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Research into the rationality and the application scopes of different melting models of nanoparticles

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Abstract

A rational melting model is indispensable to address the fundamental issue regarding the melting of nanoparticles. To ascertain the rationality and the application scopes of the three classical thermodynamic models, namely Pawlow, Rie, and Reiss melting models, corresponding accurate equations for size-dependent melting temperature of nanoparticles were derived. Comparison of the melting temperatures of Au, Al, and Sn nanoparticles calculated by the accurate equations with available experimental results demonstrates that both Reiss and Rie melting models are rational and capable of accurately describing the melting behaviors of nanoparticles at different melting stages. The former (surface pre-melting) is applicable to the stage from initial melting to critical thickness of liquid shell, while the latter (solid particles surrounded by a great deal of liquid) from the critical thickness to complete melting. The melting temperatures calculated by the accurate equation based on Reiss melting model are in good agreement with experimental results within the whole size range of calculation compared with those by other theoretical models. In addition, the critical thickness of liquid shell is found to decrease with particle size decreasing and presents a linear variation with particle size. The accurate thermodynamic equations based on Reiss and Rie melting models enable us to quantitatively and conveniently predict and explain the melting behaviors of nanoparticles at all size range in the whole melting process.

Both Reiss and Rie melting models are rational and capable of accurately describing the melting behaviors of nanoparticles at different melting stages. The former is applicable to the stage from initial melting to critical thickness of liquid shell, while the latter from the critical thickness to complete melting. The critical thickness of liquid shell decreases with decreasing particle size and a linear relationship between them is observed. This paper provides us an effective and convenient method to address the fundamental issue regarding the melting temperature of nanoparticles.

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References

  • Buffat P, Borel JP (1976) Size effect on the melting temperature of gold particles. Phys Rev A 13(6):2287–2297

    Article  Google Scholar 

  • Castro T, Reifenberger R, Choi E, Andres RP (1990) Size-dependent melting temperature of individual nanometer-sized metallic clusters. Phys Rev B 42(13):8548–8556

    Article  Google Scholar 

  • Chernyshev AP (2008) Melting of surface layers of nanoparticles: Landau model. Mater Chem Phys 112(1):226–229

    Article  Google Scholar 

  • Couchman PR, Jesser WA (1977) Thermodynamic theory of size dependence of melting temperature in metals. Nature 269(5628):481–483

    Article  Google Scholar 

  • Cui ZX, Zhao MZ, Lai WP, Xue YQ (2011) Thermodynamics of size effect on phase transition temperatures of dispersed phases. J Phys Chem C 115(46):22796–22803

    Article  Google Scholar 

  • Curzon A (1959) PhD Thesis, University of London

  • Delogu F (2005) Thermodynamics on the nanoscale. J Phys Chem B 109(46):21938–21941

    Article  Google Scholar 

  • Delogu F (2007) Demixing phenomena in NiAl nanometre-sized particles. Nanotechnology 18(6):065708

    Article  Google Scholar 

  • Dick K, Dhanasekaran T, Zhang Z, Meisel D (2002) Size-denpendent melting of silica-encapsulated gold nanoparticles. J Am Chem Soc 124(10):2312–2317

    Article  Google Scholar 

  • Ercolessi F, Andreoni W, Tosatti E (1991) Melting of small gold particles: mechanism and size effects. Phys Rev Lett 66(7):911–914

    Article  Google Scholar 

  • Font F, Myers TG (2013) Spherically symmetric nanoparticle melting with a variable phase change temperature. J Nanopart Res 15(12):1–13

    Article  Google Scholar 

  • Goldstein AN, Echer CM, Alivisatos AP (1992) Melting in semiconductor nanocrystals. Science 256(5062):1425–1427

    Article  Google Scholar 

  • Guenther G, Guillon O (2014) Models of size-dependent nanoparticle melting tested on gold. J Mater Sci 49(23):7915–7932

    Article  Google Scholar 

  • Guisbiers G, Abudukelimu G (2013) Influence of nanomorphology on the melting and catalytic properties of convex polyhedral nanoparticles. J Nanopart Res 15(2):1431–1442

    Article  Google Scholar 

  • Guisbiers G, Buchaillot L (2009) Universal size/shape-dependent law for characteristic temperatures. Phys Lett A 374(2):305–308

