Monte Carlo Study of Triblock Self-Assembly by Cooperative Motion Algorithm
Wołoszczuk Sebastian 1, Banaszak Michał 1,2*
1 Faculty of Physics, Adam Mickiewicz University
ul. Uniwersytetu Poznańskiego 2, 61-614 Poznań, Poland2 NanoBioMedical Centre, Adam Mickiewicz University
ul. Wszechnicy Piastowskiej 3, 61-614 Poznań, Poland
*E-mail: michal.banaszak@amu.edu.pl
Received:
Received: 30 August 2020; revised: 21 September 2020; accepted: 22 September 2020; published online: 30 September 2020
DOI: 10.12921/cmst.2020.0000025
Abstract:
We perform a comprehensive Monte Carlo study of the ABA triblock self-assembly by the Cooperative Motion Algorithm. Our attention is focused on three series of triblocks which are grown from parent AB diblocks of varying asymmetry. Unlike the previous studies in which the total length of the chain varies upon growing the terminal A-block, here we keep the fixed chain length for a given series. Moreover, we determine the order-disorder transition temperature as the τ parameter (being the ratio of the grown A-block to the length of the parent diblock) increases. In this case we find that the order-disorder transition temperature monotonically decreases for two asymmetric series which is different from the non-monotonic depression of T_ODT reported previously. We also construct a phase diagram which shows a variety of nanostructures as τ is increased.
Key words:
cooperative motion algorithm, Monte Carlo, triblock copolymers
References:
[1] I.W. Hamley, The Physics of Block Copolymers, Oxford University Press (1998).
[2] S. Wołoszczuk, M. Banaszak, R.J. Spontak, Monte-Carlo simulations 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).
[3] 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), 168306 (2005).
[4] M. Banaszak, S. Wołoszczuk, T. Pakula, S. Jurga, Computer simulation of structure and microphase separation in model A-B-A triblock copolymers, Phys. Rev. E 66, 031804 (2002).
[5] A. Gauger, A. Weyersberg, T. Pakula, Monte Carlo studies of static properties of interacting lattice polymers with the cooperative-motion algorithm, Makromol. Chem., Theory Simul. 2(4), 531–560 (1993).
[6] A. Weyersberg, T.A. Vilgis, Phase transitions in diblock copolymers: Theory and Monte Carlo simulations, Phys. Rev. E 48(1), 377–390 (1993).
[7] T. Pakula, K. Karatasos, S.H. Anastasiadis, G. Fytas, Computer Simulation of Static and Dynamic Behavior of Di-block Copolymer Melts, Macromolecules 30(26), 8463–8472 (1997).
[8] T. Pakula, Simulations on the Completely Occupied Lattice, [In:] M.J. Kotelyanskii, D.N. Thedorou (eds.), Simulation Methods for Polymers, chap. 5. Marcel-Dekker (2004).
[9] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, Equation of State Calculations by Fast Computing Machines, J. Chem. Phys. 21, 1087 (1953).
[10] R.H. Swendsen, J.S. Wang, Replica Monte Carlo Simulation of Spin-Glasses, Phys. Rev. Lett. 57, 2607 (1986).
[11] A. Sikorski, Properties of star-branched polymer chains. Application of the replica exchange Monte Carlo method, Macromolecules 35(18), 7132–7137 (2002).
[12] D.J. Earl, M.W. Deem, Parallel tempering: Theory, applications, and new perspectives, Phys. Chem. Chem. Phys. 7, 3910–3916 (2005).
[13] P. Knychala, M. Dziecielski, M. Banaszak, N.P. Balsara, Phase Behavior of Ionic Block Copolymers Studied by a Minimal Lattice Model with Short-Range Interactions, Macromolecules 46(14), 5724–5730 (2013).
[14] G.H. Fredrickson, The Equlibrium Theory of Inhomogeneous Polymers, Clarendon Press, Oxford (2006).
[15] P. Knychala, M. Banaszak, N.P. Balsara, Effect of Composition on the Phase Behavior of Ion-Containing Block Copolymers Studied by a Minimal Lattice Model, Macromolecules 47(7), 2529–2535 (2014).
We perform a comprehensive Monte Carlo study of the ABA triblock self-assembly by the Cooperative Motion Algorithm. Our attention is focused on three series of triblocks which are grown from parent AB diblocks of varying asymmetry. Unlike the previous studies in which the total length of the chain varies upon growing the terminal A-block, here we keep the fixed chain length for a given series. Moreover, we determine the order-disorder transition temperature as the τ parameter (being the ratio of the grown A-block to the length of the parent diblock) increases. In this case we find that the order-disorder transition temperature monotonically decreases for two asymmetric series which is different from the non-monotonic depression of T_ODT reported previously. We also construct a phase diagram which shows a variety of nanostructures as τ is increased.
Key words:
cooperative motion algorithm, Monte Carlo, triblock copolymers
References:
[1] I.W. Hamley, The Physics of Block Copolymers, Oxford University Press (1998).
[2] S. Wołoszczuk, M. Banaszak, R.J. Spontak, Monte-Carlo simulations 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).
[3] 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), 168306 (2005).
[4] M. Banaszak, S. Wołoszczuk, T. Pakula, S. Jurga, Computer simulation of structure and microphase separation in model A-B-A triblock copolymers, Phys. Rev. E 66, 031804 (2002).
[5] A. Gauger, A. Weyersberg, T. Pakula, Monte Carlo studies of static properties of interacting lattice polymers with the cooperative-motion algorithm, Makromol. Chem., Theory Simul. 2(4), 531–560 (1993).
[6] A. Weyersberg, T.A. Vilgis, Phase transitions in diblock copolymers: Theory and Monte Carlo simulations, Phys. Rev. E 48(1), 377–390 (1993).
[7] T. Pakula, K. Karatasos, S.H. Anastasiadis, G. Fytas, Computer Simulation of Static and Dynamic Behavior of Di-block Copolymer Melts, Macromolecules 30(26), 8463–8472 (1997).
[8] T. Pakula, Simulations on the Completely Occupied Lattice, [In:] M.J. Kotelyanskii, D.N. Thedorou (eds.), Simulation Methods for Polymers, chap. 5. Marcel-Dekker (2004).
[9] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, Equation of State Calculations by Fast Computing Machines, J. Chem. Phys. 21, 1087 (1953).
[10] R.H. Swendsen, J.S. Wang, Replica Monte Carlo Simulation of Spin-Glasses, Phys. Rev. Lett. 57, 2607 (1986).
[11] A. Sikorski, Properties of star-branched polymer chains. Application of the replica exchange Monte Carlo method, Macromolecules 35(18), 7132–7137 (2002).
[12] D.J. Earl, M.W. Deem, Parallel tempering: Theory, applications, and new perspectives, Phys. Chem. Chem. Phys. 7, 3910–3916 (2005).
[13] P. Knychala, M. Dziecielski, M. Banaszak, N.P. Balsara, Phase Behavior of Ionic Block Copolymers Studied by a Minimal Lattice Model with Short-Range Interactions, Macromolecules 46(14), 5724–5730 (2013).
[14] G.H. Fredrickson, The Equlibrium Theory of Inhomogeneous Polymers, Clarendon Press, Oxford (2006).
[15] P. Knychala, M. Banaszak, N.P. Balsara, Effect of Composition on the Phase Behavior of Ion-Containing Block Copolymers Studied by a Minimal Lattice Model, Macromolecules 47(7), 2529–2535 (2014).
