Regardless of the absorption, surface area, wavelength, absolute potential, simply considering the lifetime of exciton of semiconductor, does this give it better dye degradation, water splitting efficiencies, or a better solar cell?
Do I conclude that indirect transition eventually dissipate exciton energy through heat (phonon) or radical species (suppose nanoparticles in solvent/oxygen) Different from the direct transition results in fluorescence?
In my opinion, the 1st question : the photocatalytic activity is not only affected by band gap but also the concentration of catalyst (doped or compounded) and of dye (water) or other factors. So there is still a limitation.
the 2nd question : I think it's dependent on the data you have collected from the experiment supporting your conclusion.
In addition to the factors Rudy has mentioned in his answer,in photodegradation of dyes by photocatalysts type of dye is also very important, . Because some dyes can absorb to catalyst and reduce its activity. So I think we can`t guess the ability of water splitting and its convenience in solar cells from dye degradation.
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