    Article  Google Scholar 

  • Guisbiers G, Wautelet M (2006) Size, shape and stress effects on the melting temperature of nano-polyhedral grains on a substrate. Nanotechnology 17(8):192–198

    Article  Google Scholar 

  • Guisbiers G, Abudukelimu G, Clement F, Wautelet M (2007) Effects of shape on the phase stability of nanoparticles. J Comput Theor Nanosci 4(2):309–315

    Article  Google Scholar 

  • Hanszen KJ (1960) The melting points of small spherules. Z Phys 157:523–553

    Article  Google Scholar 

  • Jiang Q, Shi HX, Zhao M (1999) Melting thermodynamics of organic nanocrystals. J Chem Phys 111(5):2176–2180

    Article  Google Scholar 

  • Jiang Q, Zhang Z, Li JC (2000) Melting thermodynamics of nanocrystals embedded in a matrix. Acta Mater 48(20):4791–4795

    Article  Google Scholar 

  • Johari GP (1998) Thermodynamic contributions from pre-melting or pre-transformation of finely dispersed crystals. Philos Mag A 77(6):1367–1380

    Article  Google Scholar 

  • Jones DRH (1974) Free energies of solid-liquid interfaces. J Mater Sci 9(1):1–17

    Article  Google Scholar 

  • Kuntová Z, Rossi G, Ferrando R (2008) Melting of core-shell Ag-Ni and Ag-Co nanoclusters studied via molecular dynamics simulations. Phys Rev B 77(20):205431

    Article  Google Scholar 

  • Lai SL, Guo JY, Petrova V, Ramanath G, Allen LH (1996) Size-dependent melting properties of small tin particles: nanocalorimetric measurements. Phys Rev Lett 77(1):99–102

    Article  Google Scholar 

  • Lai SL, Carlsson JRA, Allen LH (1998) Melting point depression of al clusters generated during the early stages of film growth: nanocalorimetry measurements. Appl Phys Lett 72(9):1098–1100

    Article  Google Scholar 

  • Lim HS, Ong CK, Ercolessi F (1993) Surface effects in vibrational and melting properties of Pb clusters. Z Phys D 26:45–47

    Article  Google Scholar 

  • Lindemann FA (1910) The calculation of molecular vibration frequencies. Z Phys 11:609–612

    Google Scholar 

  • Lubashenko VV (2010) Size-dependent melting of nanocrystals: a self-consistent statistical approach. J Nanopart Res 12(5):1837–1844

    Article  Google Scholar 

  • Mott NF (1934) The resistance of liquid metals. Proc R Soc Lond A 146(857):465–472

    Article  Google Scholar 

  • Mottet C, Rossi G, Baletto F, Ferrando R (2005) Single impurity effect on the melting of nanoclusters. Phys Rev Lett 95(3):035501

    Article  Google Scholar 

  • Nanda KK (2006) A simple classical approach for the melting temperature of inert-gas nanoparticles. Chem Phys Lett 419(1–3):195–200

    Article  Google Scholar 

  • Nanda KK, Sahu SN, Behera SN (2002) Liquid-drop model for the size-dependent melting of low-dimensional systems. Phys Rev A 66(1):013208

    Article  Google Scholar 

  • Pavan L, Baletto F, Novakovic R (2015) Multiscale approach for studying melting transitions in CuPt nanoparticles. Phys Chem Chem Phys 17(42):28364–28371

    Article  Google Scholar 

  • Pawlow P (1909) Relation between melting point and surface energy. Z Phys Chem 65:545–548

    Google Scholar 

  • Perry RH, Green D (1984) Perry’s chemical engineers’ handbook, 6th. McGraw- Hill, New York, pp 3–128

    Google Scholar 

  • Reiss H, Wilson IB (1948) The effect of surface on melting point. J Colloid Sci 3:551–561

    Article  Google Scholar 

  • Rie E (1923) Influence of surface tension on melting and freezing. Z Phys Chem 104:354–362

    Google Scholar 

  • Rytkonen A, Valkealahti S, Manninen M (1997) Melting and evaporation of argon clusters. J Chem Phys 106(5):1888–1892

    Article  Google Scholar 

  • Safaei A, Attarian Shandiz M, Sanjabi S, Barber ZH (2007) Modelling the size effect on the melting temperature of nanoparticles, nanowires and nanofilms. J Phys Condens Mat 19(21):216216

