Rotational effects equilibrium assumption

As for the theoretical treatment, we could only try to include the eleetrostatie solute-solvent interaetions and, in faet, we corrected the electronic potential energies for the solvation effeets by simply adding as calculated according to the solvaton model [eq. (2)]. The resulting potential curves are to be seen as effective potentials at equilibrium, i.e. refleeting orientational equilibrium distributions of the solvent dipoles around the eharged atoms of the solute molecule. In principle, the use of potentials thus corrected involves the assumption that solvent equilibration is more rapid than internal rotation of the solute molecule. Fig. 4 points out the effects produced on the potential... 

In this Section we will derive the effective rotational Hamiltonian within the rigid nuclear frame approximation, i.e., under the simplifying assumption that the nuclei may be considered as frozen at their equilibrium positions within the molecule, (For a discussion of vibrational effects compare Appendix III.) Furthermore all intramolecular magnetic interactions are neglected since they lead only to comparatively small shifts and splittings of the rotational absorption lines, which in most cases cannot be observed with the standard resolution of a micro-wave spectrograph. 

The assumption of free rotation about each C-C bond in an alkyl chain can give conformations of molecules that are precluded on grounds of excluded-volume effects. Following Tsutsumi, a jump model was employed [8.11] to describe trans-gauche isomerisms in the chain of liquid crystals by allowing jumps about one bond at any one time. To evaluate internal correlation functions gi t), not only the equilibrium probabilities of occupation given by Eq. (8.4) are needed, but also the conditional probability P(7, t 7o,0), where 7 and 70 denote one of the three equilibrium states (1, 2, 3) at times t and zero, respectively,... 

Here a simple extension of the master equation method developed for macromolecules in solution [8.4, 8.22] is used to model correlated internal motions in liquid crystals. By explicitly generating all of the possible conformations in a mesogen and weighing these conformers according to their equilibrium probabilities imposed by the nematic mean field [8.12, 8.14], those improbable conformations that were obtained based on the assumption of independent rotations about different C-C bonds may be effectively eliminated. Thus, internal rotations about different axes are considered to be highly correlated. A similar approach has been used to model correlated internal motions in lamellar mesophases of lyotropic liquid crystals [8.20]. All of the studies still retain the simplifying assumption of decoupling internal rotations from the reorientation of the whole molecule. First, the decoupled model of correlated internal motions is considered. 

New mathematical techniques [22] revealed the structure of the theory and were helpful in several derivations to present the theory in a simple form. The assumption of small transient (elastic) strains and transient relative rotations, employed in the theory, seems to be appropriate for most LCPs, which usually display a small macromolecular flexibility. This assumption has been used in Ref [23] to simplify the theory to symmetric type of anisotropic fluid mechanical constitutive equations for describing the molecular elasticity effects in flows of LCPs. Along with viscoelastic and nematic kinematics, the theory nontrivially combines the de Gennes general form of weakly elastic thermodynamic potential and LEP dissipative type of constitutive equations for viscous nematic liquids, while ignoring inertia effects and the Frank elasticity in liquid crystalline polymers. It should be mentioned that this theory is suitable only for monodomain molecular nematics. Nevertheless, effects of Frank (orientation) elasticity could also be included in the viscoelastic nematody-namic theory to describe the multidomain effects in flows of LCPs near equilibrium. 

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