A Nosé-Hoover Thermostat Adapted to a Slab Geometry
Maćkowiak Sz. 1, Pieprzyk Sławomir 2, Brańka A.C. 2, Heyes D.M. 3
1 Institute of Physics, Poznań University of Technology
Piotrowo 3, 60-965 Poznań, Poland
E-mail: szymon.mackowiak@put.poznan.pl2 Institute of Molecular Physics, Polish Academy of Sciences
M. Smoluchowskiego 17, 60-179 Poznań, Poland
E-mail: pieprzyk@ifmpan.poznan.pl, branka@ifmpan.poznan.pl3 Department of Physics, Royal Holloway
University of London, Egham, Surrey TW20 0EX, UK
E-mail: david.heyes@rhul.ac.uk
Received:
Received: 01 December 2016; revised: 22 February 2017; accepted: 27 February 2017; published online: 06 April 2017
DOI: 10.12921/cmst.2016.0000060
Abstract:
A Nosé-Hoover (NH) type thermostat is considered for Molecular Dynamics (MD) simulations of confined systems. This is based on a generalised velocity of the same generic form as the NH thermostat of Allen and Schmid, [Mol. Sim. 33, 21 (2007)]. An unthermostatted confined region is sandwiched between two walls which are thermostatted. No external shearing is imposed. Non-equilibrium Molecular Dynamics (NEMD) simulations were carried out of the time evolution of the wall and confined region temperature after a jump in temperature of the walls. Relaxation of the confined region temperature to the target value was found to be typically slower than that of the wall. An analysis of the system parameter dependence of the lag time, τ , and departures from what would be expected from Fourier’s law suggest that a boundary transmission heat flux bottleneck is a significant factor in the time delay. This delayed thermal equilibration would therefore become an important factor when a time-dependent (e.g., oscillatory) temperature or shearing of the walls is implemented using NEMD. Adjustments between the response time of the wall thermostat should be made compatible with that of the rest of the system, to minimise its effects on the observed behaviour.
Key words:
References:
[1] W.G. Hoover, Computational Statistical Mechanics (Elsevier,
Amsterdam, 1991).
[2] S. Nosé, A Molecular Dynamics Method for Simulations in
the Canonical Ensemble, Mol. Phys. 52, 255 (1984).
[3] W.G. Hoover, Canonical dynamics: Equilibrium phase-space
distributions, Phys. Rev. A 31, 1695 (1985).
[4] P. Hunenberger, Thermostat Algorithms for Molecular Dynamics Simulations, Adv. Polym. Sci. 173, 105 (2005).
[5] A. Bulgac, D. Kusnezov, Canonical ensemble averages from
pseudomicrocanonical dynamics, Phys. Rev. A 42, 5045
(1990).
[6] G.J. Martyna, M.L. Klein, M.Tuckerman, Nosé-Hoover
chains: The canonical ensemble via continuous dynamics,
J. Chem. Phys. 97, 2635 (1992).
[7] W.G. Hoover, B.L. Holian, Kinetic moments method for
the canonical ensemble distribution, Phys. Lett. A 211, 253
(1996).
[8] A.C. Brańka, M. Kowalik, K.W. Wojciechowski, Generalization of the Nosé-Hoover approach, J. Chem. Phys. 119, 1929
(2003).
[9] A.C. Brańka, K.W. Wojciechowski, Generalization of Nosé
and Nosé-Hoover isothermal dynamics, Phys. Rev. E 62, 3281
(2000).
[10] H.H. Rugh, Dynamical Approach to Temperature, Phys. Rev.
Lett. 78, 772 (1997).
[11] O.G. Jepps, G. Ayton, D.J. Evans, Microscopic expressions
for the thermodynamic temperature, Phys. Rev. E 62, 4757
(2000).
[12] G. Rickayzen, J.G. Powles, Temperature in the classical microcanonical ensemble, J. Chem. Phys. 114, 4333 (2001).
[13] C. Braga, K.P. Travis, A configurational temperature NoséHoover thermostat, J. Chem. Phys. 123, 134101 (2005).
[14] M.P. Allen, F. Schmid, A thermostat for molecular dynamics
of complex fluids, Mol. Simul. 33, 21 (2007).
[15] S. Pieprzyk, D.M. Heyes, Sz. Maćkowiak, A.C. Brańka,
Galilean-invariant Nosé-Hoover-type thermostats, Phys. Rev.
E 91, 033312 (2015).
[16] D. Kusnezov, A. Bulgac, W. Bauer, Canonical ensembles from
chaos, Ann. Phys. 204, 155 (1990).
[17] C. Gattinoni, D. M. Heyes, C. D. Lorenz, D. Dini, Traction
and nonequilibrium phase behavior of confined sheared liquids at high pressure, Phys. Rev. E 88, 052406 (2013).
