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Register a new userCorrelation between thermodynamic anomalies and pathways of ice nucleation in supercooled water
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The well-known classical nucleation theory (CNT) for the free energy barrier towards formation of a nucleus of critical size of the new stable phase within the parent metastable phase fails to take into account the influence of other metastable phases having density/order intermediate between the parent metastable phase and the final stable phase. This lacuna can be more serious than capillary approximation or spherical shape assumption made in CNT. This issue is particularly significant in ice nucleation because liquid water shows rich phase diagram consisting of two (high and low density) liquid phases in supercooled state. The explanations of thermodynamic and dynamic anomalies of supercooled water often invoke the possible influence of a liquid-liquid transition between two metastable liquid phases. To investigate both the role of thermodynamic anomalies and presence of distinct metastable liquid phases in supercooled water on ice nucleation, we employ density functional theoretical approach to find nucleation free energy barrier in different regions of phase diagram. The theory makes a number of striking predictions, such as a dramatic lowering of nucleation barrier due to presence of a metastable intermediate phase and crossover in the dependence of free energy barrier on temperature near liquid-liquid critical point. These predictions can be tested by computer simulations as well as by controlled experiments.
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Liquid polyamorphism is the intriguing possibility for a single component substance to exist in multiple liquid phases. We propose a minimal model for this phenomenon. Starting with a classical binary lattice model with critical azeotropy and liquid-liquid demixing, we allow interconversion of the two species, turning the system into a single-component fluid with two states differing in energy and entropy. Changing one interaction parameter allows to continuously switch from a liquid-liquid transition, terminated by a critical point, to a singularity-free scenario, exhibiting water-like anomalies but without polyamorphism. This resolves a controversy about how a liquid-liquid critical point can be found or not in simulations. The model provides a unified theoretical framework to describe supercooled water and a variety of polyamorphic liquids with water-like anomalies.
Deeply supercooled water exhibits complex dynamics with large density fluctuations, ice coarsening and characteristic time scales extending from picoseconds to milliseconds. Here, we discuss implications of these time scales as they pertain to two-phase coexistence and to molecular simulations of supercooled water. Specifically, we argue that it is possible to discount liquid-liquid criticality because the time scales imply that correlation lengths for such behavior would be bounded by no more than a few nanometers. Similarly, it is possible to discount two-liquid coexistence because the time scales imply a bounded interfacial free energy that cannot grow in proportion to a macroscopic surface area. From time scales alone, therefore, we see that coexisting domains of differing density in supercooled water can be no more than nano-scale transient fluctuations.
We investigate the energetics of droplets sourced by the thermal fluctuations in a system undergoing a first-order transition. In particular, we confine our studies to two dimensions with explicit calulations in the plane and on the sphere. Using an isoperimetric inequality from the differential geometry literature and a theorem on the inequalitys saturation, we show how geometry informs the critical droplet size and shape. This inequality establishes a mean field result for nucleated droplets. We then study the effects of fluctuations on the interfaces of droplets in two dimensions, treating the droplet interface as a fluctuating line. We emphasize that care is needed in deriving the line curvature energy from the Landau-Ginzburg energy functional and in interpreting the scalings of the nucleation rate with the size of the droplet. We end with a comparison of nucleation in the plane and on a sphere.
Estimating the homogeneous ice nucleation rate from undercooled liquid water is at the same time crucial for understanding many important physical phenomena and technological applications, and challenging for both experiments and theory. From a theoretical point of view, difficulties arise due to the long time scales required, as well as the numerous nucleation pathways involved to form ice nuclei with different stacking disorders. We computed the homogeneous ice nucleation rate at a physically relevant undercooling for a single-site water model, taking into account the diffuse nature of ice-water interfaces, stacking disorders in ice nuclei, and the addition rate of particles to the critical nucleus.We disentangled and investigated the relative importance of all the terms, including interfacial free energy, entropic contributions and the kinetic prefactor, that contribute to the overall nucleation rate.There has been a long-standing discrepancy for the predicted homogeneous ice nucleation rates, and our estimate is faster by 9 orders of magnitude compared with previous literature values. Breaking down the problem into segments and considering each term carefully can help us understand where the discrepancy may come from and how to systematically improve the existing computational methods.
The equilibrium properties of a Janus fluid made of two-face particles confined to a one-dimensional channel are revisited. The exact Gibbs free energy for a finite number of particles $N$ is exactly derived for both quenched and annealed realizations. It is proved that the results for both classes of systems tend in the thermodynamic limit ($Ntoinfty$) to a common expression recently derived (Maestre M A G and Santos A 2020 J Stat Mech 063217). The theoretical finite-size results are particularized to the Kern--Frenkel model and confirmed by Monte Carlo simulations for quenched and (both biased and unbiased) annealed systems.
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