Simulation of Ionic Copolymers by Molecular Dynamics
Dzięcielski Michał 1, Knychała Piotr 2, Banaszak Michał 3*
1 Faculty of Geographical and Geological Sciences, Adam Mickiewicz University
ul. Krygowskiego 10, 61-680 Poznań, Poland2 Faculty of Polytechnic, The President Stanislaw Wojciechowski University School of Applied Sciences in Kalisz
ul. Nowy Świat 4, 62-800 Kalisz, Poland3 Faculty of Physics, A. Mickiewicz University
ul. Umultowska 85, 61-614 Poznan, Poland
∗E-mail: mbanasz@amu.edu.pl
Received:
Received: 19 November 2016; revised: 27 November 2016; accepted: 28 November 2016; published online: 09 December 2016
DOI: 10.12921/cmst.2016.0000055
Abstract:
Using GROMACS (a molecular dynamics package) we simulate ionic copolymers and compare the numerical results with those obtained by the lattice Monte Carlo simulations. While the results are qualitatively similar for both methods, the simulation times are significantly longer for the molecular dynamics simulations than those for the corresponding Monte Carlo runs.
Key words:
GROMACS, ion diblock copolymer, microphase separation, molecular dynamics
References:
[1] L. Leibler, Theory of Microphase Separation in Block Copoly-
mers, Macromolecules 13(6), 1602 (1980).
[2] A.E. Likhtman and A.N. Semenov, Stability of the OBDD
structure for diblock copolymer melts in the strong segregation
limit, Macromolecules 27(11), 3103 (1994).
[3] M.W. Matsen and M. Schick, Stable and unstable phases
of a diblock copolymer melt, Phys. Rev. Lett. 72(16), 2660
(1994).
[4] M.W. Matsen and F.S. Bates, Block copolymer microstruc-
tures in the intermediate-segregation regime, J. Chem. Phys.
106, 2436 (1997).
[5] M. Takenaka, T. Wakada, S. Akasaka, S. Nishitsuji, K. Saijo,
H. Shimizu, M.I. Kim, and H. Hasegawa, Orthorhombic
Fddd Network in Diblock Copolymer Melts, Macromolecules
40(13), 4399 (2007).
[6] B. Miao and R.A. Wickham, Fluctuation effects and the sta-
bility of the Fddd network phase in diblock copolymer melts,
J. Chem. Phys. 128, 054902 (2008).
[7] M.W. Matsen, The standard Gaussian model for block copoly-
mer melts, J. Phys.: Condens. Matter 14(2), R21 (2002).
[8] K.A. Mauritz and R.B. Moore, State of Understanding of
Nafion, Chem. Rev. 104, 4535 (2004).
[9] Michael Hickner, Hossein Ghassemi, Yu Seung Kim, Brian R
Einsla, and James E McGrath, Alternative polymer systems
for proton exchange membranes (PEMs), Chemical Reviews
104(10), 4587 (2004).
[10] M.J. Park and N.P. Balsara, Phase Behavior of Symmet-
ric Sulfonated Block Copolymers, Macromolecules 41, 3678
(2008).
[11] Xin Wang, Sergey Yakovlev, Keith M. Beers, Moon J. Park,
Scott a. Mullin, Kenneth H. Downing, and Nitash P. Balsara,
On the Origin of Slow Changes in Ionic Conductivity of Model
Block Copolymer Electrolyte Membranes in Contact with Hu-
mid Air, Macromolecules 43(12), 5306 (2010).
[12] Y. Rabin and J.F. Marko, Microphase separation in charged
diblock copolymers: the weak segregation limit, Macro-
molecules 24(8), 2134 (1991).
[13] R. Kumar and M. Muthukumar, Microphase separation in
polyelectrolytic diblock copolymer melt: weak segregation
limit, J. Chem. Phys. 126, 214902 (2007).
[14] I. Nakamura, I., N.P. Balsara, and Z.-G. Wang, Thermodynam-
ics of Ion-Containing Polymer Blends and Block Copolymers,
Phys. Rev. Lett. 107, 198301 (2011).
