A fundamental measure theory for the sticky hard sphere fluid

We construct a density functional theory (DFT) for the sticky hard sphere (SHS) fluid which, like Rosenfeld's fundamental measure theory (FMT) for the hard sphere fluid [Phys. Rev. Lett. {\bf 63}, 980 (1989)], is based on a set of weighted densities and an exact result from scaled particle theory (SPT). It is demonstrated that the excess free energy density of the inhomogeneous SHS fluid $\Phi_{\text{SHS}}$ is uniquely defined when (a) it is solely a function of the weighted densities from Kierlik and Rosinberg's version of FMT [Phys. Rev. A {\bf 42}, 3382 (1990)], (b) it satisfies the SPT differential equation, and (c) it yields any given direct correlation function (DCF) from the class of generalized Percus-Yevick closures introduced by Gazzillo and Giacometti [J. Chem. Phys. {\bf 120}, 4742 (2004)]. The resulting DFT is shown to be in very good agreement with simulation data. In particular, this FMT yields the correct contact value of the density profiles with no adjustable parameters. Rather than requiring higher order DCFs, such as perturbative DFTs, our SHS FMT produces them. Interestingly, although equivalent to Kierlik and Rosinberg's FMT in the case of hard spheres, the set of weighted densities used for Rosenfeld's original FMT is insufficient for constructing a DFT which yields the SHS DCF.Comment: 11 pages, 3 figure

Theory of ice premelting in porous media

Premelting describes the confluence of phenomena that are responsible for the stable existence of the liquid phase of matter in the solid region of its bulk phase diagram. Here we develop a theoretical description of the premelting of water ice contained in a porous matrix, made of a material with a melting temperature substantially larger than ice itself, to predict the amount of liquid water in the matrix at temperatures below its bulk freezing point. Our theory combines the interfacial premelting of ice in contact with the matrix, grain boundary melting in the ice, and impurity and curvature induced premelting, the latter occurring in regions which force the ice-liquid interface into a high curvature configuration. These regions are typically found at points where the matrix surface is concave, along contact lines of a grain boundary with the matrix, and in liquid veins. Both interfacial premelting and curvature induced premelting depend on the concentration of impurities in the liquid, which, due to the small segregation coefficient of impurities in ice are treated as homogeneously distributed in the premelted liquid. Our principal result is an equation for the fraction of liquid in the porous medium as a function of the undercooling, which embodies the combined effects of interfacial premelting, curvature induced premelting, and impurities. The result is analyzed in detail and applied to a range of experimentally relevant settings.Comment: 14 pages, 10 figures, accepted for publication in Physical Review

Grain boundary melting in ice

We describe an optical scattering study of grain boundary premelting in water ice. Ubiquitous long ranged attractive polarization forces act to suppress grain boundary melting whereas repulsive forces originating in screened Coulomb interactions and classical colligative effects enhance it. The liquid enhancing effects can be manipulated by adding dopant ions to the system. For all measured grain boundaries this leads to increasing premelted film thickness with increasing electrolyte concentration. Although we understand that the interfacial surface charge densities $q_s$ and solute concentrations can potentially dominate the film thickness, we can not directly measure them within a given grain boundary. Therefore, as a framework for interpreting the data we consider two appropriate $q_s$ dependent limits; one is dominated by the colligative effect and one is dominated by electrostatic interactions.Comment: 6 pages, 5 figure

Bifurcation in the growth of continental crust

Is the present-day water-land ratio a necessary outcome of the evolution of plate tectonic planets with a similar age, volume, mass, and total water inventory as the Earth? This would be the case - largely independent of initial conditions - if Earth's present-day continental volume were at a stable unique equilibrium with strong self-regulating mechanisms of continental growth steering the evolution to this state. In this paper, we question this conjecture. Instead we suggest that positive feedbacks in the plate tectonics model of continental production and erosion may dominate and show that such a model can explain the history of continental growth. We investigate the main mechanisms that contribute to the growth of the volume of the continental crust. In particular, we analyze the effect of the oceanic plate speed, depending on the area and thickness of thermally insulating continents, on production and erosion mechanisms. Effects that cause larger continental production rates for larger values of continental volume are positive feedbacks. In contrast, negative feedbacks act to stabilize the continental volume. They are provided by the increase of the rate of surface erosion, subduction erosion, and crustal delamination with the continental volume. We systematically analyze the strengths of positive and negative feedback contributions to the growth of the continental crust. Although the strengths of some feedbacks depend on poorly known parameters, we conclude that a net predominance of positive feedbacks is plausible. We explore the effect of the combined feedback strength on the feasibility of modeling the observed small positive net continental growth rate over the past 2-3 billion years

Density functional theory for hard-sphere mixtures: the White-Bear version Mark II

In the spirit of the White-Bear version of fundamental measure theory we derive a new density functional for hard-sphere mixtures which is based on a recent mixture extension of the Carnahan-Starling equation of state. In addition to the capability to predict inhomogeneous density distributions very accurately, like the original White-Bear version, the new functional improves upon consistency with an exact scaled-particle theory relation in the case of the pure fluid. We examine consistency in detail within the context of morphological thermodynamics. Interestingly, for the pure fluid the degree of consistency of the new version is not only higher than for the original White-Bear version but also higher than for Rosenfeld's original fundamental measure theory.Comment: 16 pages, 3 figures; minor changes; J. Phys.: Condens. Matter, accepte

On the decay of the pair correlation function and the line of vanishing excess isothermal compressibility in simple fluids

We re-visit the competition between attractive and repulsive interparticle forces in simple fluids and how this governs and connects the macroscopic phase behavior and structural properties as manifest in pair correlation functions. We focus on the asymptotic decay of the total correlation function $h(r)$ which is, in turn, controlled by the form of the pair direct correlation function $c(r)$. The decay of $r h(r)$ to zero can be either exponential (monotonic) if attraction dominates repulsion and exponentially damped oscillatory otherwise. The Fisher-Widom (FW) line separates the phase diagram into two regions characterized by the two different types of asymptotic decay. We show that there is a new and physically intuitive thermodynamic criterion which approximates well the actual FW line. This new criterion defines a line where the isothermal compressibility takes its ideal gas value $\chi_T=\chi_T^\text{id}$. We test our hypothesis by considering four commonly used models for simple fluids. In all cases the new criterion yields a line in the phase diagram that is close to the actual FW line for the thermodynamic state points that are most relevant. We also investigate (Widom) lines of maximal correlation length, emphasizing the importance of distinguishing between the true and Ornstein-Zernike correlation length

A hard-sphere model on generalized Bethe lattices: Statics

We analyze the phase diagram of a model of hard spheres of chemical radius one, which is defined over a generalized Bethe lattice containing short loops. We find a liquid, two different crystalline, a glassy and an unusual crystalline glassy phase. Special attention is also paid to the close-packing limit in the glassy phase. All analytical results are cross-checked by numerical Monte-Carlo simulations.Comment: 24 pages, revised versio