Journal of Non-Newtonian Fluid Mechanics, Vol.165, No.13-14, 698-711, 2010
Structure and phase transitions of carbonaceous mesophase binary mixtures under uniaxial extensional flow
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 (perpendicular to, parallel to) and scalene (perpendicular to, parallel to), where the symbols (perpendicular to, parallel to) 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 perpendicular to nematic -> biaxial nematic -> uniaxial parallel to 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 reversible arrow prolate) and orientation (perpendicular to reversible arrow parallel to) 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. (C) 2010 Elsevier B.V. All rights reserved.
Keywords:Discotic nematic liquid crystals;Thermodynamics of mesophase mixtures;Uniaxial extensional flow of binary mesogenic mixtures;Thermo-rheological phase diagram;X-ray intensity