[15] I. Nakamura, I. and Z.-G. Wang, Salt-doped block copoly-
mers: ion distribution, domain spacing and effective [small
chi] parameter, Soft Matter 8, 9356 (2012).
[16] P. Knychała, M. Banaszak, Park M. J., and N.P. Balsara, Mi-
crophase Separation in Sulfonated Block Copolymers Studied
by Monte Carlo Simulations, Macromolecules 42(22), 8925
(2009).
[17] P. Knychała, M. Dzi ̨ ecielski, M. Banaszak, and N.P. Bal-
sara, Phase Behavior of Ionic Block Copolymers Studied
by a Minimal Lattice Model with Short-Range Interactions,
Macromolecules 46(14), 5724 (2013).
[18] P. Knychała, M. Banaszak, and N.P. Balsara, Effects of
Composition on the Phase Behavior of Ion-Containing Block
Copolymers Studied by a Minimal Lattice Model, Macro-
molecules 47(7), 2529 (2014).
[19] P. Knychała and M. Banaszak, Simulations on a swollen
gyroid nanostructure in thin films relevant to systems of ionic
block copolymers, European Physical Journal E 37, 67 (2014).
[20] J.E. Lennard-Jones, In On the Determination of Molecular
Fields, volume 106, page 463 The Royal Society, 1924.
[21] S. Blonski, W. Brostow, and J. Kubat, Molecular-Dynamics
Simulations of Stress-Relaxation in Metals and Polymers,
Physical Review B 49, 6494 (1994).
[22] K. Kremer and G.S. Grest, ynamics of Entangled Linear
Polymer Melts: A Molecular-Dynamics Simulation, J. Chem.
Phys. 92, 5057 (1990).
[23] B. Hess, H. Bekker, H.J.C. Berendsen, and J.G.E.M Fraaije,
LINCS: A Linear Constraint Solver for Molecular Simulations,
Journal of Computational Chemistry 18, 1463 (1997).
[24] J.P. Ryckaert, G. Ciccotti, and H.J.C. Berendsen, Numerical
Integration of the Cartesian Equations of Motion of a System
with Constraints: Molecular Dynamics of n-Alkanes, Journal
of Computational Physics 23, 327 (1977).
[25] T. Darden, D. York, and L. Pedersen, Particle Mesh Ewald:
An N-log(N) Method for Ewald Sums in Large Systems, J.
Chem. Phys. 98, 10089 (1993).
[26] P. Ewald, Die Berechnung optischer und elektrostatischer
Gitterpotentiale, Ann. Phys. 369, 253 (1921).
[27] M.P. Allen and D. Tildesley, Computer Simulation of Liquids,
Clarendon Press Oxford, 1989.
[28] J. Kolafa and J.W. Perram, Cutoff Errors in the Ewald Sum-
mation Formulae for Point Charge Systems, Molecular Simu-
lation 9, 351 (1992).
[29] S. Nose, A Unified Formulation of the Constant Temperature
Molecular-Dynamics Methods, J. Chem. Phys. 81, 511 (1984).
[30] W.G. Hoover, Canonical Dynamics: Equilibrium Phase-
Space Distribution, Phys. Rev. A 31, 1695 (1984).
[31] W.F. Van Gunsteren and H.J.C. Berendsen, A Leap-frog Al-
gorithm for Stochastic Dynamics, Molecular Simulation 1,
173 (1988).
[32] L. Verlet, Computer Experiments on Classical Fluids. I.
Thermodynamical Properties of Lennard-Jones Molecules,
Physical Review 159, 98 (1967).
[33] Gromacs User Manual 4.0, ftp://ftp.gromacs.org/pub/manual/
manual-4.0.pdf, Available: 30.08.2015.
[34] T.M. Beardsley and M.W. Matsen, Monte Carlo phase dia-
gram for diblock copolymer melts, Eur. Phys. J. E 32(3), 155
(2010).
[35] D. Van Der Spoel, E. Lindahl, B. Hess, G. Groenhof, A.E.
