×

Molecular dynamics study of the thermal conductivity of amorphous nanoporous silica. (English) Zbl 1227.82059

Summary: This study reports, for the first time, non-equilibrium molecular dynamics (MD) simulations predicting the thermal conductivity of amorphous nanoporous silica. The heat flux was imposed using the Müller-Plathe method and interatomic interactions were modeled using the widely used van Beest, Kramer and van Santen potential. Monodisperse spherical pores organized in a simple cubic lattice were introduced in an amorphous silica matrix by removing atoms within selected regions. The simulation cell length ranged from 17 to 189 Å, the pore diameter from 12 to 25 Å, and the porosity varied between 10% and 35%. Results establish that the thermal conductivity of nanoporous silica at room temperature was independent of pore size and depended only on porosity. This qualitatively confirms recent experimental measurements for cubic and hexagonal mesoporous silica films with pore diameter and porosity ranging from 3 to 18 nm and 20% to 48%, respectively. Moreover, predictions of MD simulations agreed well with predictions from the coherent potential model. By contrast, finite element analysis simulating the same nanoporous structures, but based on continuum theory of heat conduction, agreed with the well-known Maxwell Garnett model.

MSC:

82C35 Irreversible thermodynamics, including Onsager-Machlup theory
Full Text: DOI

References:

