2.3 Free radical polymerization

Fundamentals of Free Radical Polymerization

Free radical polymerization is one of the most widely used methods for producing commercial polymers like polyethylene, polystyrene, PVC, and synthetic rubbers. The core idea: generate a reactive species (a free radical) that opens a monomer's carbon-carbon double bond, creating a new radical at the chain end that reacts with the next monomer, and the next, building a long polymer chain very quickly.

The process follows three distinct stages: initiation, propagation, and termination. Each stage has its own kinetics, and the balance between them determines the molecular weight, polydispersity, and structure of the final polymer.

Mechanism of Free Radical Polymerization

1. An initiator molecule decomposes to produce free radicals (species with an unpaired electron).
2. A radical attacks the $\pi$ bond of a vinyl monomer ($CH_2=CHX$), breaking it open and forming a new $\sigma$ bond. The unpaired electron moves to the end of the chain.
3. This radical chain end reacts with another monomer unit, extending the chain. This repeats thousands of times in a fraction of a second.
4. The chain stops growing when two radicals encounter each other (termination) or when the radical transfers to another molecule (chain transfer).

Because each chain grows to full length almost instantly before the next one starts, high molecular weight polymer coexists with unreacted monomer throughout the reaction. This is a hallmark of chain-growth polymerization.

Key Steps: Initiation, Propagation, Termination

• Initiation has two parts: (1) decomposition of the initiator into radicals, and (2) the radical's addition to the first monomer unit. The decomposition step is usually rate-limiting.
• Propagation is the repeated addition of monomer to the active chain end. It's fast and accounts for most of the monomer consumption.
• Termination stops chain growth. It can happen by combination (two chain radicals coupling together) or disproportionation (hydrogen transfer between two radicals, producing one saturated and one unsaturated chain end).

Each step has its own rate constant ($k_d$, $k_p$, $k_t$), and the interplay of these constants governs the overall rate and the molecular weight of the product.

Chain Transfer Reactions

Chain transfer occurs when a growing radical abstracts an atom (usually hydrogen) from another molecule, killing the original chain but generating a new radical that can start a fresh chain.

Transfer can happen to:

• Solvent molecules
• Monomer molecules
• Polymer chains already formed (which causes branching)
• Chain transfer agents (CTAs) added on purpose to limit molecular weight

The key effect: chain transfer reduces the average molecular weight without significantly changing the overall polymerization rate. Deliberately added CTAs like thiols (e.g., dodecanethiol) are a practical tool for molecular weight control.

Initiators and Initiation

The initiator is what gets the whole reaction going. Its choice affects the rate of radical generation, the polymer's end groups, and even the temperature window for the reaction.

Types of Free Radical Initiators

• Peroxides contain a weak O–O bond that breaks homolytically. Benzoyl peroxide (BPO) is a classic example, generating two oxygen-centered radicals upon heating.
• Azo compounds decompose by releasing $N_2$ gas and forming two carbon-centered radicals. AIBN (azobisisobutyronitrile) is the most common, with a well-characterized half-life around 10 hours at 65 °C.
• Redox initiators generate radicals through electron transfer at lower temperatures. An example is the $Fe^{2+}/H_2O_2$ (Fenton) system, commonly used in emulsion polymerization.
• Photoinitiators absorb UV or visible light to produce radicals. These are essential in UV-curable coatings and dental composites.

Thermal vs. Photochemical Initiation

Thermal initiation relies on heat to supply the activation energy for bond homolysis. You control the rate by adjusting temperature and choosing an initiator with the right half-life for your conditions. The downside is that thermal methods offer limited spatial control.

Photochemical initiation uses light energy instead. This gives you spatial control (only irradiated areas polymerize) and temporal control (turn the light off, radicals stop forming). It's widely used in lithography, 3D printing, and coatings. The tradeoff is that the monomer system must be transparent enough for light to penetrate.

Initiation Efficiency

Not every radical generated actually starts a polymer chain. The initiator efficiency ($f$) is the fraction that does, and it's typically between 0.3 and 0.8.

Why less than 1.0? The main culprit is the cage effect: when an initiator decomposes in solution, the two radicals are initially trapped in a "cage" of solvent molecules. They may recombine before diffusing apart. Higher solvent viscosity increases the cage effect and lowers $f$.

The rate of initiation is given by:

$R_i = 2fk_d[I]$

where $k_d$ is the initiator decomposition rate constant and $[I]$ is the initiator concentration. The factor of 2 accounts for two radicals produced per initiator molecule.

