The Trommsdorff-Norrish Effect: Runaway Autoacceleration in Radical Polymerization

The paradox: a reaction that speeds up as it thickens

Free-radical polymerization is supposed to be a well-behaved chain reaction. Initiator decomposes to give radicals, those radicals add monomer one unit at a time (propagation), and two growing radicals eventually meet and annihilate each other (termination). Under the steady-state approximation, the rate of initiation equals the rate of termination, and the polymerization rate settles into the textbook form Rₚ = kₚ [M] (kd f [I] / kₜ)^½, where kₚ and kₜ are the propagation and termination rate constants, [M] and [I] the monomer and initiator concentrations, kd the initiator decomposition constant, and f the initiator efficiency. Everything about that expression predicts a rate that decays monotonically as monomer and initiator are consumed.

The gel effect is the flat contradiction of that expectation. In an undiluted (bulk) polymerization of a monomer like methyl methacrylate (MMA), styrene, or methyl acrylate, the rate first falls gently as expected — and then, somewhere around 20–40% conversion, it reverses and climbs steeply, often overshooting the initial rate several-fold before finally choking off at high conversion when even monomer can no longer diffuse. Plotted as conversion versus time, the curve develops a distinctive S-shaped acceleration; plotted as rate versus conversion it shows a dramatic hump. Because the phenomenon coincides with the point where the reacting mass turns to a viscous gel, it acquired the name gel effect, and the whole rate anomaly is called autoacceleration.

The resolution of the paradox is that not all three elementary steps depend on diffusion the same way. Termination requires two large, sluggish macroradicals to find each other and bring their radical ends into contact — a process that becomes hopelessly slow in a thickening medium. Propagation only requires a small, nimble monomer molecule to reach a radical chain end. As viscosity climbs, kₜ falls off a cliff while kₚ barely notices. Since Rₚ scales as kₚ/kₜ^½, a collapsing denominator makes the rate rise. The reaction does not violate kinetics — it obeys a rate law in which one constant is quietly becoming a variable.

Two labs, one effect: Norrish, Smith, and Trommsdorff

The anomaly was documented in stages across the 1940s. In 1942 Ronald George Wreyford Norrish — later the 1967 Nobel laureate in chemistry for flash photolysis, shared with Porter and Eigen — published with R. R. Smith a careful kinetic study of MMA in Nature showing the rate rising with conversion in a way no steady-state treatment could accommodate. They correctly attributed it to a decrease in the termination rate as the medium became viscous. A few years later, in 1947, G. V. (Gunter) Schulz and G. Harborth reported abnormally fast ("explosive") bulk MMA polymerizations, reinforcing the same picture. For this reason the phenomenon is often called the Norrish-Smith effect or, most commonly, the Trommsdorff-Norrish effect.

The name that stuck to the German literature belongs to Ernst Trommsdorff, whose 1947 work (and the widely cited 1948 paper with Köhle and Lagally in Die Makromolekulare Chemie) laid out the diffusion-controlled-termination picture in quantitative detail for MMA. Trommsdorff's insight was that the falling termination rate not only accelerates the reaction but simultaneously lengthens the kinetic chain, so the average molecular weight climbs during the autoacceleration window. Both consequences flow from a single cause: radicals live longer because they cannot find each other to die.

It is worth being precise about a naming collision that trips up students. The Norrish reactions of carbonyl photochemistry — the α-cleavage (Norrish Type I) and the intramolecular γ-hydrogen abstraction (Norrish Type II) — are entirely different chemistry, also named for R. G. W. Norrish. The gel effect shares his name only because he studied both. When someone says 'the Norrish effect' in a polymer context they almost always mean autoacceleration; in a photochemistry context they mean the cleavage reactions. Same chemist, two legacies.

The mechanism: diffusion control and the collapse of kₜ

Termination between two macroradicals is a multistage diffusion problem, and each stage can become rate-limiting as conditions change. Modern treatments (following Benson and North in the 1960s and later Buback, Russell, and others) decompose it into three sequential steps, so that the overall termination coefficient is a series resistance: 1/kₜ ≈ 1/k_trans + 1/k_seg + 1/k_react.

• Translational diffusion (center-of-mass): the two whole chains must migrate through the entangled melt until their coils overlap. This is exquisitely sensitive to bulk viscosity and molar mass, scaling roughly as the self-diffusion coefficient D ∝ M^(−1) below entanglement and ∝ M^(−2) (reptation) above it.
• Segmental diffusion: once the coils interpenetrate, the reactive chain ends must wriggle into contact — internal, short-range motion. This dominates at moderate conversion and is much less viscosity-sensitive than translation.
• Reaction-diffusion / chemical step: at very high conversion, chains barely move at all; a radical end effectively 'walks' by adding monomer (propagation moves the radical), and termination becomes limited by that residual mobility. This is why kₜ eventually tracks kₚ[M] at the tail end.

