Chain Polymerization: Free-Radical Kinetics & Molecular Weight Distribution (2D)

Initiation

Initiator [I]₀ 8.0 mmol/L

Temperature 60 °C

Propagation

Monomer [M]₀ 6.0 mol/L

Chain control

Chain-transfer C_m 0.0040

Termination mode

Live Readout

Conversion

0.0%

[M] remaining

6.00 mol/L

Active radicals

Dead chains

Xn (simulated)

Đ = Xw/Xn

0.00

Kinetic chain length ν

DPn (Mayo, theory)

How it works

A kinetic Monte-Carlo model of free-radical chain-growth polymerization. Each simulated tick applies the real rate laws stochastically to every chain:

Initiation:  Ri = 2·f·kd·[I]        (kd scales with Temperature)
Propagation: Rp = kp·[M]·[R•]       (per-radical prob. = kp·[M]·dt)
Transfer:    Rtr = Cm·kp·[M]·[R•]   (ends chain, spawns new radical)
Termination: Rt = kt·[R•]²          (paired radicals meet at random)

Kinetic chain length:  ν = Rp / Ri
Mayo equation:  1/DPn = 1/(x·ν) + Cm     (x=2 combination, x=1 disproportionation)

[I] decays exponentially (kd·[I]) and [M] depletes with every real propagation event, so the run self-terminates as conversion approaches 100%. Every dead chain — from termination or transfer — is binned into a live molecular-weight-distribution histogram, with the theoretical most-probable (Flory) distribution overlaid as a dashed curve so you can check the stochastic run against the closed-form prediction.

Combination termination merges two radicals into one chain (narrower Đ, →1.5).
Disproportionation ends both radicals separately, unchanged (broader Đ, →2.0).
Raising Cm shortens chains via the Mayo equation independent of termination mode — a real, verifiable trade-off between initiator, temperature, monomer and transfer-agent levels.

Active radical chain Dead (terminated) chain MWD vs. Flory theory