Abstract
AbstractThe uniaxial orientational order in a macromolecular system is usually specified using the Hermans factor which is equivalent to the second moment of the system's orientation distribution function (ODF) expanded in terms of Legendre polynomials. In this work, we show that for aligned materials that are two‐dimensional (2D) or have a measurable 2D intensity distribution, such as carbon nanotube (CNT) textiles, the Hermans factor is not appropriate. The ODF must be expanded in terms of Chebyshev polynomials and therefore, its second moment is a better measure of orientation in 2D. We also demonstrate that both orientation parameters (Hermans in three dimensional (3D) and Chebyshev in 2D) depend not only on the respective full‐width‐at‐half‐maximum of the peaks in the ODF but also on the shape of the fitted functions. Most importantly, we demonstrate a method to rapidly estimate the Chebyshev orientation parameter from a sample's 2D Fourier power spectrum, using an analysis program written in Python which is available for open access. As validation examples, we use digital photographs of dry spaghetti as well as scanning electron microscopy images of direct‐spun carbon nanotube fibers, proving the technique's applicability to a wide variety of fibers and images.
Highlights
The physical properties of anisotropic materials such as carbon nanotube (CNT) yarns,[1] carbon fibers or drawn polymer fibers and films are highly correlated with the degree of internal orientation, which can be increased by post-treatments such as mechanical drawing
We have demonstrated a method to facilitate the estimation of alignment in anisotropic materials, such as carbon nanotube yarns and similar aligned systems, using an analysis program which we have made available online
This method relies on analyzing photographs or scanning electron micrographs of the samples to arrive at an orientation distribution function (ODF) which is used to calculate order parameters
Summary
The physical properties of anisotropic materials such as carbon nanotube (CNT) yarns,[1] carbon fibers or drawn polymer fibers and films are highly correlated with the degree of internal orientation, which can be increased by post-treatments such as mechanical drawing. Stretched (and reinforced) electro-spun cellulose fibers show great improvements in tensile strength and thermal stability, and reduced bursting.[2] The use of oriented dye molecules in luminescent solar concentrators increases emission into preferred waveguide modes, thereby increasing their optical quantum efficiency.[3] CNT buckypapers, films and fibers aligned in-situ or by post-processing exhibit considerable enhancements in their electrical and thermal conductivities, carrier mobility, current carrying capacities, tensile strengths and elastic moduli.[4,5,6,7,8,9,10,11,12] The degree of internal alignment is considered an important metric to understand structure–property relations in macroscopic materials.
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