694 research outputs found
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
Model B4 : multi-decade creep and shrinkage prediction of traditional and modern concretes
To improve the sustainability of concrete infrastructure, engineers face the challenge of incorporating new concrete materials while pushing the expected design life beyond 100 years. The time-dependent creep and shrinkage response of concrete governs the serviceability and durability in this multi-decade time frame. It has been shown that current prediction equations for creep and shrinkage underestimate material deformations observed in structures outside of a laboratory environment. A new prediction model for creep and shrinkage is presented that can overcome some of the shortcomings of the current equations. The model represents an extension and systematic recalibration of model B3, a 1995 RILEM Recommendation, which derives its functional form from the phenomena of diffusion, chemical hydration, moisture sorption, and the evolution of micro-stresses in the cement structure. The model is calibrated through a joint optimization of a new enlarged laboratory test database and a new database of bridge deflection records to overcome the bias towards short-term behavior. A framework for considering effects of aggregates, admixtures, additives, and higher temperatures is also incorporated
Size scaling of strength in thin film delamination
We investigate by numerical simulation the system size dependence of the
shear delamination strength of thin elastic films. The films are connected to a
rigid substrate by a disordered interface containing a pre-existing crack. The
size dependence of the strength of this system is found to depend crucially on
the crack shape. For circular cracks, we observe a crossover between a
size-independent regime at large crack radii which is controlled by propagation
of the pre-existing crack, and a size-dependent regime at small radii which is
dominated by nucleation of new cracks in other locations. For cracks of finite
width that span the system transversally, we observe for all values of the
crack length a logarithmic system size dependence of the failure stress. The
results are interpreted in terms of extreme value statistics.Comment: 10 pages, 4 figure
Steady advection-diffusion around finite absorbers in two-dimensional potential flows
We perform an exhaustive study of the simplest, nontrivial problem in
advection-diffusion -- a finite absorber of arbitrary cross section in a steady
two-dimensional potential flow of concentrated fluid. This classical problem
has been studied extensively in the theory of solidification from a flowing
melt, and it also arises in Advection-Diffusion-Limited Aggregation. In both
cases, the fundamental object is the flux to a circular disk, obtained by
conformal mapping from more complicated shapes. We construct the first accurate
numerical solution using an efficient new method, which involves mapping to the
interior of the disk and using a spectral method in polar coordinates. Our
method also combines exact asymptotics and an adaptive mesh to handle boundary
layers. Starting from a well-known integral equation in streamline coordinates,
we also derive new, high-order asymptotic expansions for high and low P\'eclet
numbers (\Pe). Remarkably, the `high' \Pe expansion remains accurate even
for such low \Pe as . The two expansions overlap well near \Pe =
0.1, allowing the construction of an analytical connection formula that is
uniformly accurate for all \Pe and angles on the disk with a maximum relative
error of 1.75%. We also obtain an analytical formula for the Nusselt number
() as a function of the P\'eclet number with a maximum relative error of
0.53% for all possible geometries. Because our finite-plate problem can be
conformally mapped to other geometries, the general problem of two-dimensional
advection-diffusion past an arbitrary finite absorber in a potential flow can
be considered effectively solved.Comment: 29 pages, 12 figs (mostly in color
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