At low conversion, termination is fast and the chemical encounter is not limiting — kₜ for MMA is on the order of 10⁷–10⁸ M⁻¹s⁻¹, near diffusion control for small radicals. As conversion climbs, the entangled macroradicals can no longer translate, k_trans plummets, and kₜ falls by two to three orders of magnitude — from ~10⁷ down toward 10⁴–10⁵ M⁻¹s⁻¹. Propagation, meanwhile, holds near its intrinsic value (kₚ for MMA is ≈ 500–1000 M⁻¹s⁻¹ at 50–70 °C) because a monomer molecule the size of a solvent molecule still diffuses freely. With kₜ in free fall and kₚ constant, the steady-state radical concentration [M•] = (Rᵢ/2kₜ)^½ swells, and both Rₚ (∝ kₚ[M•]) and the kinetic chain length ν = kₚ[M]/(2kₜ[M•]) rise together. The runaway is self-reinforcing: faster reaction means more heat, higher temperature accelerates initiator decomposition, and higher viscosity from newly formed polymer suppresses kₜ further.

Worked example: bulk MMA at 50 °C, by the numbers

Take the canonical system: neat MMA (bulk density ≈ 0.94 g/mL, so [M]₀ ≈ 9.4 M) initiated by AIBN (2,2′-azobis(2-methylpropionitrile)) at 50 °C. AIBN's decomposition constant kd ≈ 2 × 10⁻⁶ s⁻¹ at 50 °C, with efficiency f ≈ 0.6. Representative low-conversion constants for MMA at 50 °C are kₚ ≈ 570 M⁻¹s⁻¹ and kₜ ≈ 2.5 × 10⁷ M⁻¹s⁻¹. With [I] ≈ 0.02 M, the initiation rate Rᵢ = 2 f kd [I] ≈ 2(0.6)(2×10⁻⁶)(0.02) ≈ 4.8 × 10⁻⁸ M/s, giving a steady-state radical concentration [M•] = (Rᵢ/2kₜ)^½ ≈ (4.8×10⁻⁸ / 5×10⁷)^½ ≈ 3.1 × 10⁻⁸ M — a startlingly tiny population of active chains, on the order of one radical per 10⁸ monomer units.

The initial rate is then Rₚ = kₚ[M][M•] ≈ 570 × 9.4 × 3.1×10⁻⁸ ≈ 1.7 × 10⁻⁴ M/s, or roughly 0.1% conversion per minute — sedate. Now let the reaction run to ~40% conversion, where translational termination has become impossible for the entangled chains and kₜ has dropped by a factor of ~100 to ≈ 2.5 × 10⁵ M⁻¹s⁻¹. Since [M•] ∝ kₜ^(−½), the radical concentration rises by √100 = 10×, to ~3 × 10⁻⁷ M. The rate, Rₚ ∝ kₜ^(−½) at fixed [M], likewise jumps ~10×, even as [M] itself has fallen by 40%. Net: the observed rate roughly quintuples relative to its low-conversion value — precisely the autoacceleration hump seen in Trommsdorff's original data.

The molar-mass consequence follows from the same √kₜ scaling. The kinetic chain length ν ∝ kₚ[M]/(kₜ[M•]) ∝ kₚ[M]/(Rᵢ kₜ)^½, so a 100-fold drop in kₜ multiplies ν by ~10 (partly offset by the lower [M]). Polymer formed during the gel-effect window is therefore markedly higher in molar mass, and the molecular-weight distribution broadens because chains born before, during, and after autoacceleration experience wildly different termination environments — dispersities Đ can climb well above the 1.5–2.0 expected for ideal termination.

Limits, subtleties, and what the simple picture misses

The heuristic 'kₜ collapses, kₚ is constant' is right in spirit but hides real subtlety. First, kₚ is not perfectly constant: at very high conversion (typically > 80% for MMA) even monomer diffusion becomes hindered and the reaction enters the glass effect (or 'glass transition effect'). If the reaction temperature is below the Tg of the forming polymer-monomer mixture, the system vitrifies, kₚ finally collapses too, and the polymerization stops dead — often at incomplete conversion, leaving residual monomer trapped in glassy PMMA. This is why cast acrylic sheet is post-cured at elevated temperature: to push above Tg and burn off the last few percent of monomer.