[18] D. M. Heyes, E. R. Smith, D. Dini, H. A. Spikes, T. A. Zaki,
Pressure dependence of confined liquid behavior subjected to
boundary-driven shear, J. Chem. Phys. 136, 134705 (2012).
[19] C. Gattinoni, Sz. Maćkowiak, D. M. Heyes, A. C. Brańka,
D. Dini, Boundary-controlled barostats for slab geometries
in molecular dynamics simulations, Phys. Rev. E 90, 043302
(2014).
[20] M. Teodorescu, S. Theodossiades, H. Rahnejat, Impact dynamics of rough and surface protected MEMS gears, Tribol.
Int. 42, 197 (2009).
[21] S. Bernardi, B. D. Todd D. J. Searles, Thermostating highly
confined fluids, J. Chem. Phys. 132, 244706 (2010).
[22] B. D. Todd, D. J. Evans, P. J. Daivis, Pressure tensor for
inhomogeneous fluids, Phys. Rev. E 52, 1627 (1995).
[23] S. Butler, P. Harrowell, Simulation of the coexistence of
a shearing liquid and a strained crystal, J. Chem. Phys. 118,
4115 (2003).
[24] J. Petravic, P. Harrowell, The boundary fluctuation theory of
transport coefficients in the linear-response limit, J. Chem.
Phys. 124, 014103 (2006).
[25] Sz. Maćkowiak, D. M. Heyes, D. Dini, A. C. Brańka, Nonequilibrium phase behavior and friction of confined molecular
films under shear: A non-equilibrium molecular dynamics
study, J. Chem. Phys. 145, 164704 (2016).
[26] X. Yong, L. T. Zhang, Thermostats and thermostat strategies
for molecular dynamics simulations of nanofluidics, J. Chem.
Phys. 138, 084503 (2013).
[27] S. De Luca, B. D. Todd, J. S. Hansen, P. J. Daivis, A new and
effective method for thermostatting confined fluids, J. Chem.
Phys. 140, 054502 (2014).
[28] D. M. Heyes, The Liquid State, (John Wiley & Sons, Chichester, 1997).
[29] B.L. Holian, A.F. Voter, R. Ravelo, Thermostatted molecular
dynamics: How to avoid the Toda demon hidden in NoséHoover dynamics, Phys. Rev. E 52, 2338 (1995).
[30] G.E. Valenzuela, J.H. Saavedra, R.E. Rozasn P.G. Toledo,
Analysis of energy and friction coefficient fluctuations of
a Lennard-Jones liquid coupled to the Nosé-Hoover thermostat, Mol. Simul. 41, 521, (2014).
[31] S. Nosé, Constant-temperature molecular dynamics, Progress
of Theoretical Physics Supplement 103, 1 (1991).
[32] A.C. Brańka, Nosé-Hoover chain method for nonequilibrium molecular dynamics simulation, Phys. Rev. E 61, 4769,
(2000).
A Nosé-Hoover (NH) type thermostat is considered for Molecular Dynamics (MD) simulations of confined systems. This is based on a generalised velocity of the same generic form as the NH thermostat of Allen and Schmid, [Mol. Sim. 33, 21 (2007)]. An unthermostatted confined region is sandwiched between two walls which are thermostatted. No external shearing is imposed. Non-equilibrium Molecular Dynamics (NEMD) simulations were carried out of the time evolution of the wall and confined region temperature after a jump in temperature of the walls. Relaxation of the confined region temperature to the target value was found to be typically slower than that of the wall. An analysis of the system parameter dependence of the lag time, τ , and departures from what would be expected from Fourier’s law suggest that a boundary transmission heat flux bottleneck is a significant factor in the time delay. This delayed thermal equilibration would therefore become an important factor when a time-dependent (e.g., oscillatory) temperature or shearing of the walls is implemented using NEMD. Adjustments between the response time of the wall thermostat should be made compatible with that of the rest of the system, to minimise its effects on the observed behaviour.
Key words:
References:
[1] W.G. Hoover, Computational Statistical Mechanics (Elsevier,
Amsterdam, 1991).
[2] S. Nosé, A Molecular Dynamics Method for Simulations in
the Canonical Ensemble, Mol. Phys. 52, 255 (1984).
[3] W.G. Hoover, Canonical dynamics: Equilibrium phase-space
distributions, Phys. Rev. A 31, 1695 (1985).
[4] P. Hunenberger, Thermostat Algorithms for Molecular Dynamics Simulations, Adv. Polym. Sci. 173, 105 (2005).
[5] A. Bulgac, D. Kusnezov, Canonical ensemble averages from
pseudomicrocanonical dynamics, Phys. Rev. A 42, 5045
(1990).
