714 research outputs found
On the efficient numerical solution of lattice systems with low-order couplings
We apply the Quasi Monte Carlo (QMC) and recursive numerical integration
methods to evaluate the Euclidean, discretized time path-integral for the
quantum mechanical anharmonic oscillator and a topological quantum mechanical
rotor model. For the anharmonic oscillator both methods outperform standard
Markov Chain Monte Carlo methods and show a significantly improved error
scaling. For the quantum mechanical rotor we could, however, not find a
successful way employing QMC. On the other hand, the recursive numerical
integration method works extremely well for this model and shows an at least
exponentially fast error scaling
Free energy of cluster formation and a new scaling relation for the nucleation rate
Recent very large molecular dynamics simulations of homogeneous nucleation
with Lennard-Jones atoms [Diemand et al. J. Chem. Phys. {\bf
139}, 074309 (2013)] allow us to accurately determine the formation free energy
of clusters over a wide range of cluster sizes. This is now possible because
such large simulations allow for very precise measurements of the cluster size
distribution in the steady state nucleation regime. The peaks of the free
energy curves give critical cluster sizes, which agree well with independent
estimates based on the nucleation theorem. Using these results, we derive an
analytical formula and a new scaling relation for nucleation rates: is scaled by , where the supersaturation ratio is ,
is the dimensionless surface energy, and is a dimensionless
nucleation rate. This relation can be derived using the free energy of cluster
formation at equilibrium which corresponds to the surface energy required to
form the vapor-liquid interface. At low temperatures (below the triple point),
we find that the surface energy divided by that of the classical nucleation
theory does not depend on temperature, which leads to the scaling relation and
implies a constant, positive Tolman length equal to half of the mean
inter-particle separation in the liquid phase.Comment: 7 figure
PHP167 Analysis of the IQWIG Comments on the Evidence Searches of Dossiers in the German Amnog Process
Systematic Improvement of Classical Nucleation Theory
We reconsider the applicability of classical nucleation theory (CNT) to the
calculation of the free energy of solid cluster formation in a liquid and its
use to the evaluation of interface free energies from nucleation barriers.
Using two different freezing transitions (hard spheres and NaCl) as test cases,
we first observe that the interface-free-energy estimates based on CNT are
generally in error. As successive refinements of nucleation-barrier theory, we
consider corrections due to a non-sharp solid-liquid interface and to a
non-spherical cluster shape. Extensive calculations for the Ising model show
that corrections due to a non-sharp and thermally fluctuating interface account
for the barrier shape with excellent accuracy. The experimental solid
nucleation rates that are measured in colloids are better accounted for by
these non-CNT terms, whose effect appears to be crucial in the interpretation
of data and in the extraction of the interface tension from them.Comment: 20 pages (text + supplementary material
Test of classical nucleation theory on deeply supercooled high-pressure simulated silica
We test classical nucleation theory (CNT) in the case of simulations of
deeply supercooled, high density liquid silica, as modelled by the BKS
potential. We find that at density ~g/cm, spontaneous nucleation
of crystalline stishovite occurs in conventional molecular dynamics simulations
at temperature T=3000 K, and we evaluate the nucleation rate J directly at this
T via "brute force" sampling of nucleation events. We then use parallel,
constrained Monte Carlo simulations to evaluate , the free energy
to form a crystalline embryo containing n silicon atoms, at T=3000, 3100, 3200
and 3300 K. We find that the prediction of CNT for the n-dependence of fits reasonably well to the data at all T studied, and at 3300 K yields a
chemical potential difference between liquid and stishovite that matches
independent calculation. We find that , the size of the critical nucleus,
is approximately 10 silicon atoms at T=3300 K. At 3000 K, decreases to
approximately 3, and at such small sizes methodological challenges arise in the
evaluation of when using standard techniques; indeed even the
thermodynamic stability of the supercooled liquid comes into question under
these conditions. We therefore present a modified approach that permits an
estimation of at 3000 K. Finally, we directly evaluate at T=3000
K the kinetic prefactors in the CNT expression for J, and find physically
reasonable values; e.g. the diffusion length that Si atoms must travel in order
