  Polymer chains decorated with a fraction of monomers capable of forming
reversible bonds form transient polymer networks that are important in soft and
biological systems. If chains are flexible and the attractive monomers are all
of the same species, the network formation occurs continuously as density
increases. By contrast, it has been recently shown [L. Rovigatti and F.
Sciortino, Phys. Rev. Lett. 129, 047801 (2022)] that, if the attractive
monomers are of two different and alternating types, the entropic gain of
swapping intra-molecular bonds for inter-molecular connections induces a first
order phase transition in the fully-bonded (\textit{i.e.} low-temperature or,
equivalently, large monomer-monomer attraction strength) limit and the network
forms abruptly on increasing density. Here we use simulations to show that this
phenomenon is robust with respect to thermal fluctuations, disorder and change
in the polymer architecture, demonstrating its generality and likely relevance
for the wide class of materials that can be modelled as associative (transient)
polymer networks.
