1,015 research outputs found
Computer simulation of low-energy excitations in amorphous silicon with voids
We use empirical molecular dynamics technique to study the low-energy
vibrations in a large 4096 atom model for pure amorphous silicon and a set of
models with voids of different size based on it. Numerical vibrational
eigenvalues and eigenvectors for our models are obtained by exact
diagonalization of their dynamical matrices. Our calculations show that
localized low-energy vibrational excitations of rather complex structure are
present in amorphous silicon models with voids. According to their spatial
localization patterns we make an attempt to classify these excitations as modes
associated with the void and "mixed" modes associated with the interaction of
the void with strained regions of silicon network.Comment: Was presented at ICAMS18 conference, Snowbird UT, August 1999.
Submitted to J. of Non-Cryst. Solid
Effects of Nanoparticle Geometry and Size Distribution on Diffusion Impedance of Battery Electrodes
The short diffusion lengths in insertion battery nanoparticles render the
capacitive behavior of bounded diffusion, which is rarely observable with
conventional larger particles, now accessible to impedance measurements.
Coupled with improved geometrical characterization, this presents an
opportunity to measure solid diffusion more accurately than the traditional
approach of fitting Warburg circuit elements, by properly taking into account
the particle geometry and size distribution. We revisit bounded diffusion
impedance models and incorporate them into an overall impedance model for
different electrode configurations. The theoretical models are then applied to
experimental data of a silicon nanowire electrode to show the effects of
including the actual nanowire geometry and radius distribution in interpreting
the impedance data. From these results, we show that it is essential to account
for the particle shape and size distribution to correctly interpret impedance
data for battery electrodes. Conversely, it is also possible to solve the
inverse problem and use the theoretical "impedance image" to infer the
nanoparticle shape and/or size distribution, in some cases, more accurately
than by direct image analysis. This capability could be useful, for example, in
detecting battery degradation in situ by simple electrical measurements,
without the need for any imaging.Comment: 30 page
Induced-charge Electrokinetic Phenomena: Theory and Microfluidic Applications
We give a general, physical description of ``induced-charge electro-osmosis''
(ICEO), the nonlinear electrokinetic slip at a polarizable surface, in the
context of some new techniques for microfluidic pumping and mixing. ICEO
generalizes ``AC electro-osmosis'' at micro-electrode arrays to various
dielectric and conducting structures in weak DC or AC electric fields. The
basic effect produces micro-vortices to enhance mixing in microfluidic devices,
while various broken symmetries -- controlled potential, irregular shape,
non-uniform surface properties, and field gradients -- can be exploited to
produce streaming flows. Although we emphasize the qualitative picture of ICEO,
we also briefly describe the mathematical theory (for thin double layers and
weak fields) and apply it to a metal cylinder with a dielectric coating in a
suddenly applied DC field.Comment: 4 pages, 4 figs; revsion with more refs, one new fig, and more
emphasis on microfluidic
Induced-Charge Electro-Osmosis
We describe the general phenomenon of `induced-charge electro-osmosis' (ICEO)
-- the nonlinear electro-osmotic slip that occurs when an applied field acts on
the ionic charge it {\sl induces} around a polarizable surface. Motivated by a
simple physical picture, we calculate ICEO flows around conducting cylinders in
steady (DC), oscillatory (AC), and suddenly-applied electric fields. This
picture, and these systems, represent perhaps the clearest example of nonlinear
electrokinetic phenomena. We complement and verify this physically-motivated
approach using a matched asymptotic expansion to the electrokinetic equations
in the thin double-layer and low potential limits. ICEO slip velocities vary
like , where is the field strength and is a
geometric length scale, and are set up on a time scale , where is the screening length and is the ionic diffusion
constant. We propose and analyze ICEO microfluidic pumps and mixers that
operate without moving parts under low applied potentials. Similar flows around
metallic colloids with fixed total charge have been described in the Russian
literature (largely unnoticed in the West). ICEO flows around conductors with
