  We numerically study a simple fluid composed of particles having a hard-core
repulsion, complemented by two short-ranged attractive (sticky) spots at the
particle poles, which provides a simple model for equilibrium polymerization of
linear chains. The simplicity of the model allows for a close comparison, with
no fitting parameters, between simulations and theoretical predictions based on
the Wertheim perturbation theory, a unique framework for the analytic
prediction of the properties of self-assembling particle systems in terms of
molecular parameter and liquid state correlation functions. This theory has not
been subjected to stringent tests against simulation data for ordering across
the polymerization transition. We numerically determine many of the
thermodynamic properties governing this basic form of self-assembly (energy per
particle, order parameter or average fraction of particles in the associated
state, average chain length, chain length distribution, average end-to-end
distance of the chains, and the static structure factor) and find that
predictions of the Wertheim theory accord remarkably well with the simulation
results.
