Non-equilibrium Computer Simulations of Coupling Effects under Thermal Gradients
Department of Chemistry, Imperial College London, SW7 2AZ, United Kingdom
and
Department of Chemistry, Norwegian University of Science and Technology
E-mail: f.bresme@imperial.ac.uk
Received:
Received: 09 March 2017; revised: 12 April 2017; accepted: 06 May 2017; published online: 30 September 2017
DOI: 10.12921/cmst.2017.0000018
Abstract:
In this work, we discuss recent developments in the computer simulations of molecular fluids under thermal gradients. Non-equilibrium simulations allow performing numerical tests of fundamental questions of non-equilibrium thermodynamics. These tests show that non-equilibrium simulations provide an efficient approach to quantify within a single
simulation the thermophysical properties of fluids along an isobar. We discuss aspects connected to the computation of local temperatures in systems under the influence of heat fluxes, and how the combination of non-equilibrium molecular dynamics and non-equilibrium thermodynamics allows understanding phenomena arising from the coupling of internal molecular variables and heat fluxes, which lead, e.g. to thermo-molecular orientation. The behavior of these orientational effects near a fluid critical point is also discussed.
Key words:
configurational tempera- ture, local equilibrium hypothesis, non-equilibrium molecular dynamics, thermal gradients, thermal polarization
References:
[1] C. Ludwig, Sitz. ber. Akad. Wiss. Wien Math.-Nat. wiss. Kl 50, 539 (1856).
[2] C. Soret, Etat d’équilibre des dissolutions dont deux parties sont portées à des températures différentes, Arch. Sci. Phys. Nat., Geneve 2, 48 (1879).
[3] S. Wiegand, Thermal diffusion in liquid mixtures and polymer solutions, J. Phys.: Condens. Matter 16, R357 (2004).
[4] R. Piazza, A. Parola, Thermophoresis in colloidal suspensions, J. Phys.: Condens. Matter 20, 153102 (2008).
[5] S. Putnam, D. Cahill, G. Wong, Temperature Dependence of Thermodiffusion in Aqueous Suspensions of Charged Nanoparticles, Langmuir 23, 9221 (2007).
[6] M. Reichl, M. Herzog, A. Götz, D. Braun, Temperature Dependence of Thermodiffusion in Aqueous Suspensions of Charged Nanoparticles, Langmuir 23, 9221 (2007).
[7] T. Kirkpatrick, J.O. de Zarate, J.V. Sengers, Nonequilibrium Casimir-like Forces in Liquid Mixtures, Phys. Rev. Lett. 115, 035901 (2015).
[8] P. Baaske, F. Weinert, S. Duhr, K. Lemke, M. Russel, D. Braun, Extreme accumulation of nucleotides in simulated hydrothermal pore systems, Proc. Natl. Acad. Sci. USA 104, 9346 (2007).
[9] S. Duhr, D. Braun, Thermophoretic Depletion Follows Boltzmann Distribution, Phys. Rev. Lett. 96, 168301 (2006).
[10] C. Debuschewitz, W. Köhler, Molecular Origin of Thermal Diffusion in Benzene + Cyclohexane Mixtures, Phys. Rev. Lett. 87, 055901 (2001).
[11] K. Eslahian, A. Majee, M. Maskos, A. Würger, Specific salt effects on thermophoresis of charged colloids, Soft Matter 10, 1931 (2014).
[12] S. Di Lecce, T. Albrecht, F. Bresme, A computational approach to calculate the heat of transport of aqueous solutions, Sci. Rep., 7, 44833 (2017).
[13] W.G. Hoover, Nonequilibrium Molecular Dynamics, Ann. Rev. Phys. Chem. 34, 103 (1983).
[14] D. J. Evans, G. P. Morris, Statistical Mechanics of Non-equilibrium Liquids, Academic Press, New York, 1990.
[15] F. Bresme, A. Lervik, J. Armstrong, Non-equilibrium Molecular Dynamics, Chapter 6, in Experimental Thermodynamics Volume X: Non-Equilibrium Thermodynamics with Applications, D. Bedeaux, S. Kjelstrup, J.V. Sengers eds., IUPAC, p. 105 (2016).
[16] D.J. Evans, Homogeneous NEMD algorithm for thermal conductivity—Application of non-canonical linear response theory, Phys. Lett., 91A, 457 (1982).
