
The mean molecular lengths ( l M) are displayed in Table 1, calculated from the molecular structure taking into account the molar ratio of the compounds employed in the mixtures. In this context, we have studied the same samples previously investigated composed of pure C 9 and C 14, and binary mixtures of C 14 - C 9 and C 9 - C 6. With a view of investigating the correlation length behavior in our systems, we extended the previous work making use of the X-ray scattering technique to explore the values of e within the N * and A phases domain as well as along the A- N * phase transition. It is well known that the average correlation length (e) in a second order phase transition diverges continuously in the vicinities of the transition. Recently, we have investigated the possible existence of a second order phase transition at r 0.92 for a particular mixture of C 6- C 9 (63.1 mol% of C 9) through density measurements. In fact, calorimetric measurements performed by two of us on binary mixtures composed of cholesteryl palmitate ( C 16), cholesteryl myristate ( C 14), cholesteryl nonanoate ( C 9) and cholesteryl caproate ( C 6) and C 9, cholesteryl heptanoate ( C 7) and C 6, that present a A- N * phase transition, gave evidence of a tricritical point around r 0.90 - 0.92. Several calorimetric measurements were performed on binary mixtures (where the molar ratio was varied between two different homologous liquid crystal molecules of distinct lengths) and showed that the reduced temperature can vary from 0.89 to 0.99. , the theoretical results point out that the energy associated to the smectic ordering increases with molecular length and r, occurring a second order phase transition for r 0.88. In a extension of the McMillan's model proposed by Lee et al. The reduced temperature is defined as : r = T AN/ T NI, where T AN and T NI represent, respectively, the A- N and N-Isotropic ( I) phase transition temperatures, also known as McMillan ratio. In particular, the Smectic A ( A) - Nematic ( N) or cholesteric ( N *) phase transition was demostrated to be of either first order or second order, depending on the smectic layer thickness and the reduced temperature, according to McMillan's molecular model. The first (discontinuous) and second (continuous) order nature of the liquid crystal phase transitions have been the subject of many works along the last 30 years. Such effect induces a second order A N* phase transition for a particular mixture of 63.1 mol% of C 9 and 36.9 mol% of C 6, evidenced by viscosity measurements in good agreement with previous density data.

The results show a decrease in A phase domain and an expansion of the N* domain as the mean molecular length is diminished. We have studied the in influence of the mean molecular length on the nature of the cholesteric ( N*) smectic A ( A) liquid crystal phase transition for thermotropic compounds of cholesteryl myristate ( C 14), cholesteryl nonanoate ( C 9), and binary mixtures of C 14 C 9 and cholesteryl caproate ( C 6) phase ( dA), the mean molecular length ( ) in the N* domain, and the correlation length (e), as well as changes along the N* A phase transition, were determined from the X-ray diffraction data.
