Chain Reaction Fundamentals
Free-radical polymerization proceeds through three stages: initiation, propagation, and termination. An initiator molecule decomposes into radicals that add to a monomer double bond, starting a chain. Each subsequent monomer addition extends the chain by one unit in a propagation step that repeats hundreds to thousands of times. The chain finally stops when two radicals meet and combine or disproportionate.
The Kinetic Chain Length
The average number of monomers added per radical — the kinetic chain length — determines molecular weight. It equals the ratio of propagation rate to termination rate: Xₙ = kₚ[M]/√(kₜ·f·kd·[I]). This square-root dependence on initiator concentration means that to halve the molecular weight, you must quadruple the initiator loading — a fundamental constraint in polymer manufacturing.
Steady-State Radical Concentration
Within seconds of reaction start, radical production from initiator decomposition balances radical consumption by termination, establishing a steady-state concentration [R•] = √(f·kd·[I]/kₜ). This typically hovers around 10⁻⁸ mol/L — extraordinarily low, yet sufficient to drive rapid polymerization because kₚ is large. The simulation shows how [R•] varies with initiator and termination kinetics.
Industrial Implications
Controlling polymerization kinetics is essential for manufacturing consistent polymer products. LDPE is made by free-radical polymerization at extreme pressures (1500–3000 atm) to achieve high conversion rates. Emulsion polymerization confines radicals in micelles to achieve both high rate and high molecular weight simultaneously — circumventing the usual inverse relationship. This simulator reveals how each parameter affects the kinetic tradeoffs that govern polymer production.