Radical Reactions

While most organic reactions taught in introductory courses involve heterolytic bond cleavage (both electrons go to one atom), an equally important class of reactions proceeds through homolytic cleavage, where each atom retains one electron from the broken bond. The resulting species — free radicals — are highly reactive intermediates with an unpaired electron.

Radical reactions are fundamentally different from ionic reactions in several ways: they are not sensitive to solvent polarity, they are not influenced by nucleophilicity or electrophilicity in the usual sense, and they propagate through chain mechanismswhere a single initiation event can trigger thousands of productive cycles before termination.

Radicals are ubiquitous in nature and technology. They drive combustion (the rapid oxidation of fuels), polymerization (the synthesis of polyethylene, polystyrene, and PVC), atmospheric chemistry (ozone depletion involves chlorine radicals), and biological processes (oxidative stress, enzyme mechanisms, and DNA damage).

2.1 Defining BDE

The bond dissociation energy (BDE, or $D°$) is the enthalpy change for the homolytic cleavage of a bond in the gas phase at 298 K:

BDE is always positive (bond breaking is endothermic). A larger BDE means a stronger bond. BDE values are specific to particular bonds in specific molecular environments — unlike average bond energies, which are averaged over many molecules.

2.2 C–H Bond Strengths and Radical Stability

The BDE of a C–H bond measures the stability of the radical formed when that hydrogen is removed. A weaker C–H bond produces a more stable radical:

2.3 Radical Stability Order

The stabilization of alkyl radicals follows from hyperconjugation: adjacent C–H $\sigma$ bonds donate electron density into the half-filled$p$ orbital of the radical center. More alkyl groups provide more hyperconjugative stabilization.

Allylic and benzylic radicals enjoy additional stabilization through resonance delocalization. The unpaired electron is spread over multiple atoms via overlap with the adjacent $\pi$ system:

Radical reactions proceed through a characteristic chain mechanismwith three distinct phases: initiation, propagation, and termination.

3.1 Initiation

Initiation creates radicals from non-radical precursors. Common methods:

• Homolytic cleavage by heat (thermolysis): Molecules with weak bonds (peroxides, azo compounds) decompose on heating:
  $$\text{ROOR} \xrightarrow{\Delta} 2\;\text{RO}\cdot$$
• Photolysis (UV light): Absorption of a photon provides the energy for homolysis:
  $$\text{Br}_2 \xrightarrow{h\nu} 2\;\text{Br}\cdot$$

The energy required for initiation equals the BDE of the weakest bond:$D°(\text{Br-Br}) = 193 \;\text{kJ/mol}$,$D°(\text{Cl-Cl}) = 242 \;\text{kJ/mol}$,$D°(\text{O-O}) \approx 155 \;\text{kJ/mol}$ (peroxides).

3.2 Propagation

Propagation steps are the productive steps that convert reactants to products. Each propagation step consumes one radical and produces one radical, sustaining the chain. For the chlorination of methane:

The sum of all propagation steps gives the overall reaction:

3.3 Chain Length

The chain length is the average number of propagation cycles that occur per initiation event. Typical chain lengths range from $10^2$ to$10^4$. This means a single radical initiation can produce thousands of product molecules before termination occurs.

3.4 Termination

Termination destroys radicals by combining two radical species. Since these reactions consume two radicals without producing any, they break the chain:

• Combination: $\text{Cl}\cdot + \cdot\text{CH}_3 \to \text{CH}_3\text{Cl}$
• Combination: $\cdot\text{CH}_3 + \cdot\text{CH}_3 \to \text{C}_2\text{H}_6$
• Combination: $\text{Cl}\cdot + \text{Cl}\cdot \to \text{Cl}_2$
• Disproportionation: Two radicals exchange an H atom, producing one saturated and one unsaturated product

Termination steps are rare compared to propagation because radical concentrations are very low (typically $10^{-8}$ to $10^{-10} \;\text{M}$), and termination requires two radicals to encounter each other (second-order kinetics).

4.1 Chlorination vs. Bromination

Chlorination and bromination differ dramatically in their selectivity for different types of C–H bonds. The key is the Hammond postulate: for an endothermic step, the transition state resembles the product (radical); for an exothermic step, it resembles the reactant (alkane).

The hydrogen abstraction step determines selectivity:

• Chlorination ($\text{Cl}\cdot + \text{R-H}$): slightly endothermic (+8 kJ/mol for methane). Early, reactant-like transition state. Low selectivity — all C–H bonds react at somewhat similar rates.
• Bromination ($\text{Br}\cdot + \text{R-H}$): significantly endothermic (+73 kJ/mol for methane). Late, product-like transition state. High selectivity — the more stable radical is preferentially formed.

4.2 Relative Reactivity Per Hydrogen

For bromination, the selectivity is so high that practically only the tertiary C–H bond reacts when one is available. This makes bromination synthetically useful for selective functionalization.

4.3 Derivation: Product Distribution for Propane Chlorination

Propane ($\text{CH}_3\text{CH}_2\text{CH}_3$) has 6 primary hydrogens and 2 secondary hydrogens. The expected product ratio is:

This gives approximately 43% 1-chloropropane and 57% 2-chloropropane. For bromination:

This gives approximately 3.5% 1-bromopropane and 96.5% 2-bromopropane — essentially exclusive secondary bromination.

