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I'm working on a research project involving absorption spectra of particulates in solution. I was curious if someone could clarify or direct me to a resource that explains broadening mechanisms specifically for absorption spectra. For example, the oft-cited Heisenberg and Doppler broadening effects both make sense to me in the context of emission spectra, but I don't see the mechanism by which they would be influential in absorption spectra. But I also can't find a source to verify this, since emission and absorption spectra are often lumped together in the familiar statement "the absorption spectrum is simply the inverse of the emission spectrum"

Thanks very much for any advice.

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I can do absorption peak broadening in the context of the transport equation, but you're coming from an entirely different perspective. I think we would need more specification as to whether you just need the mathematics for the absorption peak broadening itself or something about to the attenuation related to it. To start off with, is this broadening due to a change in the temperature, or do I just not understand the context at all? –  AlanSE Jun 8 '11 at 14:01
    
I apologize, the question was ambiguous. I'm more interested in the qualitative reasons why absorption peaks are broadened. If you could direct me to a resource on the math, I'd appreciate it, but there's no need to waste your effort writing any of the math up for me. The spectroscopy is being done at a fixed low temperature, and so Doppler effects are likely less important than others. Thanks! –  wil3 Jun 10 '11 at 14:24
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2 Answers 2

The reason the statement is made

"the absorption spectrum is simply the inverse of the emission spectrum"

is because broadening mechanisms depend on kinematics, and kinematics is reversible.

By this I mean that if an emitting atom because of its thermal kinetic energy emits a photon of energy which, instead of E, is E+delta(E), where the extra energy comes because of its motion, the same atom instead of absorbing E will absorb E+delta(E) again because of its motion when the photon hits it. Statistically the broadening curves will be the same.

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This makes sense to me thermodynamically. But I know that certain photosynthetic spectra fall prey to things like the Stokes shift, in which thermal energy is lost uniformly between excitation and emission, and so the emission spectrum is redshifted relative to the absorption spectrum. It seems to me like there could be non-uniform phenomena like this effect, which is why I'm curious whether the inverse rule is true in all cases. thanks very much for your answer –  wil3 Jun 10 '11 at 14:29
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It should be emphasized that you are measuring absorption spectra in solutions. This means that the spectral broadening is dominated by interactions with solvent molecules and lines will be much broader compared to gas-phase spectra.

It is nearly impossible to calculate time-dependent interactions of absorbing species with hundreds of solvent molecules but there are some empirical rules. For example, polar solvents (methanol) will perturb the electronic state of a molecule stronger compared to unpolar solvents (hexane), so, generally, linewidth in hexane is smaller. Also, this interaction is generally stronger for the excited state (because the electron cloud "expands") and thus absorption bands will be shifted in wavelength compared to gas-phase spectra - normally, to longer wavelength.

You can find these rules in any old textbook on UV-Vis spectroscopy. I say old to exclude books on high-resolution gas-phase spectroscopy which is the major topic of the last 30 years.

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This got me thinking- I'm dealing primarily with an RET between chromophores in a biological system, and so I've been assuming that effects due to motion in liquid are second order compared to perturbations and broadening effects due to the actual coupling and energy distribution within the system. Is this a faulty assumption? I'd be interested in knowing if there's a handy rule--of-thumb for the magnitude of the effects of various broadening mechanisms. thank you! –  wil3 Jun 10 '11 at 14:32
    
@wil3: It is not just the motion of the liquid (which is nevertheless very fast, in the picosecond range). There is (nearly) no order and every molecule is perturbed in a different way. This is called inhomegenous broadening - every molecule absorbs at slightly different wavelength. You get linewidth of 10-20 nanometers due to this broadening. Only very fast energy transfer (10 femtoseconds?) can lead to comparable broadening. –  gigacyan Jun 10 '11 at 18:22
    
I agree that the broadening is inhomogenous because we are observing Gaussian peaks. Could you recommend a specific text, article, or site where I could find out more about these solvent interactions? Most of the papers I've read attribute the Gaussian line shape to dipole coupling in exciton transfer systems, and so I'd like to examine these other, faster interactions you describe. Thanks very much! –  wil3 Jun 12 '11 at 18:58
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