Dual Self-Assembly in Strongly Asymmetric A-B-A Triblock Copolymer Melts Studied by Self-Consistent Field Theory and Monte Carlo Simulations
Dzięcielski Michał 1, Wołoszczuk Sebastian 2, Banaszak Michał 3*
1 Faculty of Geographical and Geological Sciences, Adam Mickiewicz University
ul. Krygowskiego 10, 61-680 Poznań, Poland2 Faculty of Physics, Adam Mickiewicz University
ul. Umultowska 85, 61-614 Poznan, Poland3* Faculty of Physics and NanoBioMedical Centre, Adam Mickiewicz University ul. Umultowska 85, 61-614 Poznan, Poland
*E-mail: mbanasz@amu.edu.pl
Received:
Received: 29 November 2018; revised: 12 December 2018; accepted: 14 December 2018; published online: 24 December 2018
DOI: 10.12921/cmst.2018.0000059
Abstract:
Using the Self-Consistent Field Theory (SCFT) we study the dual self-assembly of ABA triblock copolymers melts 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 shorter for the SCFT calculations than those for the corresponding Monte Carlo simulations.
Key words:
Monte Carlo simulation, self-assembly, self-consistent field theory, triblock copolymer
References:
[1] I.W.HamleyThePhysicsofBlockCopolymers,1998.
[2] M.Lazzari,G.Liu,S.Lecommandoux,BlockCopolymersin Nanoscience, pp. 1–428. Block Copolymers in Nanoscience,
2008.
[3] V.Abetz,P.F.W.Simon,Phasebehaviourandmorphologies
of block copolymers, Advances in Polymer Science, 189 2005. [4] A.N.SemenovSov.Phys.JETP61,733–742(1985).
[5] F.S.BatesG.H.Fredrickson,Blockcopolymers-designersoft
materials, Physics Today 52(2), 32–38 (1999).
[6] C. Park, J. Yoon, E.L. Thomas, Enabling nanotechnology with self assembled block copolymer patterns, Polymer 44(22),
6725–6760 (2003).
[7] V.Abetz,Blockcopolymers,ternarytriblocks,Encyclopedia
of Polymer Science and Technology 1, 482–523 (2003).
[8] Z.Guo,G.Zhang,F.Qiu,H.Zhang,Y.Yang,A..Shi,Discovering ordered phases of block copolymers: New results from
a generic fourier-space approach, Physical Review Letters
101(2) (2008).
[9] M.W.Matsen,R.B.Thompson,Equilibriumbehaviorofsym-
metric aba triblock copolymer melts, Journal of Chemical
Physics 111(15), 7139–7146 (1999).
[10] M.W. Matsen, Equilibrium behavior of asymmetric aba tri-
block copolymer melts, Journal of Chemical Physics 113(13),
5539–5544 (2000).
[11] P. Alexandridis, U. Olsson, B. Lindman, A record nine dif-
ferent phases (four cubic, two hexagonal, and one lamellar lyotropic liquid crystalline and two micellar solutions) in a
ternary isothermal system of an amphiphilic block copolymer and selective solvents (water and oil), Langmuir 14(10), 2627–2638 (1998).
[12] A.S. Krishnan, S.D. Smith, R.J. Spontak, Ternary phase behavior of a triblock copolymer in the presence of an endblockselective homopolymer and a midblock-selective oil, Macromolecules 45(15), 6056–6067 (2012).
[13] M.W. Matsen, F.S. Bates, Origins of complex self-assembly in block copolymers, Macromolecules 29(23), 7641–7644 (1996).
[14] J.T.Chen,E.L.Thomas,C.K.Ober,G..Mao,Self-assembled smectic phases in rod-coil block copolymers, Science 273, 343–346 (1996).
[15] J. Raez, I. Manners, M.A. Winnik, Nanotubes from the selfassembly of asymmetric crystalline-coil poly(ferrocenylsilanesiloxane) block copolymers, Journal of the American Chemical Society, 124(35), 10381–10395 (2002).
[16] M.W. Matsen, M. Schick, Lamellar phase of a symmetric triblock copolymer, Macromolecules 27(1), 187–192 (1994).
[17] M.W. Hamersky, S.D. Smith, A.O. Gozen, R.J. Spontak,
Phase behavior of triblock copolymers varying in molecular
asymmetry, Physical Review Letters 95(16), (2005).
[18] S.Woloszczuk,M.Banaszak,R.J.Spontak,Monte-carlosimulations of the order-disorder transition depression in aba
triblock copolymers with a short terminal block, Journal of Polymer Science, Part B: Polymer Physics 51(5), 343–348 (2013).
