arXiv subjects

Ignacio Urrutia

Publications and source records attributed to Ignacio Urrutia.

17 recordsLinked to original sources

arXiv2021

The fourth virial coefficient for hard spheres in even dimension

The fourth virial coefficient is calculated exactly for a fluid of hard spheres in even dimensions. For this purpose the complete star cluster integral is expressed as the sum of two three-folded integrals only involving spherical angular coordinates. These integrals are solved anallytically for any even dimension d and working with existing expressions for the other terms of the fourth cluster integral we obtain an expression for the fourth virial coefficient B4(d) for even d that sums a finite number of simple terms, with the number of terms increasing with d.

cond-mat.stat-mech↗

arXiv2019

Generalization of the Wall Theorem to Out-of-equilibrium Conditions

The well-known Wall theorem states a simple and precise relation among temperature, pressure and density of a fluid at contact with a confining hard wall in thermodynamic equilibrium. In this Letter we develop an extension of the Wall theorem to out-of-equilibrium conditions, providing an exact relation between pressure, density and temperaure at the wall, valid for strong non-equilibrium situations. We derive analytically this Non-equilibrium Wall theorem for stationary states and validate it with non-equilibrium event-driven molecular-dynamics simulations. We compare the analytical expression with simulations by direct evaluation of temperature, density and pressure on the wall in linear regime, medium and very strong out-of-equilibrium conditions of a nanoconfined liquid under flow in stationary state, presenting viscous heating and heat transport. The agreement between theory and simulation is excellent, allowing for a conclusive validation. In addition, we explore the degree of accuracy of using the equilibrium Wall theorem and different expressions for the local temperature, employed in non-equilibrium molecular-dynamics simulations.

cond-mat.stat-mech↗

arXiv2016

Bending and Gaussian rigidities of confined soft spheres from second-order virial series

We use virial series to study the equilibrium properties of confined soft-spheres fluids interacting through the inverse-power potentials. The confinement is induced by hard walls with planar, spherical and cylindrical shapes. We evaluate analytically the coefficients of order two in density of the wall-fluid surface tension $γ$ and analyze the curvature contributions to the free energy. Emphasis is in bending and Gaussian rigidities, which are found analytically at order two in density. Their contribution to $γ(R)$ and the accuracy of different truncation procedures to the low curvature expansion are discussed. Finally, several universal relations that apply to low-density fluids are analyzed.

cond-mat.soft↗

arXiv2016

Virial series for inhomogeneous fluids applied to the Lennard-Jones wall-fluid surface tension at planar and curved walls

We formulate a straightforward scheme of statistical mechanics for inhomogeneous systems that includes the virial series in powers of the activity for the grand free energy and density distributions. There, cluster integrals formulated for inhomogeneous systems play a main role. We center on second order terms that were analyzed in the case of hard-wall confinement, focusing in planar, spherical and cylindrical walls. Further analysis was devoted to the Lennard-Jones system and its generalization the 2k-k potential. For this interaction potentials the second cluster integral was evaluated analytically. We obtained the fluid-substrate surface tension at second order for the planar, spherical and cylindrical confinement. Spherical and cylindrical cases were analyzed using a series expansion in the radius including higher order terms. We detected a $\ln R^{-1}/R^{2}$ dependence of the surface tension for the standard Lennard-Jones system confined by spherical and cylindrical walls, no matter if particles are inside or outside of the hard-walls. The analysis was extended to bending and Gaussian curvatures, where exact expressions were also obtained.

cond-mat.soft↗

arXiv2015

Fluids confined in wedges and by edges: From cluster integrals to thermodynamic properties referred to different regions

Recently, new insights in the relation between the geometry of the vessel that confines a fluid and its thermodynamic properties were traced through the study of cluster integrals for inhomogeneous fluids. In this work I analyze the thermodynamic properties of fluids confined in wedges or by edges, emphasizing on the question of the region to which these properties refer. In this context, the relations between the line-thermodynamic properties referred to different regions are derived as analytic functions of the dihedral angle $α$ , for $0<α<2π$ , which enables a unified approach to both edges and wedges. As a simple application of these results, I analyze the properties of the confined gas in the low-density regime. Finally, using recent analytic results for the second cluster integral of the confined hard sphere fluid, the low density behavior of the line thermodynamic properties is analytically studied up to order two in the density for $0<α<2π$ and by adopting different reference regions.

cond-mat.soft↗

arXiv2015

Structure, thermodynamic properties, and phase diagrams of few colloids confined in a spherical pore

