I was quite happy last week to post a news item about a colorless transparent luminescent solar concentrator developed at Michigan State University (East Lansing, MI), as I have had a long-term fascination with luminescent solar concentrators. So why am I so fascinated by such devices?
One reason is that at first glance they seem to violate the second law of thermodynamics, which says that the entropy of any isolated system never decreases. In the field of optics, the second law sorta translates in a hand-waving way to the fact that the étendue (solid angle multiplied by beam cross-section) of a light beam can never decrease: for example, one can't focus a low-quality laser beam to a spot as small as that that can be produced by a high-quality laser beam (given the same lens used for both, with lens pupil optimally filled).
As for solar concentrators: the sun has a viewing angle of 0.27°; with the sun as the object, the theoretical maximum concentration ratio for a conventional solar concentrator with optimal optics turns out to be about 46,000. As the viewing angle of the light source gets larger, the theoretical maximum concentration ratio decreases, until with a 180° viewing angle (in other words, a uniformly cloudy day), the theoretical maximum concentration ratio is only 1.
Demoted from law to allegation?
But a luminescent solar concentrator is different. It is a thin, flat transparent sheet doped with luminescent material; when light strikes the sheet, part of the light is absorbed and re-emitted at a longer wavelength. Most of the light is totally internally reflected to the edge of the sheet, where photovoltaic cells can be placed to collect the light.
Because this process can occur for a wide angular range of incoming light, a luminescent solar concentrator can theoretically reach significant concentration ratios even on uniformly cloudy days (that 180° viewing angle).
So has the second law of thermodynamics been violated (for the first time ever!)? To be specific, could we take a luminescent solar concentrator and concentrate light from a uniform bath of radiation, producing a reduction in entropy?
Surely not. For a proper high-entropy experiment, the "uniform bath of radiation" would have to be all-surrounding blackbody radiation, and the luminescent solar concentrator would have to be also at the blackbody temperature. What happens then? For one, everything will (or should!) come to thermodynamic equilibrium, emitting blackbody spectra, which are certainly not as well-fitted as sunlight to the absorption spectrum of a luminescent dopant. Not to mention the fact that a surrounding blackbody spectrum containing significant visible light would attain a blackbody temperature high enough to destroy the concentrator.
More fundamentally, whatever physical effects come into play here will balance; the second law of thermodynamics will still hold.
Right?
(If you have something to say about this, please email me at [email protected])