Mark, and H.J.C. Berendsen, GROMACS: Fast, Flexible, and
Free, J. Comput. Chem. 26, 1701 (2005).
[36] Tabulated Potentials, http://www.gromacs.org/Documenta
tion/How-tos/Tabulated_Potentials, Available: 30.08.2015.
[37] User Specified non-bonded potentials in gromacs, http://www.
gromacs.org/@api/deki/files/94/=gromacs_nb.pdf, Available:
29.10.2016.
Using GROMACS (a molecular dynamics package) we simulate ionic copolymers and compare the numerical results with those obtained by the lattice Monte Carlo simulations. While the results are qualitatively similar for both methods, the simulation times are significantly longer for the molecular dynamics simulations than those for the corresponding Monte Carlo runs.
Key words:
GROMACS, ion diblock copolymer, microphase separation, molecular dynamics
References:
[1] L. Leibler, Theory of Microphase Separation in Block Copoly-
mers, Macromolecules 13(6), 1602 (1980).
[2] A.E. Likhtman and A.N. Semenov, Stability of the OBDD
structure for diblock copolymer melts in the strong segregation
limit, Macromolecules 27(11), 3103 (1994).
[3] M.W. Matsen and M. Schick, Stable and unstable phases
of a diblock copolymer melt, Phys. Rev. Lett. 72(16), 2660
(1994).
[4] M.W. Matsen and F.S. Bates, Block copolymer microstruc-
tures in the intermediate-segregation regime, J. Chem. Phys.
106, 2436 (1997).
[5] M. Takenaka, T. Wakada, S. Akasaka, S. Nishitsuji, K. Saijo,
H. Shimizu, M.I. Kim, and H. Hasegawa, Orthorhombic
Fddd Network in Diblock Copolymer Melts, Macromolecules
40(13), 4399 (2007).
[6] B. Miao and R.A. Wickham, Fluctuation effects and the sta-
bility of the Fddd network phase in diblock copolymer melts,
J. Chem. Phys. 128, 054902 (2008).
[7] M.W. Matsen, The standard Gaussian model for block copoly-
mer melts, J. Phys.: Condens. Matter 14(2), R21 (2002).
[8] K.A. Mauritz and R.B. Moore, State of Understanding of
Nafion, Chem. Rev. 104, 4535 (2004).
[9] Michael Hickner, Hossein Ghassemi, Yu Seung Kim, Brian R
Einsla, and James E McGrath, Alternative polymer systems
for proton exchange membranes (PEMs), Chemical Reviews
104(10), 4587 (2004).
[10] M.J. Park and N.P. Balsara, Phase Behavior of Symmet-
ric Sulfonated Block Copolymers, Macromolecules 41, 3678
(2008).
[11] Xin Wang, Sergey Yakovlev, Keith M. Beers, Moon J. Park,
Scott a. Mullin, Kenneth H. Downing, and Nitash P. Balsara,
On the Origin of Slow Changes in Ionic Conductivity of Model
Block Copolymer Electrolyte Membranes in Contact with Hu-
mid Air, Macromolecules 43(12), 5306 (2010).
[12] Y. Rabin and J.F. Marko, Microphase separation in charged
diblock copolymers: the weak segregation limit, Macro-
molecules 24(8), 2134 (1991).
[13] R. Kumar and M. Muthukumar, Microphase separation in
polyelectrolytic diblock copolymer melt: weak segregation
limit, J. Chem. Phys. 126, 214902 (2007).
[14] I. Nakamura, I., N.P. Balsara, and Z.-G. Wang, Thermodynam-
ics of Ion-Containing Polymer Blends and Block Copolymers,
Phys. Rev. Lett. 107, 198301 (2011).
[15] I. Nakamura, I. and Z.-G. Wang, Salt-doped block copoly-
mers: ion distribution, domain spacing and effective [small
chi] parameter, Soft Matter 8, 9356 (2012).
[16] P. Knychała, M. Banaszak, Park M. J., and N.P. Balsara, Mi-
crophase Separation in Sulfonated Block Copolymers Studied
by Monte Carlo Simulations, Macromolecules 42(22), 8925
(2009).
