Core-softened potentials and the anomalous properties of waterE. A. Jaglaa)The Abdus Salam International Centre for Theoretical Physics (ICTP), I-34014 Trieste, Italy共Received 1 June 1999; accepted 4 August 1999兲We study the phase diagram of a system of spherical particles interacting in three dimensionsthrough a potential consisting of a strict hard core plus a linear repulsive shoulder at larger distances.The phase diagram 共obtained numerically, and analytically in a limiting case兲 shows anomalousproperties that are similar to those observed in water. Specifically, we find maxima of density andisothermal compressibility as a function of temperature, melting with volume contraction, andmultiple stable crystalline structures. If in addition a long range attraction between the particles isincluded, the usual liquid–gas coexistence curve with its critical point is obtained. But moreinterestingly, a first order line in the metastable fluid branch of the phase diagram appears, endingin a new critical point, as it was suggested to occur in water. In this way the model provides acomprehensive, consistent and unified picture of most of the anomalous thermodynamical propertiesof water, showing that all of them can be qualitatively explained by the existence of two competingequilibrium values for the interparticle distance. © 1999 American Institute of Physics.关S0021-9606共99兲50241-9兴I. INTRODUCTIONWater is an anomalous substance in many respects.1Liq-uid water has a maximum as a function of temperature inboth density and isothermal compressibility. It solidifies withvolume increasing at low pressures, and the solid phase 共ice兲shows a remarkable variety of crystalline structures in differ-ent sectors of the pressure–temperature plane. Some of theseproperties are known from long ago, but their origin is stillcontroversial. In an effort to rationalize these anomalousproperties, the supercooled 共metastable兲 sector of the phasediagram of liquid water has received much attention in thelast years.2–6It was observed that when appropriately cooled共using techniques for preventing crystallization兲 water be-comes a viscous fluid with many properties 共as heat capacityand isothermal compressibility兲 displaying a tendency thathas suggested even a thermodynamic singularity at somelower temperature.7Although there is a limit of about 235 Kbelow which water cannot be cooled without crystallization,amorphous states of water at much lower temperatures canbe obtained by different techniques. All these amorphousstates are observed to correspond to one of two differentstructures 关referred to as low-density amorphous 共LDA兲 andhigh-density amorphous 共HDA兲兴 that differ by about 20% indensity, which transform reversibly one into the other uponchanges of pressure.8There is evidence that these amorphousstates are thermodynamically connected with fluid water, al-though a direct verification is not possible due to recrystalli-zation at intermediate temperatures.9The observation of LDA and HDA was an experimentalclue that led to the proposal of the second critical pointhypothesis.3,10,11This hypothesis states that in the deeply su-percooled region water can exist in two different amorphousconfigurations, separated by a line of first order transitions.This line should end in a critical point very much as theusual liquid–vapor line ends in a critical point. This hypoth-esis, in addition to obviously explain the reversible transfor-mation between LDA and HDA, provides a natural thoughphenomenological explanation for the anomalous behaviorof density and isothermal compressibility. However, the veryexistence of the second critical point is known to be unnec-essary for the appearance of other anomalies,12,13and theissue of what the microscopic properties of water moleculesare that may produce the appearance of the second criticalpoint is poorly understood. In all cases it seems to be crucialthat water 共because of the particular form of its moleculesand peculiarities of the hydrogen bond兲 exhibits competitionbetween more expanded structures 共preferred at low pres-sures兲 and more compact ones 共which are favored at highpressures兲. But it is not obvious to what extent this simplefact can be made responsible for all the anomalies of water,or if more subtle properties of the interaction potential 共inparticular, cooperative hydrogen bonding兲13,14are crucial.Numerical simulations based on some of the availablepair potentials for the interaction between water moleculesreproduce many of its properties reasonably well, althoughthe systems that have been studied are strongly limited insize, due to computational constraints.15,16These simulationsonly suggest the existence of the second critical point, but upto now they were not able to prove its existence unambigu-ously. Other simplified and in some cases ad hoc modelshave been devised to show the appearance of anomalousproperties in the phase diagram.17Some of these modelshave a second critical point, but in these cases a global char-acterization of the phase diagram that includes all otheranomalies has not been achieved. In all cases, the modelsused have as a fundamental ingredient the competition be-tween expanded, less dense structures, and compressed, moredense ones.It is the goal of the present work to show that a verya兲Electronic mail: [email protected] OF CHEMICAL PHYSICS VOLUME 111, NUMBER 19 15 NOVEMBER 199989800021-9606/99/111(19)/8980/7/$15.00 © 1999 American Institute of PhysicsDownloaded 05 May 2004 to 198.11.27.55. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jspsimple model of spherical particles interacting through a re-pulsive potential that possesses two different preferred equi-librium positions has a phase diagram in which: 共a兲 lines ofmaxima for the density and the isothermal compressibility ofthe liquid exist; 共b兲 the fluid phase freezes with an increase involume in some pressure range; and 共c兲 the solid phase hasmultiple different crystalline structures depending on P andT. When a long range van der Waals attraction is includedon top of the previous, exclusively repulsive potential, thesystem 共d兲 preserves the anomalies that exist in the nonat-tractive case; 共e兲 develops a liquid-gas first order coexistingline that ends in a critical point in the usual fashion; and 共f兲depending on the strength of the attractive
View Full Document
Unlocking...