagating active centers involve free radicals.

� Anionic: require nucleophilic reactive centers.

� Cationic: whose propagating species are electrophiles.

� Coordination: whose active centers are complexes formed coordination between monomer molecules and transition metal atoms.

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� The initiator is a radical, and the propagating site of reactivity (*) is a carbon radical.

� Cationic Polymerization The initiator is an acid, and the propagating site of reactivity (*) is a carbocation.

� Anionic Polymerization The initiator is a nucleophile, and the propagating site of reactivity (*) is a carbanion.

� Coordination Catalytic Polymerization The initiator is a transition metal complex, and the propagating site of reactivity (*) is a terminal catalytic complex.

Reactions Compatible with Chain Poly.

� Monomers carrying unsaturated groups;

� Cyclic strained monomers;

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i.e.

� In general, initiation requires energy

� And, propagation produces energy.

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� When temperature is raised, the entropy term increases as well until becoming equal to enthalpy term. -> The polymerization cannot proceed.

� The maximum temperature is called ceiling temperature.

� As temperature increases, at some point the entropy contribution overwhelms the enthalpy contribution. Above this temperature, depolymerization is faster than polymerization. The polymer "unzips" back to monomer.

Free Radical Chain Polymerization

� Most of the polymers are prepared by free radical polymerization.

� Free radicals form by homolytic bond cleavage.

� A species containing an atom with a single unpaired electron is called a radical (often free radical).

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Double bonds

� the two pairs of electrons which make up the double bond are not the same.

� One pair is held securely on the line between the two carbon nuclei in a bond called a sigma bond.

� The other pair is more loosely held in an orbital above and below the plane of the molecule known as a pi bond.

Equivalent views of C=C

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� The free radical, Ra, uses one of the electrons in the pi bond to help to form a new bond between itself and the left hand carbon atom. The other electron returns to the right hand carbon.

� This is energetically worth doing because the new bond between the radical and the carbon is stronger than the pi bond which is broken.

� You would get more energy out when the new bond is made than was used to break the old one. The more energy that is given out, the more stable the system becomes.

Planar to Tetrahedral

� sp2-hybridized carbon atoms are transformed into sp3 ones.

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Tacticity

� This notion is particularly interesting in the case of vinyl and related polymers.

� Chiral Carbon: C atom with 4 different groups.

� Enantiomer: is one of two stereoisomers that are mirror images of each other that are non-superposable.

� Enantiomers form different crystals.

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Free Radical Chain Polymerization

� Free radicals can be involved in six reactions;

1. Addition R*+CH2=CR’R’’�RCH2C*R’R’’

2. Abstraction/transfer R*+R’X�RX+*R’

3. Disproportionation 2 RCH2CH2*�RCH2CH3+RCH=CH2

4. Combination R*+*R’�R-R’

5. Fragmentation RA*�R*+A

6. Rearrangement R’’R’R*�*R’’R’R

Free radical polymerization kinetics

� Initiation:� kc is non-negligible, the proportion really active is

called efficiency (f) of this initiator.

Ri = 2f kd[I] ; dissociation step is slower, each initiator forms two radicals.

Ikd

2R.

ki

RM.

R.+ M

kc

R-RR.+ R.

as side reaction

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Free radical polymerization kinetics

� Propagation:

� Rp = kp[RM*][M]

� Termination: combination or disproportionation

� Rt = kt[RM*]2

Free radical polymerization kinetics

� Assuming that the number of active chains remains constant;

Ri=Rt

2f kd[I] = kt[RM*]2

Rp = kp (f [I]kd/kt)1/2[M]

Xn=<=

<>=

?=(@ A BCB�

)D [E]

�?C4[F]=K’’

[E]

[F]D/

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Some conclusions

� The rate of propagation α [M] and α [I]1/2.

� The rate of termination α [I].

� The av. MW α [M] and α1/ [I]1/2.

� The first chain is that is initiated rapidly produces a HMW polymer.

� Increasing the temperature increases the concentration of free radicals and thus rate of reactions, but it decreases the av. MW.

� If the temperature exceeds the ceiling temperature the polymer will decompose and no propagation will take place.

Initiation of FR Polymerizations

� A. Generation of Initial Free Radicals� Most of the generators are unstable molecules that can

homolytically dissociate under thermal effect, due to their weak covalent

� The electronegativity of the elemets is high.

Ed0-0 < EdN-N < EdC-C

� The stabilization (by electron-donor and/or resonance effects) of the radicals resulting from the dissociation

Molecule Ed Estab.(kJ/mol)H-CH3 426 0H-CH2-CH3 393 33H-C(CH3) 376 50H-CH2-Ph 322 104

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Thermal Initiators

� Organic peroxides and hypoperoxides are very commonly used.

� Decomposition of peroxides can be single or multi-steps.

