Quantifying alignment in carbon nanotube yarns and similar two?dimensional anisotropic systems

The uniaxial orientational order in a macromolecular system is usually specified using the Hermans factor which equivalent to second moment of system's orientation distribution function (ODF) expanded terms Legendre polynomials. In this work, we show that for aligned materials are two-dimensional (2D) or have measurable 2D intensity distribution, such as carbon nanotube (CNT) textiles, not appropriate. ODF must be Chebyshev polynomials and therefore, its better measure 2D. We also demonstrate both parameters (Hermans three dimensional (3D) 2D) depend only on respective full-width-at-half-maximum peaks but shape fitted functions. Most importantly, method rapidly estimate parameter from sample's Fourier power spectrum, an analysis program written Python available open access. As validation examples, use digital photographs dry spaghetti well scanning electron microscopy images direct-spun fibers, proving technique's applicability wide variety fibers images.