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Particle scattering function P(q) of RDD model. Examples of the influence of shape randomness and size polydispersity. b ¼ 90 Àa (deg).
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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...
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... instead of PðqÞ and R G , P(q) and R G denote the whole particle scattering function and the whole radius of gyration, respectively. Figure 8 shows examples of the influence of the cases in which the randomness of the shape and polydispersity of sizes changed. In these cases, randomizing the sizes of divided areas (partial sub-planes) gave the simplest curves, which had fewer peaks and valleys. ...
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Citations
... [ 33 ] Further moleculardynamics simulations by Abraham and Nelson [ 34,35 ] provided a detailed discussion of oriented and orientationally averaged structure factors [ 36 ] and demonstrated that the original analysis in terms of the Flory exponent (5) was indeed fl awed. Grest [ 37 ] studied sheets in three to eight space dimensions, where the anisotropic structure factor turns out to be a particularly valuable tool (for a detailed discussion of the structure factor, see the report by Hirata [ 38 ] ). He found that sheets are fl at for d ≤ 4 and crumpled for d ≥ 5 dimensions where, in the crumpled cases, the exponent ν is signifi cantly larger than the Flory exponent ν F . ...
Scaling behavior of one-dimensional (1D) and two-dimensional (2D) polymers in dilute solution is discussed with the goal of stimulating experimental work by chemists, physicists, and material scientists in the emerging field of 2D polymers. The arguments are based on renormalization-group theory, which is explained for a general audience. Many ideas and methods successfully applied to 1D polymers are found not to work if one goes to 2D polymers. The role of the various states exhibiting universal behavior is turned upside down. It is expected that solubility will be a serious challenge for 2D polymers. Therefore, given the crucial importance of solutions in characterization and processing, synthetic concepts are proposed that allow the local bending rigidity and the molar mass to be tuned and the long-range interactions to be engineered, all with the goal of preventing the polymer from falling into flat or compact states.
... 5,6 Highly functionalized forms of graphene such as graphene oxide (GO) show a far greater degree of wrinkling due to the interruptions the functional groups cause to the network of sp 2 bonded carbon, increasing the possibility for deformation. 7 Indeed, graphene oxide within a polystyrene matrix has been visualized by SEM as a well-dispersed array of crumpled sheets where the high aspect ratio of the GO is evident along with a disordered and heterogeneous distribution of material. 8 This flexibility of conformation draws parallels between graphene oxide or similarly flexible "two-dimensional macromolecules" with a one-dimensional chain-like polymer molecule that adopts its conformation as a function of its physical and chemical environment. ...
... 8 This flexibility of conformation draws parallels between graphene oxide or similarly flexible "two-dimensional macromolecules" with a one-dimensional chain-like polymer molecule that adopts its conformation as a function of its physical and chemical environment. 7,9 These departures from the ideal flat platelet conformation have a significant effect upon composite properties, with more wrinkled and folded morphologies having the most detrimental effect on material properties improvements. 10 Furthermore, as the conformation of GO is dependent upon the surrounding matrix, an outstanding question rests upon how the GO shape varies with chemical environment and how this variation is related to good nanoparticle dispersion, which is seen to be an important factor in the production of a successful polymer nanocomposite. ...
We study the conformation of graphene oxide as the filler in nanocomposites of polystyrene and poly(methyl methacrylate) using inverse-space scattering techniques and atomic force microscopy. By subtracting the polymer scattering to estimate the scattering contribution from the graphene oxide, we discover surface fractal scattering that spans a range of more than two decades in reciprocal space, indicating that the graphene oxide within these materials is rough on a very wide range of length scales and implying extensive extrinsic wrinkling and folding. We discover that well-exfoliated, locally flat sheets of graphene oxide produce a crossover in the scattering at a length scale of 16 nm, which becomes dominated by the signature of mass fractal scattering from thin disks or sheets. We show that the local graphene oxide structure in these polymer–graphene oxide nanocomposites is identical to that of graphene oxide in a water solution studied on the same length scale. Our results confirm the presence of well-exfoliated sheets that are key to achieving high interfacial areas between polymers and high aspect ratio filler in nanocomposites.
