The Need for Higher Order Terms in

As stated in Sec. 3, the retention of only the first term in Eq. [14] leads to the mean field theory of Maier and Saupe and the equivalent theory of the previous chapter. This version of the theory has been shown to provide a good qualitative picture of the nematic phase and its transition to the isotropic liquid. What, then, is it about the experimental facts that indicate the necessity of higher order terms in Fi  

In Fig. 2 we display (schematically) the comparison of several experiments with the mean field theory, including only the term in 1/2. We use T — Tp as the abscissa, so that the two materials depicted can be conveniently compared on the same graph. The dashed line is the theoretical curve computed from the mean field theory using only the term in t/o We note that there is a striking difference in the properties of the two materials, PAA (para-azoxyanisole) and PAP (para-azoxyphenetol). We note further that the simple theory cannot account for the order parameter of either material. Fig. 2 is, in fact, clear evidence for the necessity of higher-order terms in the potential. That the two substances have different values of T. must mean that 

The mean field theory with higher-order terms included is capable of reproducing the experimental data of Fig. 2. The addition of the term in JJ y Eq. [14], is found to be sufficient. The data on PAP can be accounted for by having U4 -f-0.12 U2, while the data on PAA are fit by assuming —0.19 1/2. In the case of PAP, adds to the ordering effects of U2 and P2 is raised above that predicted by the simple theory. In the case of PAA, on the other hand, decreases the ordering effects of the U2 term and a lowered P2 results. Similar results on these two materials have also been reported by Chandrasekhar and Madhusudana.  

The most dramatic evidence that the interaction potential must be quite complicated comes from recent experiments by Jen, Clark, Pershan, and Priestley on MBBA (N-(p -methoxybenzylidene)-p-n butylaniline). Using the Raman scattering technique these authors were able to determine the temperature dependences of both P2 and P4 . The experimental data are shown (with their error bars) 

Our most promising attempt at describing the experiments on MBBA was realized by using the following single molecule potential  

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