[1] Semiconductor Industry Association, The international technology roadmap for semiconductors 2006.
[2] Choi, S. G.; Ha, T. J.; Yu, B. G.; Jaung, S. P.; Kwon, O.; Park, H. H.: Improvement of uncooled infrared imaging detector by using mesoporous silica as a thermal isolation layer, Ceramics int. 34, No. 4, 833-836 (2008)
[3] Coquil, T.; Richman, E. K.; Hutchinson, N.; Tolbert, S. H.; Pilon, L.: Thermal conductivity of cubic and hexagonal mesoporous silica thin films, J. appl. Phys. 106, No. 3, 034910 (2009)
[4] Allen, M. P.; Tildesley, D. J.: Computer simulation of liquids, (2002) · Zbl 0703.68099
[5] Green, M. S.: Markoff random processes and the statistical mechanics of time-dependent phenomena. II. irreversible processes in fluids, J. chem. Phys. 22, No. 3, 398-413 (1954)
[6] Kubo, R.; Yokota, M.; Nakajima, S.: Statistical-mechanical theory of irreversible processes. II. response to thermal disturbance, J. phys. Soc. jpn 12, No. 11, 1203-1211 (1957)
[7] Schelling, P. K.; Phillpot, S. R.; Keblinski, P.: Comparison of atomic-level simulation methods for computing thermal conductivity, Phys. rev. B 65, No. 14, 144306 (2002)
[8] Müller-Plathe, F.: A simple nonequilibrium molecular dynamics method for calculating the thermal conductivity, J. chem. Phys. 106, No. 14, 6082-6085 (1997)
[9] Mahajan, S. S.; Subbarayan, G.; Sammakia, B. G.: Estimating thermal conductivity of amorphous silica nanoparticles and nanowires using molecular dynamics simulations, Phys. rev. E 76, No. 5, 056701 (2007)
[10] Vogelsang, R.; Hoheisel, C.; Ciccotti, G.: Thermal conductivity of the lennard – Jones liquid by molecular dynamics calculations, J. chem. Phys. 86, No. 11, 6371-6375 (1987)
[11] Che, J.; &ccedil, T.; Agin; Iii, W. A. Goddard: Thermal conductivity of carbon nanotubes, Nanotechnology 11, No. 2, 65-69 (2000)
[12] Li, J.; Porter, L.; Yip, S.: Atomistic modeling of finite-temperature properties of crystalline \(\beta \)- sic: II. Thermal conductivity and effects of point defects, J. nuclear mater. 255, No. 2 – 3, 139-152 (1998)
[13] Volz, S. G.; Chen, G.: Molecular-dynamics simulation of thermal conductivity of silicon crystals, Phys. rev. B 61, No. 4, 2651-2656 (2000)
[14] Mcgaughey, A. J. H.; Kaviany, M.: Thermal conductivity decomposition and analysis using molecular dynamics simulations: part II. Complex silica structures, Int. J. Heat mass transfer 47, No. 8 – 9, 1799-1816 (2004) · Zbl 1056.80004 · doi:10.1016/j.ijheatmasstransfer.2003.11.009
[15] Stillinger, F. H.; Weber, T. A.: Computer simulation of local order in condensed phases of silicon, Phys. rev. B 31, No. 8, 5262-5271 (1985)
[16] Huang, Z.; Tang, Z.; Yu, J.; Bai, S.: Thermal conductivity of amorphous and crystalline thin films by molecular dynamics simulation, Phys. B condens. Matter 404, No. 12 – 13, 1790-1793 (2009)
[17] Yoon, Y. G.; Car, R.; Srolovitz, D. J.; Scandolo, S.: Thermal conductivity of crystalline quartz from classical simulations, Phys. rev. B 70, No. 1, 012302 (2004)
[18] Jund, P.; Jullien, R.: Molecular-dynamics calculation of the thermal conductivity of vitreous silica, Phys. rev. B 59, No. 21, 13707-13711 (1999)
[19] Van Beest, B. W. H.; Kramer, G. J.; Van Santen, R. A.: Force fields for silicas and aluminophosphates based on ab initio calculations, Phys. rev. Lett. 64, No. 16, 1955-1958 (1990)
[20] Horbach, W.; Kob, J.; Binder, K.; Angell, C. A.: Finite size effects in simulations of Glass dynamics, Phys. rev. E 54, No. 6, R5897-R5900 (1996)
[21] Sun, L.; Murthy, J. Y.: Domain size effects in molecular dynamics simulation of phonon transport in silicon, Appl. phys. Lett. 89, No. 17, 171919 (2006)
[22] Sellan, D. P.; Landry, E. S.; Turney, J. E.; Mcgaughey, A. J. H.; Amon, C. H.: Size effects in molecular dynamics thermal conductivity predictions, Phys. rev. B 81, No. 21, 214305 (2010)
[23] Lukes, J. R.; Tien, C. L.: Molecular dynamics simulation of thermal conduction in nanoporous thin films, Microsc. thermophys. Eng. 8, No. 4, 341-359 (2004)
[24] Lee, J. H.; Grossman, J. C.; Reed, J.; Galli, G.: Lattice thermal conductivity of nanoporous si: molecular dynamics study, Appl. phys. Lett. 91, No. 22, 223110 (2007)
[25] Thomas, J. A.; Turney, J. E.; Iutzu, R. M.; Amon, C. H.; Mcgaughey, A. J. H.: Predicting phonon dispersion relations and lifetimes from the spectral energy density, Phys. rev. B 81, No. 8, 081411 (2010)
