  Self-assembled linear structures like giant cylindrical micelles or discotic
molecules in solution stacked in flexible columns are systems reminiscent of
polydisperse polymer solutions.These supramolecular polymers have an
equilibrium length distribution, the result of a competition between the random
breakage of chains and the fusion of chains to generate longer ones. In the
present work, we review the basic theoretical concepts of these ``equilibrium
polymers" and some of the important results obtained by simulation approaches.
We propose a new version of a mesoscopic model in continuous space based on the
bead and FENE spring polymer model which is treated by Brownian Dynamics and
Monte-Carlo binding/unbinding reversible changes for adjacent monomers in
space, characterized by an attempt frequency parameter. For a dilute and a
moderately semi-dilute state-points which both correspond to dynamically
unentangled regimes, the dynamic properties are found to depend upon $\omega$
through the effective life time $\tau_b$ of the average size chain which, in
turn, yields the kinetic reaction coefficients of the mean-field kinetic model
proposed by Cates. Simple kinetic theories seem to work for times $ t \geq
\tau_b$ while at shorter time, strong dynamical correlation effects are
observed.
