Some Isoperimetric Inequalities in Electrochemistry and Hele Shaw Flows

Isoperimetric inequalities are applied to a moving-boundaryproblem for doubly-connected domains. This problem occurs forexample in electrochemistry, in which case the domains in questionare the electrolyte of an electrolytic cell. The two electrodessurrounding the electrolyte are assumed to grow or dissolve,at different rates in general, by electrochemical reaction.We obtain optimal estimates showing, for example, that the leastchange in volume of each electrode always occurs in sphericalsymmetry.     

Influence of Ions on Aqueous Acid–Base Reactions

We study the effects of bromide salts on the rate and mechanism of the aqueous proton/deuteron‐transfer reaction between the photoacid 8‐hydroxy‐1,3,6‐pyrenetrisulfonic acid (HPTS) and the base acetate. The proton/deuteron release is triggered by exciting HPTS with 400 nm femtosecond laser pulses. Probing the electronic and vibrational resonances of the photoacid, the conjugate photobase, the hydrated proton/deuteron and the accepting base with femtosecond visible and mid‐infrared pulses monitors the proton transfer. Two reaction channels are identified: 1) direct long‐range proton transfer over hydrogen‐bonded water bridges that connect the acid and base and 2) acid dissociation to produce fully solvated protons followed by proton scavenging from solution by acetate. We observe that the addition of salt affects the long‐range reaction pathway, and reduces both the rate at which protons are released to solution by HPTS and the rate at which solvated protons are scavenged from solution by acetate. We study the dependence of these effects on the nature and concentration of the dissolved salt.     

Characterization of ultrashort electron pulses by electron-laser pulse cross correlation

An all-optical method to determine the duration of ultrashort electron pulses is presented. This technique makes use of the laser pulse ponderomotive potential to effectively sample the temporal envelope of the electron pulse by sequentially scattering different sections of the pulse out of the main beam. Using laser pulse parameters that are easily accessible with modern tabletop chirped-pulse amplification laser sources, it is possible to measure the instantaneous duration of electron pulses shorter than 100 fs in the energy range that is most useful for electron diffraction studies, 10-300 keV.     

Long-range proton transfer in aqueous Acid-base reactions

We study the mechanism of proton transfer (PT) in the aqueous acid-base reaction between the photoacid 8-hydroxy-1,3,6-pyrenetrisulfonic acid (HPTS) and acetate by probing the vibrational resonances of HPTS, acetate, and the hydrated proton with femtosecond mid-infrared laser pulses. We find that PT takes place in a distribution of hydrogen-bound reaction complexes that differ in the number of water molecules separating the acid and the base. The number of intervening water molecules ranges from 0 to 5, which, together with a strongly distance-dependent PT rate, explains the observed highly nonexponential reaction kinetics. The kinetic isotope effect for the reaction is determined to be 1.5, indicating that tunneling does not play a significant role in the transfer of the proton. Rather, the transfer mechanism is best described in terms of the adiabatic PT picture as it has been formulated by Hynes and co-workers [Staib, A.; Borgis, D.; Hynes, J. T. J. Chem. Phys. 1995, 102, 2487. Ando, K.; Hynes, J. T. J. Phys. Chem. B 1997, 101, 10464.], where solvent fluctuations play an essential role in forming the correct hydrogen-bond configuration and solvent polarization to facilitate PT.     

On the role of water in intermolecular proton-transfer reactions

We study the mechanism of proton transfer (PT) between the photoacid (8-hydroxy-1,3,6-pyrenetrisulfonic acid (HPTS)) and the base acetate in aqueous solution using femtosecond vibrational spectroscopy. By probing the vibrational resonances of the photoacid, the accepting base, and the hydrated proton we find that intermolecular PT in this model system involves the transfer of the proton across several water molecules linking the donor-acceptor pair by hydrogen bonds (H-bonds). We find that at high base concentration the rate of PT is not determined by the mutual diffusion of acid and base but rather by the rate of Grotthuss-like conduction of the proton between molecules. This long-range PT requires an activated solvent configuration to facilitate the charge transfer.