Radical polymerization is one of the most common methods of polymer synthesis. It involves the follo — Physical Chemistry — Thermodynamics Chemistry Question
Radical polymerization
Radical polymerization is one of the most common methods of polymer synthesis. It involves the following stages:
Initiation – the stage at which active particles usually referred to as radicals appear as a result of particular chemical reaction and/or changes of physical properties of the system (heating, irradiation).
Chain propagation – consecutive addition of monomer molecules to a radical resulting in formation of new radicals of bigger size. Usually the rate constant of propagation is considered to be independent of polymerization degree of a growing radical (assumption of equal reactivity).
Chain termination – the stage at which chain growth is stopped due to bimolecular interaction of radicals. Recombination and disproportionation are possible ways of chain termination.
Chain transfer – the stage at which an inactive polymer molecule is formed due to interaction of a propagating radical with a chain transfer agent. This process is accompanied by transformation of the transfer agent into new radical. The latter can either initiate growth of a new polymer chain or terminate the chain. Molecules of the monomer, solvent or special additives can act as chain transfer agents.
To obtain poly-(methyl methacrylate) (poly-MMA), its monomer (9.4 g) was heated to 60 °C in the presence of 0.1 g of α,α’-azodiisobutyronitrile (AIBN) and 0.5 g of α-chlorotoluene. The density of the reaction mixture is 0.91 g cm-3. The rate constants of elementary stages are: kin = 7.2×10–4 s–1 (initiation), kp = 7.1×102 l mol–1 s–1 (propagation), kt = 2.6×107 l mol–1 s–1 (termination). Initiation efficiency is fin = 0.8. Constants of chain transfer are: CA = 4.2×10–4 (to α-chlorotoluene) and CM = 1.0×10–5 (to the monomer).
Hint: chain transfer constant is defined as the ratio of the rate constants of chain transfer to a given species and chain propagation (C = ktr / kp).
[VISUAL]
Write down reaction equations for initiation, chain propagation, chain termination, and chain transfer in the above given system.
Model Answer
Initiation:
(CH3)2C(CN-N=N-C(CH3)2(CN) → 2 (CH3)2C•(CN) + N2
Chain propagation:
(CH3)2C(CN)• + CH2=C(CH3)COOCH3 → (CH3)2C(CN-CH2-C•(CH3)COOCH3
~(PMMA)• + MMA → ~(PMMA-CH2-C•(CH3)COOCH3
Chain termination via recombination:
2 ~(PMMA-CH2-C•(CH3)COOCH3 → ~(PMMA-CH2-C(CH3)(COOCH3)-C(CH3)(COOCH3)-CH2-~(PMMA)
Chain termination via disproportionation:
2 ~(PMMA-CH2-C•(CH3)COOCH3 → ~(PMMA-CH2-CH(CH3)COOCH3 + ~(PMMA-CH=C(CH3)COOCH3
Chain transfer to α-chlorotoluene:
~(PMMA)• + C6H5CH2Cl → ~(PMMA-H + C6H5C•HCl
Chain transfer to the monomer:
~(PMMA)• + CH2=C(CH3)COOCH3 → ~(PMMA-H + CH2=C(COOCH3)CH2•
Write down reaction equation(s) which decrease(s) initiation efficiency fin.
Model Answer
Recombination of primary radicals inside the solvent cage: 2 (CH3)2C•(CN) → (CH3)2C(CN-C(CH3)2(CN)
Write rate equations for:
a) generation of active radicals
b) monomer consumption
c) changes of the concentration of radicals
Model Answer
a) d[P•]/dt = 2 * kin * fin * [In]
b) -d[M]/dt = kp * [P•] * [M]
c) d[P•]/dt = 2 * kin * fin * [In] - 2 * kt * [P•]^2
Express equilibrium concentration of radicals under steady-state conditions as a function of kinetic parameters of elementary stages.
Model Answer
[P•] = (kin * fin * [In] / kt)^(1/2)
Express the rate of monomer consumption (rate of polymerization) as a function of immediate concentrations of the monomer and initiator and kinetic parameters of elementary stages. Find the order of polymerization reaction on the monomer and initiator.
Model Answer
-d[M]/dt = kp * [M] * (kin * fin * [In] / kt)^(1/2)
The reaction order is 1 with respect to the monomer, and 1/2 (or 0.5) with respect to the initiator.
Determine the value of the rate constant of termination via disproportionation. Arrange the following processes in the decreasing order of their influence on Pn value.
a) chain termination
b) chain transfer to monomer
c) chain transfer to α-chlorotoluene
Model Answer
kt,d = 1.8×10^7 dm^3 mol^-1 s^-1 (or L mol^-1 s^-1).
Decreasing order of influence: chain termination >> chain transfer to α-chlorotoluene > chain transfer to monomer (a >> c > b).
Deduce the structure of the polymer using integral intensities of characteristic peaks given in the table.
Signal Integral intensity
a 5.0
b 1.0
c 1.0
d 42
e 2.0
f 27
g 39
h 4.5
Model Answer
The polymer has the structure: Cl-CH(C6H5)-[CH2-C(CH3)(COOCH3)]13-CH=C(CH3)COOCH3 (one end is a chlorotoluene residue, containing 13 MMA monomer units, and the other is an unsaturated PMMA end-group formed via disproportionation).