On the theory of the Sternndash;Volmer coefficient for dense fluids

摘要

In phenomenological theories of fluorescence quenching in dense fluids, one assumes that the Sternndash;Volmer coefficientKhas a dependence upon a limited number of parameters. Denoting byK0the value ofKwhen the quencher molecules are infinitely dilute, our starting point is thatK0=K0(D,tgr;,k,R), whereDis the sum of the diffusion coefficients of the fluorophore and quencher,kis a rate constant, tgr; is the unquenched lifetime of the fluorophore, andRis the range of interaction between fluorophore and quencher. We then find by dimensional analysis thatK0can be simplified toK0=DRtgr;sdot;F(k/DR,Dtgr;/R2), whereF(x,y) is a function of just two variables. Furthermore, ifSis a function specifying the region of configuration space in which fluorophores and quenchers interact lsqb;G. Wilemski and M. Fixman, J. Chem. Phys. 58, 4009 (1973)rsqb;, we find thatK0depends only upon an average ofSover the steady state fluorophorendash;quencher pair correlation function. Under ordinary conditions,k/DRandDtgr;/R2will be large. We note that in this limitK0approaches the Smoluchowski value 4pgr;DRtgr;. Correction terms to the Smoluchowski value are explicitly computed, however, whenSis a delta function or a step function. Inasmuch as both forms lead to corrections tending in the same direction, it may be difficult to distinguish them by experiment. Thus, we conclude that future theoretical work should focus on a more realistic form forS.