Photochemistry: UV curing

[Danijel Gorupec]

UV curable dyes/paints are, for example, used in high-speed offset printing. UV light 'dries' the dye in a fraction of a second... My understanding is that UV light polymerizes certain component of the dye turning it from liquid to solid.

 

But for years one thing I cannot understand... In this particular offset printing example, there is a claim that UV curing speed is proportional to about fourth power of the UV light intensity. As a result, parabolic reflectors are made to concentrate UV light from lamps into a few-millimeters thin line across the web (instead of the light being spread over a larger surface).

 

How can UV curing speed depend on fourth power of light density? For me, it is only intuitive that UV curing speed is directly proportional to the light density (not to the fourth power). Can anyone here explain (provide hints on microscopic level) how this fourth-power dependence came to be?

 

(Please be gentle with your wording because I dedicated my life to learn about women, not chemistry.)

[DrP]

My first guess (I haven't looked anything up) - is that not all incident UV beams cause a cross linking action to take place... Say, for argument sake, that 25% of the incident UV radiation activates a cross linking reaction... then it would take 4 times the UV light to double the amount of cross linking taking place.

 

It is probably more complicated that this, but these are my first thoughts.

[swansont]

A couple of possibilities I can think of -

 

Nonlinear processes depend on a higher exponent of intensity, often I^2. This may be a nonlinear effect. You might need two reactions to occur near each other in a short period of time.

 

This is a process in a material with some thickness, and the intensity drops off exponentially with penetration distance (Beer's law). So the additional power may be so that there is sufficient intensity on the far side of the material. The fourth power claim might just be an approximation for this exponential behavior, possibly combined with a nonlinear effect.

[Danijel Gorupec]

These are good possible explanations, Swansont, thank you. I particularly like "two reactions to occur near each other in a short period of time" because I was not thinking in this direction.

 

I can also confirm that the fourth-power law is most likely an empirical approximation, at least according to wording used in documents where it was mentioned.