Structure and phase transitions of carbonaceous mesophase binary mixtures under uniaxial extensional flow

Abstract

The Maier–Saupe model for binary mixtures of uniaxial discotic nematogens, formulated in previous studies [1], is extended to simulate the effect of uniaxial extensional flow on the phase behavior and structure. The rotational diffusivity of each disk-like component in the mixture of a high molecular weight (Mw) and a low molecular weight species, is derived based on: (i) a power law that relates molecular size to molecular weight and (ii) the excluded volume of binary disc-like molecules. The thermo-rheological phase diagram of a 50/50 mixture, given in terms of temperature ( T) and Deborah ( De) number show the existence of four T– De regions and six solutions: oblate (⊥, ∥), prolate (⊥, ∥) and scalene (⊥, ∥), where the symbols (⊥, ∥) indicate alignment of the tensor order ellipsoid with respect to the extension axis. It is found that, with increasing T, the higher molecular weight component exhibits weak deviations from the well-known pure species response to uniaxial extensional flow (uniaxial ⊥ nematic → biaxial nematic → uniaxial ∥ paranematic). In contrast, the low molar mass component is always uniaxial and the orientation of the oblate or prolate states is dictated by the coupling effects emanating from the high molar mass component. Analysis of the coupling effects reveals that the changes in conformation ( oblate ⇄ prolate ) and orientation ( ⊥ ⇄ ∥ ) is effected through changes in pairs of eigenvalues. At high temperature, extensional flow acting on an isotropic phase produces an oblate paranematic state in the high Mw species and a prolate paranematic state in the low Mw species. Finally we show that X-ray intensity calculations are able to detect the different regions of the thermo-rheological phase diagram characterized by the presence of oblate, prolate, scalene nematic and paranematic states.