337 research outputs found
Theory of Sorption Hysteresis in Nanoporous Solids: II. Molecular condensation
Motivated by the puzzle of sorption hysteresis in Portland cement concrete or
cement paste, we develop in Part II of this study a general theory of vapor
sorption and desorption from nanoporous solids, which attributes hysteresis to
hindered molecular condensation with attractive lateral interactions. The
classical mean-field theory of van der Waals is applied to predict the
dependence of hysteresis on temperature and pore size, using the regular
solution model and gradient energy of Cahn and Hilliard. A simple "hierarchical
wetting" model for thin nanopores is developed to describe the case of strong
wetting by the first monolayer, followed by condensation of nanodroplets and
nanobubbles in the bulk. The model predicts a larger hysteresis critical
temperature and enhanced hysteresis for molecular condensation across nanopores
at high vapor pressure than within monolayers at low vapor pressure. For
heterogeneous pores, the theory predicts sorption/desorption sequences similar
to those seen in molecular dynamics simulations, where the interfacial energy
(or gradient penalty) at nanopore junctions acts as a free energy barrier for
snap-through instabilities. The model helps to quantitatively understand recent
experimental data for concrete or cement paste wetting and drying cycles and
suggests new experiments at different temperatures and humidity sweep rates.Comment: 26 pages, 10 fig
Tuning the stability of Electrochemical Interfaces by Electron Transfer reactions
The morphology of interfaces is known to play fundamental role on the
efficiency of energy-related applications, such light harvesting or ion
intercalation. Altering the morphology on demand, however, is a very difficult
task. Here, we show ways the morphology of interfaces can be tuned by driven
electron transfer reactions. By using non-equilibrium thermodynamic stability
theory, we uncover the operating conditions that alter the interfacial
morphology. We apply the theory to ion intercalation and surface growth where
electrochemical reactions are described using Butler-Volmer or coupled
ion-electron transfer kinetics. The latter connects microscopic/quantum
mechanical concepts with the morphology of electrochemical interfaces. Finally,
we construct non-equilibrium phase diagrams in terms of the applied driving
force (current/voltage) and discuss the importance of engineering the density
of states of the electron donor in applications related to energy harvesting
and storage, electrocatalysis and photocatalysis.Comment: 10 pages, 6 figure
Phase Separation Dynamics in Isotropic Ion-Intercalation Particles
Lithium-ion batteries exhibit complex nonlinear dynamics, resulting from
diffusion and phase transformations coupled to ion intercalation reactions.
Using the recently developed Cahn-Hilliard reaction (CHR) theory, we
investigate a simple mathematical model of ion intercalation in a spherical
solid nanoparticle, which predicts transitions from solid-solution radial
diffusion to two-phase shrinking-core dynamics. This general approach extends
previous Li-ion battery models, which either neglect phase separation or
postulate a spherical shrinking-core phase boundary, by predicting phase
separation only under appropriate circumstances. The effect of the applied
current is captured by generalized Butler-Volmer kinetics, formulated in terms
of diffusional chemical potentials, and the model consistently links the
evolving concentration profile to the battery voltage. We examine sources of
charge/discharge asymmetry, such as asymmetric charge transfer and surface
"wetting" by ions within the solid, which can lead to three distinct phase
regions. In order to solve the fourth-order nonlinear CHR
initial-boundary-value problem, a control-volume discretization is developed in
spherical coordinates. The basic physics are illustrated by simulating many
representative cases, including a simple model of the popular cathode material,
lithium iron phosphate (neglecting crystal anisotropy and coherency strain).
Analytical approximations are also derived for the voltage plateau as a
function of the applied current
Homogenization of the Poisson-Nernst-Planck Equations for Ion Transport in Charged Porous Media
Effective Poisson-Nernst-Planck (PNP) equations are derived for macroscopic
ion transport in charged porous media under periodic fluid flow by an
asymptotic multi-scale expansion with drift. The microscopic setting is a
two-component periodic composite consisting of a dilute electrolyte continuum
(described by standard PNP equations) and a continuous dielectric matrix, which
is impermeable to the ions and carries a given surface charge. Four new
features arise in the upscaled equations: (i) the effective ionic diffusivities
and mobilities become tensors, related to the microstructure; (ii) the
effective permittivity is also a tensor, depending on the electrolyte/matrix
permittivity ratio and the ratio of the Debye screening length to the
macroscopic length of the porous medium; (iii) the microscopic fluidic
convection is replaced by a diffusion-dispersion correction in the effective
diffusion tensor; and (iv) the surface charge per volume appears as a
continuous "background charge density", as in classical membrane models. The
coefficient tensors in the upscaled PNP equations can be calculated from
periodic reference cell problems. For an insulating solid matrix, all gradients
are corrected by the same tensor, and the Einstein relation holds at the
macroscopic scale, which is not generally the case for a polarizable matrix,
unless the permittivity and electric field are suitably defined. In the limit
of thin double layers, Poisson's equation is replaced by macroscopic
electroneutrality (balancing ionic and surface charges). The general form of
the macroscopic PNP equations may also hold for concentrated solution theories,
based on the local-density and mean-field approximations. These results have
broad applicability to ion transport in porous electrodes, separators,
membranes, ion-exchange resins, soils, porous rocks, and biological tissues
Electrochemical Impedance Imaging via the Distribution of Diffusion Times
We develop a mathematical framework to analyze electrochemical impedance
spectra in terms of a distribution of diffusion times (DDT) for a parallel
array of random finite-length Warburg (diffusion) or Gerischer
(reaction-diffusion) circuit elements. A robust DDT inversion method is
presented based on Complex Nonlinear Least Squares (CNLS) regression with
Tikhonov regularization and illustrated for three cases of nanostructured
electrodes for energy conversion: (i) a carbon nanotube supercapacitor, (ii) a
silicon nanowire Li-ion battery, and (iii) a porous-carbon vanadium flow
battery. The results demonstrate the feasibility of non-destructive "impedance
imaging" to infer microstructural statistics of random, heterogeneous
materials
Theory of voltammetry in charged porous media
We couple the Leaky Membrane Model, which describes the diffusion and
electromigration of ions in a homogenized porous medium of fixed background
charge, with Butler-Volmer reaction kinetics for flat electrodes separated by
such a medium in a simple mathematical theory of voltammetry. The model is
illustrated for the prototypical case of copper electro-deposition/dissolution
in aqueous charged porous media. We first consider the steady state with three
different experimentally relevant boundary conditions and derive analytical or
semi-analytical expressions for concentration profiles, electric potential
profiles, current-voltage relations and overlimiting conductances. Next, we
perform nonlinear least squares fitting on experimental data, consider the
transient response for linear sweep voltammetry and demonstrate good agreement
of the model predictions with experimental data. The experimental datasets are
for copper electrodeposition from copper(II) sulfate solutions in a variety of
nanoporous media, such as anodic aluminum oxide, cellulose nitrate and
polyethylene battery separators, whose internal surfaces are functionalized
with positively and negatively charged polyelectrolyte polymers.Comment: 39 pages, 12 figures, 5 tables; clarified where other parameters are
taken from and fixed typo
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