JACS ART I CLES Published on Web 08/26/2008 Nanosolids,Slushes,and Nanoliquids:Characterization of Nanophases in Metal Clusters and Nanoparticles Zhen Hua Li*t and Donald G.Truhlar*+ Department of Chemistry,Fudan University,Shanghai,200433,China and Department of Chemistry and Supercomputing Institute,University of Minnesota, Minneapolis,Minnesota 55455-0431 Received April 3,2008;E-mail:lizhenhua@fudan.edu.cn;truhlar@umn.edu Abstract:One of the keys to understanding the emergent behavior of complex materials and nanoparticles is understanding their phases.Understanding the phases of nanomaterials involves new concepts not present in bulk materials;for example,the phases of nanoparticles are quantum mechanical even when no hydrogen or helium is present.To understand these phases better,molecular dynamics(MD)simulations on size-selected particles employing a realistic analytic many-body potential based on quantum mechanical nanoparticle calculations have been performed to study the temperature-dependent properties and melting transitions of free Aln clusters and nanoparticles with n=10-300 from 200 to 1700 K.By analyzing properties of the particles such as specific heat capacity (c),radius of gyration,volume,coefficient of thermal expansion (B),and isothermal compressibility (K),we developed operational definitions of the solid,slush,and liquid states of metal clusters and nanoparticles.Applying the definitions,which are based on the temperature dependences of c.B,and In k,we determined the temperature domains of the solid,slush,and liquid states of the Al particles.The results show that Al clusters(n<18,diameter of less than 1 nm)are more like molecules,and it is more appropriate to say that they have no melting transition,but Al nanoparticles (n>19,diameter of more than 1 nm)do have a melting transition and are in the liquid state above 900-1000 K.However,all aluminum nanoparticles have a wide temperature interval corresponding to the slush state in which the solid and liquid states coexist in equilibrium,unlike a bulk material where coexistence occurs only at a single temperature (for a given pressure).The commonly accepted operational marker of the melting temperature,namely,the peak position of c,is not unambiguous and not appropriate for characterizing the melting transition for aluminum particles with the exception of a few particle sizes that have a single sharp peak(as a function of temperature)in each of the three properties,c,B,and In K. 1.Introduction we "borrow"concepts from well-studied ones.However,one Metal clusters and nanoparticles,as an intermediate form of must be careful when applying macroconcepts to finite systems matter!-7 between the composing atoms and the corresponding because these concepts may be ill defined for finite systems. bulk materials,have distinct electrical,optical,magnetic. For example,melting is well defined on the macroscale but not chemical,and catalytic properties and have been the subjects on the nanoscale.-13 Molecular dynamics simulations of metal of extensive experimental and theoretical study.Understanding nanoparticles have covered dynamic phase coistenc phe- the evolution of various physical and chemical properties from nomena not present in bulk metals.14- the atomic to the bulk limit is also of great fundamental and Understanding the molecular thermodynamics of nanophases practical interest.Often,when we face a new class of phenomena is a key enabler for the bottom-up approach to nanodesign.For macroscopic systems,a phase is a state with uniform20 or t Fudan University. continuously varying21 physical and chemical properties (in- University of