Folding behaviors of two-dimensional flexible polymers

Unlike one-dimensional polymers, the theoretical framework on the behaviors of two-dimensional (2D) polymers is far from completeness. In this study, we model single-layer flexible 2D polymers of different sizes and examine their scaling behaviors in solution, represented by R-g similar to L-nu, where R-g is the radius of gyration and L is the side length of a 2D polymer. We find that the scaling exponent nu is 0.96 for a good solvent and 0.64 for under poor solvent condition. Interestingly, we observe a previously unnoticed phenomenon: under intermediate solvent conditions, the 2D polymer folds to maintain a flat structure, and as L becomes larger, multiple folded structures emerge. We introduce a shape parameter Q to diagram the relationship of folded structures with the polymer size and solvent condition. Theoretically, we explain the folding transitions by the competition between bending and solvophobic free energies.