The shape of ribbons: from polymers to surfaces

Ribbons are a subset of polymerized networks that occupy an intermediate space between polymers and surfaces. We perform extensive numerical simulations to understand how to interpolate the statistical properties of ribbons across the two limits by studying their behavior as a function of their widths and bending rigidities, taking into consideration both ideal and self-avoiding ribbons. We map out a two-dimensional phase diagram of the morphology of ideal ribbons, and uncover the onset of a crumpling transition for ribbons of sufficiently large width. We also discuss the onset width above which a ribbon behaves effectively as a surface. Finally, we suggest scaling laws and functional forms that properly link and interpolate the shape of self-avoiding polymers to that of self-avoiding surfaces.