[19] S.S. Tallury, K.P. Mineart, S. Woloszczuk, D.N. Williams, R.B. Thompson, M.A. Pasquinelli, M. Banaszak, R.J. Spontak, Communication: Molecular-level insights into asymmetric triblock copolymers: Network and phase development, Journal of Chemical Physics 141(12), (2014).
[20] S. Woloszczuk, K.P. Mineart, R.J. Spontak, M. Banaszak,
Dual modes of self-assembly in superstrongly segregated bicomponent triblock copolymer melts, Physical Review E – Statistical, Nonlinear, and Soft Matter Physics 91(1), (2015).
[21] S. Woloszczuk, S. Jurga, M. Banaszak, Towards entropydriven interstitial micelles at elevated temperatures from selective a1-b-a2 triblock solutions, Physical Review E 94(2), (2016).
[22] S. Woloszczuk, M.O. Tuhin, S.R. Gade, M.A. Pasquinelli, M. Banaszak, R.J. Spontak, Complex phase behavior and network characteristics of midblock-solvated triblock copolymers as physically cross-linked soft materials, ACS Applied Materials and Interfaces 9(46), 39940–39944 (2017).
[23] S. Woloszczuk, M. Banaszak, Interstitial micelles in binary blends of aba triblock copolymers and homopolymers, Physical Review E 97(1), (2018).
[24] I.A. Nyrkova, A.R. Khokhlov, M. Doi, Microdomains in block copolymers and multiplets in ionomers: Parallels in behavior, Macromolecules 26(14), 3601–3610 (1993).
[25] A.N. Semenov, I.A. Nyrkova, A.R. Khokhlov, Polymers with strongly interacting groups: Theory for nonspherical multiplets, Macromolecules 28(22), 7491–7500 (1995).
[26] C. Burger, M.A. Micha, S. Oestreich, S. Förster, M. Antonietti, Characterization of two new stable block copolymer mesophases by synchrotron small-angle scattering, Europhysics Letters 42(4), 425–429 (1998).
[27] T.P. Lodge, M.A. Hillmyer, Z. Zhou, Y. Talmon, Access to the superstrong segregation regime with nonionic abc copolymers, Macromolecules 37(18), 6680–6682 (2004).
[28] R.R. Taribagil, M.A. Hillmyer, T.P. Lodge, Hydrogels from aba and abc triblock polymers, Macromolecules 43(12), 5396– 5404 (2010).
[29] S.Qin,H.Li,W.Yuan,Y.Zhang,Hierarchicalself-assembly of fluorine-containing diblock copolymer:from onion-like nanospheres to superstructured microspheres, Polymer 52(4), 1191–1196 (2011).
[30] J. . Deng, W. . Wang, Z. . Zheng, X. . Ding, Y. . Peng, Selfassembly behavior of copolymers with super segregated structure containing fluorinated segments, Chinese Journal of Polymer Science (English Edition) 32, 817–822 (2014).
[31] D.J.Pochan,Z.Chen,H.Cui,K.Hales,K.Qi,K.L.Wooley, Toroidal triblock copolymer assemblies, Science 306(5693), 94–97 (2004).
[32] A. Gauger, A. Weyersberg, T. Pakula, Monte carlo studies of static properties of interacting lattice polymers with the cooperative-motion algorithm, Die Makromolekulare Chemie, Theory uSimulations 2(4), 531–560 (1993).
[33] A. Weyersberg, T.A. Vilgis, Phase transitions in diblock copolymers: Theory and monte carlo simulations, Physical Review E 48(1), 377–390 (1993).
[34] T. Pakula, K. Karatasos, S.H. Anastasiadis, G. Fytas, Computer simulation of static and dynamic behavior of diblock copolymer melts, Macromolecules 30(26), 8463–8472 (1997).
[35] T.Pakula,Simulationsonthecompletelyoccupiedlattice,in Simulation Methods for Polymers (M.J. Kotelyanskii, D.N. Thedorou, eds.), ch. 5, Marcel-Dekker, 2004.
[36] M.Banaszak,S.Woloszczuk,T.Pakula,S.JurgaPhys.Rev. E 66(031804), (2003).
[37] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller J. Chem. Phys. 21(1087), (1953).
[38] R.H. Swendsen, J.S. Wang, Replica monte carlo simulation of spin-glasses, Physical Review Letters 57(12), 2607–2609 (1986).
[39] D.J.Earl,M.W.Deem,Paralleltempering:Theory,applications, and new perspectives, Physical Chemistry Chemical Physics 7(23), 3910–3916 (2005).