Minnesota. tensive thermodynamic variables)in a well-defined temperature (1)Bonacic-Koutecky,V.;Fantucci,P.;Koutecky,J.Chem.Rev.1991. and pressure range.The change from one phase to another phase 91,1035.de Heer,W.A.Rev.Mod.Phys.1993,65,611. (2)Feldheim,D.L.:Foss.C.A.Metal Nanoparticles:Synthesis, Characterization,and Applications;Marcel Dekker.New York,2002. (8)Berry,R.S.;Jellinek,J.;Natanson,G.Phys.Rev.A 1984,30,919. (3)Buchachenko,A.L.Russ.Chem.Rev.2003,72,375. (9)Beck,T.L.;Jellinek,J.:Berry,R.S.J.Chem.Phrys.1987,87,545. (4)Schmid,G.Nanoparticles:From Theory to Applications;Wiley-VCH: (10)Berry.R.S.:Wales,D.J.Phys.Rev.Lett.1989,63,1156.(a)Wales. Weinheim,2004. D.J.:Berry,R.S.J.Chem.Phys.1990.92.4473.Berry.R.S. (5)Chan,K.-Y.;Ding,J.:Ren,J.:Cheng,S.:Tsang,K.Y.J.Mater. J.Chem.Soc.,Faraday Trans.1990,86,2343.Berry,R.S.Sci.Am. Chem.2004,14,505.Heiz,U.;Bullock,E.L.J.Mater.Chem.2004. 1990,26368. 14.564.O'Hair.R.A.J.:Khairallah.G.N.J.Cluster Sci.2004./5. (11)Berry,R.S.In Clusters of Atoms and Molecules;Haberland,H.. 331. Ed.;Springer Series in Chemical Physics 52;Springer:Berlin,1994: (6)Baletto,F.:Ferrando.R.Rev.Mod.Phys.2005,77.371 p 187.Berry,R.S.Microscale Thermoplrys.Eng.1997,1,1. (7)Astruc,D.:Lu.F.:Aranzaes.T.R.Angew.Chem..Int.Ed.2005. Proykova,A.:Berry,R.S.J.Phys.B:At.Mol.Opt.Phys.2006.39. 44.7852.Watanabe,K.:Menzel,P.;Nilius,N.:Freund,H.-J.Chem. R167. Rev.2006,106,4301.Perepichka,D.F.:Rosei.F.Angew.Chem.. (12)Berry,R.S.C.R.Phys.2002.3,319. Int.Ed.2007.46,6006.Jellinek,J.Faraday Discuss.2008.138.11. (13)Schmidt,M.;Haberland,H.C.R.Phys.2002,3,327. 12698■J.AM.CHEM.S0C.2008,130,12698-12711 10.1021/ja802389d CCC:$40.75 2008 American Chemical SocietyNanosolids, Slushes, and Nanoliquids: Characterization of Nanophases in Metal Clusters and Nanoparticles Zhen Hua Li*,† and Donald G. Truhlar*,‡ Department of Chemistry, Fudan UniVersity, Shanghai, 200433, China and Department of Chemistry and Supercomputing Institute, UniVersity of Minnesota, Minneapolis, Minnesota 55455-0431 Received April 3, 2008; E-mail: lizhenhua@fudan.edu.cn; truhlar@umn.edu Abstract: One of the keys to understanding the emergent behavior of complex materials and nanoparticles is understanding their phases. Understanding the phases of nanomaterials involves new concepts not present in bulk materials; for example, the phases of nanoparticles are quantum mechanical even when no hydrogen or helium is present. To understand these phases better, molecular dynamics (MD) simulations on size-selected particles employing a realistic analytic many-body potential based on quantum mechanical nanoparticle calculations have been performed to study the temperature-dependent properties and melting transitions of free Aln clusters and nanoparticles with n ) 10-300 from 200 to 1700 K. By analyzing properties of the particles such as specific heat capacity (c), radius of gyration, volume, coefficient of thermal expansion (
), and isothermal compressibility (κ), we developed operational definitions of the solid, slush, and liquid states of metal clusters and nanoparticles. Applying the definitions, which are based on the temperature dependences of c,
, and ln κ, we determined the temperature domains of the solid, slush, and liquid states of the Aln particles. The results show that Aln clusters (n e 18, diameter of less than 1 nm) are more like molecules, and it is more appropriate to say that they have no melting transition, but Aln nanoparticles (n g 19, diameter of more than 1 nm) do have a melting transition and are in the liquid state above 900-1000 K. However, all aluminum nanoparticles have a wide temperature interval corresponding to the slush state in which the solid and liquid states coexist in equilibrium, unlike a bulk material where coexistence occurs only at a single temperature (for a given pressure). The commonly accepted operational marker of the melting temperature, namely, the peak position of c, is not unambiguous and not appropriate for characterizing the melting transition for aluminum particles with the exception of a few particle sizes that have a single sharp peak (as a function of temperature) in each of the three properties, c,