[17] D.P. Hansen, D.J. Evans, A generalized heat flow algorithm, Mol. Phys. 81, 767 (1994).
[18] J. Armstrong, F. Bresme, Water polarization induced by thermal gradients: The extended simple point charge model (SPC/E), J. Chem. Phys. 139, 014504 (2013).
[19] A. Tenenbaum, Local equilibrium in stationary states by molecular dynamics, Phys. Rev. A 28, 3132 (1983).
[20] B. Hafskjold, in Thermal Nonequilibrium Phenomena in Fluid Mixtures, Lecture Notes in Physics, ed. W. Köhler, S. Wiegand, Springer, p. 3, (2001).
[21] F. Müller-Plathe, A simple nonequilibrium molecular dynamics method for calculating the thermal conductivity, J. Chem. Phys. 106, 6082 (1997).
[22] I. Iriarte-Carretero, M.A. Gonzalez, J. Armstrong, F. Fernandez-Alonso, F. Bresme, The rich phase behavior of the thermopolarization of water: from a reversal in the polarization, to enhancement near criticality conditions, Phys. Chem. Chem. Phys. 18, 19894 (2016).
[23] G. Bussi, D. Donadio, M. Parrinello, Canonical sampling through velocity rescaling, J. Chem. Phys. 126, 014101 (2007).
[24] J. H. Irving, J. G. Kirkwood, The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics, J. Chem. Phys. 18, 817 (1950).
[25] B.D. Todd, D.J. Evans, P.J. Daivis, Pressure tensor for inhomogeneous fluids, Phys. Rev. E, 52, 1627 (1995).
[26] A.S. Tascini, J. Armstrong, E. Chiavazzo, M. Fasano, P. Asinari, F. Bresme, Thermal transport across nanoparticle–fluid interfaces: the interplay of interfacial curvature and nanoparticle–fluid interactions, Phys. Chem. Chem. Phys. 19, 3244 (2017).
[27] J. Armstrong, F. Bresme, Temperature inversion of the thermal polarization of water, Phys. Rev. E 92, 060103 (2015).
[28] S.R. de Groot, P. Mazur P., Non-equilibrium thermodynamics, New York, Dover, (1984).
[29] F. Römer, A. Lervik, F. Bresme, Nonequilibrium molecular dynamics simulations of the thermal conductivity of water: A systematic investigation of the SPC/E and TIP4P/2005 models, J. Chem. Phys. 137, 074503 (2012).
[30] J. Casas-Vázquez J, D. Jou, Temperature in non-equilibrium states: a review of open problems and current proposals, Rep. Prog. Phys. 66, 1937 (2003).
[31] L.D. Landau, E.M. Lifschitz, Statistical physics, part 1. Oxford: Pergamon, (1969).
[32] J.P. Hansen, I.R. Macdonald, Theory of simple liquids, 3rd ed. Amsterdam: Academic Press (2013).
[33] O. Jepps, G. Ayton, D. Evans, Microscopic expressions for the thermodynamic temperature, Phys. Rev. E. 62, 4757 (2000).
[34] A. Lervik A, O. Wilhelmsen, T.T. Trinh, H.R. Nagel, Finite-size and truncation effects for microscopic expressions for the temperature at equilibrium and nonequilibrium, J. Chem. Phys. 143, 114106 (2015).
[35] N. Jackson, J. M. Rubi, F. Bresme, Non-equilibrium molecular dynamics simulations of the thermal transport properties of Lennard-Jones fluids using configurational temperatures, Mol. Sim. 42, 1214 (2016).
[36] H.H. Rugh, Dynamical Approach to Temperature, Phys. Rev. Lett. 78, 772 (1997).
[37] D.G. Grier, Y. Han, Anomalous interactions in confined charge-stabilized colloid, J. Phys.: Condens. Matter. 16, S4145 (2004).
[38] F. Römer, F. Bresme, J. Muscatello, D. Bedeaux, J.M. Rubi, Thermomolecular Orientation of Nonpolar Fluids, Phys. Rev. Lett. 108, 105901 (2012).
[39] C.D. Daub, J. Tafjord, S. Kjesltrup, D. Bedeaux, F. Bresme, Molecular alignment in molecular fluids induced by coupling between density and thermal gradients, Phys. Chem. Chem. Phys. 18, 12213 (2016).
