chain
Paul Cochrane
Example simulation of free-radical chain polymerisation.
Adapted for xmds from "Mathematica computer programs for physical
chemistry", William H. Cropper, Springer Verlag (1998)
Calculates [M], concentration of monomer, [P.], concentration of
chain radicals, [I], concentration of initiator, [R.],
concentration of initiator radicals, and [P],
concentration of polymer, during the first 10 s
of a free-radical chain polymerization process.
The various rates involved are
Rate of initiation: Ri = 2 f kd [I]
Rate of propagation: Rp = kp [M] [P.] + kp [M] [R.]
Rate of termination: Rt = 2 kt [P.]^2,
where kp, kd and kt are rate constants and f is the
initiation efficiency factor. Rate equations are:
d[M]/dt = -kp [M] [P.] - kp [M] [R.]
d[P.]/dt = 2 f kd [I] - 2 kt [P.]^2
d[I]/dt = -2 f kd [I]
d[R.]/dt = 2 f kd [I] - kp [M] [R.]
d[P]/dt = kt [P.]^2.
The program also calculates the average degree of polmerization
according to Eq. (10.47), as given in
"Mathematica computer programs for physical chemistry"
xave = -(d[M]/dt)/(d[P]/dt).
t
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main
1
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double
Monomer Chain Initiator Radical Polymer
RK4IP
10
100000
1000
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