文档库 最新最全的文档下载
当前位置:文档库 › NaCl nanodroplet on NaCl(100) at the melting point

NaCl nanodroplet on NaCl(100) at the melting point

a r X i v :c o n d -m a t /0410047v 1 [c o n d -m a t .m t r l -s c i ] 2 O c t 2004NaCl nanodroplet on NaCl(100)at the melting point T.Zykova-Timan a ,

b ,?,U.Tartaglino a ,b ,D.Ceresoli a ,b ,W.Sekkal-Zaoui

c an

d E.Tosatti a ,b ,c a International School for Advanced Studies (SISSA-ISAS),via Beirut 2,34014Trieste,Italy b INFM Democritos National Simulation Center,Trieste,Italy c International Center for Theoretical Physics (ICTP),Strada Costiera 11,34014,Trieste,Italy 1Introduction

A long known unusual property of molten alkali halide salts is their remarkable inability to wet their own solid surface at the melting point,giving rise,in particular to a partial wetting angle as large as 48?on NaCl(100)[1,2].While partial self-wetting must generically arise when there is non-melting of the solid surface,as has been long known e.g.for metal surfaces [4],there are so

far no theoretical studies of either e?ects in ionic systems.In our work[3]we have investigated the properties of solid NaCl(100)near to the melting point in contact with a droplet of its own liquid.

2Method of calculation

We carried out extensive classical molecular dynamics simulations of a nan-odroplet of liquid NaCl deposited on the solid NaCl surface.For NaCl,whose molecular model was described by the Born-Mayer-Huggins potential as pa-rameterized by Fumi and Tosi[5,6],the Coulomb long-range interactions were treated by the standard3-dimensional Ewald method[7].The convergence parameters for the Ewald summations were chosen in order to converge the real and reciprocal space sums to a given tolerance(10?5Hartree per atom). We simulated NaCl bulk systems and slabs with(100)orientation,consist-ing of about4000–5000molecular units.The chosen time step was1fs,and the typical simulation time was200ps.After verifying that the bulk ther-modynamic properties of solid NaCl(melting temperature,lattice expansion, volume jump at melting point[3])are very well described we simulated the approach of a NaCl droplet on NaCl(100)surface.

We prepared a7200atom crystalline slab,8atomic planes thick(15×15×4(NaCl)4conventional cubic cells).The slab was gradually heated up to the bulk melting point,keeping two atomic layers rigidly?xed at the bottom of the slab,however with a lattice spacing growing with T,in order to simulate a thermally expanding semi-in?nite solid.Separately we prepared a small NaCl cluster consisting of500NaCl molecular units.The size of this cluster was large enough to yield after melting a near-spherical drop,and also a well-de?ned shape when the drop is deposited on the surface.The cluster was melted by heating above the bulk melting temperature(T M=1066±20K in our model in good agreement with the experimental value T exp M=1074K[3]),and then it was equilibrated at T=T M for100ps,yielding a well-de?ned spherical liquid droplet of radius18?A.

Finally,we placed the drop near the solid NaCl(100)slab surface,the lower-most atoms of the drop a distance4?A from the surface(?g.1a).Zero vertical velocity was assigned to the drop center of mass but the drop expanded any-way to touch the surface.As soon as the drop contacted the surface,attempts at equilibrating the system at the theoretical melting temperature(T M)failed, and the whole solid NaCl slab melted very quickly,which is compatible with the‘fragile’nature of non-melting of solid NaCl(100)[3].At a much lower temperature than T M(1000K)on the contrary,the substrate remained solid, while the drop spread slightly only at the beginning but then crystallized,

forming a nice“stepped”pyramid,made up of(100)facets.We succeeded ?nally in equilibrating the liquid nanodroplet on the solid surface at the inter-

mediate temperature of1050K,which is only slightly below T M of our model. This is described in the following section.

3Results

The nanodroplet and the solid slab were separately equilibrated at1050K.

During the?rst100ps after contact,the droplet settled down on the substrate, gradually approaching the?nal shape(?g.1b-d).In the next130ps,the droplet survived in a(not clear if metastable or unstable,but long lived)state

without spreading appreciably(?g.1e-f).At the end of our simulation,the droplet–substrate system looked like?g.1h.The top view of?g.2shows

that the drop spread almost circularly.

Before proceeding with further descriptions,it is important to specify the thermodynamics of this situation.Because we are below T M(even if slightly) the?nal equilibrium state should consist of a?at solid NaCl(100)surface,i.e.

the nanodroplet should completely spread and recrystallize.That however will take a very long time.While the nanodroplet exists,it will form an external wetting angleθL V(?g.1),as well as an internal angleθSL.The latterθSL is

irrelevant here,because it depends critically on the temperature and on the time.In particular at short times and not too far from T M we expectθSL≈0. The external angleθL V is instead signi?cant,as it should equal the macroscopic wetting angle measured in the bubble experiment[1,2].

