INVESTIGADORES
IDIART Martin Ignacio
congresos y reuniones científicas
Título:
A model problem concerning the ionic transport in microstructured solid electrolytes
Autor/es:
I. J. CURTO SILLAMONI; M. I. IDIART
Lugar:
Bariloche
Reunión:
Congreso; XXI Congreso sobre Métodos Numéricos y sus Aplicaciones; 2014
Resumen:
Current
efforts to develop polymeric electrolytes for all-solid-state lithium
batteries are hampered by the unsatisfactory ionic conductivity of
available polymers at room temperature. The most promising polymers
available to date consist of poly-ethylene-oxide (PEO) complexes
doped with a lithium salt such as lithium perclorate
or lithium iodide. These are semi-crystalline polymers which
often exhibit spherulitic microstructural morphologies. Now, early
experimental works on semi-crystalline polymers claimed that only the
amorphous phase supported fast ionic transport, thus promoting
efforts to produce PEO complexes of low crystallinity. However, more
recent works have revealed that when a PEO specimen is deformed the
ionic conductivity in the direction of elongation increases by orders
of magnitude. This strongly suggests that actually the crystalline
phase can be more conductive than the amorphous phase in certain
directions, and that highly conductive PEO complexes could result
from high crystallinities with suitable crystallographic textures.
The purpose of this work is to develop a multi-scale constitutive
theory that rationalize these observations.
We
begin by deriving the field equations of ionic transport in
microstructured solids by combining the principles of mass
conservation, electrodynamics, and thermodynamics in a consistent
fashion. We consider common forms of the energies and dissipation
rates characterizing the various phases. The nonlinear field
equations are then homogenized by making use of the notion of
two-scale convergence. At the microscopic scale, the various field
equations become a set of decoupled linear conductivity equations; at
the macroscopic scale, the field equations remain nonlinear but the
effective behavior is characterized by a set of second-order
conductivity tensors which can be computed by traditional means. The
theory is applied to two-dimensional material systems with
spherulitic microstructural morphologies. These microstructures are
modeled with two-scale microgeometries consisting of Shulgasser?s
spheres (higher lengthscale) composed of two-phase laminates (lower
lengthscale) radially oriented. An analytic expression is obtained
for the ionic conductivity in terms of the various microstructural
parameters, including the crystallinity. Assuming reasonable values
for the various material parameters characterizing the amorphous and
crystalline phases, the predictions do support the idea that the
crystalline phase exhibits a higher (lower) ionic mobility than the
amorphous phase along (perpendicular to) the direction of the
polymeric chains.