687 research outputs found
A Dynamical Theory of Electron Transfer: Crossover from Weak to Strong Electronic Coupling
We present a real-time path integral theory for the rate of electron transfer
reactions. Using graph theoretic techniques, the dynamics is expressed in a
formally exact way as a set of integral equations. With a simple approximation
for the self-energy, the rate can then be computed analytically to all orders
in the electronic coupling matrix element. We present results for the crossover
region between weak (nonadiabatic) and strong (adiabatic) electronic coupling
and show that this theory provides a rigorous justification for the salient
features of the rate expected within conventional electron transfer theory.
Nonetheless, we find distinct characteristics of quantum behavior even in the
strongly adiabatic limit where classical rate theory is conventionally thought
to be applicable. To our knowledge, this theory is the first systematic
dynamical treatment of the full crossover region.Comment: 11 pages, LaTeX, 8 Postscript figures to be published in J. Chem.
Phy
Distribution of Interacting Ionic Particles in Disordered Media
Equilibrium distribution of interacting ionic particles in a charged
disordered background is studied using the nonlinear Poisson-Boltzmann
equation. For an arbitrarily given realization of the disorder, an exact
solution of the equation is obtained in one dimension using a mapping of the
nonlinear Poisson-Boltzmann equation to a self-consistent Schrodinger equation.
The resulting density profile shows that the ions are delocalized, despite what
the equivalent Schrodinger formulation in one dimension would suggest. It is
shown that the ions are not distributed so as to locally neutralize the
background, presumably due to their mutual interactions
Direct optical observations of surface thermal motions at sub-shot noise levels
We measure spectral properties of surface thermal fluctuations of liquids,
solids, complex fluids and biological matter using light scattering methods.
The random thermal fluctuations are delineated from random noise at sub-shot
noise levels. The principle behind this extraction, which is quite general and
is not limited to surface measurements, is explained. An optical lever is used
to measure the spectrum of fluctuations in the inclinations of surfaces down to
at W optical intensity, corresponding
to in the vertical displacement, in the
frequency range . The dynamical evolution of the
surface properties is also investigated. The measurement requires only a short
amount of time and is essentially passive, so that it can be applied to a wide
variety of surfaces.Comment: 5pp, 5 figure
Spectral properties of thermal fluctuations on simple liquid surfaces below shot noise levels
We study the spectral properties of thermal fluctuations on simple liquid
surfaces, sometimes called ripplons. Analytical properties of the spectral
function are investigated and are shown to be composed of regions with simple
analytic behavior with respect to the frequency or the wave number. The derived
expressions are compared to spectral measurements performed orders of magnitude
below shot noise levels, which is achieved using a novel noise reduction
method. The agreement between the theory of thermal surface fluctuations and
the experiment is found to be excellent.Comment: 9 pages, 5 figure
Large Scale Structures a Gradient Lines: the case of the Trkal Flow
A specific asymptotic expansion at large Reynolds numbers (R)for the long
wavelength perturbation of a non stationary anisotropic helical solution of the
force less Navier-Stokes equations (Trkal solutions) is effectively constructed
of the Beltrami type terms through multi scaling analysis. The asymptotic
procedure is proved to be valid for one specific value of the scaling
parameter,namely for the square root of the Reynolds number (R).As a result
large scale structures arise as gradient lines of the energy determined by the
initial conditions for two anisotropic Beltrami flows of the same helicity.The
same intitial conditions determine the boundaries of the vortex-velocity tubes,
containing both streamlines and vortex linesComment: 27 pages, 2 figure
Anomalous temperature dependence of surface tension and capillary waves at liquid gallium
The temperature dependence of surface tension \gamma(T) at liquid gallium is
studied theoretically and experimentally using light scattering from capillary
waves. The theoretical model based on the Gibbs thermodynamics relates the
temperature derivative of \gamma to the surface excess entropy -\Delta S.
