Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

154 EXPERIMENTAL METHODS FOR FAST REACTIONSallowing k2 to be determined from the variation of $/I$~ with cB, provided thatT~ is known. This equation is associated with the names of Stern and Volmer.In one important respect, this derivation is not quite complete. Just as there aretwo ways in which the encounter complex A*-B can be formed, so there are twoways in which it can react. Because the average reaction time is comparable to thetime taken for the steady state to be set up, only a certain fraction w of the excitedmolecules will obey the Stern-Volmer equation. The remaining (1- w) reacts immediatelyafter excitation and so does not contribute to the relative fluorescenceyield. Put another way, if a molecule of A has a B within the “reaction distance”when it is excited, it may react “immediately” and so will not fluoresce. As may bepredicted, the effect of this transient excess reactivity is more important the harderit is for A* and B to diffuse apart, i.e., the greater the viscosity of the medium, andthe more efficient is the reaction. Thus 4/40 = w/(l +kzcB~,), and the stationaryrate coefficient may be evaluated if w is known. The latter can be calculated fromthe expression w = exp( - V,C,), where VD is a characteristic reaction volume surroundingA* and w represents the probability that no B molecule will be foundinside this space. V,, is a fun~tion’~ of the diffusion coefficients of A and B, the meanlifetime of A* in the absence of B(T,) and the effective encounter distance. In mostcases approximate values of w can be calculated and then, by successive approximations,the stationary rate coefficients and encounter distances which best fit thedata are computed.It sometimes happens that one of the products of the reaction of A* with B is stillexcited and can itself fluoresce. Such a situation arises in “fluorescence transformation”and, if the spectrum of the fluorescing product is sufficiently different fromthat of A*, some very useful additional information about the main reaction maybe gained. The quantum yield for the species formed in the fluorescence transformation(B*) is given by(neglecting the factor w). Using the fact that-+’/c$b+Q/+o = 1, plots of the respectiveratios of fluorescence intensities against concentration of B should be of theform shown in Fig. 18. Z’/Zh tends to unity as the concentration of B is increased,while Z/Zo tends to zero. Should an important side reaction not have been consideredin the reaction scheme, the shape of the relative intensity us. concentration plotswill show this.Before discussing reactions that have been studied fluorimetrically it should bepointed out that the excited form A* may be expected to have very different reactivitypatterns from the ground state form of A. Such differences arise because of