P RUEBA

The product of the calculated molecular order parameters, Sθ, arising from the alignment of the dyes within the E7 host presented in this chapter, and the order parameters, Sβ, arising from the alignment of the TDMs within the dyes, presented in Chapter 3, enables the overall order parameters, Sϕ, of the TDMs against the host director to be calculated. Sϕ is a calculated value that should, in principle, be directly comparable to the Sexp values obtained experimentally by polarised UV-visible absorption measurements. Table 4.8 lists calculated values of Sϕ for the dyes, alongside the Sexp

values first given in Table 4.2 for comparison. The trend in the experimental Sexp values and the calculated Sϕ values for the dyes is good, but it is evident that the calculated order parameters are uniformly higher than those obtained experimentally, as can also be seen by the graphical comparison presented in Figure 4.23. This discrepancy is likely to be largely as a result of the overestimation of the molecular alignment within the MD simulations, as obtained for the host alone and discussed above, but it may also be partly due to the Sβ values being calculated for static all-trans geometries which may represent “best-case” conformations.

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Table 4.8 Calculated dichroic order parameters, Sϕ, of the dyes in E7 obtained from the product of calculated Sθ and Sβ values.

Dye Sϕ Sexp

15SB3 0.829 0.73

15NB3 0.794 0.61

15NB3OH 0.748 0.51

26B3 0.853 0.68

26B3OH 0.894 0.74

Figure 4.23 Graphical comparison of the experimental order parameters of the dyes in E7, Sexp, with the calculated order parameters, Sϕ, calculated as the product of Sθ and Sβ values.

A plot of Sϕ vs. Sexp also enables further assessment of the match between the experimental and calculated dichroic order parameters, as shown in Figure 4.24, which would have a gradient of 1, an intercept of 0, and an R² value of 1 for a perfect correlation between calculated and experimental values. Figure 4.24 shows that there is a strong positive correlation between the calculated and experimental values, quantified by the value of R² = 0.8299 and the positive gradient of 0.532 from the fit, suggesting this method is appropriate for calculating trends in experimental dichroic order parameters. However, the fitted gradient of <1 and the fitted intercept of 0.476 highlight a potential limitation of the approach for replicating absolute values.

Figure 4.24 Plot of calculated dichroic order parameters, S_ϕ, vs. experimental order parameters, Sexp. The grey line indicates a perfect match between calculated and experimental values.

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The value of an order parameter Sθ arises from a distribution of θ angles between the director and the long axes of individual molecules, as observed in the MD simulations (Figure 4.17). For discussion, it can sometimes be useful to express such a value in terms of a single θ angle, equivalent to a δ-distribution that would give the same order parameter,²⁸ as given by Equation (4.12).

The angles, θ, calculated using Equation (4.12) for the host molecules and the dye molecules in the guest-host simulations starting from pseudo-nematic starting geometries are given in Table 4.9. The relative molecular orientations using these θ angles and TDM orientations using the β angles listed originally in Table 3.10 and again in Table 4.9 are presented schematically in Figure 4.25.

Table 4.9 Angles, θ, obtained from the average order parameters of the host molecules and dye molecules from the guest-host MD simulations starting from pseudo-nematic configurations, calculated using Equation (4.12). β angles originally given in Table 3.10 are listed again here for clarity.

Dye θhost / ° θdye / ° β / °

15SB3 16.4 19.3 4.4

15NB3 17.1 17.2 13.8

15NB3OH 17.3 18.9 15.9

26B3 16.9 16.4 8.4

26B3OH 16.5 15.3 1.7

Figure 4.25 Schematic diagram of the relative calculated alignments of the dye molecular axes, the host molecular axes and the dye TDMs using the values in Table 4.9 and Table 3.10.

1 2 1

cos 3

S_

  ^{ } (4.12)

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The orientations shown in Figure 4.25 indicate that the major limiting factor in terms of the alignments of the dye TDMs against the host director is the molecular alignment of the dyes within the host, particularly given the likely overestimation of the degree of molecular alignment in the MD simulations. However the consistency between the θdye

values suggests that there is relatively little variation between the molecular alignments of the different dye molecules, which are calculated to be comparable to the molecular alignment exhibited by the E7 host species. The main cause of the variation in the calculated order parameters between the dyes is shown to be the orientations of the TDMs within the dyes. This comparison enables the lower experimental order parameters of the amine dyes to be rationalised in terms of their large β values when compared with the other dyes studied here. The high observed order parameter of 26B3OH may be attributed primarily to the small value of β, but also to slightly better orientational order of the dye within the host than the other dyes.

179 4.4 Conclusions

Experimental order parameters obtained from polarised UV-visible absorption spectra showed significant variation in the dichroic order parameters of the dyes in E7. The MD simulations indicate there is little variation in the molecular alignment of the dyes within the host, and subsequent combination with results of the TD-DFT calculations replicates the experimentally observed alignment trend, indicating that the primary cause of the observed variation in alignment is due to differences in TDM alignments within the dyes, defined by the β angles. The ability to consider the two contributions to the observed alignment independently, by MD and DFT calculations provides information not readily obtainable from experiment. Hence, the approach developed here may be extremely useful from the perspective of molecular design, as it may potentially enable dyes for guest-host applications to be engineered in such a way that both contributions to the overall alignment are optimised.

The combined computational approach presented here overestimates the alignment of the dye TDMs within the host, but the nature of the calculations employed means the approach provides a predictive capability, enabling the behaviour of different dyes to be compared within a nematic environment. This is an approach that can be readily extended to other guest and host systems, and could be readily applied to hypothetical systems.

The MD simulations also enabled the conformations explored by the dyes to be analysed, showing that the dyes exhibiting higher experimental order parameters than the host (15SB3, 26B3 and 26B3OH) had higher calculated aspect ratios than the host molecules, but that the dyes exhibiting lower experimental order parameters than the host (15NB3 and 15NB3OH) had lower calculated aspect ratios than the host molecules.

However, this common trend was not fully matched by the trend in calculated order parameters, Sθ, for which 15SB3 was calculated to have the lowest order parameter of the dyes studied. This discrepancy is surprising, and is potentially indicative that some assumptions made in the theoretical treatment of the calculation of alignment are not valid, because it does not match the generally accepted theory that more rod-like structures exhibit increased molecular alignment.

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Chapter 5