Molecular potentials anisotropic molecules

Since their discovery in the nineteenth century [1], hquid crystals have fascinated scientists due to their unusual properties and their wide range of potential apphcations, especially in optoelectronics. LC systems can be divided into two categories thermotropic LC phases and lyotropic LC phases. Thermotropic LC systems result from anisotropic molecules or molecular parts (so called mesogens or mesogenic moieties, respectively), and form hquid crystalline phases between the soHd state and the isotropic hquid state, where they flow like liquids but possess some of the characteristic physical properties of crys-... 

Figure 16. Measure of translational order of N2 patches on graphite with respect to the ideal adsorption sites on the (VS x J3)R3Q° lattice from molecular dynamics simulations. Anisotropic molecule-surface potential (3.3) with 7 = 0.4 and 7r = -0.9 (triangles), 7 = 0.4 and 7 = —0.54 (cirlces), and isotropic special case 7.4 = 0 and Jr = 0 (squares). Unfilled (filled) symbols refer to 140 (210) molecules. (Adapted from Fig. 1 of Ref. 165.)...

Figure 17. Molecular dynamics trajectories above the melting transition at a coverage of 0.5 monolayers. The center of mass of the N2 molecules is projected on the graphite basal plane (a) for the isotropic molecule-surface potential (3.3) with 7 = 7 = 0 at 44 K and (b) for the anisotropic molecule-surface potential (3.3) with = 0.4 and y — —0.54 at 55 K. (c) Top view of the final configuration of (Z>). (Adapted from Figs. 3 and 9 of Ref. 165.)...

Perhaps the most significant difficulty in the computer simulation of polyatomic fluids is the formulation of the intermolecular potential function. Extremely little is known about the details of anisotropic molecular interactions, and the possibilities for modeling are restricted by considerations of practicality for computer applications. In this section we shall discuss several approaches that have been used to model the interactions of anisotropic molecules. 

Without interactions with potential host molecules and in diluted solutions to avoid excimeric formations, pyrene presents in solution an intense and anisotropic fluorescence, as well as a high fluorescence quantum yield [34-37], Direct evidence of ground-state interactions of pyrene with potential host molecules is provided by the emission spectra. The vibrational structure of the emission spectrum of pyrene is constituted by five fine peaks, named I, I2, h, I4, and I5 (Fig. 13.2) [38]. An increase of the intensity of peak Ii is observed in polar solvents, while I, is solvent insensitive. Thus, the evolution of the ratio of intensities /1//3 gives information on the evolution of the polarity of the environment close to molecular pyrene, and consequently on the encapsulation of this guest in a host molecular or supramolecular object [39]. This sensitivity of pyrene, and of peri-fused polycyclic aromatic hydrocarbon molecules in general, to the polarity of the environment is a photophysic property that is extensively used to study host-guest interactions [40]. 

Besides the remarkable directionality of the motion, the images also demonstrate a periodic variation of the cluster from an elongated to a circular shape (Fig. 39). The diagrams in Fig. 39 depict the time dependence of the displacement and the cluster size. Until the cluster was finally trapped, the speed remained fairly constant as can be seen from the constant slope in Fig. 39 a. The oscillatory variation of the cluster shape is shown in Fig. 39b. Although a coarse model for the motion has been presented in Fig. 39, the actual cause of the motion remains unknown. The ratchet model proposed by J. Frost requires a non-equiUb-rium variation in the energetic potential to bias the Brownian motion of a molecule or particle under anisotropic boundary conditions [177]. Such local perturbations of the molecular structure are believed to be caused by the mechanical contact with the scaiming tip. A detailed and systematic study of this question is still in progress. 

Molecules may vibrate and when they vibrate, their interaction with other molecules is modified. Vibrating molecules often appear bigger and more anisotropic. For selected systems, for example for hydrogen-rare gas pairs, vibrational dependences have been carefully modeled [227]. However, relatively few molecular interaction potentials are well known and for specific cases, one will have to search the recent literature for state of the art models. 