Assuming quasi equilibrium for the liquid nanodroplet in the sense speci?ed above,this angle will obey Young’s equation(?g.3)

γSL+γL V cosθL V=γSV(1) where theγ’s are the interface free energies.

To determine the external wetting angleθL V of the nanodroplet we analyzed

100con?gurations in last100ps.The instantaneous atomic positions were plotted in cylindrical coordinates(r and z,where r is parallel to the surface),

and from the pro?le of the drop,we determined the best approximation to a portion of a sphere,by determining the center position and the radius.The contact angle follows immediately by simple geometry from these two quanti-

ties.Our best estimate slightly below T M isθL V=50?±5?which is in excellent agreement with the experiment value at the melting point(48?)[1].At the end of the simulation the internal solid-liquid interface was still relatively sharp

and?at,consistent with our assumptionθSL≈0.

The thermodynamical reason leading to the large observedθL V can now be analyzed.As eq.(1)shows,a large value ofθL V may arise either due to a large valueγSL,or to a smallγSV,relative toγL V or to both.These free energies at T≈T M are all presently unknown.While simulations are presently under way to calculateγSV[3],we can already anticipate on purely physical arguments that both factors namely,a largeγSL and a smallγSV,will indeed occur on NaCl(100).The liquid and the solid di?er enormously,in density and other properties,and this does suggest thatγSL has no reason to be small,as it was instead in the case of metals.The solid surface free energy is instead small due to a good cancellation of the Coulomb potential outside the(100)surface, and also to a good vibrational free energy of the hot solid surface[3].

4Discussion

We can now try to relate further the wetting angleθL V to more microscopic quantities.Di Tolla et al.[4]showed that for a non-melting metal surface,the angleθL V could be related through a simple model to the surface spinodal temperature T S,that is the maximum temperature above T M to which the non-melting surface can be overheated.As discussed in a companion paper to this[3],the very same model must be improved in order to describe NaCl, owing to the larger di?erences between solid and liquid.The free energy gain upon crystallizing the surface at T=T M,?γ∞=(γL V+γSL)?γSV is related to the partial contact angle through Young’s equation(1)

cosθL V=1?

?γ∞

2cos

2πl

With our value of?γ∞,and L=4.813×109erg/gr,a=5.9?A we predict T S=1210K,very close to that seen in simulations.[3]

5Conclusion

In conclusion,molecular dynamics simulations indicate that metastable liquid NaCl nanodroplets on solid NaCl(100)can exist for some time close to T M. They are found to exhibit an unusually large partial wetting angle,whose value is in agreement with the large macroscopic wetting angle observed in the bubble experiment.Thermodynamically this appears to be caused by an unusual small value of the solid-vapor interface free energy,as well as by a large solid-liquid interface free energy.The free energy di?erences extracted via Young’s equation can also be connected well with other properties,such as the solid surface spinodal temperature.

Acknowledgments

Project was sponsored by Italian Ministry of University and Research,through COFIN02,COFIN03,and FIRB RBAU01LX5H;and by INFM,through PRA NANORUB and and“Iniziativa Trasversale calcolo parallelo”.Calculations were performed on the IBM-SP4at CINECA,Casalecchio(Bologna). References

[1]G.Grange and B.Mutaftschiev,Surf.Sci.47,723(1975).

[2] B.Mutaftschiev,J.Cryst.Growth182,205(1997).

[3]T.Zykova-Timan,U.Tartaglino,D.Ceresoli,W.Sekkal-Zaoui,E.A.Jagla and

E.Tosatti,to be published.

[4] F.D.Di Tolla,F.Ercolessi and E.Tosatti,Phys.Rev.Lett.74,3201(1995);

F.D.Di Tolla,E.Tosatti and F.Ercolessi,Interplay of melting,wetting,

overheating and faceting on metal surfaces:theory and simulation,in Monte Carlo and molecular dynamics of condensed matter systems(ed.by K.Binder and G.Ciccotti),SIF,Bologna,1996.

[5]M.P.Tosi and F.Fumi,J.Chem.Phys.Solids25,45(1964).

[6]M.J.L.Sangster and M.Dixon,Adv.Phys.23,247(1976).

[7]M.A.Allen and D.J.Tildesley,“Computer Simulation of Liquids”,Oxford

Science Press,Oxford,1987.

[8] B.Pluis,T.N.Taylor,D.Frenkel and J.F.van der Veen,Phys.Rev.B40

(1989)1353.

c)d)a)b)e)t = 0 ps t = 30 ps t = 87 ps g)t = 115 ps t = 170 ps t = 230 ps f)h)t = 143 ps t = 200 ps Fig.1.Time evolution of the liquid NaCl drop on NaCl(100).Dark and light circles stand for the Na +and Cl ?ions respectively.

Fig.2.Top view of the liquid droplet on the NaCl(100)after230ps.Dark and light circles stand for the Na+and Cl?ions respectively.

Fig.3.Sketch of the liquid drop partially wetting a solid substrate,showing the balance of the forces acting at the interfaces.

相关文档
相关文档 最新文档