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Photoinitiator Efficiencies Calculator

This website allows simulating the initiation reaction of radical photopolymerizations according to the following model:

Formulas used in model

The rate of radical generation (see equation (1)) depends on the concentration [I] of the photoinitiator, its extinction coefficient ε at the desired irradiation wavelength, as well as the dissociation quantum yield Φ and the intensity of the light source I0 (photon flux). These parameters can be freely chosen in the model below. The layer thickness d is set to 1 cm in the simulations.

Equations (2)-(3) describe the addition of the primary radicals A• an B• to the monomer M. The concentration of the monomer [M] as well as the rate constants k1 and k2 can be freely chosen.

Equations (4)-(5) describe the quenching of the primary radicals by molecular oxygen O2. Again, the oxygen concentration [O2] as well as the quenching rate constants k3 and k4 can be set to the desired values.

The output of the simulation is a graph showing concentration of the individual species versus time. You can also download the input file for COPASI and the result file generated by it. Caution: please only enter numbers within the range specified for each parameter.

Parameter Quantity Unit Range
Concentration of initiator, [I] mol/L 0 - 10
Concentration of monomer, [M] mol/L 0 - 10
Concentration of oxygen, [O2] mol/L 0 - 10
Quantum yield, Φ 0 - 1
Photon flux, I0 mol/(L·s) 0 - 1000
Extinction coefficient, ε L/(mol·cm) >0 - 2000
Rate constant of addition of A•, k1 L/(mol·s) 0 - 1e10
Rate constant of addition of B•, k2 L/(mol·s) 0 - 1e10
Rate constant of oxygen quenching of A•, k3 L/(mol·s) 0 - 1e10
Rate constant of oxygen quenching of B•, k4 L/(mol·s) 0 - 1e10

For a full explanation please see:

A. Eibel, D. E. Fast, G. Gescheidt, Polym. Chem. 2018, 9, 5107-5115.

The calculations are performed using the program COPASI (version 4.23.184), available under the Artistic License 2.0. We are grateful to the authors of COPASI for allowing us to integrate it into this website.

Financial support by the Austrian Research Promotion Agency (FFG) is gratefully acknowledged. This page was developed in connection with the SOH4PEM (State of Health Monitoring for Proton Exchange Membrane Fuel Cell Stacks) project. For further information see: institute.tuwien.ac.at/soh4pem.

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