to move from the liquid to the crystal embryo is approximately 0.2 nm. We are
thereby able to compare the results for J at 3000 K obtained both directly and
based on CNT, and find that they agree within an order of magnitude.Comment: corrected calculation, new figure, accepted in JC
Sustainable Electrochemical Depolymerization of Lignin in Reusable Ionic Liquids
Lignin’s aromatic building blocks provide a chemical resource that is, in theory, ideal for substitution of
aromatic petrochemicals. Moreover, degradation and valorization of lignin has the potential to generate
many high-value chemicals for technical applications. In this study, electrochemical degradation
of alkali and Organosolv lignin was performed using the ionic liquids 1-ethyl-3-methylimidazolium
trifluoromethanesulfonate and triethylammonium methanesulfonate. The extensive degradation of
the investigated lignins with simultaneous almost full recovery of the electrolyte materials provided
a sustainable alternative to more common lignin degradation processes. We demonstrate here that
both the presence (and the absence) of water during electrolysis and proton transport reactions had
significant impact on the degradation efficiency. Hydrogen peroxide radical formation promoted certain
electrochemical mechanisms in electrolyte systems “contaminated” with water and increased yields of
low molecular weight products significantly. The proposed mechanisms were tentatively confirmed by
determining product distributions using a combination of liquid chromatography-mass spectrometry
and gas-chromatography-mass spectrometry, allowing measurement of both polar versus non-polar as
well as volatile versus non-volatile components in the mixtures
Collective Behavior of Asperities in Dry Friction at Small Velocities
We investigate a simple model of dry friction based on extremal dynamics of
asperities. At small velocities, correlations develop between the asperities,
whose range becomes infinite in the limit of infinitely slow driving, where the
system is self-organized critical. This collective phenomenon leads to
effective aging of the asperities and results in velocity dependence of the
friction force in the form .Comment: 7 pages, 8 figures, revtex, submitted to Phys. Rev.
Homogeneous nucleation of colloidal melts under the influence of shearing fields
We study the effect of shear flow on homogeneous crystal nucleation, using
Brownian Dynamics simulations in combination with an umbrella sampling like
technique. The symmetry breaking due to shear results in anisotropic radial
distribution functions. The homogeneous shear rate suppresses crystal
nucleation and leads to an increase of the size of the critical nucleus. These
observations can be described by a simple, phenomenological extension of
classical nucleation theory. In addition, we find that nuclei have a
preferential orientation with respect to the direction of shear. On average the
longest dimension of a nucleus is along the vorticity direction, while the
shortest dimension is preferably perpendicular to that and slightly tilted with
respect to the gradient direction.Comment: 10 pages, 8 figures, Submitted to J. Phys.: Condens. Matte
Simulation of fluid-solid coexistence in finite volumes: A method to study the properties of wall-attached crystalline nuclei
The Asakura-Oosawa model for colloid-polymer mixtures is studied by Monte
Carlo simulations at densities inside the two-phase coexistence region of fluid
and solid. Choosing a geometry where the system is confined between two flat
walls, and a wall-colloid potential that leads to incomplete wetting of the
crystal at the wall, conditions can be created where a single nanoscopic
wall-attached crystalline cluster coexists with fluid in the remainder of the
simulation box. Following related ideas that have been useful to study
heterogeneous nucleation of liquid droplets at the vapor-liquid coexistence, we
estimate the contact angles from observations of the crystalline clusters in
thermal equilibrium. We find fair agreement with a prediction based on Young's
equation, using estimates of interface and wall tension from the study of flat
surfaces. It is shown that the pressure versus density curve of the finite
system exhibits a loop, but the pressure maximum signifies the "droplet
evaporation-condensation" transition and thus has nothing in common with a van
der Waals-like loop. Preparing systems where the packing fraction is deep
inside the two-phase coexistence region, the system spontaneously forms a "slab
state", with two wall-attached crystalline domains separated by (flat)
interfaces from liquid in full equilibrium with the crystal in between;
analysis of such states allows a precise estimation of the bulk equilibrium
properties at phase coexistence
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