Use of ultra-small-angle X-ray scattering to measure grain size of lamellar styrene-butadiene block copolymers

Simultaneous determination of the lamellar morphological length scale and t he grain size of several low molecular weight heterogeneous styrene-butadie ne block copolymers was accomplished through the use of ultra-small-angle X -ray scattering measurements. NIST's X23A3 Ultra SAXS beamline of the Natio nal Synchotron Light Source in the Brookhaven National Laboratory provided a scattering vector, q, from 0.0004 to 0.1 A(-1). Many of the block copolym er specimens display a clearly resolvable peak in the Ultra SAXS region, an d grain size was determined using the spherical form factor. Determination of Pored's law constant and the value of the scattering invariant provided a preliminary verification of the proposed scattering mechanism by solving for the contrast factor and the volume fraction of the grain boundaries in these specimens. Grain size in a given polymer was a function of annealing temperature and time. For the case of a block copolymer swollen with varyin g amounts of cumene, both the lamellar repeat distance, d, and the grain si ze, D, increased with the cube root of the volume fraction of solvent over the concentration range examined.