In this case, 𝑅 𝑝 serves as both the radius of dispersed polymer and also the elliptical major radius of the assembled polymers (minor radius 𝜀𝑅 𝑝 ) and 𝛾 is the contrast ratio Δ𝜌 𝑓 2 /Δ𝜌 𝑝 2 . The radius of the fibril cross-section 𝑅 𝑓 is then calculated from 𝑅 𝑝 by equating areas using 𝑅 𝑓 = (𝜀𝑅 𝑝 2 𝑁 𝑝 / 𝜙 𝑝 ) 1/2 where 𝑁 𝑝 /𝜙 𝑝 is treated as a single parameter and corresponds to the number of polymers within a fibril cross-section divided by the packing fraction. Because 𝜙 𝑝 is the cross-sectional packing fraction of polymers within the fibril aggregate it is approximately 1 and therefore 𝑁 𝑝 ~ 𝑁 𝑝 /𝜙 𝑝 , which gives an estimate of the number of polymers that constitute the aggregate's cross-section. For the internal structure factor we use a Schulz-Zimm distributed Percus-Yevick hard sphere structure factor 𝑆 𝐻𝑆 with an effective spacing of 𝐷 𝑒𝑓𝑓 = 2𝑅 𝑝 and an effective volume fraction 𝜙 𝐻𝑆 . This therefore couples the lamellar stacking distance to the major diameter of the polymer. Polydispersity is then applied to 𝑅 𝑝 and all subsequent functions of 𝑅 𝑝 using a Schulz-Zimm distribution with width parameter 𝜎 𝑝 and mean radius 𝑅 𝑝 ̅̅̅̅ . The relevant terms in equation ( ) are then averages according to the distribution (denoted by an overbar). We find that the hard sphere structure factor is sufficient to model the lamellar peak due to the fact that the fibril term 𝛾𝑁 𝑝 Σ 𝐶𝑆,𝑓 dominates the internal structure factor (the term in brackets) at low 𝑞 and the large polydispersity also drastically smooths out the features of the internal structure factor which occur at high 𝑞. We find that the overall structure factor 𝑆(𝑞) = 𝛾𝑁 𝑝 Σ 𝐶𝑆,𝑓 + 𝑆 𝐻𝑆 developed with this theory is similar to the structure factor for explicitly positioned, monodisperse, rigid cylinder bundles (Figure ) but is of course more generally applicable.