fixed potential, on the other hand, have no colloidal analog and offer further
possibilities for microfluidic applications.Comment: 36 pages, 8 figures, to appear in J. Fluid Mec
Front dynamics during diffusion-limited corrosion of ramified electrodeposits
Experiments on the diffusion-limited corrosion of porous copper clusters in
thin gap cells containing cupric chloride are reported. By carefully comparing
corrosion front velocities and concentration profiles obtained by phase-shift
interferometry with theoretical predictions, it is demonstrated that this
process is well-described by a one-dimensional mean-field model for the generic
reaction A + B (static) -> C (inert) with only diffusing reactant (cupric
chloride) and one static reactant (copper) reacting to produce an inert product
(cuprous chloride). The interpretation of the experiments is aided by a
mathematical analysis of the model equations which allows the reaction-order
and the transference number of the diffusing species to be inferred. Physical
arguments are given to explain the surprising relevance of the one-dimensional
mean-field model in spite of the complex (fractal) structure of the copper
clusters.Comment: 26 pages, 10 figures, submitted to J. Phys. Chem. B, high quality eps
figures available at http://www-math.mit.edu/~bazant/paper
Attractive forces in microporous carbon electrodes for capacitive deionization
The recently developed modified Donnan (mD) model provides a simple and
useful description of the electrical double layer in microporous carbon
electrodes, suitable for incorporation in porous electrode theory. By
postulating an attractive excess chemical potential for each ion in the
micropores that is inversely proportional to the total ion concentration, we
show that experimental data for capacitive deionization (CDI) can be accurately
predicted over a wide range of applied voltages and salt concentrations. Since
the ion spacing and Bjerrum length are each comparable to the micropore size
(few nm), we postulate that the attraction results from fluctuating bare
Coulomb interactions between individual ions and the metallic pore surfaces
(image forces) that are not captured by meanfield theories, such as the
Poisson-Boltzmann-Stern model or its mathematical limit for overlapping double
layers, the Donnan model. Using reasonable estimates of the micropore
permittivity and mean size (and no other fitting parameters), we propose a
simple theory that predicts the attractive chemical potential inferred from
experiments. As additional evidence for attractive forces, we present data for
salt adsorption in uncharged microporous carbons, also predicted by the theory.Comment: 19 page
Interfacial dynamics in transport-limited dissolution
Various model problems of ``transport-limited dissolution'' in two dimensions
are analyzed using time-dependent conformal maps. For diffusion-limited
dissolution (reverse Laplacian growth), several exact solutions are discussed
for the smoothing of corrugated surfaces, including the continuous analogs of
``internal diffusion-limited aggregation'' and ``diffusion-limited erosion''. A
class of non-Laplacian, transport-limited dissolution processes are also
considered, which raise the general question of when and where a finite solid
will disappear. In a case of dissolution by advection-diffusion, a tilted
ellipse maintains its shape during collapse, as its center of mass drifts
obliquely away from the background fluid flow, but other initial shapes have
more complicated dynamics.Comment: 5 pages, 4 fig
Diffusion-Limited Aggregation on Curved Surfaces
We develop a general theory of transport-limited aggregation phenomena
occurring on curved surfaces, based on stochastic iterated conformal maps and
conformal projections to the complex plane. To illustrate the theory, we use
stereographic projections to simulate diffusion-limited-aggregation (DLA) on
surfaces of constant Gaussian curvature, including the sphere () and
pseudo-sphere (), which approximate "bumps" and "saddles" in smooth
surfaces, respectively. Although curvature affects the global morphology of the
aggregates, the fractal dimension (in the curved metric) is remarkably
insensitive to curvature, as long as the particle size is much smaller than the
radius of curvature. We conjecture that all aggregates grown by conformally
invariant transport on curved surfaces have the same fractal dimension as DLA
in the plane. Our simulations suggest, however, that the multifractal
dimensions increase from hyperbolic () geometry, which
we attribute to curvature-dependent screening of tip branching.Comment: 4 pages, 3 fig
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