Method of Planes Normal Pressure for Slit Geometries in Molecular Dynamics Simulations
Maćkowiak Sz. 1, Heyes D.M. 2, Dini D. 2, Brańka A.C. 3*
1 Institute of Physics
Poznań University of Technology
Nieszawska 13a
60-965 Poznań, Poland2 Department of Mechanical Engineering
Imperial College London, Exhibition Road
South Kensington, London SW7 2AZ
United Kingdom3 Institute of Molecular Physics
Polish Academy of Sciences
M. Smoluchowskiego 17
60-179 Poznań. Poland
∗E-mail: branka@ifmpan.poznan.pl
Received:
Received: 13 May 2013; revised: 1 August 2013; accepted: 2 August 2013; published online: 5 September 2013
DOI: 10.12921/cmst.2013.19.03.167-173
OAI: oai:lib.psnc.pl:452
Abstract:
The resolution and convergence properties of the Method of Planes (MOP) local pressure tensor method is analyzed for a slit geometry in which a system of interacting particles is placed between movable walls composed of atoms. Boundary-driven Molecular Dynamics (BMD) simulations were performed for different situations in which solid or fluid phases are formed between crystalline or amorphous walls. It is shown that for these inhomogeneous, steady state structures the total force exerted by a wall atoms on the inside particles is consistent with the normal pressure component obtained from the MOP method if a sufficiently small integration time step is applied. The work demonstrates that the numerical errors associated with computing the MOP pressure can be non-negligible and should be a consideration when determining the BMD algorithm parameters.
Key words:
computer simulations, inhomogeneous systems, method of planes, molecular dynamics, pressure tensor, slit geometry
References:
[1] M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids,
Oxford University Press: 1987.
[2] Z. Zhou, Fluctuations and thermodynamics properties of the
constant shear strain ensemble, J. Chem. Phys. 114, 8769-
8774 (2001).
[3] H.W. Graben and J.R. Ray, Unified treatment of adiabatic
ensembles, Phys. Rev. A 43, 4100-4103 (1991).
[4] J.R. Ray and A. Rahman, Statistical ensembles and molecular
dynamics studies of anisotropic solids, J. Chem. Phys. 80,
4423-4428 (1984).
[5] H.C. Andersen, Molecular dynamics simulations at constant
pressure and/or temperature, J. Chem. Phys. 72, 2384-2393
(1980).
[6] W.G. Hoover, Constant-pressure equations of motion, Phys.
Rev. A 34, 2499-2500 (1986).
[7] J.R. Ray, Pressure fluctuations in statistical physics, Am.
J. Phys. 50, 1035 (1982).
[8] M. Parrinello and A. Rahman, Crystal Structure and Pair Po-
tentials: A Molecular-Dynamics Study, Phys. Rev. Lett. 45,
1196–1199 (1980).
[9] M. Parrinello and A. Rahman, Polymorphic transitions in sin-
gle crystals: A new molecular dynamics method, J. Appl. Phys.
52, 7182-7190 (1981).
[10] E. Hernández, Metric-tensor flexible-cell algorithm for
isothermal-isobaric molecular dynamics simulations, J. Chem.
Phys. 115, 10282-10290 (2001).
[11] D.J. Evans and G.P. Morriss, Isothermal-isobaric molecular
dynamics, Chem. Phys. 77, 63-66 (1983).
[12] H.J.C. Berendsen, J.P.M. Postma, W.F. van Gunsteren, A. Di-
Nola and J.R. Haak, Molecular dynamics with coupling to an
external bath, J. Chem. Phys. 81, 3684-3690 (1984).
[13] J.-C. Wang and K.A. Fichthorn, A method for molecular dy-
namics simulation of confined fluids, J. Chem. Phys. 112,
8252-8259 (2000).
[14] M. Lupkowski and F. van Swol, Computer simulation of fluids
interacting with fluctuating walls, J. Chem. Phys. 93, 737-745
(1990).
[15] M. Lupkowski and F. van Swol, Ultrathin films under shear,
J. Chem. Phys. 95, 1995 (1991).
[16] H. Eslami, F. Mozaffari, J. Moghadasi and F. Müller-
Plathe, Molecular dynamics simulation of confined fluids
in isosurface-isothermal-isobaric ensemble, J. Chem. Phys.
129, 194702 (2008).
[17] H. Takaba, Y. Onumata and S.-I. Nakao, Molecular simula-
tion of pressure-driven fluid flow in nanoporous membranes,
J. Chem. Phys. 127, 054703 (2007).
[18] J. Cormier, J.M. Rickman and T.J. Delph, Stress calculation
in atomistic simulations of perfect and imperfect solids, J. App.
Phys. 89, 99-104 (2001).
[19] B.D. Todd, D.J. Evans and P.J. Davis, Pressure tensor for
inhomogeneous fluids, Phys. Rev. E 52, 1627–1638 (1995).
[20] D.M. Heyes, E.R. Smith, D. Dini and T.A. Zaki, The equiva-
lence between volume averaging and method of planes defi-
nitions of the pressure tensor at a plane, J. Chem. Phys. 135,
24512 (2011).
[21] J. Petravic and P. Harrowell, The boundary fluctuation theory
of transport coefficients in the linear-response limit, J. Chem.
Phys. 124, 014103 (2006).
[22] D.M. Heyes, E.R. Smith, D. Dini and H.A. Spikes and T.A.
Zaki, Pressure dependence of confined liquid behavior sub-
jected to boundary-driven shear, J. Chem. Phys. 136, 134705
(2012).
