Light scattering from a random collection of cylinder-symmetrical particles

Light-Scattering Patterns from Collagen Films in Relation to the Texture of a Random Assembly of Anisotropic Rods in Three Dimensions

“…As one of the generalizations of the rod assembly model, van Aartsen has recently formulated the concept of polarized light scattering from the three-dimensional random assembly of circular as well as lozenge rods being definite in size. 21 Unfortunately the orientation of scattering elements within the rod was limited to the case where the principal optical axes of the elements were parallel to the rod axis. Further generalizations, taking into account the orientation distribution of scattering elements within the rod, can only be made after more research has been…”

Light Scattering and Microscopy from Block Copolymers with Cylindrical Morphology

“…One potential candidate that is consistent with the rectilinear textures seen in microscopy is an anisotropic rod model. If either the amplitude or correlation function method is applied to randomly oriented anisotropic rods with an optic axis at a fixed angle with respect to the rod axis, one obtains a 4-fold scattering pattern [ref 15 and section III.F.l of this paper]. If the angle is 0°, one gets x-type scattering, whereas if the angle is 45°, the pattern is of the + type.…”

“…2 " A (Vcgp2> (15) //dr' dr" Psame gTain(r',r") = N(VA2 + VB2) //dr' dr" Psame CGP(r',r") = N(VCGP2) (10) We define the relative difference in grain volumes E. Evaluation of the Scattering Patterns. By relating the shape functions in eq 4 to probabilities (eqs 5-8), and those probabilities to correlation functions (eqs 13 and 14), we can show that the Hv intensity for the CGP orientation in the differential solid angle centered at {9g, fig} is proportional to //dr'dr"(CA+B,A+B(r'-r")-2CA,A(r'-r")) ei(jKr'-r")) (16) where F(9g,iug,00a,fi0) = sin2(0a) sin(2wa) (17) and the a subscript stands for A or B (see Appendix A).…”

Polarized Light Scattering from Polymer Textures

“…The fibrillar structure in fibres and films is often modelled by the use of uniaxially anisotropic rod-like entities. The study of the independent light scattering from anisotropic rods was pioneered by Rhodes and Stein [27] and generalized by van Aartsen [28]. It provided the formalism for the later extension t o coherent scattering by assemblies of rods through t h e introduction of correlation statistics.…”