Rigid rods Onsager approach

An alternative approach to phase separation for rigid and freely jointed rods (38) and for worm-like chains (39,40) has been proposed by Khokhlov and coworkers. Their work is based not on lattice models but on Onsager s theory for the phase separation of rigid rods. These theories are valid only for very low concentrations, so their applicability to the phase separation of cellulose based mesophases may be questionable. 

Figure 3 Experimental and theoretical osmotic pressure, II, of PBLG in DMF versus solute volume fraction, b is the molecular volume. The datapoints are taken from Refs. 27 and 28 (data set B), and encompass measurements between 15°C and 45°C. Solid line theory based on the Khokhlov-Semenov approach to flexibility in combination with the decoupling approximation and the dimensional separation approach based on Eq. (8) [29]. Upper dotted line extension of isotropic branch. Lower dotted line extension of nematie branch. Dashed-dotted line result for completely rigid molecules. Dashed line Onsager s second virial coefficient-approximation for rigid rods.

The Onsager method is thus applicable with low concentrations of a solution of rods (high concentrations (O 1) [8, 12-16]. Parsons approach [13] is distinguished by the greatest simplicity and generality with respect to application to solutions of rigid-chain macromolecules. The central approximation in [13] consists of the hypothesis that the pair correlation... 

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