Second, the onset conversion is not universal — it depends strongly on chain length, temperature, dilution, and monomer identity. Longer chains entangle sooner, so higher-molar-mass systems autoaccelerate earlier; dilution with solvent delays or suppresses the effect by keeping viscosity down; higher temperature both speeds initiation and softens the medium. Styrene shows a milder gel effect than MMA partly because its bulkier propagating radical and lower kₚ change the balance. Vinyl acetate and acrylates, with their fast propagation and strong chain-transfer, show their own idiosyncratic acceleration behavior.

Third, modeling the effect quantitatively is genuinely hard and still somewhat empirical. Early treatments used free-volume theory (Bueche; the Chiu-Carratt-Soong and Marten-Hamielec models) to make kₜ and later kₚ functions of conversion and temperature via the fractional free volume. Diffusion-based approaches tie kₜ to the polymer self-diffusion coefficient and reptation dynamics. Pulsed-laser polymerization (PLP) combined with size-exclusion chromatography, pioneered by Olaj and refined by an IUPAC working party under Buback in the 1990s, finally gave reliable, model-independent kₚ values and let researchers isolate the kₜ behavior — confirming that the gel effect is overwhelmingly a termination phenomenon until the glass regime. Even so, no single closed-form law captures the full conversion range, and reactor models still stitch together separate expressions for the pre-gel, gel, and glass regimes.

Why it matters: runaway reactors, cast acrylic, and controlled polymerization

The gel effect is not an academic curiosity — it is a process-safety hazard. Bulk radical polymerizations are strongly exothermic (MMA releases ≈ 55 kJ/mol, styrene ≈ 70 kJ/mol on polymerization), and autoacceleration dumps that heat faster and faster into a medium whose viscosity has just crippled convective and conductive cooling. In an inadequately controlled batch reactor the positive feedback loop — more rate → more heat → hotter → faster initiation and lower viscosity-limited kₜ → still more rate — can drive a thermal runaway. Adiabatic temperature rises exceeding 100–200 °C are possible; the monomer boils, pressure spikes, and reactors have vented, foamed over, or ruptured. Industrial guidance for bulk acrylic and styrenic processes explicitly addresses gel-effect runaway, favoring solution or suspension polymerization, staged monomer feeds, dilution, and aggressive temperature control to keep the reaction out of the autoaccelerating regime.

The same physics is exploited where high molar mass and rapid, complete cure are desirable. Cast poly(methyl methacrylate) — Plexiglas and Perspex sheet — is made by bulk polymerizing MMA between glass plates precisely because the gel effect drives conversion high and pushes molar mass up, giving the tough, high-Mw material acrylic glazing needs. Bone cement (PMMA) used in orthopedic arthroplasty relies on a fast bulk cure at body-adjacent temperatures; surgeons manage a real, tactile gel point as the dough sets, and the cure exotherm is clinically relevant. Dental composites, adhesives, and thick-section castings all live with autoacceleration by design.

Finally, the gel effect is the foil that motivates reversible-deactivation radical polymerization (RDRP) — ATRP (Matyjaszewski; Sawamoto), RAFT (the CSIRO group, 1998), and NMP. By keeping the instantaneous radical concentration extremely low and reversibly capping dormant chains, these methods dramatically suppress irreversible bimolecular termination, which is the very step that misbehaves in the gel effect. The result is controlled molar mass, narrow dispersity, and — importantly for engineers — a far tamer, more predictable rate profile without the autoacceleration hump. Understanding why classical free-radical polymerization runs away is, in a real sense, understanding why controlled radical polymerization was worth inventing.

The two rate constants that govern free-radical polymerization respond very differently as the medium thickens — the asymmetry is the whole story.

Feature	Propagation kₚ	Termination kₜ
Reacting partners	Polymer radical + small monomer	Two polymer radicals (macroradicals)
Diffusion needed	Small-molecule (segmental) diffusion	Whole-chain (translational) diffusion
Effect of rising viscosity	Nearly unaffected until very high conversion	Falls sharply — becomes diffusion-limited early
Behavior at gel-effect onset	Roughly constant (≈ 10²–10³ M⁻¹s⁻¹)	Collapses 10²–10³-fold
Net effect on rate Rₚ ∝ kₚ/kₜ^½	Numerator steady	Shrinking denominator drives autoacceleration
Net effect on chain length	—	Longer radical lifetime → higher molar mass