32 research outputs found
Phase field modeling of electrochemistry I: Equilibrium
A diffuse interface (phase field) model for an electrochemical system is
developed. We describe the minimal set of components needed to model an
electrochemical interface and present a variational derivation of the governing
equations. With a simple set of assumptions: mass and volume constraints,
Poisson's equation, ideal solution thermodynamics in the bulk, and a simple
description of the competing energies in the interface, the model captures the
charge separation associated with the equilibrium double layer at the
electrochemical interface. The decay of the electrostatic potential in the
electrolyte agrees with the classical Gouy-Chapman and Debye-H\"uckel theories.
We calculate the surface energy, surface charge, and differential capacitance
as functions of potential and find qualitative agreement between the model and
existing theories and experiments. In particular, the differential capacitance
curves exhibit complex shapes with multiple extrema, as exhibited in many
electrochemical systems.Comment: v3: To be published in Phys. Rev. E v2: Added link to
cond-mat/0308179 in References 13 pages, 6 figures in 15 files, REVTeX 4,
SIUnits.sty. Precedes cond-mat/030817
Irreversible reorganization in a supercooled liquid originates from localised soft modes
The transition of a fluid to a rigid glass upon cooling is a common route of
transformation from liquid to solid that embodies the most poorly understood
features of both phases1,2,3. From the liquid perspective, the puzzle is to
understand stress relaxation in the disordered state. From the perspective of
solids, the challenge is to extend our description of structure and its
mechanical consequences to materials without long range order. Using computer
simulations, we show that the localized low frequency normal modes of a
configuration in a supercooled liquid are causally correlated to the
irreversible structural reorganization of the particles within that
configuration. We also demonstrate that the spatial distribution of these soft
local modes can persist in spite of significant particle reorganization. The
consequence of these two results is that it is now feasible to construct a
theory of relaxation length scales in glass-forming liquids without recourse to
dynamics and to explicitly relate molecular properties to their collective
relaxation.Comment: Published online: 20 July 2008 | doi:10.1038/nphys1025 Available from
http://www.nature.com/nphys/journal/v4/n9/abs/nphys1025.htm
Making Space for Failure in Geographic Research
The idea that field research is an inherently âmessyâ process has become widely accepted by geographers in recent years. There has thus far been little acknowledgment, however, of the role that failure plays in doing human geography. In this article we push back against this, arguing that failure should be recognized as a central component of what it means to do qualitative geographical field research. This article seeks to use failure proactively and provocatively as a powerful resource to improve research practice and outcomes, reconsidering and giving voice to it as everyday, productive, and necessary to our continual development as researchers and academics. This article argues that there is much value to be found in failure if it is critically examined and shared, andâcruciallyâif there is a supportive space in which to exchange our experiences of failing in the field
Jamming percolation and glassy dynamics
We present a detailed physical analysis of the dynamical glass-jamming
transition which occurs for the so called Knight models recently introduced and
analyzed in a joint work with D.S.Fisher \cite{letterTBF}. Furthermore, we
review some of our previous works on Kinetically Constrained Models.
The Knights models correspond to a new class of kinetically constrained
models which provide the first example of finite dimensional models with an
ideal glass-jamming transition. This is due to the underlying percolation
transition of particles which are mutually blocked by the constraints. This
jamming percolation has unconventional features: it is discontinuous (i.e. the
percolating cluster is compact at the transition) and the typical size of the
clusters diverges faster than any power law when . These
properties give rise for Knight models to an ergodicity breaking transition at
: at and above a finite fraction of the system is frozen. In
turn, this finite jump in the density of frozen sites leads to a two step
relaxation for dynamic correlations in the unjammed phase, analogous to that of
glass forming liquids. Also, due to the faster than power law divergence of the
dynamical correlation length, relaxation times diverge in a way similar to the
Vogel-Fulcher law.Comment: Submitted to the special issue of Journal of Statistical Physics on
Spin glasses and related topic
Cooperative Behavior of Kinetically Constrained Lattice Gas Models of Glassy Dynamics
Kinetically constrained lattice models of glasses introduced by Kob and
Andersen (KA) are analyzed. It is proved that only two behaviors are possible
on hypercubic lattices: either ergodicity at all densities or trivial
non-ergodicity, depending on the constraint parameter and the dimensionality.
But in the ergodic cases, the dynamics is shown to be intrinsically cooperative
at high densities giving rise to glassy dynamics as observed in simulations.
The cooperativity is characterized by two length scales whose behavior controls
finite-size effects: these are essential for interpreting simulations. In
contrast to hypercubic lattices, on Bethe lattices KA models undergo a
dynamical (jamming) phase transition at a critical density: this is
characterized by diverging time and length scales and a discontinuous jump in
the long-time limit of the density autocorrelation function. By analyzing
generalized Bethe lattices (with loops) that interpolate between hypercubic
lattices and standard Bethe lattices, the crossover between the dynamical
transition that exists on these lattices and its absence in the hypercubic
lattice limit is explored. Contact with earlier results are made via analysis
of the related Fredrickson-Andersen models, followed by brief discussions of
universality, of other approaches to glass transitions, and of some issues
relevant for experiments.Comment: 59 page