Monte-Carlo Simulations of Two-Dimensional Polymer Solutions with Explicit Solvent Treatment
Polanowski Piotr, Jeszka Jeremiasz, Sikorski Andrzej
1 Department of Molecular Physics, Technical University of Łódź, 90-924 Łódz, Poland
2 Department of Man-Made Fibres, Technical University of Łódź, 90-924 Łódz ́, Poland
3 Department of Chemistry, University of Warsaw Pasteura 1, 02-093 Warszawa, Poland
*E-mail: sikorski@chem.uw.edu.pl
Received:
Received: 06 November 2017; revised: 04 December 2017; accepted: 08 December 2017; published online: 31 December 2017
DOI: 10.12921/cmst.2017.0000050
Abstract:
he static properties of two dimensional athermal polymer solutions with explicit solvent molecules were studied by Monte Carlo lattice simulations using the cooperative motion algorithm (CMA). The simulations were performed for a wide range of polymer chain length N (from 16 to 1024) and polymer concentration (from 0.0156 to 1.00). The results obtained for short chains (N < 256) were in good agreement with theoretical predictions and previous simulations. For the longest chains (512 or 1024 beads) some unexpected behavior in the dilute and semidilute regimes was found. A rapid change in the concentration dependence of the end-to-end distance, the radius of gyration and the chain asphericity was observed below a critical concentration of the microphase separation, φc = 0.6 (for N = 1024). At concentrations lower than φc, the chains tends to be more rod-like. Single chain scattering structure factors showed changes in the fractal dimension of the chain as a function of the polymer concentration. The observed phenomena can be related to the excluded volume of solvent molecules, which leads to a modification of chain statistics in the vicinity of other chains.
Key words:
cooperative motion algorithm, lattice models, Monte Carlo simulations, polymer melts, thin films
References:
[1] A. Yethiraj, Computer Simulation Study of Two-Dimensional Polymer Solutions, Macromolecules 36, 5854–5862 (2003).
[2] C. Vlahos, M. Kosmas, On the miscibility of chemically identical linear homopolymers of different size, Polymer 44, 503–507 (2003).
[3] B. Maier, J. O. Radler, Conformation and Self-Diffusion of Single DNA Molecules Confined to Two Dimensions, Phys. Rev. Lett. 82, 1911–1914 (1999).
[4] B. Maier, J. O. Radler, DNA on Fluid Membranes: A Model Polymer in Two Dimensions, Macromolecules 33, 7185–7194 (2000).
[5] B. Maier, J. O. Radler, Shape of Self-Avoiding Walks in Two Dimensions, Macromolecules 34, 5723–5724 (2001).
[6] Y. M. Wang, I. Teraoka, Structures and Thermodynamics of Nondilute Polymer Solutions Confined between Parallel Plates, Macromolecules 33, 3478–3484 (2000).
[7] I. Teraoka, Y. M. Wang, Crossover from Two- to Three-Dimensional Contraction of Polymer Chains in Semidilute Solutions Confined to a Narrow Slit, Macromolecules 33, 6901–6903 (2000).
[8] H. Aoki, S. Morita, R. Sekine, S. Ito, Conformation of Single Poly(methyl methacrylate) Chains in an Ultra-Thin Film Studied by Scanning Near-Field Optical Microscopy, Polymer J. 40, 274–280 (2008).
[9] H. Aoki, M. Anryu, S. Ito, On the Miscibility of Chemically Identical Linear Homopolymers of Different Size, Polymer 46, 5896–5902 (2005).
[10] P. K. Lin, C. C. Fu, Y. L. Chen, Y. R. Chen, P. K. Wei, C. H. Kuan, W. S. Fann, Static Conformation and Dynamics of Single DNA Molecules Confined in Nanoslits. Phys. Rev. E 76, 011806 (2007).
[11] J. Sakamoto, J. van Heijst, O. Lukin, A. D. Schlüter, Two-Dimensional Polymers: Just a Dream of Synthetic Chemists?, Angew. Chem.-Int. Edit. 48, 1030–1069 (2009).
[12] P. P. Wen, N. Zheng, L. S. Li, G. Sun, Q. F. Shi, Polymerlike Statistical Characterization of Two-Dimensional Granular Chains, Phys. Rev. E 85, 031301 (2012).
