  We present a new simulation technique to study systems of polymers
functionalized by reactive sites that bind/unbind forming reversible linkages.
Functionalized polymers feature self-assembly and responsive properties that
are unmatched by systems lacking selective interactions. The scales at which
the functional properties of these materials emerge are difficult to model,
especially in the reversible regime where such properties result from many
binding/unbinding events. This difficulty is related to large entropic barriers
associated with the formation of intra-molecular loops. In this work we present
a simulation scheme that sidesteps configurational costs by dedicated Monte
Carlo moves capable of binding/unbinding reactive sites in a single step.
Cross-linking reactions are implemented by trial moves that reconstruct chain
sections attempting, at the same time, a dimerization reaction between pairs of
reactive sites. The model is parametrized by the reaction equilibrium constant
of the reactive species free in solution. This quantity can be obtained by
means of experiments or atomistic/quantum simulations. We use the proposed
methodology to study self-assembly of single--chain polymeric nanoparticles,
starting from flexible precursors carrying regularly or randomly distributed
reactive sites. During a single run, almost all pairs of reactive monomers
interact at least once. We focus on understanding differences in the morphology
of chain nanoparticles when linkages are reversible as compared to the well
studied case of irreversible reactions. Intriguingly, we find that the size of
regularly functionalsized chains, in good solvent conditions, is non-monotonous
as a function of the degree of functionalization. We clarify how this result
follows from excluded volume interactions and is peculiar of reversible
linkages and regular functionalizations.