[17] P. Knychała, M. Dzi ̨ ecielski, M. Banaszak, and N.P. Bal-
sara, Phase Behavior of Ionic Block Copolymers Studied
by a Minimal Lattice Model with Short-Range Interactions,
Macromolecules 46(14), 5724 (2013).
[18] P. Knychała, M. Banaszak, and N.P. Balsara, Effects of
Composition on the Phase Behavior of Ion-Containing Block
Copolymers Studied by a Minimal Lattice Model, Macro-
molecules 47(7), 2529 (2014).
[19] P. Knychała and M. Banaszak, Simulations on a swollen
gyroid nanostructure in thin films relevant to systems of ionic
block copolymers, European Physical Journal E 37, 67 (2014).
[20] J.E. Lennard-Jones, In On the Determination of Molecular
Fields, volume 106, page 463 The Royal Society, 1924.
[21] S. Blonski, W. Brostow, and J. Kubat, Molecular-Dynamics
Simulations of Stress-Relaxation in Metals and Polymers,
Physical Review B 49, 6494 (1994).
[22] K. Kremer and G.S. Grest, ynamics of Entangled Linear
Polymer Melts: A Molecular-Dynamics Simulation, J. Chem.
Phys. 92, 5057 (1990).
[23] B. Hess, H. Bekker, H.J.C. Berendsen, and J.G.E.M Fraaije,
LINCS: A Linear Constraint Solver for Molecular Simulations,
Journal of Computational Chemistry 18, 1463 (1997).
[24] J.P. Ryckaert, G. Ciccotti, and H.J.C. Berendsen, Numerical
Integration of the Cartesian Equations of Motion of a System
with Constraints: Molecular Dynamics of n-Alkanes, Journal
of Computational Physics 23, 327 (1977).
[25] T. Darden, D. York, and L. Pedersen, Particle Mesh Ewald:
An N-log(N) Method for Ewald Sums in Large Systems, J.
Chem. Phys. 98, 10089 (1993).
[26] P. Ewald, Die Berechnung optischer und elektrostatischer
Gitterpotentiale, Ann. Phys. 369, 253 (1921).
[27] M.P. Allen and D. Tildesley, Computer Simulation of Liquids,
Clarendon Press Oxford, 1989.
[28] J. Kolafa and J.W. Perram, Cutoff Errors in the Ewald Sum-
mation Formulae for Point Charge Systems, Molecular Simu-
lation 9, 351 (1992).
[29] S. Nose, A Unified Formulation of the Constant Temperature
Molecular-Dynamics Methods, J. Chem. Phys. 81, 511 (1984).
[30] W.G. Hoover, Canonical Dynamics: Equilibrium Phase-
Space Distribution, Phys. Rev. A 31, 1695 (1984).
[31] W.F. Van Gunsteren and H.J.C. Berendsen, A Leap-frog Al-
gorithm for Stochastic Dynamics, Molecular Simulation 1,
173 (1988).
[32] L. Verlet, Computer Experiments on Classical Fluids. I.
Thermodynamical Properties of Lennard-Jones Molecules,
Physical Review 159, 98 (1967).
[33] Gromacs User Manual 4.0, ftp://ftp.gromacs.org/pub/manual/
manual-4.0.pdf, Available: 30.08.2015.
[34] T.M. Beardsley and M.W. Matsen, Monte Carlo phase dia-
gram for diblock copolymer melts, Eur. Phys. J. E 32(3), 155
(2010).
[35] D. Van Der Spoel, E. Lindahl, B. Hess, G. Groenhof, A.E.
Mark, and H.J.C. Berendsen, GROMACS: Fast, Flexible, and
Free, J. Comput. Chem. 26, 1701 (2005).
[36] Tabulated Potentials, http://www.gromacs.org/Documenta
tion/How-tos/Tabulated_Potentials, Available: 30.08.2015.
[37] User Specified non-bonded potentials in gromacs, http://www.
gromacs.org/@api/deki/files/94/=gromacs_nb.pdf, Available:
29.10.2016.
