Comparison of the Onsager and Flory Theories

The Onsager and Flory theories are both statistical theories on rigid rod liquid crystalline polymers, but the former is a virial approximation while the latter is a lattice model. The first is more applicable to dilute solutions while the latter works especially well for high concentrations and a highly ordered phase. These theories with experiments, especially critical volume fractions 4 i and critical order parameter Sc at nematic-isotropic transition are made below. 

The Onsager theory points out that liquid crystalline polymers enter from the liquid crystal phase to the isotropic phase at the volume fraction 

It is shown that the predictions of the Onsager theory are smaller than that of the experimental data. This discrepancy is due to the second virial approximation. Adopting higher terms of virial coefficients may improve the predictions. 

Meanwhile, Flory predicts a higher critical volume fraction. It is thought that the Flory lattice model is comparatively simple, even though the addition of the soft interactions does not change this shortcoming. 

The real liquid crystalline polymers exhibit finite flexibility. This kind of polymer was studied extensively by Khokhlov and his co-workers. Assume that the semiflexible chain has the total contour length L, and Kuhn length l and diameter D, and L l D. Analogous to the Onsager model, the free energy of the polymer in solution is composed of the conformational 

---

Figure 2.13. Critical volume fraction vs. ratio of persistence length to molecular diameter (l/D) comparisons of the Onsager and Flory theories with experimental data. (Modified from Ciferri, 1991. Reproduced by permission of John Wiley Sons, Inc.)...

---