[40] A. Sikorski, Properties of star-branched polymer chains. application of the replica exchange monte carlo method, Macromolecules 35(18), 7132–7137 (2002).
[41] P. Knychała, M. Dzięcielski, M. Banaszak, N.P. Balsara, Phase behavior of ionic block copolymers studied by a minimal lattice model with short-range interactions, Macromolecules 46(14), 5724 (2013).
[42] G. Fredrickson, The Equilibrium Theory of Inhomogeneous Polymers. 2007.
Using the Self-Consistent Field Theory (SCFT) we study the dual self-assembly of ABA triblock copolymers melts 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 shorter for the SCFT calculations than those for the corresponding Monte Carlo simulations.
Key words:
Monte Carlo simulation, self-assembly, self-consistent field theory, triblock copolymer
References:
[1] I.W.HamleyThePhysicsofBlockCopolymers,1998.
[2] M.Lazzari,G.Liu,S.Lecommandoux,BlockCopolymersin Nanoscience, pp. 1–428. Block Copolymers in Nanoscience,
2008.
[3] V.Abetz,P.F.W.Simon,Phasebehaviourandmorphologies
of block copolymers, Advances in Polymer Science, 189 2005. [4] A.N.SemenovSov.Phys.JETP61,733–742(1985).
[5] F.S.BatesG.H.Fredrickson,Blockcopolymers-designersoft
materials, Physics Today 52(2), 32–38 (1999).
[6] C. Park, J. Yoon, E.L. Thomas, Enabling nanotechnology with self assembled block copolymer patterns, Polymer 44(22),
6725–6760 (2003).
[7] V.Abetz,Blockcopolymers,ternarytriblocks,Encyclopedia
of Polymer Science and Technology 1, 482–523 (2003).
[8] Z.Guo,G.Zhang,F.Qiu,H.Zhang,Y.Yang,A..Shi,Discovering ordered phases of block copolymers: New results from
a generic fourier-space approach, Physical Review Letters
101(2) (2008).
[9] M.W.Matsen,R.B.Thompson,Equilibriumbehaviorofsym-
metric aba triblock copolymer melts, Journal of Chemical
Physics 111(15), 7139–7146 (1999).
[10] M.W. Matsen, Equilibrium behavior of asymmetric aba tri-
block copolymer melts, Journal of Chemical Physics 113(13),
5539–5544 (2000).
[11] P. Alexandridis, U. Olsson, B. Lindman, A record nine dif-
ferent phases (four cubic, two hexagonal, and one lamellar lyotropic liquid crystalline and two micellar solutions) in a
ternary isothermal system of an amphiphilic block copolymer and selective solvents (water and oil), Langmuir 14(10), 2627–2638 (1998).
[12] A.S. Krishnan, S.D. Smith, R.J. Spontak, Ternary phase behavior of a triblock copolymer in the presence of an endblockselective homopolymer and a midblock-selective oil, Macromolecules 45(15), 6056–6067 (2012).
[13] M.W. Matsen, F.S. Bates, Origins of complex self-assembly in block copolymers, Macromolecules 29(23), 7641–7644 (1996).
[14] J.T.Chen,E.L.Thomas,C.K.Ober,G..Mao,Self-assembled smectic phases in rod-coil block copolymers, Science 273, 343–346 (1996).
[15] J. Raez, I. Manners, M.A. Winnik, Nanotubes from the selfassembly of asymmetric crystalline-coil poly(ferrocenylsilanesiloxane) block copolymers, Journal of the American Chemical Society, 124(35), 10381–10395 (2002).
[16] M.W. Matsen, M. Schick, Lamellar phase of a symmetric triblock copolymer, Macromolecules 27(1), 187–192 (1994).
[17] M.W. Hamersky, S.D. Smith, A.O. Gozen, R.J. Spontak,
Phase behavior of triblock copolymers varying in molecular
asymmetry, Physical Review Letters 95(16), (2005).
[18] S.Woloszczuk,M.Banaszak,R.J.Spontak,Monte-carlosimulations of the order-disorder transition depression in aba
triblock copolymers with a short terminal block, Journal of Polymer Science, Part B: Polymer Physics 51(5), 343–348 (2013).
[19] S.S. Tallury, K.P. Mineart, S. Woloszczuk, D.N. Williams, R.B. Thompson, M.A. Pasquinelli, M. Banaszak, R.J. Spontak, Communication: Molecular-level insights into asymmetric triblock copolymers: Network and phase development, Journal of Chemical Physics 141(12), (2014).
