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Expressions for the interpretation of circular intensity differential scattering of chiral aggregates
Author(s) -
Bustamante Carlos,
Maestre Marcos F.,
Keller David
Publication year - 1985
Publication title -
biopolymers
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.556
H-Index - 125
eISSN - 1097-0282
pISSN - 0006-3525
DOI - 10.1002/bip.360240813
Subject(s) - scattering , scattering length , chemistry , dipole , wavelength , sign (mathematics) , scattering amplitude , light scattering , physics , cross section (physics) , biological small angle scattering , molecular physics , optics , mathematical analysis , quantum mechanics , mathematics , small angle neutron scattering , neutron scattering
The derivation of compact expressions of the circular intensity differential scattering (CIDS) of chiral molecules is presented in the first Born approximation of the fields. The expressions derived are valid for a suspension of scattering chiral particles free to adopt any orientation in solution. The connection is established between the preferential scattering cross section for right‐ vs left‐circularly polarized light for a given scattering angle and the geometrical parameters of the molecule. As observed experimentally, the equations predict that the circular differential scattering patterns must show as a function of the scattering angle a series of lobes of alternating sign. In between these lobes, zeros in the differential scattering cross section occur. For the case of two dipole moments arranged in chiral fashion, an expression is derived that shows how the relative arrangement of the dipoles and their separation relative to the wavelength of light control the number and the position of the zeros. A compact expression predicting the CIDS of a sample for very small angles of scattering is derived for a system of helices whose dimensions are small compared with the wavelength of light. Finally, the presence of CIDS in a sample is related to the appearance of anomalous signals in the CD spectrum of chiral systems. Expressions and computations of the magnitudes and sign of the anomalies are presented. The expressions obtained confirm the main features of the experimental CIDS patterns of chiral molecules previously published.