    Article  Google Scholar 

  • Safaei A, Attarian Shandiz M, Sanjabi S, Barber ZH (2008) Modeling the melting temperature of nanoparticles by an analytical approach. J Phys Chem C 112(1):99–105

    Article  Google Scholar 

  • Sambles JR (1971) An electron microscope study of evaporating gold particles: the Kelvin equation for liquid gold and the lowering of the melting point of solid gold particles. Proc R Soc Lond A 324(1558):339–351

    Article  Google Scholar 

  • Sinha S, Gao B, Zhou O (2004) Synthesis of silicon nanowires and novel nano-dendrite structures. J Nanopart Res 6(4):421–425

    Article  Google Scholar 

  • Skripov VP, Koverda VP, Skokov VN (1981) Size effect on melting of small particles. Phys Status Solidi (a) 66(1):109–118

    Article  Google Scholar 

  • Steenbergen KG, Gaston NA (2016) Two-dimensional liquid structure explains the elevated melting temperatures of gallium nanoclusters. Nano Lett 16(1):21–26

    Article  Google Scholar 

  • Tang J, Yang J (2015) Simultaneous melting of shell and core atoms, a molecular dynamics study of lithium–copper nanoalloys. J Nanopart Res 17(7):299–310

    Article  Google Scholar 

  • Wanyika H (2013) Sustained release of fungicide metalaxyl by mesoporous silica nanospheres. J Nanopart Res 15(8):1831–1839

    Article  Google Scholar 

  • Wautelet M (1998) On the shape dependence of the melting temperature of small particles. Phys Lett A 246(3):341–342

    Article  Google Scholar 

  • Xiao SF, Hu WY, Yang JY (2006) Melting temperature: from nanocrystalline to amorphous phase. J Chem Phys 125(18):184504/1–184504/4

    Article  Google Scholar 

  • Xue YQ, Gao BJ, Gao JF (1997) The theory of thermodynamics for chemical reactions in dispersed heterogeneous systems. J Colloid Interface Sci 191(1):81–85

    Article  Google Scholar 

  • Xue YQ, Zhao QS, Luan CH (2001) The thermodynamic relations between the melting point and the size of crystals. J Colloid Interface Sci 243(2):388–390

    Article  Google Scholar 

  • Yaws CL (1999) Chemical properties handbook, McGraw-Hill. Book, Beijing, pp (a) 154–157, a78–81, 104–107; b 207–210; c 234–237

  • Zhang M, Efremov MY, Schiettekatte F, Olson EA, Kwan AT, Lai SL, Wisleder T, Greene JE, Allen LH (2000) Size-dependent melting point depression of nanostructures: nanocalorimetric measurements. Phys Rev B 62(15):10548–10557

    Article  Google Scholar 

  • Zhang YN, Wang L, Bian XF (2003) Melting of Au nanoclusters by molecular dynamics simulation. Acta Phys -Chim Sin 19(1):35–39

    Google Scholar 

  • Zhao SJ, Wang SQ, Cheng DY, Ye HQ (2001) Three distinctive melting mechanisms in isolated nanoparticles. J Phys Chem B 105(51):12857–12860

    Article  Google Scholar 

  • Zhu JH, Fu QS, Xue YQ, Cui ZX (2016) Comparison of different models of melting transformation of nanoparticles. J Mater Sci 51(9):4462–4469

    Article  Google Scholar 

  • Zhu JH, Fu QS, Xue YQ, Cui ZX (2017) Accurate thermodynamic relations of the melting temperature of nanocrystals with different shapes and pure theoretical calculation. Mater Chem Phys 19:222–228

    Google Scholar 

Download references

Acknowledgements

All the authors acknowledge the financial support from the National Natural Science Foundation of China (No. 21373147 and No. 21573157).

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  1. Department of Applied Chemistry, Taiyuan University of Technology, Taiyuan, 030024, China

    Qingshan Fu, Yongqiang Xue, Zixiang Cui & Huijuan Duan

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  1. Qingshan Fu
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Correspondence to Yongqiang Xue.

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Fu, Q., Xue, Y., Cui, Z. et al. Research into the rationality and the application scopes of different melting models of nanoparticles. J Nanopart Res 19, 263 (2017). https://doi.org/10.1007/s11051-017-3960-1

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