Self-assembled linear structures like giant cylindrical micelles or discotic molecules in solution stacked in flexible columns are systems reminiscent of polydisperse polymer solutions, ranging from dilute to concentrated solutions as the overall monomer density and/or the chain length increases. 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. This scissionrecombination mechanism is believed to be responsible of some peculiar dynamical properties like the Maxwell fluid rheological character for entangled micelles. Simulations employing simple mesoscopic models provide a powerful approach to test mean-field theories or scaling approaches which have been proposed to rationalize the structural and kinetic properties of these soft matter systems. 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 ω. 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 ω through the effective life time τ 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 ≥ τ b while at shorter time, strong dynamical correlation effects are observed. Other dynamical properties like the overall monomer diffusion and the mobility of reactive end-monomers are also investigated.

It is commonly accepted that in concentrated solutions or melts high-molecular weight polymers display randomwalk conformational properties without long-range correlations between subsequent bonds. This absence of memory means, for instance, that the bond-bond correlation function, P (s), of two bonds separated by s monomers along the chain should exponentially decay with s. Presenting numerical results and theoretical arguments for both monodisperse chains and self-assembled (essentially Flory size-distributed) equilibrium polymers we demonstrate that some long-range correlations remain due to self-interactions of the chains caused by the chain connectivity and the incompressibility of the melt. Suggesting a profound analogy with the well-known long-range velocity correlations in liquids we find, for instance, P (s) to decay algebraically as s −3/2 . Our study suggests a precise method for obtaining the statistical segment length be in a computer experiment.

Following Flory's ideality hypothesis, the chemical potential of a test chain of length n immersed into a dense solution of chemically identical polymers of length distribution P(N) is extensive in n . We argue that an additional contribution deltamu(c)(n) approximately +1/rho (sqrt[n]) arises (rho being the monomer density) for all P(N) if n " which can be traced back to the overall incompressibility of the solution leading to a long-range repulsion between monomers. Focusing on Flory-distributed melts, we obtain deltamu(c)(n) approximately equal to (1 - 2n/ ) / rho (sqrt[n]) for n " (2) , hence, deltarho(c)(n) approximately equal to -1/rho (sqrt[n]) if n is similar to the typical length of the bath . Similar results are obtained for monodisperse solutions. Our perturbation calculations are checked numerically by analyzing the annealed length distribution P(N) of linear equilibrium polymers generated by Monte Carlo simulation of the bond fluctuation model. As predicted we find, e.g., the non-exponentiality parameter K (p) = 1 - (p)! (p) to decay as K (p) approximately equal to 1/ (sqrt[]) for all moments p of the distribution.