[13] H. Meyer, J. P. Wittmer, T. Kreer, A. Johner, J. Baschnagel, Static Properties of Polymer Melts in Two Dimensions, J. Chem. Phys. 132, 184904 (2010).
[14] V. Vaidya, S. Soggs, J. Kim, A. Haldi, J. M. Haddock, B. Kippelen, D. M. Wilson, Comparison of Pentacene and Amorphous Silicon AMOLED Display Driver Circuits, IEEE Transaction on Circuits and Systems 55, 1177–1184(2008).
[15] P. G. De Gennes, Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, NY, 1979.
[16] P. H. Nelson. T. A. Hatton, G. C. Rutledge, General Reptation and Scaling of 2D Athermal Polymers on Close-Packed Lattices, J. Chem. Phys. 107, 1269–1278 (1997).
[17] P. Adamczyk, P. Polanowski, A. Sikorski, Percolation in Polymer-Solvent Systems: A Monte Carlo Study, J. Chem. Phys. 131, 234901 (2009).
[18] S. Żerko, P. Polanowski, A. Sikorski, Percolation in Two-Dimensional Systems Containing Cyclic Chains, Soft Matter 2012, 8, 973–979.
[19] M. Bishop, C. J. Saltiel, The Shapes of Two-, Four-, and Five-Dimensional Linear and Ring Polymers, J. Chem. Phys. 85, 6728–6731 (1986).
[20] I. Carmesin, K. Kremer, Static and Dynamic Properties of Two-Dimensional Polymer Melts, J. Phys. (France) 51, 915–932 (1990).
[21] H. Meyer, T. Kreer, M. Aichele, A. Johner, J. Baschnagel, Perimeter Length and Form Factor in Two-Dimensional Polymer Melts, Phys. Rev. E 79, 50802 (2009).
[22] P. Polanowski, J. K. Jeszka, Microphase Separation in Two-Dimensional Athermal Polymer Solutions on a Triangular Lattice, Langmuir 23, 8678–8680 (2007).
[23] P. Polanowski, J. K. Jeszka, A. Sikorski, Monte-Carlo Studies of Two-Dimensional Polymer-Solvent Systems, J. Mol. Model. 23, 63 (2017).
[24] P. Polanowski, J. K. Jeszka, A. Sikorski, Dynamic Properties of Linear and Cyclic Chains in Two Dimensions. Computer Simulation Studies, Macromolecules 47, 4830–4839 (2014).
[25] T. Pakula, Cooperative Relaxations in Condensed Macromolecular Systems. 1. A Model for Computer Simulation, Macromolecules 20, 679–682 (1987)
[26] J. Reiter, Monte Carlo Simulations of Linear and Cyclic Chains on Cubic and Quadratic Lattices, Macromolecules 23, 3811–3816 (1990).
[27] T. Pakula, S. Geyler, Cooperative Relaxations in Condensed Macromolecular Systems. 2. Computer Simulation of Self-Diffusion of Linear Chains, Macromolecules 20, 2909–2914 (1987).
[28] S. Geyler, T. Pakula, J. Reiter, Monte Carlo Simulation of Dense Polymer Systems on a Lattice, J. Chem. Phys. 92, 2676–2680 (1990).
[29] J. Reiter, T. Edling, T. Pakula, Monte Carlo Simulation of Lattice Models for Macromolecules at High Densities, J. Chem. Phys. 93, 837–844 (1990).
[30] P. Polanowski, T. Pakula, Studies of Polymer Conformation and Dynamics in Two Dimensions Using Simulations Based on the Dynamic Lattice Liquid (DLL) Model, J. Chem. Phys. 117, 4022–4029 (2002).
[31] S. Wołoszczuk, M. Banaszak, S. Jurga, M. Radosz, Low-Temperature Extra Ordering Effects in Symmetric Block Copolymers from Lattice Monte Carlo Simulation, Comput. Methods Sci. Technol. 10, 219–228 (2004).
[32] T. Pakula, D. Vlassopoulos, G. Fytas G., J. Roovers, Structure and Dynamics of Melts of Multiarm Polymer Stars, Macromolecules 31, 8931–8940 (1998).
[33] T. Pakula, Computer Simulation of Polymers in Thin Layers. I. Polymer Melt Between Neutral Walls – Static Properties, J. Chem. Phys. 95, 4685–4690 (1991).
