5.1 Free radical polymerization: mechanism and kinetics

Free Radical Polymerization Mechanism

Free radical polymerization converts small monomer molecules into long polymer chains using reactive free radicals. It's one of the most widely used chain-growth techniques because it works with a broad range of vinyl monomers and doesn't require extremely pure conditions. The mechanism breaks down into three stages: initiation, propagation, and termination.

Steps of Free Radical Polymerization

Initiation happens in two sub-steps:

1. An initiator molecule (I) undergoes homolytic cleavage, meaning a covalent bond breaks so that each fragment keeps one electron, producing two free radicals: $I \rightarrow 2R\bullet$ Common initiators include benzoyl peroxide (BPO) and azobisisobutyronitrile (AIBN). Heat or UV light supplies the energy to break the bond.

2. One of those radicals adds to a monomer (M), forming a new radical with an active center at the chain end: $R\bullet + M \rightarrow RM\bullet$

Not every radical generated in step 1 successfully adds to a monomer. Some radicals recombine or undergo side reactions in the solvent cage before they ever reach a monomer. The fraction that do initiate chains is captured by the initiator efficiency ($f$), which typically falls between 0.3 and 0.8.

Propagation is the rapid, repeated addition of monomer units to the active center:

$RM_n\bullet + M \rightarrow RM_{n+1}\bullet$

Each addition regenerates the radical at the chain end, so the chain keeps growing. A single propagation step is fast ($k_p$ values are often on the order of $10^2$–$10^4 \; L \; mol^{-1} s^{-1}$), and thousands of monomers can add before the chain stops.

Termination kills the active radical and stops chain growth. Two mechanisms are common:

• Combination: two growing chains couple together, producing one dead chain with roughly double the length.

$RM_n\bullet + \bullet M_mR \rightarrow RM_{n+m}R$

• Disproportionation: a hydrogen atom transfers from one radical chain end to another, creating two dead chains (one with a saturated end, one with an unsaturated end).

$RM_n\bullet + \bullet M_mR \rightarrow RM_nH + RM_{m-1}{=}CH_2$

Which termination mode dominates depends on the monomer. For example, polystyrene terminates mostly by combination below about 60 °C, while poly(methyl methacrylate) favors disproportionation because of steric crowding around the radical.

Kinetics and Factors Affecting Free Radical Polymerization

Kinetic Rate Expression

The overall rate of polymerization is:

$R_p = k_p [M][M\bullet]$

where $k_p$ is the propagation rate constant, $[M]$ is monomer concentration, and $[M\bullet]$ is the concentration of active radical chain ends.

The problem is that $[M\bullet]$ is extremely small and hard to measure directly. To get around this, you apply the steady-state assumption: after a brief startup period, radicals are created (initiation) and destroyed (termination) at the same rate, so $[M\bullet]$ stays roughly constant.

Setting $R_i = R_t$:

1. The rate of initiation is $R_i = 2fk_d[I]$, where $k_d$ is the initiator decomposition rate constant, $[I]$ is initiator concentration, and $f$ is initiator efficiency. The factor of 2 appears because each initiator molecule produces two radicals.
2. The rate of termination is $R_t = 2k_t[M\bullet]^2$, where $k_t$ is the termination rate constant.
3. Setting these equal and solving for $[M\bullet]$: $[M\bullet] = \left(\frac{fk_d[I]}{k_t}\right)^{1/2}$
4. Substituting back into the $R_p$ expression gives: $R_p = k_p [M] \left(\frac{fk_d[I]}{k_t}\right)^{1/2}$

This result tells you two things at a glance: $R_p$ is first-order in monomer concentration but only half-order in initiator concentration. Doubling $[I]$ increases the rate by a factor of $\sqrt{2}$, not 2.

Temperature and Concentration Effects

Temperature affects every rate constant in the system, but not equally:

• $k_d$ (initiator decomposition) has the largest activation energy, so it's the most sensitive to temperature changes. Raising temperature sharply increases radical production.
• $k_p$ also increases with temperature, but more modestly.
• The net effect: higher temperature gives faster polymerization but shorter chains, because more radicals are present at any given time, which increases the termination rate.

Initiator concentration follows the same trade-off. More initiator means more radicals, faster polymerization, but lower molecular weight because chains terminate sooner.

Monomer structure influences reactivity. Monomers with electron-rich double bonds (like vinyl acetate) tend to have higher $k_p$ values and polymerize faster. Monomers with bulky or conjugating substituents (like methyl methacrylate or styrene) have more stabilized radicals, which makes them less reactive in propagation but also affects termination rates. The overall picture depends on the balance of these effects.

Chain Transfer

Chain transfer occurs when the radical active center is transferred from a growing chain to another molecule, stopping that chain's growth and starting a new one:

$RM_n\bullet + T{-}H \rightarrow RM_nH + T\bullet$

The new radical ($T\bullet$) can then re-initiate polymerization by adding to a monomer. The transfer agent (T-H) can be solvent (e.g., toluene, carbon tetrachloride), monomer itself, or a deliberately added chain transfer agent (CTA) such as a mercaptan (thiol).

Key consequences of chain transfer:

• Reduced molecular weight. Chains are cut short because the radical moves to a new molecule instead of continuing to add monomer. More chain transfer means shorter average chains.
• Broader molecular weight distribution. The polydispersity index (PDI) increases because chain lengths become less uniform.
• Polymerization rate is largely unaffected (as long as the new radical re-initiates efficiently), because the total number of radicals in the system doesn't change.
• Functional end groups. The fragment from the transfer agent ends up capping the dead chain, which can be useful if you want specific end-group chemistry.

The chain transfer constant quantifies how effective a given transfer agent is:

$C_s = \frac{k_{tr}}{k_p}$

A higher $C_s$ means the agent competes more effectively with propagation. For example, carbon tetrabromide has a much higher $C_s$ with styrene than toluene does, so even a small amount of $CBr_4$ significantly lowers molecular weight.