In an OLED, holes and electrons combine to form an excited state with a triplet:singlet ratio of 3:1. Can someone explain to me (in a way a chemist, not a mathematician or physicist, can understand!) why this is the case? The only explanation I've found just says it is based on statistical considerations, but that doesn't really explain much. I was looking for a more clear explanation. Thanks.
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physiscists might frown at the explanation in the link below but it is definitely simple :
http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Electronic_Spectroscopy/Electronic_Spectroscopy%3A_Theory
(Electron Spin section)
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so far so good for the difference between singlet and triplet, it comes from the total spin of the pair
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now for the 3:1 ratio, it is a little more complicated since you have to count the multiplicities of the S=0 and S=1 subspaces (you already know they span a 4 dimensional space)
the link below has a nice illustration :
http://www.nature.com/nphys/journal/v7/n4/fig_tab/nphys1883_F1.html
and the link below can be used as a legend for this illustration
http://www.christianhill.co.uk/teaching/tutorials/qm2/spin/singlet-and-triplet-states
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hope this helps a little but spin systems are always a little hard to "explain" ... however, they're fun to play with :
https://www.pinterest.com/pin/123637952243468206/
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unfortunately statistical consideration is the easiest. Just imagine completely random system you have only 4 possible exciton states. one with S=0 (singlet) 3 with S=1(triplet) so u get 1:3 ratio
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