Radical Chain Reactions: Initiation, Propagation, Termination

Radical chain mechanisms are the operating principle behind industrial free-radical polymerization of ethylene, vinyl chloride, styrene, and acrylates, in which an initiator (peroxide or azo compound) generates the first radical and a propagating polymer-chain radical adds monomer thousands of times before termination — the direct scale-up of exactly the initiation/propagation/termination framework built here, elaborated further in Radical Polymerization. Autoxidation, the slow radical chain oxidation of fats, oils, rubber, and plastics by atmospheric O₂, follows the identical logic with a peroxyl radical (ROO•) as the chain carrier, and is why antioxidants (radical-trapping phenols like BHT or vitamin E) are added to foods and polymers — they intercept the chain by donating a very weak O–H bond to the peroxyl radical, generating a resonance-stabilized, unreactive phenoxyl radical that cannot efficiently continue the chain, effectively acting as inhibitors that shorten chain length dramatically. Combustion chemistry, atmospheric ozone-depletion chemistry (chlorofluorocarbon photolysis generating Cl• that catalytically destroys ozone in an analogous propagation loop), and industrial halogenation processes for making chlorinated solvents all run on the same three-phase mechanism. In synthesis, radical brominations with NBS (Wohl–Ziegler conditions) remain a standard method for allylic and benzylic functionalization, and radical chain thinking is the conceptual gateway to understanding reactive intermediates more broadly, including the electron-counting and orbital arguments used for Carbenes: Structure and Generation, where analogous single-electron and two-electron bookkeeping recurs in a different guise.

Ask the tutor: How does the Evans–Polanyi principle quantitatively connect bond dissociation energies to activation energies across a whole series of radical abstractions, and how would you use it to predict a rate ratio you haven't measured?

A radical is a species with an unpaired electron in a nonbonding or partially bonding orbital — highly reactive because that orbital wants to pair up. Homolysis of a weak bond (Cl–Cl, Br–Br, O–O in a peroxide, or a C–C bond in an initiator like AIBN) supplies the first radicals; from then on, the chemistry is dictated by two facts about radicals that differ fundamentally from ions. First, radicals are usually not stabilized or destabilized by solvent polarity the way ions are, so radical reactions tolerate nonpolar, aprotic conditions (CCl₄, gas phase) where ionic mechanisms would be hopelessly slow. Second, a radical reacting with a closed-shell molecule can only do one of a few things: abstract an atom (usually H or halogen), add to a π bond, or fragment — and in each case exactly one new radical is produced, conserving the total spin. The defining topology of a chain reaction is that propagation steps link together so that the radical consumed by step $n$ is exactly the radical produced by step $n{-}1$. Draw the two propagation steps of methane chlorination stacked vertically and you see immediately that Cl• is regenerated:

Add these two equations and the radicals cancel, leaving the observed stoichiometry $\text{CH}_4 + \text{Cl}_2 \rightarrow \text{CH}_3\text{Cl} + \text{HCl}$ — but that overall equation tells you nothing about why one C–H bond reacts faster than another. That information lives entirely in the first propagation step's transition state.

Look closely at the numbers in the figure: step 1 (Cl• abstracting H from methane) is almost thermoneutral, while step 2 (methyl radical grabbing Cl from Cl₂) is strongly exothermic. This asymmetry is the rule, not the exception, in halogenation: the first propagation step, generating the carbon radical, is the slow, selectivity-determining step, while the second step, regenerating the halogen radical, is fast and essentially indiscriminate. Selectivity is decided at the first transition state, and the Hammond postulate tells you what that transition state looks like. The Hammond postulate states that a transition state resembles whichever adjacent species (reactant or product) it is closer to in energy. For an endothermic elementary step, the TS is product-like (a "late" TS, close in structure and energy to the radical intermediate); for an exothermic step, the TS is reactant-like ("early", little radical character developed). Because H-abstraction by Cl• is nearly thermoneutral (small $\Delta H$, low barrier, ~4 kJ/mol for a typical secondary C–H), the TS is early and barely distinguishes between primary, secondary, and tertiary C–H bonds — chlorination is unselective. H-abstraction by Br• is substantially endothermic (barrier ~50–75 kJ/mol), so the TS is late and product-like, meaning it already "feels" most of the stability difference between a primary and a tertiary radical — bromination is highly selective.

