Theory of concentration quenching of fluorescence polarization in two-dimensional solutions

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Abstract
The extensions of the theories of Förster, Ore and Knox of concentration quenching of fluorescence polarization presented in [6] are applied to two-dimensional solutions. The discussion is limited to two types of solutions in both of which the molecules lie in a single plane. In the first type the dipolar orientations are randomly distributed, while in the second they are restricted to a fixed angle with respect to the solution normal, but otherwise random. For both types of solution the theoretical problem is reduced to a calculation of the probability P that the fluorescent radiation is emitted by an initially excited molecule. The connection between P and the experimentally obtained degree of polarization is discussed in detail for the different types of solution and for different experimental conditions. The theoretical results are compared with three different sets of experimental data. The predictions of the two-dimensional forms of Knox's and Jablonski's cluster theories are highly consistent, and both agree quite well with the experimental data. The predictions of the two-dimensional form of Ore's theory give somewhat poorer agreement, even when the angular factors are properly taken into account.