Glassy effects in the swelling/collapse dynamics of homogeneous polymers

We investigate, using numerical simulations and analytical arguments, a sim ple one-dimensional model for the swelling or the collapse of a closed poly mer chain of size Ai, representing the dynamical evolution of a polymer in a Theta -solvent that is rapidly changed into a good solvent (swelling) or a bad solvent (collapse). In the case of swelling, the density profile for intermediate times is parabolic and expands in space as t(1/3), as predicte d by a Flory-like continuum theory. The dynamics slows down after a time pr oportional to N-2 when the chain becomes stretched, and the polymer gets st uck in metastable "zig-zag" configurations, from which it escapes through t hermal activation. The size of the polymer in the final stages is found to grow as root ln t. In the case of collapse, the chain very quickly (after. a time of order unity) breaks up into clusters of monomers ("pearls"). The evolution of the chain then proceeds through a slow growth of the size of t hese metastable clusters, again evolving as the logarithm of time. S;Ve enu merate the total number of metastable states as a function of the extension of the chain, and deduce from this computation that the radius of the chai n should decrease as 1 / ln(ln t). We compute the total number of metastabl e states with a given value of the energy, and find that the complexity is non-zero for arbitrary low energies. We also obtain the distribution of clu ster sizes, that we compare to simple "cut-in-two" coalescence models. Fina lly, we determine the aging properties of the dynamical structure. The suba ging behaviour that we find is attributed to the tail of the distribution a t small cluster sizes, corresponding to anomalously "fast" clusters (as com pared to the average). S;Ve argue that this mechanism for subaging might ho ld in other slowly coarsening systems.