Structurally complex, soft materials often display disordered low-dimensional features that are quantified by a mass-fractal dimension, df.  In small-angle scattering, power-law scattering is observed in a size range between the primary structure and the overall size.  For example, a molybdenum disulfide nano-sheet can display a power-law decay of close to -2 reflecting two dimensionality between the thickness and the overall sheet size.  Similarly a linear polymer chain in the melt can display the same nanoscale dimension, df = 2, between the persistence length and the coil size.  An analysis of scattering can resolve the difference between these structures using scaling methods developed several years ago through quantification of the minimum dimension, dmin, which reflects the degree of tortuosity to a structure.  For a sheet structure dmin is 1, while for a random walk of a linear structure dmin is 2.  A related dimension is the connectivity dimension, c, that can be defined by df = c dmin. For a linear chain c is 1 and for a two-dimensional sheet c is 2, so c reflects the native structural dimension prior to kinetic or thermodynamic (entropic) crumpling.  This approach has been useful to quantify crumpling in sheet structures on the nanoscale due to chemical modification, to understand and quantify long-chain branching in polyethylene, to verify complex macromolecular topologies in model polymers such as H-polymers, star polymers, and recently to quantify the appearance of branching in worm-like micelles.  We have also used this approach to understand hyperbranched polymers, the structure of gels and networks, the structure of cyclics, protein and nucleic acid folding, and fluctuations in bilayer membranes. <br/><br/>

Topology of soft materials using neutron and X-ray scattering

249th National Meeting (2015)

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