Rod-Like Structures with Longitudinal Density Modulation

Rod-Like Structures with Longitudinal Density Modulation 

Random crystalline-amorphous copolymers have the tendency to aggregate in rod-like structures exhibiting a density modulation along the rod (see Sect. 5.1). The form factor appropriate for an ensemble of isotropically oriented cylinders is given by the orientational average of A(Q,R,L,a), the Fourier transform of a cylinder with a as the angle between its axis of symmetry and the scattering vector Q [55]  

The integral may be decomposed into a product of radial and axial terms  

The case of a density modulation (alternating more or less dense region) along the cylinder direction can be described by modifying the axial term as 

The cosin function describes the modulation with a period h over the cylinder of length L = 2Nh. c is the average amphtude of the modulation. Unfortunately Eq. 32 and the following caimot not be solved analytically. Nevertheless, a numerical solution can describe the sahent features of the neutron cross-section, from an ensemble of cylinders of radius a and length L, which are randomly oriented and display a modulated density along the axis. 

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