Deformation behavior of a poly(ether ester) copolymer. Quantitative analysis of SAXS fiber patterns

A method for the quantitative analysis of two-dimensional small-angle X-ray scattering (SAXS) patterns with fiber symmetry is proposed and applied to a series of images recorded during straining and relaxation cycles of a two-phase polymer sample at a synchrotron beamline. The studied longitudinal scattering originates from microfibrils or lamellar stacks built from alternating soft and hard domains. The scattering intensity of the patterns is projected onto the direction of str ain, yielding one-dimensional scattering curves. From these curves, interface distribution functions are computed and analyzed using an advanced stacking model with a small set of parameters. Not only the average domain heights but also four parameters characterizing each of two height distributions (hard and soft domains) are determined as a function of elongation. These parameters are norm, mean, variance, and skewness. They describe the response of the filled elastic network to strain,For the studied poly(ester ether) thermoplastic elastomer, the quantitative analysis shows that two microfibrillar components tan intact and a damaged one) can be identified in the patterns from samples at medium elongation as well as in patterns recorded during relaxation from medium elongation. Although the scattering patterns differ considerably, the hard domain distributions extracted from the fits are identical. The difference between elongated and relaxed state is in the distribution of the soft domain heights. There are indications for a nonuniform elasticity of the soft domains. The average internal strain of the soft domains can be computed and compared to the external strain; and pull out of tie molecules taut among different microfibrils can be studied.