Additivity law of anisotropy

When the sample contains a mixture of fluorophores, each has its own emission 

From a practical point of view, we measure the components I and I , which are now the sum of all individual components  

The important consequence of this is that the total emission anisotropy is the weighted sum of the individual anisotropies4  

This relationship applies to both steady-state and time-resolved experiments. In the latter case, if each species i exhibits a single exponential fluorescence decay with lifetime tj, the fractional intensity of this species at time t is 

This equation shows that, at time t, each anisotropy term is weighted by a factor that depends on the relative contribution to the total fluorescence intensity at that time. This is surprising at first sight, but simply results from the definition used for the emission anisotropy, which is based on the practical measurement of the overall ly and I components. A noticeable consequence is that the emission anisotropy of a mixture may not decay monotonously, depending of the values of r, and Ti for each species. Thus, r(t) should be viewed as an apparent or a technical anisotropy because it does not reflect the overall orientation relaxation after photoselection, as in the case of a single population of fluorophores. 

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