4.5 Mechanical Reinforcement and the Payne Effect in Nanocomposites . . . . . . . . . . . . . . . 116
4.6 Fracture of Double Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5 Conclusions and Outlook . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 122
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Abstract The development of high-performance polymeric materials typically
involves a trade-off between desirable properties such as processability, recyclability, durability, and strength. Two common strategies in this regard are composites
and reversibly cross-linked materials. Making optimal choices in the vast design
spaces of these polymeric materials requires a solid understanding of the molecularscale mechanisms that determine the relation between their structure and their
mechanical properties. Over the past few years, a wide range of computational
techniques has been developed and employed to model these mechanisms and
build this understanding. Focusing on approaches rooted in molecular dynamics,
we present and discuss these techniques, and demonstrate their use in several
physical models of novel polymer-based materials, including nanocomposites,
toughened gels, double network elastomers, vitrimers, and reversibly cross-linked
semiflexible biopolymers.
Keywords Dynamic networks · Mechanical properties · Mechanical
reinforcement · Modelling · Nanocomposites · Polymer materials · Simulation
1 Introduction
Pretty much every talk on the mechanics of polymer materials will feature, at one
point or another, an image of a plate of spaghetti and/or a snake. Two iconic
metaphors, representing the two quintessential determinants of the mechanical
quality of classical polymer materials: structure and dynamics. Classical polymer
texts will emphasize the fact that the long polymer strands become entangled,
impeding each other’s ability to explore space much more than ordinary
non-extended particles do. As a result, polymer solutions and melts – in addition
to the viscous characteristics expected for these ultimately liquid systems – exhibit
mechanical properties usually found in solids even in the absence of chemical crosslinking and do so over broad ranges of timescales. These liquidlike traits, possibly
enhanced by elevated temperatures, facilitate the structural relaxations that provide
malleability and ensure the easy processing of entangled polymer materials: desirable properties in their own right but also beneficial to the recyclability of polymeric
materials. For these and many other reasons, regimes of deformability and plasticity
are highly sought-after in application. Those same applications, however, generally
also require that – once formed into a product – the materials are strong, are tough
64
C. Raffaelli et al.
4.6 Fracture of Double Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5 Conclusions and Outlook . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 122
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Abstract The development of high-performance polymeric materials typically
involves a trade-off between desirable properties such as processability, recyclability, durability, and strength. Two common strategies in this regard are composites
and reversibly cross-linked materials. Making optimal choices in the vast design
spaces of these polymeric materials requires a solid understanding of the molecularscale mechanisms that determine the relation between their structure and their
mechanical properties. Over the past few years, a wide range of computational
techniques has been developed and employed to model these mechanisms and
build this understanding. Focusing on approaches rooted in molecular dynamics,
we present and discuss these techniques, and demonstrate their use in several
physical models of novel polymer-based materials, including nanocomposites,
toughened gels, double network elastomers, vitrimers, and reversibly cross-linked
semiflexible biopolymers.
Keywords Dynamic networks · Mechanical properties · Mechanical
reinforcement · Modelling · Nanocomposites · Polymer materials · Simulation
1 Introduction
Pretty much every talk on the mechanics of polymer materials will feature, at one
point or another, an image of a plate of spaghetti and/or a snake. Two iconic
metaphors, representing the two quintessential determinants of the mechanical
quality of classical polymer materials: structure and dynamics. Classical polymer
texts will emphasize the fact that the long polymer strands become entangled,
impeding each other’s ability to explore space much more than ordinary
non-extended particles do. As a result, polymer solutions and melts – in addition
to the viscous characteristics expected for these ultimately liquid systems – exhibit
mechanical properties usually found in solids even in the absence of chemical crosslinking and do so over broad ranges of timescales. These liquidlike traits, possibly
enhanced by elevated temperatures, facilitate the structural relaxations that provide
malleability and ensure the easy processing of entangled polymer materials: desirable properties in their own right but also beneficial to the recyclability of polymeric
materials. For these and many other reasons, regimes of deformability and plasticity
are highly sought-after in application. Those same applications, however, generally
also require that – once formed into a product – the materials are strong, are tough
64
C. Raffaelli et al.