[40] F. Bresme, A. Lervik, D. Bedeaux, S. Kjelstrup, Water Polarization under Thermal Gradients, Phys. Rev. Lett. 101, 020602 (2008).
[41] J.V. Sengers, private communication (2016).
In this work, we discuss recent developments in the computer simulations of molecular fluids under thermal gradients. Non-equilibrium simulations allow performing numerical tests of fundamental questions of non-equilibrium thermodynamics. These tests show that non-equilibrium simulations provide an efficient approach to quantify within a single
simulation the thermophysical properties of fluids along an isobar. We discuss aspects connected to the computation of local temperatures in systems under the influence of heat fluxes, and how the combination of non-equilibrium molecular dynamics and non-equilibrium thermodynamics allows understanding phenomena arising from the coupling of internal molecular variables and heat fluxes, which lead, e.g. to thermo-molecular orientation. The behavior of these orientational effects near a fluid critical point is also discussed.
Key words:
configurational tempera- ture, local equilibrium hypothesis, non-equilibrium molecular dynamics, thermal gradients, thermal polarization
References:
[1] C. Ludwig, Sitz. ber. Akad. Wiss. Wien Math.-Nat. wiss. Kl 50, 539 (1856).
[2] C. Soret, Etat d’équilibre des dissolutions dont deux parties sont portées à des températures différentes, Arch. Sci. Phys. Nat., Geneve 2, 48 (1879).
[3] S. Wiegand, Thermal diffusion in liquid mixtures and polymer solutions, J. Phys.: Condens. Matter 16, R357 (2004).
[4] R. Piazza, A. Parola, Thermophoresis in colloidal suspensions, J. Phys.: Condens. Matter 20, 153102 (2008).
[5] S. Putnam, D. Cahill, G. Wong, Temperature Dependence of Thermodiffusion in Aqueous Suspensions of Charged Nanoparticles, Langmuir 23, 9221 (2007).
[6] M. Reichl, M. Herzog, A. Götz, D. Braun, Temperature Dependence of Thermodiffusion in Aqueous Suspensions of Charged Nanoparticles, Langmuir 23, 9221 (2007).
[7] T. Kirkpatrick, J.O. de Zarate, J.V. Sengers, Nonequilibrium Casimir-like Forces in Liquid Mixtures, Phys. Rev. Lett. 115, 035901 (2015).
[8] P. Baaske, F. Weinert, S. Duhr, K. Lemke, M. Russel, D. Braun, Extreme accumulation of nucleotides in simulated hydrothermal pore systems, Proc. Natl. Acad. Sci. USA 104, 9346 (2007).
[9] S. Duhr, D. Braun, Thermophoretic Depletion Follows Boltzmann Distribution, Phys. Rev. Lett. 96, 168301 (2006).
[10] C. Debuschewitz, W. Köhler, Molecular Origin of Thermal Diffusion in Benzene + Cyclohexane Mixtures, Phys. Rev. Lett. 87, 055901 (2001).
[11] K. Eslahian, A. Majee, M. Maskos, A. Würger, Specific salt effects on thermophoresis of charged colloids, Soft Matter 10, 1931 (2014).
[12] S. Di Lecce, T. Albrecht, F. Bresme, A computational approach to calculate the heat of transport of aqueous solutions, Sci. Rep., 7, 44833 (2017).
[13] W.G. Hoover, Nonequilibrium Molecular Dynamics, Ann. Rev. Phys. Chem. 34, 103 (1983).
[14] D. J. Evans, G. P. Morris, Statistical Mechanics of Non-equilibrium Liquids, Academic Press, New York, 1990.
[15] F. Bresme, A. Lervik, J. Armstrong, Non-equilibrium Molecular Dynamics, Chapter 6, in Experimental Thermodynamics Volume X: Non-Equilibrium Thermodynamics with Applications, D. Bedeaux, S. Kjelstrup, J.V. Sengers eds., IUPAC, p. 105 (2016).
[16] D.J. Evans, Homogeneous NEMD algorithm for thermal conductivity—Application of non-canonical linear response theory, Phys. Lett., 91A, 457 (1982).
[17] D.P. Hansen, D.J. Evans, A generalized heat flow algorithm, Mol. Phys. 81, 767 (1994).
[18] J. Armstrong, F. Bresme, Water polarization induced by thermal gradients: The extended simple point charge model (SPC/E), J. Chem. Phys. 139, 014504 (2013).