5.1 Allylic Bromination with NBS

N-Bromosuccinimide (NBS) is the reagent of choice for selective allylic bromination. NBS maintains a very low, steady concentration of$\text{Br}_2$ in solution, which prevents competing addition to the double bond:

The mechanism proceeds through allylic radical formation. The allylic C–H bond (BDE $\approx 369 \;\text{kJ/mol}$) is selectively abstracted because the resulting allylic radical is resonance-stabilized. The role of NBS is to slowly release$\text{Br}_2$ by reacting with the HBr byproduct:

5.2 Benzylic Bromination

Toluene and other alkylbenzenes undergo selective bromination at the benzylic position (the carbon adjacent to the ring) under radical conditions. The benzylic C–H bond (BDE $\approx 375 \;\text{kJ/mol}$) is weaker than typical alkyl C–H bonds because the resulting benzylic radical is stabilized by resonance with the aromatic ring.

Multiple successive brominations can occur: toluene → benzyl bromide → benzal bromide ($\text{C}_6\text{H}_5\text{CHBr}_2$) → benzotrichloride ($\text{C}_6\text{H}_5\text{CBr}_3$), though selectivity decreases with each substitution due to the electron-withdrawing effect of the halogens.

In the presence of peroxides ($\text{ROOR}$), HBr adds to alkenes with anti-Markovnikov regiochemistry — the bromine ends up on the less substituted carbon. This is the peroxide effect, first explained by Morris Kharasch and Frank Mayo in the 1930s.

6.1 Mechanism

1. Initiation: Peroxide decomposes to alkoxy radicals, which abstract H from HBr to generate $\text{Br}\cdot$:
   $$\text{RO}\cdot + \text{H-Br} \longrightarrow \text{ROH} + \text{Br}\cdot$$
2. Propagation 1: $\text{Br}\cdot$ adds to the alkene. The bromine adds to the less substituted carbon to form the more stable radical:
   $$\text{Br}\cdot + \text{CH}_3\text{CH=CH}_2 \longrightarrow \text{CH}_3\dot{\text{C}}\text{HCH}_2\text{Br}$$
3. Propagation 2: The carbon radical abstracts H from HBr:
   $$\text{CH}_3\dot{\text{C}}\text{HCH}_2\text{Br} + \text{H-Br} \longrightarrow \text{CH}_3\text{CH}_2\text{CH}_2\text{Br} + \text{Br}\cdot$$

The product is 1-bromopropane (anti-Markovnikov), not 2-bromopropane (Markovnikov). The regiochemistry is controlled by radical stability, not carbocation stability.

Radical polymerization is one of the most industrially important applications of radical chemistry. Billions of kilograms of polymers are produced annually by this method, including polyethylene (PE), polystyrene (PS), poly(vinyl chloride) (PVC), and poly(methyl methacrylate) (PMMA, Plexiglas).

7.1 Mechanism

1. Initiation: A radical initiator (e.g., benzoyl peroxide or AIBN) generates a radical that adds to the first monomer:
   $$\text{R}\cdot + \text{CH}_2\text{=CHX} \longrightarrow \text{R-CH}_2\text{-}\dot{\text{C}}\text{HX}$$
2. Propagation: The growing chain radical adds to the next monomer molecule, extending the chain by one unit:
   $$\text{R-(CH}_2\text{CHX)}_n\text{-CH}_2\dot{\text{C}}\text{HX} + \text{CH}_2\text{=CHX} \longrightarrow \text{R-(CH}_2\text{CHX)}_{n+1}\text{-CH}_2\dot{\text{C}}\text{HX}$$
3. Termination: Two growing chains meet:
   • Combination: two chain radicals couple to form one long chain
   • Disproportionation: H-atom transfer produces one saturated and one unsaturated chain end

7.2 Kinetics of Radical Polymerization

Under steady-state conditions (rate of initiation = rate of termination), the rate of polymerization is:

where $k_p$ is the propagation rate constant, $[\text{M}]$ is the monomer concentration, $f$ is the initiator efficiency, $k_d$ is the initiator decomposition rate constant, $[\text{I}]$ is the initiator concentration, and$k_t$ is the termination rate constant. The degree of polymerization (average chain length) is:

Higher monomer concentration and lower initiator concentration favor longer chains (higher molecular weight polymer).

8.1 Atmospheric Chemistry

Chlorine radicals in the stratosphere catalyze ozone destruction through a radical chain mechanism. A single chlorine atom can destroy approximately 100,000 ozone molecules before termination:

The source of these chlorine atoms is the photolysis of chlorofluorocarbons (CFCs), leading to the Montreal Protocol (1987) that phased out CFC production.

8.2 Biological Radical Chemistry

Reactive oxygen species (ROS) such as superoxide ($\text{O}_2^{\cdot-}$), hydroxyl radical ($\text{HO}\cdot$), and peroxyl radicals ($\text{ROO}\cdot$) are generated during normal metabolism. While they serve signaling functions at low concentrations, excess ROS cause oxidative damage to DNA, proteins, and lipids. Antioxidants like vitamin E (tocopherol) function as radical scavengers, donating an H atom to terminate radical chains in lipid peroxidation.

8.3 Combustion

Combustion of hydrocarbons is a radical chain reaction. The burning of methane, for instance, involves hundreds of elementary radical steps. The overall reaction ($\text{CH}_4 + 2\text{O}_2 \to \text{CO}_2 + 2\text{H}_2\text{O}$) releases$890 \;\text{kJ/mol}$, making methane an efficient fuel. Understanding radical mechanisms in combustion is critical for engine design, pollution control, and fire safety.

The following simulation computes radical reaction thermodynamics from BDE data, predicts halogenation product distributions, models radical chain kinetics, and analyzes the temperature dependence of initiator decomposition in radical polymerization.