, and ln κ. 1. Introduction Metal clusters and nanoparticles, as an intermediate form of matter1-7 between the composing atoms and the corresponding bulk materials, have distinct electrical, optical, magnetic, chemical, and catalytic properties and have been the subjects of extensive experimental and theoretical study. Understanding the evolution of various physical and chemical properties from the atomic to the bulk limit is also of great fundamental and practical interest. Often, when we face a new class of phenomena we “borrow” concepts from well-studied ones. However, one must be careful when applying macroconcepts to finite systems because these concepts may be ill defined for finite systems. For example, melting is well defined on the macroscale but not on the nanoscale.8-13 Molecular dynamics simulations of metal nanoparticles have uncovered dynamic phase coexistence phe￾nomena not present in bulk metals.14-19 Understanding the molecular thermodynamics of nanophases is a key enabler for the bottom-up approach to nanodesign. For macroscopic systems, a phase is a state with uniform20 or continuously varying21 physical and chemical properties (in￾tensive thermodynamic variables) in a well-defined temperature and pressure range. The change from one phase to another phase † Fudan University. ‡ University of Minnesota. (1) Bonacic-Koutecky, V.; Fantucci, P.; Koutecky, J. Chem. ReV. 1991, 91, 1035. de Heer, W. A. ReV. Mod. Phys. 1993, 65, 611. (2) Feldheim, D. L.; Foss, C. A. Metal Nanoparticles: Synthesis, Characterization, and Applications; Marcel Dekker: New York, 2002. (3) Buchachenko, A. L. Russ. Chem. ReV. 2003, 72, 375. (4) Schmid, G. Nanoparticles: From Theory to Applications; Wiley-VCH: Weinheim, 2004. (5) Chan, K.-Y.; Ding, J.; Ren, J.; Cheng, S.; Tsang, K. Y. J. Mater. Chem. 2004, 14, 505. Heiz, U.; Bullock, E. L. J. Mater. Chem. 2004, 14, 564. O’Hair, R. A. J.; Khairallah, G. N. J. Cluster Sci. 2004, 15, 331. (6) Baletto, F.; Ferrando, R. ReV. Mod. Phys. 2005, 77, 371. (7) Astruc, D.; Lu, F.; Aranzaes, T. R. Angew. Chem., Int. Ed. 2005, 44, 7852. Watanabe, K.; Menzel, P.; Nilius, N.; Freund, H.-J. Chem. ReV. 2006, 106, 4301. Perepichka, D. F.; Rosei, F. Angew. Chem., Int. Ed. 2007, 46, 6006. Jellinek, J. Faraday Discuss. 2008, 138, 11. (8) Berry, R. S.; Jellinek, J.; Natanson, G. Phys. ReV. A 1984, 30, 919. (9) Beck, T. L.; Jellinek, J.; Berry, R. S. J. Chem. Phys. 1987, 87, 545. (10) Berry, R. S.; Wales, D. J. Phys. ReV. Lett. 1989, 63, 1156. (a) Wales, D. J.; Berry, R. S. J. Chem. Phys. 1990, 92, 4473. Berry, R. S. J. Chem. Soc., Faraday Trans. 1990, 86, 2343. Berry, R. S. Sci. Am. 1990, 263, 68. (11) Berry, R. S. In Clusters of Atoms and Molecules; Haberland, H., Ed.; Springer Series in Chemical Physics 52; Springer: Berlin, 1994; p 187. Berry, R. S. Microscale Thermophys. Eng. 1997, 1, 1. Proykova, A.; Berry, R. S. J. Phys. B: At. Mol. Opt. Phys. 2006, 39, R167. (12) Berry, R. S. C. R. Phys. 2002, 3, 319. (13) Schmidt, M.; Haberland, H. C. R. Phys. 2002, 3, 327. Published on Web 08/26/2008 12698 9 J. AM. CHEM. SOC. 2008, 130, 12698–12711 10.1021/ja802389d CCC: $40.75  2008 American Chemical Society