A direct correlation function for mesomorphic polymers and its application to the ‘smectic’ phase of isotactic polypropylene

A general model to calculate the structure of a smectic to nematic-like order in polymer systems is proposed. The model is limited to well-aligned molecules with respect to each other. It is especially suited for systems where the packing between neighboring chains is described by liquid-like disorder with axial registration in the chain-axis direction. In such a case the diffraction pattern from the oriented structure exhibits broad liquid-like reflections on the equatorial but sharper reflections on the layer lines. An Ornstein-Zernike approach is adopted to calculate the inter-chain packing and inter-chain registration, where the direct correlation function of packing and registration are decoupled. The model is applied to quantify the structure of the smectic phase of isotactic polypropylene (i-PP).