  Reversible crosslinking is a design paradigm for polymeric materials, wherein
they are microscopically reinforced with chemical species that form transient
crosslinks between the polymer chains. Besides the potential for self-healing,
recent experimental work suggests that freely diffusing reversible crosslinks
in polymer networks, such as gels, can enhance the toughness of the material
without substantial change in elasticity. This presents the opportunity for
making highly elastic materials that can be strained to a large extent before
rupturing. Here, we employ Gaussian chain theory, molecular simulation, and
polymer self-consistent field theory for networks to construct an equilibrium
picture for how reversible crosslinks can toughen a polymer network without
affecting its linear elasticity. Maximisation of polymer entropy drives the
reversible crosslinks to bind preferentially near the permanent crosslinks in
the network, leading to local molecular reinforcement without significant
alteration of the network topology. In equilibrium conditions, permanent
crosslinks share effectively the load with neighbouring reversible crosslinks,
forming multi-functional crosslink points. The network is thereby globally
toughened, while the linear elasticity is left largely unaltered. Practical
guidelines are proposed to optimise this design in experiment, along with a
discussion of key kinetic and timescale considerations.
