111 research outputs found
Unsupervised machine learning for detection of phase transitions in off-lattice systems I. Foundations
We demonstrate the utility of an unsupervised machine learning tool for the
detection of phase transitions in off-lattice systems. We focus on the
application of principal component analysis (PCA) to detect the freezing
transitions of two-dimensional hard-disk and three-dimensional hard-sphere
systems as well as liquid-gas phase separation in a patchy colloid model. As we
demonstrate, PCA autonomously discovers order-parameter-like quantities that
report on phase transitions, mitigating the need for a priori construction or
identification of a suitable order parameter--thus streamlining the routine
analysis of phase behavior. In a companion paper, we further develop the method
established here to explore the detection of phase transitions in various model
systems controlled by compositional demixing, liquid crystalline ordering, and
non-equilibrium active forces
Unsupervised machine learning for detection of phase transitions in off-lattice systems II. Applications
We outline how principal component analysis (PCA) can be applied to particle
configuration data to detect a variety of phase transitions in off-lattice
systems, both in and out of equilibrium. Specifically, we discuss its
application to study 1) the nonequilibrium random organization (RandOrg) model
that exhibits a phase transition from quiescent to steady-state behavior as a
function of density, 2) orientationally and positionally driven equilibrium
phase transitions for hard ellipses, and 3) compositionally driven demixing
transitions in the non-additive binary Widom-Rowlinson mixture
Thermodynamics predicts how confinement modifies hard-sphere dynamics
We study how confining the equilibrium hard-sphere fluid to restrictive one-
and two-dimensional channels with smooth interacting walls modifies its
structure, dynamics, and entropy using molecular dynamics and transition-matrix
Monte Carlo simulations. Although confinement strongly affects local
structuring, the relationships between self-diffusivity, excess entropy, and
average fluid density are, to an excellent approximation, independent of
channel width or particle-wall interactions. Thus, thermodynamics can be used
to predict how confinement impacts dynamics.Comment: 4 pages, 4 figure
Graphoepitaxy for translational and orientational ordering of monolayers of rectangular nanoparticles
The combinations of particle aspect ratio and enthalpic-barrier templates
that lead to translational and orientational ordering of monolayers of
rectangular particles are determined using Monte Carlo simulations and density
functional theory. For sufficiently high enthalpic barriers, we find that only
specific combinations of particle sizes and template spacings lead to ordered
arrays. The pattern multiplication factor provided by the template extends to
approximately ten times the smallest dimension of the particle
Cofinement, entropy, and single-particle dynamics of equilibrium hard-sphere mixtures
We use discontinuous molecular dynamics and grand-canonical transition-matrix
Monte Carlo simulations to explore how confinement between parallel hard walls
modifies the relationships between packing fraction, self-diffusivity, partial
molar excess entropy, and total excess entropy for binary hard-sphere mixtures.
To accomplish this, we introduce an efficient algorithm to calculate partial
molar excess entropies from the transition-matrix Monte Carlo simulation data.
We find that the species-dependent self-diffusivities of confined fluids are
very similar to those of the bulk mixture if compared at the same,
appropriately defined, packing fraction up to intermediate values, but then
deviate negatively from the bulk behavior at higher packing fractions. On the
other hand, the relationships between self-diffusivity and partial molar excess
entropy (or total excess entropy) observed in the bulk fluid are preserved
under confinement even at relatively high packing fractions and for different
mixture compositions. This suggests that the partial molar excess entropy,
calculable from classical density functional theories of inhomogeneous fluids,
can be used to predict some of the nontrivial dynamical behaviors of fluid
mixtures in confined environments.Comment: submitted to JC
Is Random Close Packing of Spheres Well Defined?
Despite its long history, there are many fundamental issues concerning random
packings of spheres that remain elusive, including a precise definition of
random close packing (RCP). We argue that the current picture of RCP cannot be
made mathematically precise and support this conclusion via a molecular
dynamics study of hard spheres using the Lubachevsky-Stillinger compression
algorithm. We suggest that this impasse can be broken by introducing the new
concept of a maximally random jammed state, which can be made precise.Comment: 6 pages total, 2 figure
Multiscale modeling of solute diffusion in triblock copolymer membranes
We develop a multiscale simulation model for diffusion of solutes through
porous triblock copolymer membranes. The approach combines two techniques:
self-consistent field theory (SCFT) to predict the structure of the
self-assembled, solvated membrane and on-lattice kinetic Monte Carlo (kMC)
simulations to model diffusion of solutes. Solvation is simulated in SCFT by
constraining the glassy membrane matrix while relaxing the brush-like membrane
pore coating against the solvent. The kMC simulations capture the resulting
solute spatial distribution and concentration-dependent local diffusivity in
the polymer-coated pores; we parameterize the latter using particle-based
simulations. We apply our approach to simulate solute diffusion through
nonequilibrium morphologies of a model triblock copolymer, and we correlate
diffusivity with structural descriptors of the morphologies. We also compare
the model's predictions to alternative approaches based on simple lattice
random walks and find our multiscale model to be more robust and systematic to
parameterize. Our multiscale modeling approach is general and can be readily
extended in the future to other chemistries, morphologies, and models for the
local solute diffusivity and interactions with the membrane
Liquid Polymorphism and Double Criticality in a Lattice Gas Model
We analyze the possible phase diagrams of a simple model for an associating
liquid proposed previously. Our two-dimensional lattice model combines
oreintati onal ice-like interactions and \"{}Van der Waals\"{} interactions
which may be repulsive, and in this case represent a penalty for distortion of
hydrogen bonds in the presence of extra molecules. These interactions can be
interpreted in terms of two competing distances, but not necessarily soft-core.
We present mean -field calculations and an exhaustive simulation study for
different parameters which represent relative strength of the bonding
interaction to the energy penalty for its distortion. As this ratio decreases,
a smooth disappearance of the doubl e criticality occurs. Possible connections
to liquid-liquid transitions of molecul ar liquids are suggested
Intra-molecular coupling as a mechanism for a liquid-liquid phase transition
We study a model for water with a tunable intra-molecular interaction
, using mean field theory and off-lattice Monte Carlo simulations.
For all , the model displays a temperature of maximum
density.For a finite intra-molecular interaction ,our
calculations support the presence of a liquid-liquid phase transition with a
possible liquid-liquid critical point for water, likely pre-empted by
inevitable freezing. For J=0 the liquid-liquid critical point disappears at
T=0.Comment: 8 pages, 4 figure
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