Although capillary waves contribute to the surface entropy with a positive sign
the effect of dipole layer on \Delta S is negative. Experimental data collected
at a free Ga surface in the temperature range from 30 to 160 C show that the
temperature derivative of the tension changes sign near 100 C.Comment: 11 pages, 1 Postscript figure, submitted to J. Phys.
Forces on a boiling bubble in a developing boundary layer, in microgravity with g-jitter and in terrestrial conditions
Terrestrial and microgravity flow boiling experiments were carried out with the same test rig, comprising a locally heated artificial cavity in the center of a channel near the frontal edge of an intrusive glass bubble generator. Bubble shapes were in microgravity generally not far from those of truncated spheres,which permitted the computation of inertial lift and drag from potential flow theory for truncated spheres approximating the actual shape. For these bubbles, inertial lift is counteracted by drag and both forces are of the same order of magnitude as g-jitter. A generalization of the Laplace equation is found which applies to a deforming bubble attached to a plane wall and yields the pressure difference between the hydrostatic pressures in the bubble and at the wall, p. A fully independent way to determine the overpressure p is given by a second Euler-Lagrange equation. Relative differences have been found to be about 5% for both terrestrial and microgravity bubbles. A way is found to determine the sum of the two counteracting major force contributions on a bubble in the direction normal to the wall from a single directly measurable quantity. Good agreement with expectation values for terrestrial bubbles was obtained with the difference in radii of curvature averaged over the liquid-vapor interface, (1/R2 − 1/R1), multiplied with the surface tension coefficient, σ. The new analysis methods of force components presented also permit the accounting for a surface tension gradient along the liquid-vapor interface. No such gradients were found for the present measurements
Nonlinear Dynamics of Capacitive Charging and Desalination by Porous Electrodes
The rapid and efficient exchange of ions between porous electrodes and
aqueous solutions is important in many applications, such as electrical energy
storage by super-capacitors, water desalination and purification by capacitive
deionization (or desalination), and capacitive extraction of renewable energy
from a salinity difference. Here, we present a unified mean-field theory for
capacitive charging and desalination by ideally polarizable porous electrodes
(without Faradaic reactions or specific adsorption of ions) in the limit of
thin double layers (compared to typical pore dimensions). We illustrate the
theory in the case of a dilute, symmetric, binary electrolyte using the
Gouy-Chapman-Stern (GCS) model of the double layer, for which simple formulae
are available for salt adsorption and capacitive charging of the diffuse part
of the double layer. We solve the full GCS mean-field theory numerically for
realistic parameters in capacitive deionization, and we derive reduced models
for two limiting regimes with different time scales: (i) In the
"super-capacitor regime" of small voltages and/or early times where the porous
electrode acts like a transmission line, governed by a linear diffusion
equation for the electrostatic potential, scaled to the RC time of a single
pore. (ii) In the "desalination regime" of large voltages and long times, the
porous electrode slowly adsorbs neutral salt, governed by coupled, nonlinear
diffusion equations for the pore-averaged potential and salt concentration
Dynamics of Counterion Condensation
Using a generalization of the Poisson-Boltzmann equation, dynamics of
counterion condensation is studied. For a single charged plate in the presence
of counterions, it is shown that the approach to equilibrium is diffusive. In
the far from equilibrium case of a moving charged plate, a dynamical counterion
condensation transition occurs at a critical velocity. The complex dynamic
behavior of the counterion cloud is shown to lead to a novel nonlinear
force-velocity relation for the moving plate.Comment: 5 pages, 1 ps figure included using eps
Measurement of a Structured Backflow in an Open Small Channel Induced by Surface-Tension Gradients
We present experiments in which the laterally confined flow of a surfactant film driven by controlled surface tension gradients causes the subtended liquid layer to self-organize into an inner upstream microduct surrounded by the downstream flow. The anomalous interfacial flow profiles and the concomitant backflow are a result of the feedback between two-dimensional and three-dimensional microfluidics realized during flow in open microchannels. Bulk and surface particle image velocimetry data combined with an interfacial hydrodynamics model explain the dependence of the observed phenomena on channel geometry
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