Coexistence of Crumpling and Flat Sheet Conformations in Two-Dimensional Polymer Networks: An Understanding of Aggrecan Self-Assembly

We investigate the conformational properties of self-avoiding two-dimensional (2D) ideal polymer networks with tunable mesh sizes as a model of self-assembled structures formed by aggrecan. Polymer networks having few branching points and large enough mesh tend to crumple, resulting in a fractal dimension of d_f≈2.7 . The flat sheet behavior (d_f=2 ) emerges in 2D polymer networks having more branching points at large length scales; however, it coexists with crumpling conformations at intermediate length scales, a feature found in scattering profiles of aggrecan solutions. Our findings bridge the long-standing gap between theories and simulations of polymer sheets.