[23] S. Butler and P. Harrowell, Simulation of the coexistence of a
shearing liquid and a strained crystal, J. Chem. Phys. 118,
4115-4126 (2003).
[24] S. Butler and P. Harrowell, Factors determining crystal–liquid
coexistence under shear, Nature (London) 415, 1008-1011
(2002).
[25] J.H. Irving and J.G. Kirkwood, The Statistical Mechanical
Theory of Transport Processes. IV. The Equation
The resolution and convergence properties of the Method of Planes (MOP) local pressure tensor method is analyzed for a slit geometry in which a system of interacting particles is placed between movable walls composed of atoms. Boundary-driven Molecular Dynamics (BMD) simulations were performed for different situations in which solid or fluid phases are formed between crystalline or amorphous walls. It is shown that for these inhomogeneous, steady state structures the total force exerted by a wall atoms on the inside particles is consistent with the normal pressure component obtained from the MOP method if a sufficiently small integration time step is applied. The work demonstrates that the numerical errors associated with computing the MOP pressure can be non-negligible and should be a consideration when determining the BMD algorithm parameters.
Key words:
computer simulations, inhomogeneous systems, method of planes, molecular dynamics, pressure tensor, slit geometry
References:
[1] M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids,
Oxford University Press: 1987.
[2] Z. Zhou, Fluctuations and thermodynamics properties of the
constant shear strain ensemble, J. Chem. Phys. 114, 8769-
8774 (2001).
[3] H.W. Graben and J.R. Ray, Unified treatment of adiabatic
ensembles, Phys. Rev. A 43, 4100-4103 (1991).
[4] J.R. Ray and A. Rahman, Statistical ensembles and molecular
dynamics studies of anisotropic solids, J. Chem. Phys. 80,
4423-4428 (1984).
[5] H.C. Andersen, Molecular dynamics simulations at constant
pressure and/or temperature, J. Chem. Phys. 72, 2384-2393
(1980).
[6] W.G. Hoover, Constant-pressure equations of motion, Phys.
Rev. A 34, 2499-2500 (1986).
[7] J.R. Ray, Pressure fluctuations in statistical physics, Am.
J. Phys. 50, 1035 (1982).
[8] M. Parrinello and A. Rahman, Crystal Structure and Pair Po-
tentials: A Molecular-Dynamics Study, Phys. Rev. Lett. 45,
1196–1199 (1980).
[9] M. Parrinello and A. Rahman, Polymorphic transitions in sin-
gle crystals: A new molecular dynamics method, J. Appl. Phys.
52, 7182-7190 (1981).
[10] E. Hernández, Metric-tensor flexible-cell algorithm for
isothermal-isobaric molecular dynamics simulations, J. Chem.
Phys. 115, 10282-10290 (2001).
[11] D.J. Evans and G.P. Morriss, Isothermal-isobaric molecular
dynamics, Chem. Phys. 77, 63-66 (1983).
[12] H.J.C. Berendsen, J.P.M. Postma, W.F. van Gunsteren, A. Di-
Nola and J.R. Haak, Molecular dynamics with coupling to an
external bath, J. Chem. Phys. 81, 3684-3690 (1984).
[13] J.-C. Wang and K.A. Fichthorn, A method for molecular dy-
namics simulation of confined fluids, J. Chem. Phys. 112,
8252-8259 (2000).
[14] M. Lupkowski and F. van Swol, Computer simulation of fluids
interacting with fluctuating walls, J. Chem. Phys. 93, 737-745
(1990).
[15] M. Lupkowski and F. van Swol, Ultrathin films under shear,
J. Chem. Phys. 95, 1995 (1991).
[16] H. Eslami, F. Mozaffari, J. Moghadasi and F. Müller-
Plathe, Molecular dynamics simulation of confined fluids
in isosurface-isothermal-isobaric ensemble, J. Chem. Phys.
129, 194702 (2008).
[17] H. Takaba, Y. Onumata and S.-I. Nakao, Molecular simula-
tion of pressure-driven fluid flow in nanoporous membranes,
J. Chem. Phys. 127, 054703 (2007).
[18] J. Cormier, J.M. Rickman and T.J. Delph, Stress calculation
in atomistic simulations of perfect and imperfect solids, J. App.
Phys. 89, 99-104 (2001).
[19] B.D. Todd, D.J. Evans and P.J. Davis, Pressure tensor for
inhomogeneous fluids, Phys. Rev. E 52, 1627–1638 (1995).
[20] D.M. Heyes, E.R. Smith, D. Dini and T.A. Zaki, The equiva-
lence between volume averaging and method of planes defi-
nitions of the pressure tensor at a plane, J. Chem. Phys. 135,
24512 (2011).
[21] J. Petravic and P. Harrowell, The boundary fluctuation theory
of transport coefficients in the linear-response limit, J. Chem.
Phys. 124, 014103 (2006).
[22] D.M. Heyes, E.R. Smith, D. Dini and H.A. Spikes and T.A.
Zaki, Pressure dependence of confined liquid behavior sub-
jected to boundary-driven shear, J. Chem. Phys. 136, 134705
(2012).
[23] S. Butler and P. Harrowell, Simulation of the coexistence of a
shearing liquid and a strained crystal, J. Chem. Phys. 118,
4115-4126 (2003).
[24] S. Butler and P. Harrowell, Factors determining crystal–liquid
coexistence under shear, Nature (London) 415, 1008-1011
(2002).
[25] J.H. Irving and J.G. Kirkwood, The Statistical Mechanical
Theory of Transport Processes. IV. The Equation
