The steady-state emission from this sample can be characterized by its polarization, p, or anisotropy, r.
p = (IVV - IVH)/(IVV+IVH)
r = (IVV - IVH)/(IVV+2IVH)
For a random array of isolated, immobile chromophores, the expected values of p and r are 1/2 and 2/5, respectively. These values are greater than zero because the excited chromophores are not randomly oriented. The values are less than 1 because not all of the excited chromophores are precisely aligned with the polarization of the exciting beam. (Recall that the probability for excitation is proportional to the squared cosine of the angle between these two vectors.) Therefore the emission is partially depolarized for the system of isolated, immobile chromophores.
Additional depolarization can occur if the chromophores are mobile, or if they are not isolated.
The influence of mobility depends on the relationship between the lifetime of the excited state and the time required for rotational diffusion of the chromophore. If rotational diffusion occurs on a much faster time scale than the fluorescence lifetime, complete depolarization of the fluorescence is expected. The other extreme (rotational diffusion much slower than the fluorescence lifetime) gives the result expected for an immobile system.
Time-resolved fluorescence depolarization measurements can yield the rotational autocorrelation function for the chromophore, RACF(t). If the excitation is produced with a single short pulse, of duration much less than the fluorescence lifetime, the time dependence of the anisotropy of the emission is
r(t) = (IVV(t) - IVH(t))/(IVV(t)+2IVH(t))
and the rotational autocorrelation function of the chromophore is obtained as
r(t) = r0RACF(t)
where we expect r0 = 2/5, which is the result for the random sample in absence of any mobility. The rotational autocorrelation function is related to the motion of the chromophore by
RACF(t) = [3 (avcos 2 alpha ) - 1]/2
where alpha is the angle between the transition moments at times 0 and t, and "avcos 2" denotes the average of the cosine.
Another mechanism can produce depolarization even in the absence of any rotational diffusion of the chromophores. If the excitation can migrate from one chromophore to another before emission occurs, the chromophore responsible for the initial excitation may have a different orientation from the chromophore responsible for the final emission. Non-radiative singlet energy transfer is an example of a mechanism by which energy migration can occur.
Return to the index