Free Radical Photopolymerization

Photopolymerization is a special form of free-radical polymerization where light is used to initiate polymerization. This method has many advantages over conventional polymerization in terms of less energy consumption, reduced waste, higher productivity (fast cure) and lower reaction temperature. The primary limitation of light-induced polymerization is the limited light penetration depths which will depend on the wave length and spectral distribution but does not exceed a few millimeters. Since polymerization stops when the light source is removed, photopolymerization techniques are only useful for thin film applications.

The photochemical initiation is usually achieved by subjecting suitable photoinitiators to UV irradiation. The absorption of light (photons) converts the absorbing molecules (PI) to their activated form which rapidly disintegrate into radicals or ions (I). These molecule fragments then initiate polymerization and/or crosslinking reactions in a subsequent step. In the case of photosensitizers (S), the light-activated molecules (S^*) transfer their energy directly to an energy acceptor molecule which then produces radicals by either hydrogen abstraction (II) or by photocleavage (III):

(I) (II) (III)

PI + h ν → A• + B• S + h ν → S* S* + I → (S-I)* (S-I)* → S•-H + I• S + h ν → S* S* + I → S + I* I* → A• + B•

The absorption of light occurs only if the energy difference between the activated state and ground state of the in initiator molecule is equal to the energy of the photon. Its energy is proportional to its  frequency ν or wave length λ and can be calculated with the Planck-Einstein relation:

E = h ν = h c / λ = ΔE

where h is Planck's constant, λ is the wavelength of the monochromatic light source and ΔE is the energy difference between the two states of the molecule. The total energy absorbed can be estimated from the change in light intensity transmitted through a layer of solution. According to the Lambert-Beer law, the decrease in light intensity is proportional to the thickness of the irradiated layer z and the concentration [PI] of light absorbing molecules (photoinitiators):

ln [I(z) / I₀] = -α z [PI]

or

log [I(z) / I₀] = -ε z [PI]

where ε, α are the molar extinction coefficients. According to the Lambert-Beer law, the absorption coefficient (α, ε) is independent of the concentration and radiation intensity.
Assuming a steady state, the rate of vinyl polymerization is given by

R_p = -d[M] / dt = k_p [M] (R_i / 2k_t)^½

where k_t and k_p are the kinetic rate constants for polymerization and termination and R_i is the photochemical initiation rate which is given by:

R_i = 2 ε Φ [PI] I(z)

Φ is the quantum yield of the photoinitiator which is defined as

           No. of initiators activating photochemical reactions
Φ =   ----------------------------------------------------------------------
         No. of quanta absorbed by the reactive mixture

 

Inserting Lambert-Beer's equation into the equation for R_i yields

R_i = 2 ε Φ [PI] I₀ 10^{-ε z [PI]}

Knowledge of the quantum yield Φ is crucial for the understanding of the photochemical process. We can distinguish between three cases:

• Φ < 1: Other chemical reactions compete with photopolymerization process
• Φ = 1: Every photon absorbed initiates a photochmical reaction
• Φ > 1: Photochemical reactions cause a chain reaction of polymerization

References

1. J. Lee, R.K. Prud'homme, I.A. Aksay, J. Mater. Res., Vol. 16, No 12 (2001).