James K. Baird

A solution of the Debye–Smoluchowski equation for the rate of reaction of ions in dilute solution

Reactions of isolated ion pairs in solution have been modelled using the Debye–Smoluchowski equation for diffusion and conduction. An activation step was incorporated using a partially reflecting boundary condition. The method of matched expansions and the Abelian theorem of Laplace transforms was used to give an approximate solution of the Debye–Smoluchowski equation. Numerical integrations based on the finite‐difference method confirmed these approximate analytic formulas.

Uniform theory of electron kinetics in nonpolar liquids

Application of the Smoluchowski–Debye equation results in a uniform treatment of the kinetics of either of the bulk reactions e− +M+→M or e−+A→A−, and the corresponding photoionization reaction, either M⇄hνM++e− or A−⇄hνA+e−. For simplicity of terminology, the bulk reactions are referred to as class I and the photoionizations as class II. Included in the theory are the following effects: (1) solvent screening of the interaction potential between e− and either of the acceptors M+ or A, (2) spatial variation of electron transport coefficients (mobility and diffusion tensor) due to the internal electric field associated with the interaction potential, (3) electron tunneling, and (4) chemical activation processes. By use of Green’s function methods, we arrive at the result n1(r)exp[−ψ (r)]=NsP (r), where n1(r) is the pair density at a relative separation r in a reaction of class I, and P (r) is the escape probability for a pair initially at a separation r in the corresponding reaction of class II. The quantit...

On departures from the Stern–Volmer law for fluorescence quenching in liquids

Fluorescence quenching with solutions of fluorophores and quenchers in inert solvents in considered.(AIP)

Semiempirical formula for the electric field dependence of geminate ion recombination fluorescence

A semiempirical formula is derived which governs the electric field dependence of the fluorescence produced upon recombination of geminate ions. The formula is applied to some new data on the fluorescence which follows the ultraviolet irradiation of solutions of N,N,N′,N′‐tetramethylparaphenylenediamine (TMPD) in tetramethylsilane and 2,2‐dimethylbutane. From the two‐parameter‐least‐squares lines which result from the application of the formula, we determine a number of derived quantities. Among these are Φip the quantum yield for photoionization of TMPD, and P(0,0) the probability of dissociation of the electron–ion pair produced by the photoionization. The values of P(0,0) are found to be nearly equal to the ratio Gfi/(Ggi+Gfi) where Gfi and Ggi are the free ion and geminate ion yields, respectively, obtained in 60Co γ irradiations of the pure solvents. The product of Φip and P(0,0) is Φe0, the free electron quantum yield. The values of Φe0 obtained from the fluorescence measurements are compared with t...

Comment on ’’Probability of escaping neutralization when the mobility is field dependent’’

The field dependence of the electron mobility in dielectric liquids is discussed.(AIP)The field dependence of the electron mobility in dielectric liquids is discussed.(AIP)

On the theory of the Stern–Volmer coefficient for dense fluids

In phenomenological theories of fluorescence quenching in dense fluids, one assumes that the Stern–Volmer coefficient K has a dependence upon a limited number of parameters. Denoting by K0 the value of K when the quencher molecules are infinitely dilute, our starting point is that K0 = K0(D,τ,k,R), where D is the sum of the diffusion coefficients of the fluorophore and quencher, k is a rate constant, τ is the unquenched lifetime of the fluorophore, and R is the range of interaction between fluorophore and quencher. We then find by dimensional analysis that K0 can be simplified to K0 = DRτ⋅F (k/DR,Dτ/R2), where F(x,y) is a function of just two variables. Furthermore, if S is a function specifying the region of configuration space in which fluorophores and quenchers interact [G. Wilemski and M. Fixman, J. Chem. Phys. 58, 4009 (1973)], we find that K0 depends only upon an average of S over the steady state fluorophore–quencher pair correlation function. Under ordinary conditions, k/DR and Dτ/R2 will be large...

Parity and differentiability restrictions on the electric field dependence of the mobility of charged particles in gases and liquids

The electric field dependences of mobility of excess electrons in liquid neopentane, given by Mozumder and Carmichael2 is examined from the point of view of parity invarance and differentiability.(AIP)

Rate of electron capture by O2 calculated from geminate ion recombination fluorescence data

Bullot, Cordier and Gauthier1 have suggested that the observed departure in their experiments on aerated solutions, from the onsage theory was due to electron capture by dissolved oxygen. It is shown that their observations are in accord with Tachiya’s form of the Mozumder limiting law for geminate ion scavenging in the presence of an electric field. The rate constant for electron capture by oxygen are derived. (AIP)