� Water soluble initiators;

� Azo compounds;

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Photochemical initiation

� Photochemical initiation;

� Ionizing ratiations (β,γ);

AB � +AB. + e- � +A + B.

Both free radicals and radical ions can be formed upon radiation and initiate polymerization.

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Propagation of FR Polymerizations

� Propagation: Generally, is very fast and corresponds to an exothermic reaction .

� Like the initiation step, the reaction mechanism is of the free-radical-addition type.

� The relative reactivities of monomers is influenced by two factors: � the stability of the monomer toward addition of a free

radical

� the stability of the monomer radical thus formed. (!!)

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� steric effects: 1,2-disubstitution and bulky substituents decrease reactivity in radical polymerizations.

� resonance: Resonance stabilization of the radical also makes the radical less reactive towards propagation.

Effect of substituents

� Steric hindrance and electronic effects are involved in the intrinsic reactivity of R*.

� The two same effects also determine the reactivity of the monomer (M).

� The proper reactivity of M can be measured by ‘methyl affinity’.

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Unsubstituted (ethylene)

Works fine.

Monosubstituted

Works fine.

1,1-Disubstituted

Usually works.

1,2-Disubstituted

Seldom works.

Trisubstituted and

tetrasubstituted

Almost never works.

Except fluorinated monomers!

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Stabilization of Radicals

� Any substituents stabilize the chain end radical.

� Inductive (weak)

� Cl, OCH3, OCOCH3

� Resonance (strong)

� CO2CH3, CN, phenyl, etc.

� The more stable the radical that forms from the monomer, the lower the polymerization rate constant and polymerization rate.

� Vinyl acetate, a very stable monomer, has a very high kp (reactive radical forms).

� Styrene, is a very reactive monomer, but forms a stable radical, and so has a lower kp.

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� The higher the stabilization of growing radicals, the lower will be the proportion of irregular (head-to-head) placements.

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Resonance Stabilization of Radicals

Problem with alkyl groups

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� Apparently, the resonance effect of the ester group tips the balance in favor of propagation versus hydrogen abstraction.

Termination of FR Polymerizations

� Implies the collision of two growing free radicals which is less probable than their collision with monomer molecules.

� They can combine or disproportionate.

� They can combine easily when there is no steric factors.

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Chain Transfer

� Radicals are reactive beasts.

� Chain transfer occurs when a radical species reacts with a nonradical species.

� In the most common occurence, the chain end radical attacks a weak bond. An atom gets transfered to the chain end.

� In many cases, a chain transfer agent is added deliberately to the reaction mixture.

� Many compounds work well for this purpose, but mercaptans (also known as thiols; R-SH) are the most general.

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� The sulfur-centered radical reinitiates very efficiently.

� The result is a dimunition of the MW without changing the overall rate of conversion of monomer to polymer.

� (Using more initiator is another way to decrease MW, but the reaction rate would increase proportionally, a possibly dangerous situation.)

Chain Transfer

� Naturally, there are many even-electron species present in the reaction mixture (i.e., monomer, initiator, solvents, polymer chains, etc.).

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Chain Transfer to Polymer

� If the chain end radical attacks an atom on the backbone of the same or another chain, the result is a new radical that can reinitiate to form a branch. This reaction happens very commonly during the free radical polymerization of polyethylene.

� .

� The chemistry is driven by the greater stability of the secondary radical that forms, compared to the primary one at the chain end.

� The most convenient site of attack is a hydrogen atom that is a short distance back on the same chain.

� Branches disrupt chain packing, and decrease degree of crystallinity, creating low density polyethylene (LDPE). LDPE is much softer than the version that is linear (made by coordination polymerization).

� Chain transfer to polymer occurs to a lesser extent in many other systems.

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Inhibitors

� Consider what happens if chain transfer occurs, but the new radical is incapable of reinitiation.

� If so, this is a kind of termination reaction. The agent responsible is called an inhibitor. There are many kinds of inhibitors, but the most common are phenols with bulky groups ortho to the OH group.

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Autoacceleration

� Autoacceleration only occurs during polymerizations with high concentrations of monomer (i.e., little or no solvent).

� The reaction proceeds normally for a while, then suddenly the rate of polymerization goes up dramatically.

� The molecular weight of chains that grow during the accelerated period is substantially higher than that of chains that grew earlier.

� Termination involves the reaction between two chain ends.

� However, in concentrated solutions, the viscosity of the reaction mixture becomes high as polymer chains form.

� This high viscosity hinders the diffusion of chains because of entanglements, so the rate of termination slows considerably.

� However, the diffusion of small molecular monomers is hardly affected by viscosity, so propagation proceeds as before.

� In addition, initiator continues to add more free radicals to the system.

� Chains grow without termination, so the conversion is rapid and the MW is high.

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TT

T

TT

T

Conventional Radical Polymerization

Controlled Radical Polymerization

Broad MWD

Dead Polymer

Narrow MWD

Living Polymer