[19] A. Tenenbaum, Local equilibrium in stationary states by molecular dynamics, Phys. Rev. A 28, 3132 (1983).
[20] B. Hafskjold, in Thermal Nonequilibrium Phenomena in Fluid Mixtures, Lecture Notes in Physics, ed. W. Köhler, S. Wiegand, Springer, p. 3, (2001).
[21] F. Müller-Plathe, A simple nonequilibrium molecular dynamics method for calculating the thermal conductivity, J. Chem. Phys. 106, 6082 (1997).
[22] I. Iriarte-Carretero, M.A. Gonzalez, J. Armstrong, F. Fernandez-Alonso, F. Bresme, The rich phase behavior of the thermopolarization of water: from a reversal in the polarization, to enhancement near criticality conditions, Phys. Chem. Chem. Phys. 18, 19894 (2016).
[23] G. Bussi, D. Donadio, M. Parrinello, Canonical sampling through velocity rescaling, J. Chem. Phys. 126, 014101 (2007).
[24] J. H. Irving, J. G. Kirkwood, The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics, J. Chem. Phys. 18, 817 (1950).
[25] B.D. Todd, D.J. Evans, P.J. Daivis, Pressure tensor for inhomogeneous fluids, Phys. Rev. E, 52, 1627 (1995).
[26] A.S. Tascini, J. Armstrong, E. Chiavazzo, M. Fasano, P. Asinari, F. Bresme, Thermal transport across nanoparticle–fluid interfaces: the interplay of interfacial curvature and nanoparticle–fluid interactions, Phys. Chem. Chem. Phys. 19, 3244 (2017).
[27] J. Armstrong, F. Bresme, Temperature inversion of the thermal polarization of water, Phys. Rev. E 92, 060103 (2015).
[28] S.R. de Groot, P. Mazur P., Non-equilibrium thermodynamics, New York, Dover, (1984).
[29] F. Römer, A. Lervik, F. Bresme, Nonequilibrium molecular dynamics simulations of the thermal conductivity of water: A systematic investigation of the SPC/E and TIP4P/2005 models, J. Chem. Phys. 137, 074503 (2012).
[30] J. Casas-Vázquez J, D. Jou, Temperature in non-equilibrium states: a review of open problems and current proposals, Rep. Prog. Phys. 66, 1937 (2003).
[31] L.D. Landau, E.M. Lifschitz, Statistical physics, part 1. Oxford: Pergamon, (1969).
[32] J.P. Hansen, I.R. Macdonald, Theory of simple liquids, 3rd ed. Amsterdam: Academic Press (2013).
[33] O. Jepps, G. Ayton, D. Evans, Microscopic expressions for the thermodynamic temperature, Phys. Rev. E. 62, 4757 (2000).
[34] A. Lervik A, O. Wilhelmsen, T.T. Trinh, H.R. Nagel, Finite-size and truncation effects for microscopic expressions for the temperature at equilibrium and nonequilibrium, J. Chem. Phys. 143, 114106 (2015).
[35] N. Jackson, J. M. Rubi, F. Bresme, Non-equilibrium molecular dynamics simulations of the thermal transport properties of Lennard-Jones fluids using configurational temperatures, Mol. Sim. 42, 1214 (2016).
[36] H.H. Rugh, Dynamical Approach to Temperature, Phys. Rev. Lett. 78, 772 (1997).
[37] D.G. Grier, Y. Han, Anomalous interactions in confined charge-stabilized colloid, J. Phys.: Condens. Matter. 16, S4145 (2004).
[38] F. Römer, F. Bresme, J. Muscatello, D. Bedeaux, J.M. Rubi, Thermomolecular Orientation of Nonpolar Fluids, Phys. Rev. Lett. 108, 105901 (2012).
[39] C.D. Daub, J. Tafjord, S. Kjesltrup, D. Bedeaux, F. Bresme, Molecular alignment in molecular fluids induced by coupling between density and thermal gradients, Phys. Chem. Chem. Phys. 18, 12213 (2016).
[40] F. Bresme, A. Lervik, D. Bedeaux, S. Kjelstrup, Water Polarization under Thermal Gradients, Phys. Rev. Lett. 101, 020602 (2008).
[41] J.V. Sengers, private communication (2016).