Propagation and Kinetics

Propagation Rate Constants

The propagation rate constant $k_p$ measures how quickly a radical chain end adds the next monomer. Values vary widely by monomer: for example, methyl methacrylate has $k_p \approx 650 \, L \cdot mol^{-1} \cdot s^{-1}$ at 60 °C, while vinyl acetate is significantly higher.

$k_p$ depends on:

• Monomer structure: steric bulk and electronic effects of substituents
• Temperature: $k_p$ increases with temperature following the Arrhenius equation
• Pressure: high pressure generally increases $k_p$

Pulsed laser polymerization (PLP) combined with size exclusion chromatography is the IUPAC-recommended method for measuring $k_p$ accurately.

Chain Growth vs. Step Growth

Free radical polymerization is a chain-growth process. This distinction matters:

This is why you can have a reaction mixture at 20% conversion that contains high molecular weight polymer alongside unreacted monomer, with very little oligomer in between.

Kinetics of Free Radical Polymerization

The steady-state approximation assumes that the concentration of radicals stays roughly constant during polymerization (rate of initiation ≈ rate of termination). This simplifies the math considerably.

Under steady state, the radical concentration is:

$[P\bullet] = \left(\frac{R_i}{2k_t}\right)^{1/2} = \left(\frac{fk_d[I]}{k_t}\right)^{1/2}$

The overall rate of polymerization becomes:

$R_p = k_p[M]\left(\frac{fk_d[I]}{k_t}\right)^{1/2}$

Two things to notice here: $R_p$ is first-order in monomer concentration but only half-order in initiator concentration. Doubling the initiator concentration increases the rate by only $\sqrt{2} \approx 1.41$ times, not twofold.

Termination Mechanisms

Combination vs. Disproportionation

In combination, two radical chain ends couple directly, forming a single chain with roughly double the kinetic chain length. The resulting polymer has initiator fragments at both ends.

In disproportionation, one radical abstracts a $\beta$-hydrogen from the other. This produces two dead chains: one with a saturated end and one with a terminal double bond. Each chain retains the kinetic chain length.

Which dominates depends on the monomer. Polystyryl radicals terminate mostly by combination. Poly(methyl methacrylate) radicals, with their bulky $\alpha$-methyl groups that hinder coupling, terminate predominantly by disproportionation at typical reaction temperatures.

Chain Transfer to Monomer

The growing radical abstracts a hydrogen (or other atom) from a monomer molecule. The original chain is terminated, and the monomer-derived radical initiates a new chain. This sets an upper limit on achievable molecular weight even in the absence of other transfer processes.

The chain transfer constant to monomer is defined as $C_M = k_{tr,M}/k_p$. Monomers like vinyl chloride have relatively high $C_M$ values, which is one reason PVC tends to have lower molecular weight than polystyrene made under similar conditions.

Chain Transfer to Solvent

The same principle applies to solvent molecules. The transfer constant $C_S = k_{tr,S}/k_p$ varies enormously with solvent choice. Carbon tetrachloride, for instance, is a very active transfer agent, while benzene has a low $C_S$.

This is why solvent selection in solution polymerization isn't just about dissolving the monomer. The wrong solvent can drastically reduce your molecular weight.

Molecular Weight Control

Kinetic Chain Length

The kinetic chain length ($\bar{\nu}$) is the average number of monomer units consumed per radical that initiates a chain:

$\bar{\nu} = \frac{R_p}{R_i} = \frac{k_p[M]}{2(fk_dk_t[I])^{1/2}}$

If termination occurs by combination, the number-average degree of polymerization $\overline{DP_n} = 2\bar{\nu}$. If by disproportionation, $\overline{DP_n} = \bar{\nu}$.

The practical takeaway: increasing initiator concentration increases the polymerization rate but decreases the molecular weight. There's always a trade-off between speed and chain length.

Mayo Equation

The Mayo equation accounts for all chain transfer processes and relates them to the degree of polymerization:

$\frac{1}{\overline{DP_n}} = \frac{1}{\overline{DP_{n,0}}} + C_M + C_S\frac{[S]}{[M]} + C_{CTA}\frac{[CTA]}{[M]}$

Here, $\overline{DP_{n,0}}$ is the degree of polymerization in the absence of any transfer, and $C_M$, $C_S$, and $C_{CTA}$ are the transfer constants to monomer, solvent, and chain transfer agent, respectively.