[26] Thomas, J. A.; Iutzu, R. M.; Mcgaughey, A. J. H.: Thermal conductivity and phonon transport in empty and water-filled carbon nanotubes, Phys. rev. B 81, No. 4, 045413 (2010)
[27] Lukes, J. R.; Zhong, H.: Thermal conductivity of individual single-wall carbon nanotubes, ASME J. Heat transfer 129, 705-716 (2007)
[28] He, Y.; Donadio, D.; Galli, G.: Heat transport in amorphous silicon: interplay between morphology and disorder, Appl. phys. Lett. 98, No. 14, 144101 (2011)
[29] Lukes, J. R.; Li, D. Y.; Liang, X. -G.; Tien, C. -L.: Molecular dynamics study of solid thin-film thermal conductivity, ASME J. Heat transfer 122, No. 3, 536-543 (2000)
[30] Plimpton, S. J.: Fast parallel algorithms for short-range molecular dynamics, J. comput. Phys. 117, 1-19 (1995) · Zbl 0830.65120 · doi:10.1006/jcph.1995.1039
[31] Hockney, R. W.; Eastwood, J. W.: Computer simulation using particles, (1989) · Zbl 0662.76002
[32] Levien, L.; Prewitt, C. T.; Weidner, D. J.: Structure and elastic properties of quartz at pressure, P=1atm, Am. mineral. 64, 920-930 (1980)
[33] Oligschleger, C.; Schön, J. C.: Simulation of thermal conductivity and heat transport in solids, Phys. rev. B 59, No. 6, 4125-4133 (1999)
[34] Müser, M. H.: Simulation of material properties below the Debye temperature: a path-integral molecular dynamics case study of quartz, J. chem. Phys. 114, No. 14, 705-716 (2001)
[35] Guissani, Y.; Guillot, B.: A numerical investigation of the liquid – vapor coexistence curve of silica, J. chem. Phys. 104, No. 19, 7633-7644 (1996)
[36] , CRC materials science and engineering handbook (2000)
[37] Nose, S.: A unified formulation of the constant temperature molecular dynamics methods, J. chem. Phys. 81, No. 1, 511-519 (1984)
[38] Hoover, W. G.: Canonical dynamics: equilibrium phase-space distributions, Phys. rev. A 31, No. 3, 1695-1697 (1985)
[39] Vollmayr, K.; Kob, W.; Binder, K.: Cooling-rate effects in amorphous silica: a computer-simulation study, Phys. rev. B 54, No. 22, 15808-15827 (1996)
[40] Touloukian, Y. S.; Powell, R. W.; Ho, C. Y.; Klemens, P. G.: Thermal conductivity: nonmetallic solids, TPRC data series 2 (1970)
[41] Nait-Ali, B.; Haberko, K.; Vesteghem, H.; Absi, J.; Smith, D. S.: Thermal conductivity of highly porous zirconia, J. eur. Ceramic soc. 26, No. 16, 3567-3574 (2006)
[42] Kaviany, M.: Principles of heat transfer, (2002) · Zbl 0974.80001
[43] Cahill, D. G.: Heat transport in dielectric thin films and at solid-solid interfaces, Microscale energy transport, 85-118 (1998)
[44] Costescu, R. M.; Bullen, A. J.; Matamis, G.; O’hara, K. E.; Cahill, D. G.: Thermal conductivity and sound velocities of hydrogen-silsesquioxane low-k dielectrics, Phys. rev. B 65, No. 9, 094205 (2002)
[45] Garnett, J. C. Maxwell: Colours in metal glasses and in metallic films, Phil. trans. Roy. soc. Lond. A 203, 385-420 (1904) · JFM 35.0844.04 · doi:10.1098/rsta.1904.0024
[46] Nan, C. W.; Birringer, R.; Clarke, D. R.; Gleiter, H.: Effective thermal conductivity of particulate composites with interfacial thermal resistance, J. appl. Phys. 81, No. 10, 6692 (1997)
[47] Hu, C.; Morgen, M.; Ho, P. S.; Jain, A.; Gill, W. N.; Plawsky, J. L.; Wayner, P. C.: Thermal conductivity study of porous low-k dielectric materials, Appl. phys. Lett. 77, 145-147 (2000)
[48] Landauer, R.: The electrical resistance of binary metallic mixtures, J. appl. Phys. 23, No. 7, 779-784 (1952)
[49] Whitaker, S.: The method of volume averaging, Theory and applications of transport in porous media 13 (1999)
[50] Cahill, D. G.; Allen, T. H.: Thermal conductivity of sputtered and evaporated sio2 and tio2 optical coatings, Appl. phys. Lett. 65, No. 3, 309-311 (1994)
[51] Bruggeman, D. A. G.: Berechnung verschiedener physikalischer konstanten von heterogenen substanzen. I. D ielektrizitstskonstanten und leitfähigkeiten der mischkörper aus isotropen substanzen, Annalen der physik (Leipzig) 416, No. 7, 636-664 (1935)
[52] Smarsly, B.; Goltner, C.; Antonietti, M.; Ruland, W.; Hoinkis, E.: SANS investigation of nitrogen sorption in porous silica, J. phys. Chem. B 105, No. 4, 831-840 (2001)
[53] Evans, W. J.; Hu, L.; Keblinski, P.: Thermal conductivity of graphene ribbons from equilibrium molecular dynamics: effect of ribbon width, edge roughness, and hydrogen termination, Appl. phys. Lett. 96, No. 20, 203112 (2010)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.