Small angle scattering by a three component system

The intensity of small angle scattering and the characteristic length a of the correlation function for a swollen, semi‐crystalline polymer were calculated on the basis of a three component system: crystals, amorphous polymer, and solvent assuming that the distribution of the crystalline and amorphous components can be characterized by two independent correlation functions. The minimum of the scattering intensity occurs when the refractive index or electron density of the solvent (component 3) equals the mean refractive index of the polymer (components 1 and 2). The correlation function of the system is the sum of the individual correlation functions of the crystalline and amorphous component and of an interaction correlation function. The contribution of the latter decreases as 1/q with increasing swelling ratio q and hence can be neglected with sufficiently high q. The theory agrees very well with the experimental data for small angle light scattering by swollen gel cellulose samples as function of the refractive index of the solvent. In particular, the theory explains the minimum of scattering intensity when the liquid has the average refractive index of the crystalline and amorphous phase of the polymer. The theory also describes accurately the variation of correlation parameter a between that of the isolated crystalline and that for the amorphous phase.