We study a system of few colloids confined in a small spherical cavity by event driven molecular dynamics simulations in the canonical ensemble. The colloidal particles interact through a short range square-well potential, which takes into account the basic elements of attraction and excluded-volume repulsion of the interaction among colloids. We analyze the structural and thermodynamic properties of this few-body confined system in the framework of the theory of inhomogeneous fluids. Pair correlation functions and density profiles across the cavity are used to determine the structure of the system and the spatial characteristics of its inhomogeneities. Pressure on the walls, internal energy and surface quantities such as surface tension and adsorption are also analyzed for the whole range of densities, temperatures and number of particles considered. We have characterized the structure of systems from 2 to 6 confined particles as function of density and temperature, identifying the distinctive qualitative behaviors all over the thermodynamic plane $T-ρ$ in a few-particle equivalence to phase diagrams of macroscopic systems. Applying the extended law of corresponding states the square well interaction is mapped to the Asakura-Oosawa model for colloid-polymer mixtures. We link explicitly the temperature in the confined square-well fluid to the equivalent packing fraction of polymers in the Asakura-Oosawa model. Using this approach we study the confined system of few colloids in a colloid-polymer mixture.

cond-mat.soft↗

arXiv2014

An exact formalism to study the thermodynamic properties of hard-sphere systems under spherical confinement

This paper presents a modified grand canonical ensemble which provides a new simple and efficient scheme to study few-body fluid-like inhomogeneous systems under confinement. The new formalism is implemented to investigate the exact thermodynamic properties of a hard sphere (HS) fluid-like system with up to three particles confined in a spherical cavity. In addition, the partition function of this system was used to analyze the surface thermodynamic properties of the many-HS system and to derive the exact curvature dependence of both the surface tension and adsorption in powers of the density. The expressions for the surface tension and the adsorption were also obtained for the many- HS system outside of a fixed hard spherical object. We used these results to derive the dependence of the fluid-substrate Tolman length up to first order in density.

cond-mat.stat-mech↗

arXiv2014

Mean properties and Free Energy of a few hard spheres confined in a spherical cavity

We use analytical calculations and event-driven molecular dynamics simulations to study a small number of hard sphere particles in a spherical cavity. The cavity is taken also as the thermal bath so that the system thermalizes by collisions with the wall. In that way, these systems of two, three and four particles, are considered in the canonical ensemble. We characterize various mean and thermal properties for a wide range of number densities. We study the density profiles, the components of the local pressure tensor, the interface tension, and the adsorption at the wall. This spans from the ideal gas limit at low densities to the high-packing limit in which there are significant regions of the cavity for which the particles have no access, due the conjunction of excluded volume and confinement. The contact density and the pressure on the wall are obtained by simulations and compared to exact analytical results. We also obtain the excess free energy for N=4, by using a simulated-assisted approach in which we combine simulation results with the knowledge of the exact partition function for two and three particles in a spherical cavity.

cond-mat.soft↗

arXiv2013

Bending rigidity and higher order curvature terms for the hard-sphere fluid near a curved wall

In this work I derive analytic expressions for the curvature dependent fluid-substrate surface tension of a hard sphere fluid on a hard curved wall. In a first step, the curvature thermodynamic properties are found as truncated power series in the activity in terms of the known second and third order cluster integral of the hard-sphere fluid near spherical and cylindrical walls. These results are then expressed as packing fraction power series and transformed to different reference regions which is equivalent to consider different positions of the dividing surface. All the obtained series expansions are rigorous results. Based on the truncated series it is shown that the bending rigidity of the system is non-null and that higher order terms in the curvature also exist. In a second step, approximate analytic expressions for the surface tension, the Tolman length, the bending rigidity and the Gaussian rigidity as functions of the packing fraction are found by considering the known terms of the series expansion complemented with a simple fitting approach. It is found that the obtained formulas accurately describe the curvature thermodynamic properties of the system, further, they are more accurate than any of the previously published expressions.

cond-mat.soft↗

arXiv2013

Statistical mechanics of fluids confined by polytopes: The hidden geometry of the cluster integrals

This paper, about a fluid-like system of spatially confined particles, reveals the analytic structure for both, the canonical and grand canonical partition functions. The studied system is inhomogeneously distributed in a region whose boundary is made by planar faces without any particular symmetry. This type of geometrical body in the $d$-dimensional space is a polytope. The presented result in the case of $d=3$ gives the conditions under which the partition function is a polynomial in the volume, surface area, and edges length of the confinement vessel. Equivalent results for the cases $d=1,2$ are also obtained. Expressions for the coefficients of each monomial are explicitly given using the cluster integral theory. Furthermore, the consequences of the polynomial shape of the partition function on the thermodynamic properties of the system, away from the so-called thermodynamic limit, is studied. Some results are generalized to the $d$-dimensional case. The theoretical tools utilized to analyze the structure of the partition functions are largely based on integral geometry.

cond-mat.stat-mech↗

arXiv2010

Two hard spheres in a pore: Exact Statistical Mechanics for different shaped cavities