This equation is your main tool for predicting how molecular weight will change when you adjust the recipe. By plotting $1/\overline{DP_n}$ vs. $[S]/[M]$, you can extract $C_S$ from the slope.

Gel Effect (Trommsdorff-Norrish Effect)

As conversion increases, the reaction mixture becomes viscous. Large polymer radicals can no longer diffuse easily to find each other, so the termination rate drops. But small monomer molecules can still diffuse to radical chain ends, so propagation continues at nearly the same rate.

The result: the radical concentration rises, and both the polymerization rate and molecular weight increase sharply. This autoacceleration is called the gel effect or Trommsdorff-Norrish effect.

This is a serious concern in industrial bulk polymerizations because the exothermic reaction can become difficult to cool. Runaway reactions can cause thermal degradation, discoloration, or even reactor failure. Strategies to manage it include using solvents (solution polymerization), running at lower conversions, or using reactor designs with high surface-to-volume ratios.

Copolymerization in Free Radical Systems

Copolymerization lets you combine two or more monomers into a single chain, giving access to properties that neither homopolymer can provide on its own.

Reactivity Ratios

The reactivity ratios $r_1$ and $r_2$ quantify each monomer's preference for adding to its own type of radical versus the other:

$r_1 = \frac{k_{11}}{k_{12}}, \quad r_2 = \frac{k_{22}}{k_{21}}$

• If $r_1 > 1$: monomer 1 radical prefers adding monomer 1 (self-propagation favored)
• If $r_1 < 1$: monomer 1 radical prefers adding monomer 2 (cross-propagation favored)
• If $r_1 \times r_2 = 1$: ideal copolymerization (random placement)
• If $r_1 \approx r_2 \approx 0$: strong alternating tendency

These ratios are determined experimentally and used with the copolymer equation to predict the instantaneous copolymer composition from the monomer feed ratio.

Composition Drift

Unless $r_1 = r_2 = 1$, the two monomers are consumed at different rates. As the reaction proceeds, the monomer feed composition shifts, and so does the copolymer composition being formed at that instant. This is composition drift.

For example, in a styrene/methyl methacrylate system, styrene is incorporated slightly faster early on. As styrene is depleted, later-formed chains become richer in MMA. The final product is a mixture of chains with varying compositions.

To minimize drift, you can use starved-feed (semi-batch) techniques, continuously adding the faster-consumed monomer to keep the feed ratio constant.

Block vs. Random Copolymers

Conventional free radical polymerization produces random (or statistical) copolymers, where monomer placement along the chain follows the reactivity ratios.

Block copolymers, with long sequences of one monomer followed by long sequences of another, require controlled/living polymerization techniques (RAFT, ATRP, NMP) because you need to grow one block first, then switch to the second monomer while keeping the chain ends active.

Alternating copolymers can sometimes be achieved in conventional free radical systems when both $r_1$ and $r_2$ are close to zero (e.g., styrene/maleic anhydride).

Industrial Applications

Bulk vs. Solution Polymerization

Bulk polymerization uses only monomer and initiator. It gives the highest purity product and maximum yield per reactor volume. The downside: heat removal is difficult because the viscous polymer mass is a poor thermal conductor, and the gel effect can cause dangerous autoacceleration.

Solution polymerization adds a solvent, which reduces viscosity and improves heat transfer. It also mitigates the gel effect. The trade-off is that you need to remove the solvent afterward, which adds cost and energy. Solvent choice also matters because of chain transfer effects.

Emulsion Polymerization

In emulsion polymerization, monomer droplets are dispersed in water using surfactants. Polymerization actually occurs inside micelles (surfactant aggregates swollen with monomer), not in the large droplets.

This system achieves something unusual: simultaneously high molecular weight and high polymerization rate. That's because radical compartmentalization in micelles reduces the effective termination rate. The product is a stable latex (polymer particles suspended in water), which is used directly in paints, adhesives, coatings, and synthetic rubber (SBR).

Suspension Polymerization

Monomer droplets (0.01–5 mm) are suspended in water using stabilizers like polyvinyl alcohol. Each droplet is essentially a tiny bulk reactor. Heat removal is efficient because water surrounds each droplet.

The product is polymer beads, which are easy to handle and process. Suspension polymerization is the standard method for producing expandable polystyrene (EPS) beads and PVC.