[34] J. Des Cloizeaux, G. Jannik, Polymers in Solution. Their Modelling and Structure, Clarendon Press, Oxford, 1990.
[35] Teraoka, Polymer Solutions – An Introduction to Physical properties, Wiley-Interscience, New York, 2002.
[36] J. A. Aronowitz, D. R. Nelson, Universal Features of Polymer Shapes, J. Phys. (France) 47, 1445–1456 (1986).
he static properties of two dimensional athermal polymer solutions with explicit solvent molecules were studied by Monte Carlo lattice simulations using the cooperative motion algorithm (CMA). The simulations were performed for a wide range of polymer chain length N (from 16 to 1024) and polymer concentration (from 0.0156 to 1.00). The results obtained for short chains (N < 256) were in good agreement with theoretical predictions and previous simulations. For the longest chains (512 or 1024 beads) some unexpected behavior in the dilute and semidilute regimes was found. A rapid change in the concentration dependence of the end-to-end distance, the radius of gyration and the chain asphericity was observed below a critical concentration of the microphase separation, φc = 0.6 (for N = 1024). At concentrations lower than φc, the chains tends to be more rod-like. Single chain scattering structure factors showed changes in the fractal dimension of the chain as a function of the polymer concentration. The observed phenomena can be related to the excluded volume of solvent molecules, which leads to a modification of chain statistics in the vicinity of other chains.
Key words:
cooperative motion algorithm, lattice models, Monte Carlo simulations, polymer melts, thin films
References:
[1] A. Yethiraj, Computer Simulation Study of Two-Dimensional Polymer Solutions, Macromolecules 36, 5854–5862 (2003).
[2] C. Vlahos, M. Kosmas, On the miscibility of chemically identical linear homopolymers of different size, Polymer 44, 503–507 (2003).
[3] B. Maier, J. O. Radler, Conformation and Self-Diffusion of Single DNA Molecules Confined to Two Dimensions, Phys. Rev. Lett. 82, 1911–1914 (1999).
[4] B. Maier, J. O. Radler, DNA on Fluid Membranes: A Model Polymer in Two Dimensions, Macromolecules 33, 7185–7194 (2000).
[5] B. Maier, J. O. Radler, Shape of Self-Avoiding Walks in Two Dimensions, Macromolecules 34, 5723–5724 (2001).
[6] Y. M. Wang, I. Teraoka, Structures and Thermodynamics of Nondilute Polymer Solutions Confined between Parallel Plates, Macromolecules 33, 3478–3484 (2000).
[7] I. Teraoka, Y. M. Wang, Crossover from Two- to Three-Dimensional Contraction of Polymer Chains in Semidilute Solutions Confined to a Narrow Slit, Macromolecules 33, 6901–6903 (2000).
[8] H. Aoki, S. Morita, R. Sekine, S. Ito, Conformation of Single Poly(methyl methacrylate) Chains in an Ultra-Thin Film Studied by Scanning Near-Field Optical Microscopy, Polymer J. 40, 274–280 (2008).
[9] H. Aoki, M. Anryu, S. Ito, On the Miscibility of Chemically Identical Linear Homopolymers of Different Size, Polymer 46, 5896–5902 (2005).
[10] P. K. Lin, C. C. Fu, Y. L. Chen, Y. R. Chen, P. K. Wei, C. H. Kuan, W. S. Fann, Static Conformation and Dynamics of Single DNA Molecules Confined in Nanoslits. Phys. Rev. E 76, 011806 (2007).
[11] J. Sakamoto, J. van Heijst, O. Lukin, A. D. Schlüter, Two-Dimensional Polymers: Just a Dream of Synthetic Chemists?, Angew. Chem.-Int. Edit. 48, 1030–1069 (2009).
[12] P. P. Wen, N. Zheng, L. S. Li, G. Sun, Q. F. Shi, Polymerlike Statistical Characterization of Two-Dimensional Granular Chains, Phys. Rev. E 85, 031301 (2012).
[13] H. Meyer, J. P. Wittmer, T. Kreer, A. Johner, J. Baschnagel, Static Properties of Polymer Melts in Two Dimensions, J. Chem. Phys. 132, 184904 (2010).
[14] V. Vaidya, S. Soggs, J. Kim, A. Haldi, J. M. Haddock, B. Kippelen, D. M. Wilson, Comparison of Pentacene and Amorphous Silicon AMOLED Display Driver Circuits, IEEE Transaction on Circuits and Systems 55, 1177–1184(2008).
