HARD-SPHERE-CHAIN EQUATIONS OF STATE FOR LYOTROPIC POLYMER LIQUID-CRYSTALS

Using Parsons-type scaling, the Onsager theory for the isotropic-nemat ic (I-N) transition of rigid-rod lyotropic polymer liquid crystals is combined with the equation of state for hard-sphere-chain fluids of Ch apman et al. and that of Hu et al. The equation of Hu et al. gives the I-N transition pressure and density in good agreement with computer s imulation by Wilson and Alien for a semi-flexible hard-sphere chain co nsisting of seven segments. For real semi-flexible polymers, we follow the Khokhlov-Semenov theory of persistent chains that introduces chai n flexibility into the Onsager theory. Using a consistent procedure to regress the equation-of-state parameters, the equations of Chapman et al. and Hu et al. are also compared with the theory of DuPre and Yang that uses the equation of Lee for hard spherocylinders. These models are compared with experiment for two binary polymer solutions containi ng poly(hexyl isocyanate) and another solution containing polysacchari de schizophyllan. The concentration of polymer at the I-N transition i s predicted as a function of the molecular weight of polymer. All mode ls perform similarly and show semi-quantitative agreement with experim ent. (C) 1998 Elsevier Science Ltd. All rights reserved.