  Our understanding of the growth of crystals is dominated by the classical
description according to which individual atoms or molecules, driven by
supersaturation, add to crystal facets. As a result, the growth of hard matter
is still mostly considered to be fundamentally incomparable to the growth of
soft matter, like polymers or liquids. By a combination of experiment and
modeling we here show how amine-capped PbS colloidal nanoparticles grow in the
absence of supersaturation by coalescence, like droplets in an emulsion.
Specifically, we (i) determine that the rates of crystal-crystal coalescence
are remarkably high (10^-2 to 10^1 M^-1*s^-1) in spite of the steric
stabilization of the particles, and are comparable to those of bimolecular
reactions, (thereby providing a new avenue for the development of a form of
chemistry where the reactants are colloids rather than molecules), (ii)
elucidate the rate limiting steps of crystal-crystal coalescence leading us to
propose design rules to control it, and (iii) demonstrate a simple,
two-parameter model that predicts quantitatively this process and its
dependence on the ligands. Lastly, we use Brownian dynamics simulations to show
how crowding effects and the relatively large size of the particles compared to
their mean free path explain these remarkably large rates of coalescence and,
at the same time, the puzzlingly low values of activation energy previously
reported for oriented attachment processes.
