  A Brownian dynamics algorithm is used to describe the static behaviour of
associative polymer solutions. Predictions for the fractions of stickers bound
by intra-chain and inter-chain association, as a function of system parameters,
such as the number of stickers, the number of monomers between stickers, the
solvent quality, and concentration are obtained. A systematic comparison with
the scaling relations predicted by the mean-field theory of Dobrynin
(Macromolecules, 37, 3881, 2004) is carried out. Different regimes of scaling
behaviour are identified depending on the monomer concentration, the density of
stickers on a chain, and the solvent quality for backbone monomers. Simulation
results validate the predictions of the mean-field theory across a wide range
of parameter values in all the scaling regimes. The value of the des Cloizeaux
exponent proposed by Dobrynin for sticky polymer solutions, is shown to lead to
a collapse of simulation data for all the scaling relations considered here.
Three different signatures for the characterisation of gelation are identified,
with each leading to a different value of the concentration at the sol-gel
transition. The modified Flory-Stockmayer expression is found to be validated
by simulations for all three gelation signatures. Simulation results confirm
the prediction of scaling theory for the gelation line that separates sol and
gel phases, when the modified Flory-Stockmayer expression is used. Phase
separation is found to occur with increasing concentration for systems in which
the backbone monomers are under theta-solvent conditions, and is shown to
coincide with a breakdown in the predictions of scaling theory.