Every propagation step's enthalpy follows directly from bond dissociation energies (BDEs), which are tabulated, measurable, and additive:

where: BDE(bond broken) is the homolytic bond strength of the bond in the starting material of that step, and BDE(bond formed) is the strength of the new bond created in the product of that step; both are measured as positive numbers (energy required to homolyze), so a step is exothermic when it forms a stronger bond than it breaks. Summing the two propagation-step enthalpies gives the overall reaction enthalpy, since the radical intermediate's bond terms cancel:

where: $\Delta H_{\text{overall}}$ must equal the BDE of the bonds broken in reactants (C–H and X–X) minus BDE of bonds formed in products (H–X and C–X), independent of any radical intermediate. Selectivity between two C–H bonds (say tertiary vs. primary) is expressed as a rate ratio, computed from the Arrhenius form applied to the rate-determining H-abstraction step:

where: $A$ are pre-exponential (frequency/steric) factors, often assumed comparable per C–H bond for a first approximation, $E_a$ are the experimental activation energies for abstraction from each type of C–H bond, $R = 8.314\ \text{J mol}^{-1}\text{K}^{-1}$, and $T$ is the absolute temperature. Because statistical (number of equivalent H's) and electronic (bond-strength/radical-stability) effects both matter, the observed product ratio is:

where: $n_A, n_B$ are the number of chemically equivalent hydrogens of each type on the substrate, and $k_A, k_B$ are the per-hydrogen rate constants for abstraction of that type.

Example 1 (foundational): Enthalpy and feasibility of propagation steps in bromination of methane. Given BDE(Br–Br) = 193 kJ/mol, BDE(CH₃–H) = 439 kJ/mol, BDE(H–Br) = 366 kJ/mol, BDE(CH₃–Br) = 293 kJ/mol, evaluate whether a Br• chain for methane bromination is thermally sustainable. Initiation: Br₂ homolysis requires 193 kJ/mol (weaker than Cl–Cl, so Br₂ initiates more easily, e.g. thermally or with visible light). Propagation step A, $\text{Br}^{\bullet} + \text{CH}_4 \rightarrow \text{HBr} + {}^{\bullet}\text{CH}_3$:

This is substantially endothermic — much more so than the analogous chlorination step (+8 kJ/mol) — and this large positive $\Delta H$ is exactly why bromination is slower overall than chlorination, and why it needs a persistently higher temperature or continuous illumination to keep the chain alive; a chain with a strongly endothermic, high-barrier propagation step turns over less often per unit time. Propagation step B, ${}^{\bullet}\text{CH}_3 + \text{Br}_2 \rightarrow \text{CH}_3\text{Br} + \text{Br}^{\bullet}$:

Overall:

The reaction is exothermic overall but far less so than chlorination's $-100$ kJ/mol, precisely because step A costs so much more. As a limiting-case check: if step A's $\Delta H$ ever exceeded the exothermicity available from step B (i.e., if $\Delta H_A > 100$ kJ/mol), the overall reaction would become endothermic and the chain thermodynamically nonviable at ordinary temperatures — this is exactly why radical fluorination (with an enormous, explosively exothermic step B but also a huge step A cost that turns out smaller than F₂'s tiny BDE) is dangerously fast, while radical iodination fails altogether, as shown next.

Example 2 (applied): Why iodination of alkanes does not proceed as a useful chain reaction. Given BDE(I–I) = 151 kJ/mol, BDE(CH₃–H) = 439 kJ/mol, BDE(H–I) = 297 kJ/mol, BDE(CH₃–I) = 234 kJ/mol. Propagation step A, $\text{I}^{\bullet} + \text{CH}_4 \rightarrow \text{HI} + {}^{\bullet}\text{CH}_3$:

