title: Scattering Function for Branched Wormlike Chains.
abstract: Wormlike or threadlike structures with local cylindrical geometry are abundantly found in nature and technical products. A thorough structural characterization in the bulk for a whole ensemble, however, is difficult. The inherent semiordered nature of the tortuous large-scale structure and especially the quantification of branching renders an assessment difficult. In the present work we introduce a hybrid function expressing the scattering intensities for X-rays, neutrons, or light in the small-angle regime for this system. The function is termed "hybrid" because it employs terms from different approaches. The large-scale structure is described via a Guinier term as well as a concomitant power-law expression in momentum transfer q taken from the so-called unified function. The local cylindrical shape, however, is taken into account through a form factor for cylinders from rigid-body modeling. In principle, the latter form factor can be replaced by an expression for any other regular body so that the new hybrid function is a versatile tool for studying hierarchical structures assembled from uniform subunits. The appropriateness and capability of the new function for cylindrical structures is exemplified using the example of a wormlike micellar system.
authors.affiliation: †CEAS-Biomedical, Chemical, and Environmental Engineering, University of Cincinnati, Cincinnati, Ohio 45221, United States.
authors.forename: Karsten
authors.initials: K
authors.lastname: Vogtt
authors.affiliation: †CEAS-Biomedical, Chemical, and Environmental Engineering, University of Cincinnati, Cincinnati, Ohio 45221, United States.
authors.forename: Gregory
authors.initials: G
authors.lastname: Beaucage
authors.forename: Michael
authors.initials: M
authors.lastname: Weaver
authors.affiliation: †CEAS-Biomedical, Chemical, and Environmental Engineering, University of Cincinnati, Cincinnati, Ohio 45221, United States.
authors.forename: Hanqiu
authors.initials: H
authors.lastname: Jiang
mesh_terms: D001622:Betaine / Q000031:analogs & derivatives* / Q000737:chemistry; D008823:Micelles; D012967:Sodium Dodecyl Sulfate / Q000031:analogs & derivatives* / Q000737:chemistry; D013501:Surface-Active Agents / Q000737:chemistry*
chemical_list: D008823:Micelles; D013501:Surface-Active Agents; D012967:Sodium Dodecyl Sulfate; D001622:Betaine; C077055:cocamidopropyl betaine; C408148:sodium laureth sulfate