Advantages and Limitations

Advantages

• High reaction rates allow for large-scale, high-throughput production
• Tolerance to impurities: unlike ionic or coordination polymerizations, free radical systems can handle trace water and many functional groups. This enables polymerization in aqueous media and reduces raw material purification costs
• Versatility: compatible with a wide range of vinyl monomers and can be run in bulk, solution, emulsion, or suspension
• Mild conditions: many systems operate at moderate temperatures (50–80 °C) and atmospheric pressure

Limitations

• Broad molecular weight distributions: because initiation, propagation, and termination occur simultaneously and continuously, the polydispersity index ($Đ = M_w/M_n$) is typically 1.5–2.0 or higher
• Limited architectural control: conventional free radical polymerization cannot easily produce block copolymers, star polymers, or other complex architectures
• Exotherm management: the highly exothermic propagation step can lead to thermal runaway, especially in bulk systems
• Chain transfer side reactions can introduce unwanted branching or limit achievable molecular weight

Modern Developments

Controlled/Living Radical Polymerization

The term "living" in this context means that termination is suppressed or minimized, so chain ends remain active throughout the reaction. This gives you:

• Predictable molecular weights that increase linearly with conversion
• Narrow molecular weight distributions ($Đ < 1.3$)
• The ability to chain-extend or make block copolymers by adding a second monomer

The three major techniques are RAFT, ATRP, and NMP.

RAFT Polymerization

Reversible Addition-Fragmentation chain Transfer (RAFT) uses a thiocarbonylthio compound (the RAFT agent) to mediate the polymerization. The RAFT agent rapidly exchanges radical activity between chains, ensuring all chains grow at roughly the same rate.

Strengths of RAFT:

• Works with the widest range of monomers among CRP techniques
• Doesn't require metal catalysts
• Can be performed under standard free radical conditions (just add the RAFT agent)

The main limitation is that RAFT agents can impart color and odor to the product, though removal or transformation of the thiocarbonylthio end group is possible.

ATRP and NMP

Atom Transfer Radical Polymerization (ATRP) uses a transition metal complex (typically Cu(I) with a nitrogen-based ligand) to reversibly activate and deactivate chain ends. The dormant chain end is an alkyl halide; the metal oxidizes to abstract the halide, generating a radical that adds a few monomers before being deactivated again.

Nitroxide-Mediated Polymerization (NMP) uses stable nitroxide radicals (like TEMPO) that reversibly cap chain ends. At elevated temperatures, the C–O bond breaks homolytically, freeing the chain radical for propagation before recapping.

Both techniques produce well-defined polymers, but ATRP requires careful removal of metal catalyst residues, and NMP is limited to a narrower range of monomers (works best with styrenics).

Characterization Methods

Gel Permeation Chromatography (GPC)

Also called size exclusion chromatography (SEC), GPC separates polymer chains by their hydrodynamic volume (effectively their size in solution). Smaller chains enter the pores of the column packing and elute later; larger chains pass through faster.

GPC provides the full molecular weight distribution, giving you $M_n$, $M_w$, and the dispersity $Đ$. Conventional GPC requires calibration with narrow-distribution standards (usually polystyrene). For absolute molecular weights, you can couple GPC with multi-angle light scattering (MALS) detection.

NMR Spectroscopy

Nuclear Magnetic Resonance spectroscopy reveals the chemical structure of the polymer at the molecular level. For free radical polymerization, NMR is particularly useful for:

• Determining copolymer composition (the ratio of incorporated monomers)
• Identifying end groups, which tells you about initiation and termination mechanisms
• Measuring tacticity (the stereochemical arrangement of substituents along the chain)
• Detecting branching and other structural irregularities

$^1H$ NMR is most common, but $^{13}C$ NMR provides higher resolution for distinguishing subtle structural differences like monomer sequence distributions in copolymers.

Thermal Analysis Techniques

• Differential Scanning Calorimetry (DSC) measures heat flow into or out of a sample as temperature changes. It identifies the glass transition temperature ($T_g$), melting point ($T_m$), and crystallization behavior.
• Thermogravimetric Analysis (TGA) tracks mass loss as a function of temperature, revealing thermal stability and decomposition temperatures. It can also quantify residual monomer or solvent content.
• Dynamic Mechanical Analysis (DMA) applies oscillating stress to a sample and measures the storage modulus, loss modulus, and $\tan \delta$. It's the most sensitive method for detecting $T_g$ and reveals how the polymer behaves mechanically across a temperature range.