Abstract
The melting transition of a Lennard-Jones (LJ) system confined in slit pores of variable pore size, H, is studied using molecular dynamics simulations. We examine various mechanisms to locate the pore melting temperature under confinement using molecular simulations. Three types of structure-less pore walls are considered, namely strongly attractive walls, weakly attractive walls, and repulsive walls. In particular, we present details of the density–temperature hysteresis, Lindemann parameter, and non-Gaussian parameter for various pore sizes ranging from 8 to 3 molecular diameters. The methods as used in this work are found applicable for repulsive, weak, and moderately attractive pores. Using the above criteria, we estimated the melting temperature for various pore surfaces and pore sizes. The melting temperature, for an attractive surface, is observed to be elevated or depressed depending on the pore size. In contrast, depression in the melting temperature is observed in the case of weakly attractive and repulsive surfaces. Crossover behavior from three-dimensional to two-dimensional for weakly attractive and repulsive surfaces is proposed using the relation ΔT m ~ H −ν, with ν ranging from 0.66 to 0.81 and 1.59 to 2.1 for 2D and 3D, respectively. The methods, viz., Lindemann and non-Gaussian parameters, however, fail in predicting melting temperature for ε wf > 8 and α > 4 for LJ 6-12 and LJ 9-3, surfaces, respectively.
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References
Zhang Z, Gekhtman D, Dresselhaus MS, Ying JY (1999) Chem Matter 11:1659
Alcoutlabi M, McKenna GB (2005) J Phys Condens Matter 17:R461
Duffy JA, Wilkinson NJ, Fretwell HM, Alam MA (1995) J Phys Condens Matter 7:L27
Unruh KM, Huber TE, Huber CA (1993) Phys Rev B 48:9021
Klein J, Kumacheva E (1995) Science 269:816
Gelb LD, Gubbins KE, Radhakrishnan R, Sliwinska-Bartkowiak M (1999) Rep Prog Phys 62:1573
Alba-Simionesco C, Coasne B, Dosseh G, Dudziak G, Gubbins KE, Radhakrishnan R, Sliwinska-Bartkowiak M (2006) J Phys Condens Matter 16:15
Murray CA, Winkle DHV (1987) Phys Rev Lett 58:1200
Tang Y, Armstrong AJ, Mockler RC, Sullivan WJO (1989) Phys Rev Lett 62:2401
Murray CA, Sprenger WO, Wenk RA (1990) Phys Rev B 42:688
Murray CA, Sprenger WO, Wenk RA (1990) J Phys Condens Matter 2:SA385
Warnock J, Awschalom DD, Shafer MW (1986) Phys Rev Lett 57:1753
Klein J, Perahia D, Warburg S, Fetters LJ (1991) Nature 352
Klein J, Kumacheva E, Perahia D, Mahalu D, Warburg S (1994) Faraday Spec Discuss Chem Soc 98
Delogu F (2006) Phys Rev B 73:184108
Delogu F (2006) J Phys Chem B 110:12645
Delogu F (2006) J Phys Condens Matter 18:5639
Huang HC, Kwak SK, Singh JK (2009) J Chem Phys 130:164511
Schmidt M, Löwen H (1996) Phys Rev Lett 76:4552
Miyahara M, Gubbins KE (1997) J Chem Phys 106:2865
Maddox MW, Gubbins KE (1997) J Chem Phys 107:9659
Radhakrishnan R, Gubbins KE (1999) Mol Phys 96:1249
Sliwinska-Bartkowiak M, Dudziak G, Sikorski R, Gras R, Radhakrishnan R, Gubbins KE (2001) J Chem Phys 114:950
Coasne B, Czwartos J, Gubbins KE, Hung FR, Sliwinska-Bartkowiak M (2005) Adsorption 11:301
Radhakrishnan R, Gubbins KE, Sliwinska-Bartkowiak M (2002) J Chem Phys 116:1147
Radhakrishnan R, Gubbins KE, Sliwinska-Bartkowiak M (2000) J Chem Phys 112:11048
Kaneko T, Mima T, Yasuoka K (2010) Chem Phys Lett 490:165
Koga K, Tanaka H (2005) J Chem Phys 122:104711
Jin ZH, Gumbsch P, Lu K, Ma E (2001) Phys Rev Lett 87:055703
Granato AV, Joncich DM, Khonik VA (2010) Appl Phys Lett 97:171911
Born M (1939) J Chem Phys 7:591
Radhakrishnan R, Gubbins KE (1999) J Chem Phys 111:9058
Hansen JP, Verlet L (1969) Phys Rev 184:151
Gotze W, Liicke M (1976) J Low Temp Phys 25:671
Broughton JQ, Gilmer GH, Weeks JD (1982) Phys Rev B 25:4651
Ranganathan S, Pathak KN (1992) Phys Rev A 45:5789
Monson PA, Kofke DA (2000) Adv Chem Phys 115:113
Lindemann FA (1910) Z phys 11:609
Hoang VV (2011) Philos Mag 91(26):3443
Stillinger FH (1995) Science 267:1935
Cailloi JM, Levesque D, Weis JJ, Hansen JP (1982) J Stat Phys 28
Plimpton SJ (1995) J Comp Phys 117:1
Kaneko T, Yasuoka K, Zeng XC (2012) Mol Sim 38:373
Dominguez H, Allen MP, Evans R (1999) Mol Phys 96:209
Hoef MAvd (2000) J Chem Phys 113:8142
Eike DM, Brennecke JF, Maginn EJ (2005) J Chem Phys 014115:014115
Morishige K, Kawano K (2000) 104:2894
Ayappa KG, Ghatak C (2002) J Chem Phys 117:5373
Fisher ME, Nakanishi H (1981) J Chem Phys 75:5857
Singh SK, Singh JK, Kwak SK, Deo G (2010) Chem Phys Lett 494:182
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This work was supported by the Department of Science and Technology, Govt. of India.
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Published as part of the special collection of articles derived from the conference: Foundations of Molecular Modeling and Simulation 2012.
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Das, C.K., Singh, J.K. Melting transition of confined Lennard-Jones solids in slit pores. Theor Chem Acc 132, 1351 (2013). https://doi.org/10.1007/s00214-013-1351-y
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DOI: https://doi.org/10.1007/s00214-013-1351-y