Discussion of the Spectra Simulation Results
The results of the spectra simulations are presented in Fig. 8.10c and the corresponding physical parameters obtained by the combined analysis of the continuous-rotation and 90° rotation techniques, vq, S and n are shown in Fig. 8.12.
The results of the asymmetry parameter, shown in Fig. 8.12b clearly indicate that the system exhibits biaxial ordering for temperatures below 0° (273K). The difference between the Nu-Nb transition temperature found by NMR (Cruz et al., 2008; Figueirinhas et al., 2005) and that found by Vij and co-workers in 2004 (Merkel et al., 2004) by optical and infrared spectroscopy experiments is most probably due to the fact that the NMR experiments are done with a mixture (with the deuterated probe 7CBad2). The shift of the phase transition temperatures in LC mixtures in comparison with pure compounds is normally observed. In the case discussed herein, the transition temperatures, both in the mixture and in the pure compounds (Merkel et al., 2004) are shown in Figs. 8.3 and 9.4, respectively. The results regarding the biaxial ordering of the system are immediately evident from the observation of the 90° rotation experimental results as shown in Fig. 8.10a,b. The results for upper temperatures are typical of uniaxial nematic phases, showing a contraction of 1/2 for the quadrupolar splitting when the sample is rotated by 90° (as explained before and easily concluded from Eq. 8.4). However, that is strikingly not the case for lower temperatures. From this experiment alone it is possible obtain the values of n, S and vq. The rotating sample experiment provides a reliable confirmation of the 90° rotation results, since the spectra of 2D powder samples (see Fig. 8.10c) are correctly fitted with the
Figure 8.12 Physical parameters resulting from the simulation of the NMR deuterium spectra obtained as a function of temperature, combining the fits of theoretical expressions to the experimental data collected both from the 90° rotation and continuous-rotation techniques: (a) Vq and S; (b) n. Reprinted (figure) with permission from [Cruz, C., Figueirinhas, J. L., Filip, D., Feio, G., Ribeiro, A. C., Frere, Y., Meyer, T and Mehl, G. H. (2008). Biaxial nematic order and phase behavior studies in an organosiloxane tetrapode using complementary deuterium NMR experiments, Physical Review E 78, 5, p. 051702]. Copyright (2008) by the American Physical Society.
same physical parameters obtained from a completely independent experiment (90° rotation).
The simulation of the spectra involves the consideration of a partial orientation distribution of the secondary directors 1 and m characterized by the angle у (see Eq. 8.4 and Fig. 8.6), both for the 90° rotation and continuous-rotation experiments.
The distribution P(^) for a sample aligned with the NMR static magnetic field B0 is given by:
This expression corresponds to a uniform distribution in the angle у (associated with the orientation of the secondary directors) when the principal director is aligned with B0 (see Fig. 8.7).
When the principal director in the sample, initially aligned, is rotated by 90° with respect to the static NMR field B0, the directors distribution becomes
where h(y) is given by
C0 is a normalization constant and Ci, C2 and C3 are fitting parameters that account for the partially alignment of the secondary directors.
In the ideal situation of a perfectly aligned biaxial nematic phase, the function h(y) would be given by
In the case of the studied system, the results of h(y) at different temperatures for the 90° rotation and continuous-rotation experiments are given in Fig. 8.i3a and Fig. 8.i3b, respectively.
As can be seen in the figure, the partial orientation distribution of secondary directors change with the technique used (90° versus continuous rotation) and with the temperature. This is not unexpected since the experimental conditions are different with respect to the magnetic torque applied to the molecules or molecular segments (dendritic arms) in the different angular conditions. On the
Figure 8.13 Distribution of secondary directors obtained from the simulation of the NMR deuterium spectra as a function of temperature, combining the fits of theoretical expressions to the experimental data collected using (a) the 90° rotation technique and (b) the continuous-rotation technique. Reprinted (figure) with permission from [Cruz, C., Figueirinhas, J. L., Filip, D., Feio, G., Ribeiro, A. C., Frere, Y., Meyer, T. and Mehl, G. H. (2008). Biaxial nematic order and phase behavior studies in an organosiloxane tetrapode using complementary deuterium NMR experiments, Physical Review E 78, 5,p.051702]. Copyright (2008) bythe American Physical Society.
other hand, the degree of alignment of the secondary directors within the biaxial nematic domains varies with the temperature. This results can be explained by the competition between the expected increase of the material's viscosity with decreasing temperatures with the opposite tendency of alignment of secondary directors with the increasing of the asymmetry parameter n for lower temperatures.
