Hybrid Unified Analysis of Hierarchical Scattering

Modern scattering facilities can produce data over 10-orders of size enabling, for the first time, understanding of hierarchical assembly and offering structural and thermodynamic metrics correlated with important properties and growth processes. For disordered, polydisperse hierarchical materials such as carbon black, silica, synthetic polymers, and pigments the Unified Scattering Function has been widely used [1,2]. Construction of hierarchical materials from narrow-distribution structures such as spherical, lamellar, and cylindrical primary particles and micelles/vesicles can be described using a hybrid approach where the primary (and secondary) structural level(s) is (are) described by conventional, structural functions, while the hierarchical assembly at larger scales can be modeled using Unified structural levels linked by a calculation of the primary radius of gyration. Examples are shown for worm-like micelles [3], polydisperse spherical aggregates [4], and polymeric lamellar crystal assemblies [5], accessing the dimensionality, branch number, length, degree of dispersion, network percoloation, width of lamellae and thermodynamic compatibility.



1) Beaucage G J. Appl. Cryst. 28 717-728 (1995).

2) Beaucage G PRE 70 031401 (2004).

3) Vogtt K,Beaucage G, Jiang HQ Langmuir 31 8228-8234 (2015).

4) Manning J, Brambila C, Rishi K, Beaucage G, Davies G-L, Patwardhan S, submitted ACS Sus. Chem. Eng.(2023).

5) Camara M, Rishi K, Beaucage G, Sukumaran SK Polymer 237 124281 (2021).