Particle scattering function of a two-dimensional flexible macromolecule

The particle scattering function (structure factor) P(q) of a two-dimensional flexible macromolecule (2D-FM), such as thin graphite oxide and graphene oxide, was calculated. The geometrical model used for shrinking the 2D-FM particle was the developable double corrugation surface (Miura folding) of a circular or elliptic disk. This model described a three-dimensionally foldable and re-extendable shape and spontaneously exhibited a self-avoiding condition inside a single particle. Moreover, the randomness of the shrinking shape and the polydispersity of the size of the disk were also added to the model. The obtained P(q) varied greatly according to the shape of the particle, which can change from a flat extended state, like a disk, to a three-dimensionally isotropic and dense shrunken state, like a short cylinder, by changing the degree of the shrinking. In addition, the P(q) showed that the shrunken state is constructed from many small partial sub-planes that are three-dimensionally neither isotropic nor dense.