We investigate the kinetics of self-assembly by means of Brownian dynamics simulation based on a idealized fluid model (two ‘sticky’ spots on a sphere) in which the particles are known to form into dynamic polymer chains at equilibrium. To illustrate the slow evolution of the properties of these self-assembling fluids to their equilibrium assembled state values at long times, we perform Brownian dynamics simulations over a range of quench depths from the high temperature unassembled state to the low temperature assembled state. We investigate the time dependence of the average chain length (cluster mass), the order parameter for the assembly transition (fraction of particles in the chain state) and the potential energy of the fluid. The rate constant governing the self-assembly ordering process depends both on kinetic-related factors (the particle hydrodynamic radius and the fluid viscosity) and on thermodynamic energetic variables governing the self-assembly transition (i.e., the entropy and enthalpy of assembly). We provide evidence that an essentially parameter-free description of the polymerization kinetics can be formulated for this model. © 2008 IOP Publishing Ltd.