| dc.description.abstract | The origin of the glassy orientational dynamics, both single particle and collective, of nematogens near the isotropic-nematic transition has been addressed in several publications in recent years [5-7, 12]. In these studies, the similarity between dynamics of supercooled glassy liquid and liquid crystals has been discussed in detail, but no quantitative measure of the similarity was provided. The fragility index introduced here serves to remove that lacuna. It is indeed surprising that even the values of the fragility parameter are in the range observed for glassy liquids as well. This is in agreement with the repeated observation by Payer and coworkers [6] that the values of the power law exponents observed in the two systems are quite similar. Further understanding of the relaxation mechanism has been obtained from a closer look at the heterogeneous dynamics. As Figure 1.1.3 demonstrates, the rotational non-Gaussian parameter shows a dramatic enhancement of heterogeneous dynamics as the I-N phase boundary is approached. Unlike what is found near the gas-liquid critical point [36], the single-particle dynamics near the I-N phase boundary are observed to be strongly affected by the approaching thermodynamic singularity. We have discussed mode coupling theory approaches introduced to understand anomalous dynamics observed in this problem.
Let us first summarize the main results of the present work. In order to understand orientational relaxation in disk-like molecules that form discotic phase on cooling, we have performed molecular dynamics simulations of a model system that consists of oblate ellipsoids of revolution interacting with each other via a variant of the Gay-Berne pair potential. The system has been studied along two isobars so chosen that the phase sequence I-N-C appears upon cooling along the one and the sequence I-C along the other. We have investigated temperature-dependent orientational relaxation across the I-N transition and in the isotropic phase near the I-C phase boundary with a focus on the short-to-intermediate time decay behavior. While the orientational relaxation across the I-N phase boundary shows a power law decay at short-to-intermediate times, such power law relaxation is not observed in the isotropic phase near the I-C phase boundary. Study of orientational pair distribution function shows that there is a growth of orientational pair correlation near the I-N transition whereas such a growth is absent in the isotropic phase near the I-C phase boundary. As the system settles into the nematic phase, the decay of the single-particle second-rank orientational time correlation function follows a pattern that is similar to what is observed with calamitic liquid crystals and supercooled molecular liquids [31,40,41].
In order to further understand microscopic slowing down of the collective OTCF, we recall the expression [47]
ri=1+j21+j2r_i = \frac{1 + j_2}{1 + j_2}ri?=1+j2?1+j2??
where S2S_2S2? is the static second rank Kirkwood factor [48]
S2=?i?jP2(ei?ej)S_2 = \sum_i \sum_j P_2(\mathbf{e}_i \cdot \mathbf{e}_j)S2?=i??j??P2?(ei??ej?)
and j2j_2j2? is a dynamic quantity which can be expressed in terms of memory functions of orientation as [49]
j2=?…j_2 = \int \dotsj2?=?…
where df=(?????)L(ee)d f = (\alpha_\parallel - \alpha_\perp) L (\mathbf{e} \mathbf{e})df=(???????)L(ee) and QQQ is the projection operator. Here LLL is the Liouville operator and ef?e_f^\alphaef?? is the x (or y) component of the unit vector along the short axis of the oblate ellipsoid of revolution. It is non-trivial to calculate from first principles but one can always estimate it from Eq. 1.2.15 where other quantities are not hard to calculate in principle.
We have calculated static second rank Kirkwood S2S_2S2? factor which may be thought of as the average number of molecules whose orientations are perfectly correlated to that of a given molecule [50]. We find that S2S_2S2? shows the same behaviour as the order parameter variation for both the isobars studied here. Dynamic quantity j2j_2j2? has no such straightforward physical interpretation like S2S_2S2?. Because of the slow power law decay, it has not been possible to calculate the relaxation times (?1\tau_1?1? and ?2\tau_2?2?) near the I-N phase boundary. However, when calculated away from the phase boundary, when relaxation functions are nearly single exponential, the value of j2j_2j2? is found to be small. The dynamic quantity usually has small and negative value and also will not have much variation across the transitions as observed for several studies [48, 51].
In contrast to our observation of the lack of power law decay in orientational relaxation of the discotic system in the isotropic phase near the I-C phase boundary, a very recent OHD-OKE experimental study by Payer and coworkers finds a power law t?0.76t^{-0.76}t?0.76 (MCT exponents and von Schweidler power law at intermediate times) along with a long-time exponential relaxation in the isotropic phase above the I-C transition [52]. The decay pattern is somewhat similar to what was observed for the calamitic system in the isotropic phase near I-N phase transition. It is possible that nematic fluctuations were important in their experimental system depending upon the choice of temperature. This point deserves further study. | |