The Partition function of two Hard Spheres in a Hard Wall Pore is studied appealing to a graph representation. The exact evaluation of the canonical partition function, and the one-body distribution function, in three different shaped pores are achieved. The analyzed simple geometries are the cuboidal, cylindrical and ellipsoidal cavities. Results have been compared with two previously studied geometries, the spherical pore and the spherical pore with a hard core. The search of common features in the analytic structure of the partition functions in terms of their length parameters and their volumes, surface area, edges length and curvatures is addressed too. A general framework for the exact thermodynamic analysis of systems with few and many particles in terms of a set of thermodynamic measures is discussed. We found that an exact thermodynamic description is feasible based in the adoption of an adequate set of measures and the search of the free energy dependence on the adopted measure set. A relation similar to the Laplace equation for the fluid-vapor interface is obtained which express the equilibrium between magnitudes that in extended systems are intensive variables. This exact description is applied to study the thermodynamic behavior of the two Hard Spheres in a Hard Wall Pore for the analyzed different geometries. We obtain analytically the external work, the pressure on the wall, the pressure in the homogeneous zone, the wall-fluid surface tension, the line tension and other similar properties.

cond-mat.stat-mech↗

arXiv2009

Statistical Mechanics of Two Hard Spheres in a Spherical Pore, Exact Analytic Results in D Dimension

This work is devoted to the exact statistical mechanics treatment of simple inhomogeneous few-body systems. The system of two Hard Spheres (HS) confined in a hard spherical pore is systematically analyzed in terms of its dimensionality >. The canonical partition function, and the one- and two-body distribution functions are analytically evaluated and a scheme of iterative construction of the system properties is presented. We analyse in detail both the effect of high confinement, when particles become caged, and the low density limit. Other confinement situations are also studied analytically and several relations between, the two HS in a spherical pore, two sticked HS in a spherical pore, and two HS on a spherical surface partition functions are traced. These relations make meaningful the limiting caging and low density behavior. Turning to the system of two HS in a spherical pore, we also analytically evaluate the pressure tensor. The thermodynamic properties of the system are discussed. To accomplish this statement we purposely focus in the overall characteristics of the inhomogeneous fluid system, instead of concentrate in the peculiarities of a few body system. Hence, we analyse the equation of state, the pressure at the wall, and the fluid-substrate surface tension. The consequences of new results about the spherically confined system of two HS in D dimension on the confined many HS system are investigated. New constant coefficients involved in the low density limit properties of the open and closed system of many HS in a spherical pore are obtained for arbitrary. The complementary system of many HS which surrounds a hard sphere (a cavity inside of a bulk HS system) is also discussed.

cond-mat.stat-mech↗

arXiv2008

Two hard spheres in a spherical pore: Exact analytic results in two and three dimensions

The partition function and the one- and two-body distribution functions are evaluated for two hard spheres with different sizes constrained into a spherical pore. The equivalent problem for hard disks is addressed too. We establish a relation valid for any dimension between these partition functions, second virial coefficient for inhomogeneous systems in a spherical pore, and third virial coefficients for polydisperse hard spheres mixtures. Using the established relation we were able to evaluate the cluster integral $b_{2}(V)$ related with the second virial coefficient for the Hard Disc system into a circular pore. Finally, we analyse the behaviour of the obtained expressions near the maximum density.

cond-mat.stat-mech↗

arXiv2006

Surface term for the capillary condensation transitions in a slit geometry

It is shown that a bare simple fluid model (SFM) proposed some years ago for studying adsorption between two semi-infinite solid walls can be improved by modifying the surface term in the grand potential for the film phase. Such a correction substantially improves the agreement between the predictions for phase transitions provided by that SFM and results obtained from calculations carried out for $^4$He with the density-functional method at zero temperature. The corrective term depends on the strength of the adsorption potential and observables of bulk helium.

cond-mat.soft↗

arXiv2006

Capillary condensation for fluids in spherical cavities

The capillary condensation for fluids into spherical nano-cavities is analyzed within the frame of two theoretical approaches. One description is based on a widely used simplified version of the droplet model formulated for studying atomic nuclei. The other, is a more elaborated calculation performed by applying a density functional theory. The agreement between both models is examined and it is shown that a small correction to the simple fluid model improves the predictions. A connection to results previously obtained for planar slits and cylindrical pores is done.

cond-mat.soft↗

arXiv2003

Adsorption of $^4$He on a single C$_{60}$

The adsorption of $^4$He inside and outside a single fullerene C$_{60}$ is studied. A physisorption potential is proposed. The energetics and structural features of C$_{60}$-$^4$He$_N$ clusters are investigated. Particular attention is paid to the growth of the highly pronounced layered density profile. The evolution towards bulk liquid and surface thickness at the free interface are discussed.

cond-mat.soft↗

arXiv2003

Curvature effects on the surface thickness and tension at the free interface of $^4$He systems

The thickness $W$ and the surface energy $σ_A$ at the free interface of superfluid $^4$He are studied. Results of calculations carried out by using density functionals for cylindrical and spherical systems are presented in a unified way, including a comparison with the behavior of planar slabs. It is found that for large species $W$ is independent of the geometry. The obtained values of $W$ are compared with prior theoretical results and experimental data. Experimental data favor results evaluated by adopting finite range approaches. The behavior of $σ_A$ and $W σ_A$ exhibit overshoots similar to that found previously for the central density, the trend of these observables towards their asymptotic values is examined.

cond-mat.soft↗