[15] P. G. De Gennes, Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, NY, 1979.
[16] P. H. Nelson. T. A. Hatton, G. C. Rutledge, General Reptation and Scaling of 2D Athermal Polymers on Close-Packed Lattices, J. Chem. Phys. 107, 1269–1278 (1997).
[17] P. Adamczyk, P. Polanowski, A. Sikorski, Percolation in Polymer-Solvent Systems: A Monte Carlo Study, J. Chem. Phys. 131, 234901 (2009).
[18] S. Żerko, P. Polanowski, A. Sikorski, Percolation in Two-Dimensional Systems Containing Cyclic Chains, Soft Matter 2012, 8, 973–979.
[19] M. Bishop, C. J. Saltiel, The Shapes of Two-, Four-, and Five-Dimensional Linear and Ring Polymers, J. Chem. Phys. 85, 6728–6731 (1986).
[20] I. Carmesin, K. Kremer, Static and Dynamic Properties of Two-Dimensional Polymer Melts, J. Phys. (France) 51, 915–932 (1990).
[21] H. Meyer, T. Kreer, M. Aichele, A. Johner, J. Baschnagel, Perimeter Length and Form Factor in Two-Dimensional Polymer Melts, Phys. Rev. E 79, 50802 (2009).
[22] P. Polanowski, J. K. Jeszka, Microphase Separation in Two-Dimensional Athermal Polymer Solutions on a Triangular Lattice, Langmuir 23, 8678–8680 (2007).
[23] P. Polanowski, J. K. Jeszka, A. Sikorski, Monte-Carlo Studies of Two-Dimensional Polymer-Solvent Systems, J. Mol. Model. 23, 63 (2017).
[24] P. Polanowski, J. K. Jeszka, A. Sikorski, Dynamic Properties of Linear and Cyclic Chains in Two Dimensions. Computer Simulation Studies, Macromolecules 47, 4830–4839 (2014).
[25] T. Pakula, Cooperative Relaxations in Condensed Macromolecular Systems. 1. A Model for Computer Simulation, Macromolecules 20, 679–682 (1987)
[26] J. Reiter, Monte Carlo Simulations of Linear and Cyclic Chains on Cubic and Quadratic Lattices, Macromolecules 23, 3811–3816 (1990).
[27] T. Pakula, S. Geyler, Cooperative Relaxations in Condensed Macromolecular Systems. 2. Computer Simulation of Self-Diffusion of Linear Chains, Macromolecules 20, 2909–2914 (1987).
[28] S. Geyler, T. Pakula, J. Reiter, Monte Carlo Simulation of Dense Polymer Systems on a Lattice, J. Chem. Phys. 92, 2676–2680 (1990).
[29] J. Reiter, T. Edling, T. Pakula, Monte Carlo Simulation of Lattice Models for Macromolecules at High Densities, J. Chem. Phys. 93, 837–844 (1990).
[30] P. Polanowski, T. Pakula, Studies of Polymer Conformation and Dynamics in Two Dimensions Using Simulations Based on the Dynamic Lattice Liquid (DLL) Model, J. Chem. Phys. 117, 4022–4029 (2002).
[31] S. Wołoszczuk, M. Banaszak, S. Jurga, M. Radosz, Low-Temperature Extra Ordering Effects in Symmetric Block Copolymers from Lattice Monte Carlo Simulation, Comput. Methods Sci. Technol. 10, 219–228 (2004).
[32] T. Pakula, D. Vlassopoulos, G. Fytas G., J. Roovers, Structure and Dynamics of Melts of Multiarm Polymer Stars, Macromolecules 31, 8931–8940 (1998).
[33] T. Pakula, Computer Simulation of Polymers in Thin Layers. I. Polymer Melt Between Neutral Walls – Static Properties, J. Chem. Phys. 95, 4685–4690 (1991).
[34] J. Des Cloizeaux, G. Jannik, Polymers in Solution. Their Modelling and Structure, Clarendon Press, Oxford, 1990.
[35] Teraoka, Polymer Solutions – An Introduction to Physical properties, Wiley-Interscience, New York, 2002.
[36] J. A. Aronowitz, D. R. Nelson, Universal Features of Polymer Shapes, J. Phys. (France) 47, 1445–1456 (1986).
