Persistence Length of Isotactic Poly(hydroxy butyrate)

Abstract

The persistence length of isotactic poly(hydroxy butyrate) was measured using small-angle neutron scattering. The value obtained from these measurements reflects a high degree of local chain persistence. If this local persistence is accounted for, scattering from these chains can be globally fit with Gaussian scaling. A global scattering function, the unified equation, is used, which decomposes the chain structure into two levels, one corresponding to the Gaussian regime and one to the persistence regime. The persistence length obtained using this global scattering function is compared to that obtained using the graphical approach of Kratky and Porod with good agreement. Additionally, the global fitting approach of Sharp and Bloomfield is also considered. The Kratky and the Sharp and Bloomfield approaches appear to yield different values for the persistence length. Additionally, the Sharp and Bloomfield function does not allow inspection of the component parts of the fit. One advantage of both global functions is that the level of statistical confidence in the persistence length can be determined in a least-squares fit. Another advantage is the removal of ambiguity concerning an apparent regime of non-Gaussian scaling between the persistence scaling regime and the Gaussian regime.

A review of semi-rigid, stilbene-containing alternating copolymers

“…This copolymer series was studied to investigate the effects of the added extra phenyl ring of stilbene monomer and cyclic monomer structure (MAn versus maleimide) on the persistence lengths [22,25]. Based on SEC and SAXS methods [3,4,38,39], this copolymers series exhibited the persistence lengths between 2 and 6 nm. From this direct comparison and measurement, stilbene alternating copolymers are classified as semi-rigid polymers (Fig.…”

Global scattering functions: a tool for grazing incidence small angle X-ray scattering (GISAXS) data analysis of low correlated lateral structures

“…In this context density fluctuations shall be described with different idealized shapes. Beaucage introduced in a set of publications [16,17,29] a general unified fit model, which is able to describe scattering over several orders of magnitude for spherical averaged particles in transmission geometry using BA. This model describes material microstructures in terms of structural levels.…”

“…It was applied successfully in transmission scattering geometry to several particle systems [30][31][32]. In addition, it was also applied to scattering from soft matter systems [29,33,34]. Nevertheless, this global model was originally developed for analysis of scattering results in transmission geometry using BA.…”

Quantification of branching in disordered materials

“…Beaucage 19 showed that it could be possible to get branching information for polymers with this approach. In Figure 8, in which neutron scattering data for branched polystyrene are fit to the unified equation, 19,69,[71][72][73] it is shown that it is possible to calculate the parameters d min and c from such a fit. 19 These model branched polystyrene samples were synthesized with divinyl benzene (10%) as a comonomer to obtain controlled levels of branching but random placement.…”