Decay Associated Spectra

When one measures an emission spectrum of a compound or a protein in a spectrofluorometer, one is measuring the average behavior of the system. If half the sample is emitting at around 350 nm, and the other half around 360 nm, one will probably see a broad peak around 355 nm. Steady state measurements are easy and informative. However, using a lifetime instrument with a time-correlated single photon counting setup or related technique, one can measure microheterogeneity in one's system.

When one fits an emission decay to a series of exponentials, it is with the idea that each individual exponential represents a single state or process. The system is then described by the sum of all these discrete states (this isn't necessarily true: multi-exponential functions can also fit relaxation processes - processes that evolved during the lifetime of the excited state. Intead of having a finite number of discrete states, one may have a continuous distribution of them. See solvation dynamics). If this model is true, then each of the discrete states should have its own emission spectrum. If you could separate physically the 350 nm spectrum from the 360 nm spectrum, then one could map out the spectral features of each state.

If one collects the emission kinetics of a system at multiple emission wavelengths, this data can be combined to pull out component spectra. An exponential function looks as follows:

Intensity(time) = a * exp (- time/lifetime)

Where a is some pre-exponential factor and the lifetime is the time after which the intensity is 1/e of the intensity at time zero. This is a single exponential. If the decay is multi-exponential, then it is just a sum of terms with the above form, each with its own lifetime and pre-exponential factor. The normalized expression should give a sum of a_i's = one. Doing this analysis at multiple emission wavelengths, one can then construct a table of a's and lifetimes for each wavelength. If lifetime is independent of wavelength (i.e. each discrete state has a distinct lifetime), then the only thing to change with wavelength is the a_i. The technique for fitting a large collection of data to a set of parameters is known as global analysis. In this analysis, the lifetimes would be linked so that they remain constant as a function of emission wavelength.

Now, one knows the total spectral intensity at a given wavelength from the steady state measurements, and the relative percentage of that intensity belonging to each decay component from the lifetime measurements. Plotting each component as a fraction of the total intensity gives the emission spectrum of that microstate. This is a decay-associated spectrum. A spectrum that represents the emission of a state with a particular decay lifetime.

See also:
time resolved emission spectra