Theory Of Diffusion-controlled Reactions Research Articles

Effect of an Electric Field on Electron Attachment to SF6 in Liquid Ethane and Propane

Abstract The effect of an external electric field, E, on the electron attachment rate constant, ke, of SF6 was studied by a pulsed-conductivity technique in liquid ethane and propane at temperatures ranging from 133-176 K and 156-216 K, respectively. At constant temperature, ke was independent of E at fields less than Ec , the critical field above which the mobility becomes field-dependent, but at E> Ec, ke increased proportionally with De, the diffusion coefficient of the electron. Application of diffusion-controlled reaction theory to the ke - De dependence yielded an effective encounter radius of 14.5 Å for the e--SF6 reaction pair in both liquids. This encounter radius is discussed in terms of the electron-SF6 interaction energy and models of electron transport and attachment in low-mobility liquids.

The kinetic boundary layer for the Fokker-Planck equation with absorbing boundary

The Fokker-Planck equation for the distribution of position and velocity of a Brownian particle is a particularly simple linear transport equation. Its normal solutions and an apparently complete set of stationary boundary layer solutions can be determined explicitly. By a numerical algorithm we select linear combinations of them that approximately fulfill the boundary condition for a completely absorbing plane wall, and that approach a linearly increasing position space density far from the wall. Various aspects of these approximate solutions are discussed. In particular we find that the extrapolated asymptotic density reaches zero at a distance xM beyond the wall. We find xM=1.46 in units of the velocity persistence length of the Brownian particle. This study was motivated by certain problems in the theory of diffusion-controlled reactions, and the results might be used to test approximate theories employed in that field.

Electron transfer from 2-methyltetrahydrofuran radical to tetracyanoethylene at low temperatures

The formation mechanism of tetracyanoethylene(TCNE) radical anions in irradiated 2-methyltetrahydrofuran(2-MTHF) solutions of TCNE has been studied at low temperatures using matrix isolation and pulse radiolysis techniques. TCNE radical anions are produced not only by electron attachment but also by electron transfer from 2-MTHF radicals to TCNE molecules. The latter process (electron transfer) was found to proceed much more slowly than the former process. On the basis of the diffusion controlled reaction theory and free volume theory, the bimolecular rate constant of the electron transfer reaction can be expressed as follows k=6.7 × 10 9T 1 2 exp[-450/(T-75)]dm 3 mol −1s −1 . Electron transfer from 2-MTHF radicals to pyrene, 1,3-dinotrobenzene, and 1,4-dicyanobenzene has not been observed.

The binding of a neutral aromatic molecule to a negatively-charged lipid membrane

The kinetics of the binding of the fluorescence indicator N-phenyl naphthylamine to bilayer vesicles of C12-methyl-phosphatidic acid have been investigated by means of the temperature-jump relaxation technique utilizing fluorescence light detection. Single-exponential relaxation curves were observed, with time constants in the range 0.2-3 ms. The concentration dependence of the relaxation time yielded an apparent association rate constant (expressed in terms of monomeric phospholipid) of k(on) = 5 x 10(6) M(-1) s(-1) in aqueous solution at 25 degrees . The activation energy and viscosity dependence associated with the binding rate show that this process is actually diffusion-controlled. The theory of diffusion-controlled reactions then allows a determination of the average size of the bilayer vesicles and of the true rate constant for the association of the indicator molecules with the vesicles. Assuming spherical geometry for the vesicles, the values are: r(ves) = 190 A, which corresponds to 20000 lipid molecules per vesicle and k'(on) = 1 x 10(11) M(-1) s(-1) (25 degrees). The correctness of this size-determination was confirmed semi-quantitatively by electron microscopy. Since in fact a distribution of vesicle sizes must be present, a discussion is included of the relaxation function which the system is expected to take in the general case. Biological implications of diffusion control for the transport of non-polar substances and for lipid mixing are indicated.

Kinetic Studies of Oxygen Chemisorption on the Rutile Single-crystal Surface by Means of Electrical Conductivity

Abstract The reaction of oxygen with the surface of a rutile single crystal was studied in the temperature range from 212 to 362°C and in the pressure range from 10−1 to 102 Torr. The process of the surface oxidation was examined by monitoring the electrical conductance change due to oxygen chemisorption. Two types of chemisorption kinetics were found for the rutile which had been reduced to different extents in vacuo before the introduction of oxygen. For the low-reduced rutile, the kinetics obeyed the parabolic rate law; this was interpreted by the diffusion-controlled reaction theory. On the other hand, it was found for the high-reduced rutile that the kinetics obeyed the Elovich equation; this could be explained by the boundary layer theory. The apparent activation energy for the former was 14.2 kcal/mol. For the latter, it was 4 kcal/mol and increased with an increase in the chemisorbed surface-charge density. In addition, the rate of oxygen chemisorption in the latter case was proportional to the pressure at a constant density of the chemisorbed surface charge.

The direct observation of transient effects in diffusion-controlled fluorescence quenching

Direct observation of the influence of so-called transient terms in the theory of diffusion-controlled reactions is reported for the fluorescence decay of a quenched system. It is found that the decay law of the quenched system accurately follows exp (- At - Br 1 2 ) as required by simple continuum theory. Values for the two adjustable parameters, R′ and D, the encounter distance and the sum of the diffusion coefficients are obtained and compared with values obtained from steady-state measurements.

Theory of kinetic salt effects in diffusion-controlled reactions. Part 2.—One reactant ion with no ion atmosphere

From the theory of diffusion-controlled reactions, kinetic salt effects have been computed for the case where one ionic reactant has no ion atmosphere. When the diffusion coefficients of the reactants are equal, the predicted effects are almost exactly half those calculated for the fully-relaxed case. The ratio of the diffusion coefficients is then an important parameter, causing the calculated salt effect to increase markedly if the newly-generated species becomes more, and to decrease if less, mobile than the other ion present initially.