[20] S. Woloszczuk, K.P. Mineart, R.J. Spontak, M. Banaszak,
Dual modes of self-assembly in superstrongly segregated bicomponent triblock copolymer melts, Physical Review E – Statistical, Nonlinear, and Soft Matter Physics 91(1), (2015).
[21] S. Woloszczuk, S. Jurga, M. Banaszak, Towards entropydriven interstitial micelles at elevated temperatures from selective a1-b-a2 triblock solutions, Physical Review E 94(2), (2016).
[22] S. Woloszczuk, M.O. Tuhin, S.R. Gade, M.A. Pasquinelli, M. Banaszak, R.J. Spontak, Complex phase behavior and network characteristics of midblock-solvated triblock copolymers as physically cross-linked soft materials, ACS Applied Materials and Interfaces 9(46), 39940–39944 (2017).
[23] S. Woloszczuk, M. Banaszak, Interstitial micelles in binary blends of aba triblock copolymers and homopolymers, Physical Review E 97(1), (2018).
[24] I.A. Nyrkova, A.R. Khokhlov, M. Doi, Microdomains in block copolymers and multiplets in ionomers: Parallels in behavior, Macromolecules 26(14), 3601–3610 (1993).
[25] A.N. Semenov, I.A. Nyrkova, A.R. Khokhlov, Polymers with strongly interacting groups: Theory for nonspherical multiplets, Macromolecules 28(22), 7491–7500 (1995).
[26] C. Burger, M.A. Micha, S. Oestreich, S. Förster, M. Antonietti, Characterization of two new stable block copolymer mesophases by synchrotron small-angle scattering, Europhysics Letters 42(4), 425–429 (1998).
[27] T.P. Lodge, M.A. Hillmyer, Z. Zhou, Y. Talmon, Access to the superstrong segregation regime with nonionic abc copolymers, Macromolecules 37(18), 6680–6682 (2004).
[28] R.R. Taribagil, M.A. Hillmyer, T.P. Lodge, Hydrogels from aba and abc triblock polymers, Macromolecules 43(12), 5396– 5404 (2010).
[29] S.Qin,H.Li,W.Yuan,Y.Zhang,Hierarchicalself-assembly of fluorine-containing diblock copolymer:from onion-like nanospheres to superstructured microspheres, Polymer 52(4), 1191–1196 (2011).
[30] J. . Deng, W. . Wang, Z. . Zheng, X. . Ding, Y. . Peng, Selfassembly behavior of copolymers with super segregated structure containing fluorinated segments, Chinese Journal of Polymer Science (English Edition) 32, 817–822 (2014).
[31] D.J.Pochan,Z.Chen,H.Cui,K.Hales,K.Qi,K.L.Wooley, Toroidal triblock copolymer assemblies, Science 306(5693), 94–97 (2004).
[32] A. Gauger, A. Weyersberg, T. Pakula, Monte carlo studies of static properties of interacting lattice polymers with the cooperative-motion algorithm, Die Makromolekulare Chemie, Theory uSimulations 2(4), 531–560 (1993).
[33] A. Weyersberg, T.A. Vilgis, Phase transitions in diblock copolymers: Theory and monte carlo simulations, Physical Review E 48(1), 377–390 (1993).
[34] T. Pakula, K. Karatasos, S.H. Anastasiadis, G. Fytas, Computer simulation of static and dynamic behavior of diblock copolymer melts, Macromolecules 30(26), 8463–8472 (1997).
[35] T.Pakula,Simulationsonthecompletelyoccupiedlattice,in Simulation Methods for Polymers (M.J. Kotelyanskii, D.N. Thedorou, eds.), ch. 5, Marcel-Dekker, 2004.
[36] M.Banaszak,S.Woloszczuk,T.Pakula,S.JurgaPhys.Rev. E 66(031804), (2003).
[37] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller J. Chem. Phys. 21(1087), (1953).
[38] R.H. Swendsen, J.S. Wang, Replica monte carlo simulation of spin-glasses, Physical Review Letters 57(12), 2607–2609 (1986).
[39] D.J.Earl,M.W.Deem,Paralleltempering:Theory,applications, and new perspectives, Physical Chemistry Chemical Physics 7(23), 3910–3916 (2005).
[40] A. Sikorski, Properties of star-branched polymer chains. application of the replica exchange monte carlo method, Macromolecules 35(18), 7132–7137 (2002).
[41] P. Knychała, M. Dzięcielski, M. Banaszak, N.P. Balsara, Phase behavior of ionic block copolymers studied by a minimal lattice model with short-range interactions, Macromolecules 46(14), 5724 (2013).
[42] G. Fredrickson, The Equilibrium Theory of Inhomogeneous Polymers. 2007.
