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Characterizing the Three‐Dimensional Orientation in Polymers using FT‐IR Spectroscopy with Linear Polarized Light
Author(s) -
Brüll Robert,
Maria Raquel,
Rode Karsten
Publication year - 2010
Publication title -
macromolecular chemistry and physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.57
H-Index - 112
eISSN - 1521-3935
pISSN - 1022-1352
DOI - 10.1002/macp.201000135
Subject(s) - legendre polynomials , absorbance , linear dichroism , orientation (vector space) , dichroism , optics , transition dipole moment , axial symmetry , moment (physics) , spectroscopy , physics , chemistry , molecular physics , circular dichroism , mathematics , crystallography , geometry , molecule , classical mechanics , quantum mechanics
The quantity of absorbance of linear polarized light depends for a given wavelength on the angle between an absorbing transition moment vector and the electric vector of the polarized light. Fraser used this relationship to interpret the infrared dichroism in axially oriented polymers. This model can be extended to calculate the orientation in three dimensions by transforming the Fraser's equation into a P 2 ‐Legendre polynomial. As a result the orientation in three directions— f x , f y , and f z —can be calculated directly from the individual absorbances measured with an electric vector along the axes of interest, the structural absorbance A 0 of the sample, and the angle of the transition moment vector in reference to the chain axis. Applying the f values into ‘Hermans’ Orientation function', it becomes possible to calculate the average angle of the chain axis with reference to the axes of interest.