Adv Polym Sci (2020) 285: 63–126
https://doi.org/10.1007/12_2020_61
© Springer Nature Switzerland AG 2020
Published online: 14 June 2020
Rheology, Rupture, Reinforcement
and Reversibility: Computational
Approaches for Dynamic Network
Materials
Chiara Raffaelli, Anwesha Bose, Cyril H. M. P. Vrusch, Simone Ciarella,
Theodoros Davris, Nicholas B. Tito, Alexey V. Lyulin,
Wouter G. Ellenbroek, and Cornelis Storm
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2 Background: Topology and Dynamics in Network Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.1 Composite Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.2 Reversible and Exchange Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3 Computational Approaches . . . . . . . .. . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .. . . . . . . . 73
3.1 Coarse-Grained Strategies for Polymer Networks in Molecular Dynamics . . . . . . . . . 73
3.2 Modelling Reversible Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.3 Modelling Exchange Reactions: Three-Body Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.4 Generation of Multiple Network Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.5 Computational Rheology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4 Structure and Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.1 Spatial Distributions of Reversibly Linked Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.2 Dynamic Bulk Rheology of Reversibly Linked Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.3 Effect of Reversible Cross-Links Near Percolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.4 Stress Relaxation in Vitrimers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
C. Raffaelli, A. Bose, C. H. M. P. Vrusch, S. Ciarella, T. Davris, and A. V. Lyulin
Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The
Netherlands
N. B. Tito, W. G. Ellenbroek, and C. Storm (*)
Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The
Netherlands
Institute for Complex Molecular Systems, Eindhoven University of Technology, Eindhoven,
The Netherlands
e-mail: c.storm@tue.nl
https://doi.org/10.1007/12_2020_61
© Springer Nature Switzerland AG 2020
Published online: 14 June 2020
Rheology, Rupture, Reinforcement
and Reversibility: Computational
Approaches for Dynamic Network
Materials
Chiara Raffaelli, Anwesha Bose, Cyril H. M. P. Vrusch, Simone Ciarella,
Theodoros Davris, Nicholas B. Tito, Alexey V. Lyulin,
Wouter G. Ellenbroek, and Cornelis Storm
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2 Background: Topology and Dynamics in Network Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.1 Composite Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.2 Reversible and Exchange Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3 Computational Approaches . . . . . . . .. . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .. . . . . . . . 73
3.1 Coarse-Grained Strategies for Polymer Networks in Molecular Dynamics . . . . . . . . . 73
3.2 Modelling Reversible Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.3 Modelling Exchange Reactions: Three-Body Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.4 Generation of Multiple Network Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.5 Computational Rheology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4 Structure and Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.1 Spatial Distributions of Reversibly Linked Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.2 Dynamic Bulk Rheology of Reversibly Linked Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.3 Effect of Reversible Cross-Links Near Percolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.4 Stress Relaxation in Vitrimers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
C. Raffaelli, A. Bose, C. H. M. P. Vrusch, S. Ciarella, T. Davris, and A. V. Lyulin
Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The
Netherlands
N. B. Tito, W. G. Ellenbroek, and C. Storm (*)
Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The
Netherlands
Institute for Complex Molecular Systems, Eindhoven University of Technology, Eindhoven,
The Netherlands
e-mail: c.storm@tue.nl