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 $J_\sigma$, using mean field theory and off-lattice Monte Carlo simulations. For all $J_\sigma\geq 0$, the model displays a temperature of maximum density.For a finite intra-molecular interaction $J_\sigma > 0$,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