This is a huge endothermicity for an elementary bimolecular step — by the Hammond postulate the TS is not just "late" but essentially beyond the product in character, with an activation energy so high (well above 140 kJ/mol, since $E_a \geq \Delta H$ for an endothermic step) that at ordinary temperatures this step simply does not turn over at a useful rate. This single fact — not the overall thermodynamics — is why "radical iodination" is not a synthetically useful reaction, even though the second propagation step remains favorable:

giving an overall $\Delta H_{\text{overall}} = 142 - 83 = +59$ kJ/mol — the overall reaction is endothermic, consistent with (and reinforcing) the kinetic failure of step A. This is the clearest illustration in this entire family of reactions that a chain's feasibility is set by its slowest, most endothermic elementary step, not by whether the total reaction happens to be downhill — indeed here both diagnoses agree, but Examples 1 and this one together show the two criteria (kinetic step-by-step, thermodynamic overall) must both be checked, since they can in principle disagree (as they do for bromination's exothermic-overall-but-kinetically-sluggish first step).

Example 3 (competition-level): Stereochemistry and rate ratio in allylic bromination with NBS. Predict the product distribution (ignoring stereochemistry first, then addressing it) when 4-methylcyclohexene undergoes radical allylic bromination with N-bromosuccinimide (NBS), and explain why the allylic radical intermediate scrambles the position of substitution. Mechanism. NBS serves as a slow, continuous low-concentration source of Br₂ (via reaction with trace HBr, keeping $[\text{Br}_2]$ low enough to favor the radical chain over ionic addition — the "Wohl–Ziegler" conditions). The propagating radical is still Br•, which abstracts one of the two allylic C–H bonds (weaker than ordinary sp³ C–H, roughly 360–370 kJ/mol, because the resulting radical is resonance-stabilized). Fishhook arrows: one from the allylic C–H bonding pair to the incoming H (forming H–Br), one from Br•'s unpaired electron into that same bond — identical topology to Mechanism 1's step 2, but now the resulting carbon radical is allylic, i.e., delocalized. Once formed, the allylic radical is best drawn as a resonance hybrid with unpaired spin density on both termini of the original allyl system: two fishhook-connected resonance structures,

drawn with a curved arrow from the p orbital bearing the radical, through the adjacent π bond, shifting the double bond and relocating the unpaired electron. This delocalization is why radical allylic bromination characteristically gives a mixture of the "direct" substitution product and the "transposed" (allylic-shift) product: the second propagation step, ${}^{\bullet}\text{C}_a{=}\text{C}_b{-}\text{C}_c \text{ (or resonance partner)} + \text{Br}_2 \rightarrow \text{product} + \text{Br}^{\bullet}$, can deliver bromine to either terminus of the delocalized radical, because Br₂ can approach either lobe of the SOMO with comparable ease. For 4-methylcyclohexene, abstraction occurs preferentially at C3 (or equivalently C6 by symmetry), generating an allylic radical delocalized over C1–C2–C3 (numbering the alkene carbons C1=C2), and Br delivery at the less hindered terminus is typically favored, but both allylic bromides (direct and transposed double-bond-shifted product) are observed experimentally in ratios that depend on sterics and the stability of the resulting alkene (Zaitsev-type stabilization of the more substituted double bond in the product often biases the ratio). The key exam point: the regiochemical scrambling is a direct, structural consequence of spin delocalization in the intermediate, not a separate mechanism — it is built into the resonance structure of the radical itself, exactly as allylic cation scrambling is built into carbocation resonance in $S_N1$/$S_N1'$ chemistry, but here the delocalized species is a radical rather than a cation, so no external nucleophile or solvent effect is needed to see both products form.

The systematic understanding of chain reactions — the concept that a single initiating event could multiply into thousands of product-forming cycles via a self-propagating loop — emerged from the study of gas-phase kinetics and combustion in the 1920s–30s, most famously through the work of Nikolay Semyonov and Cyril Hinshelwood, who shared the 1956 Nobel Prize in Chemistry for elucidating the mechanism of chemical chain reactions, including the branched chains responsible for explosive combustion. Their insight — that reaction rates in many gas-phase and combustion systems could not be explained by simple bimolecular collision theory alone, but required a self-multiplying radical mechanism with distinct initiation, propagation, and (for explosions) branching steps — reshaped physical organic chemistry's entire vocabulary for describing radical processes, the same vocabulary (fishhook arrows, chain length, inhibitor) used for organic halogenation, autoxidation, and polymerization chemistry ever since.