[6] G.J. Martyna, M.L. Klein, M.Tuckerman, Nosé-Hoover
chains: The canonical ensemble via continuous dynamics,
J. Chem. Phys. 97, 2635 (1992).
[7] W.G. Hoover, B.L. Holian, Kinetic moments method for
the canonical ensemble distribution, Phys. Lett. A 211, 253
(1996).
[8] A.C. Brańka, M. Kowalik, K.W. Wojciechowski, Generalization of the Nosé-Hoover approach, J. Chem. Phys. 119, 1929
(2003).
[9] A.C. Brańka, K.W. Wojciechowski, Generalization of Nosé
and Nosé-Hoover isothermal dynamics, Phys. Rev. E 62, 3281
(2000).
[10] H.H. Rugh, Dynamical Approach to Temperature, Phys. Rev.
Lett. 78, 772 (1997).
[11] O.G. Jepps, G. Ayton, D.J. Evans, Microscopic expressions
for the thermodynamic temperature, Phys. Rev. E 62, 4757
(2000).
[12] G. Rickayzen, J.G. Powles, Temperature in the classical microcanonical ensemble, J. Chem. Phys. 114, 4333 (2001).
[13] C. Braga, K.P. Travis, A configurational temperature NoséHoover thermostat, J. Chem. Phys. 123, 134101 (2005).
[14] M.P. Allen, F. Schmid, A thermostat for molecular dynamics
of complex fluids, Mol. Simul. 33, 21 (2007).
[15] S. Pieprzyk, D.M. Heyes, Sz. Maćkowiak, A.C. Brańka,
Galilean-invariant Nosé-Hoover-type thermostats, Phys. Rev.
E 91, 033312 (2015).
[16] D. Kusnezov, A. Bulgac, W. Bauer, Canonical ensembles from
chaos, Ann. Phys. 204, 155 (1990).
[17] C. Gattinoni, D. M. Heyes, C. D. Lorenz, D. Dini, Traction
and nonequilibrium phase behavior of confined sheared liquids at high pressure, Phys. Rev. E 88, 052406 (2013).
[18] D. M. Heyes, E. R. Smith, D. Dini, H. A. Spikes, T. A. Zaki,
Pressure dependence of confined liquid behavior subjected to
boundary-driven shear, J. Chem. Phys. 136, 134705 (2012).
[19] C. Gattinoni, Sz. Maćkowiak, D. M. Heyes, A. C. Brańka,
D. Dini, Boundary-controlled barostats for slab geometries
in molecular dynamics simulations, Phys. Rev. E 90, 043302
(2014).
[20] M. Teodorescu, S. Theodossiades, H. Rahnejat, Impact dynamics of rough and surface protected MEMS gears, Tribol.
Int. 42, 197 (2009).
[21] S. Bernardi, B. D. Todd D. J. Searles, Thermostating highly
confined fluids, J. Chem. Phys. 132, 244706 (2010).
[22] B. D. Todd, D. J. Evans, P. J. Daivis, Pressure tensor for
inhomogeneous fluids, Phys. Rev. E 52, 1627 (1995).
[23] S. Butler, P. Harrowell, Simulation of the coexistence of
a shearing liquid and a strained crystal, J. Chem. Phys. 118,
4115 (2003).
[24] J. Petravic, P. Harrowell, The boundary fluctuation theory of
transport coefficients in the linear-response limit, J. Chem.
Phys. 124, 014103 (2006).
[25] Sz. Maćkowiak, D. M. Heyes, D. Dini, A. C. Brańka, Nonequilibrium phase behavior and friction of confined molecular
films under shear: A non-equilibrium molecular dynamics
study, J. Chem. Phys. 145, 164704 (2016).
[26] X. Yong, L. T. Zhang, Thermostats and thermostat strategies
for molecular dynamics simulations of nanofluidics, J. Chem.
Phys. 138, 084503 (2013).
[27] S. De Luca, B. D. Todd, J. S. Hansen, P. J. Daivis, A new and
effective method for thermostatting confined fluids, J. Chem.
Phys. 140, 054502 (2014).
[28] D. M. Heyes, The Liquid State, (John Wiley & Sons, Chichester, 1997).
[29] B.L. Holian, A.F. Voter, R. Ravelo, Thermostatted molecular
dynamics: How to avoid the Toda demon hidden in NoséHoover dynamics, Phys. Rev. E 52, 2338 (1995).
[30] G.E. Valenzuela, J.H. Saavedra, R.E. Rozasn P.G. Toledo,
Analysis of energy and friction coefficient fluctuations of
a Lennard-Jones liquid coupled to the Nosé-Hoover thermostat, Mol. Simul. 41, 521, (2014).
[31] S. Nosé, Constant-temperature molecular dynamics, Progress
of Theoretical Physics Supplement 103, 1 (1991).
[32] A.C. Brańka, Nosé-Hoover chain method for nonequilibrium molecular dynamics simulation, Phys. Rev. E 61, 4769,
(2000).
