A Note on the Theory of Diffusion Controlled Reactions with Application to the Quenching of Fluorescence

Abstract

The principles of Smoluchowski's collision theory of reactions in solution are outlined. This theory is applicable to reactions which occur immediately on the collision of two reactant particles; that is, diffusion controlled reactions. The rate of such reactions depends on the collision frequency of reactants. In this paper an expression for the collision frequency is derived as a function of time when initially there is a Boltzmann distribution of particles around any particular reactant molecule. Both the Brownian motion of and the forces between reactant molecules are considered in the calculation. The general results are applied to the theory of quenching of fluorescence. It is shown that the quenching constant, k_Q, defined by $$\left(\frac{I_0}{I}\text{−1}\right){\mathrm{⧸n}}_Q{\mathrm{=k}}_Q,$$ (where I₀ is the intensity of fluorescence in the absence of quencher and I the intensity in the presence of quencher of concentration n_Q) can be expressed as a sum of two terms, one proportional to the reciprocal of the viscosity of the solvent and the other to the reciprocal of the square root of the viscosity.