McKean 182> considered the matrix shifts and lattice contributions from a classical electrostatic point of view, using a multipole expansion of the electrostatic energy to represent the vibrating molecule and applied this to the XY4 molecules trapped in noble-gas matrices. Mann and Horrocks 183) discussed the environmental effects on the IR frequencies of polyatomic molecules, using the Buckingham potential 184>, and applied it to HCN in various liquid solvents. Decius, 8S) analyzed the problem of dipolar vibrational coupling in crystals composed of molecules or molecular ions, and applied the derived theory to anisotropic Bravais lattices the case of calcite (which introduces extra complications) is treated separately. Freedman, Shalom and Kimel, 86) discussed the problem of the rotation-translation levels of a tetrahedral molecule in an octahedral cell. 

Within the dielectric continuum model, the electrostatic interactions between a probe and the surrounding molecules are described in terms of the interaction between the charges contained in the molecular cavity, and the electrostatic potential these changes experience, as a result of the polarization of the environment (the so-called reaction field). A simple expression is obtained for the case of an electric dipole, /a0, homogeneously distributed within a spherical cavity of radius a embedded in an anisotropic medium [10-12], by generalizing the Onsager model [13]. For the dipole parallel (perpendicular) to the director, the reaction field is parallel (perpendicular) to the dipole, and can be calculated as [10] ... 

As a final example in this subsection we mention the recent study of Zillich and Whaley who examined LiH solvated in He clusters with up to 100 atoms. The authors used a path integral Monte Carlo simulation approach, whose details shall not be discussed further here. The LiH-He interaction potential was found to be highly anisotropic with attractions for He approaching the molecule in a direction parallel to the molecular axis, but with strong repulsions for He approaching the molecule in a direction perpendicular to the molecular bond. Despite these repulsions, the authors found that LiH prefers to occupy central regions of the LiH He clusters for n larger than 10-15. 

In their original theory, Maier and Saupe supposed that the molecular interactions responsible for the nematic state are anisotropic van der Waals interactions (discussed in Section 2.3), in which case mms should be temperature-independent. However, it is now recognized that shape anisotropy is also important, even for small-molecule thermotropic nematics. By making mms temperature-dependent, the Maier-Saupe potential can, in principle, accommodate both energetic and entropic effects. In fact, if the function sin(u, u) in the purely entropic Onsager potential Eq. (2-5) is approximated by the expansion 1 — V2 cos (u, u)+. . ., then to lowest order the Maier-Saupe potential (2-7) is obtained with C/ms — Uo bT/S, where we have defined the dimensionless Maier-Saupe energy constant by Uus = ums/ksT, Thus, the Maier-Saupe potential can be used as an approximation to describe orientational order in either lyotropic (solvent-based) or thermotropic nematics. For a thermotropic melt, the Maier-Saupe theory predicts a first-order transition from the isotropic to the nematic phase when mms/ bT = U s — t i.MS = 4.55, and at this transition the scalar order parameter S jumps from zero to 0.43. S increases toward unity with further increases in Uus- The spinodal point at which the isotropic phase is unstable to even small orientational perturbations occurs atU — = 5 for the Maier-... 

In spite of the single form of these distance fuiK ions and the usual assumption that the angular expansion can be truncated after very few terms (for instance, only the isotropic and die first anisotropic L, Lg 0 terms), the number of parameters is mostly too large and these parameters are too strongly interdependent in affecting the measured properties, for a fully experimental determination of these parameters to be possible. Only for very simple systems such as atom- liatom systems or atom-tetrahedral molecule systems the experimental data could be used to yield a parametrized anisotropic potential of the form (1) and even there it appeared advantageous to extract part of the parameters from ab initio calculations. For other molecular systems only isotropic potentials are knovm mostly in simplified forms sudi as (6) or (7). 

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