Orientation-dependent interactions

A segment inclined at an angle v / with respect to the domain axis experiences an energy 

8 Orientational energy from this source provides the basis for the Maier and Saupe theory asymmetry of molecular shape and its influence on molecular packing in the fluid are not taken into account. Consequently, in order to reconcile this theory with experiments, it has been necessary to postulate unreasonably large orientation-dependent energies and, by implication, excessively large value of Aa 

kT is the orientation-dependent energy Soriem due to interactions between a segment and its neighbors in the perfectly ordered (vj/ = 0 and s = 1) neat fluid. The characteristic temperature is related to Aa according to 

The orientation-dependent energy for the system as a whole, obtained as the averaged sum of the mean field interactions of all segments, is 

The direct contribution of the orientation-dependent interactions to the reduced 

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Besseling, N. A. M. (1993). Statistical Thermodynamics of Fluids with Orientation-Dependent Interactions. Applications to Water in Homogeneous and Heterogeneous Systems. Ph.D. Thesis, Wageningen University. 

Besseling, N. A. M. and Scheutjens, J. M. H. M. (1994). Statistical thermodynamics of fluids with orientation-dependent interactions in homogeneous and inhomogeneous systems, J. Phys. Chem., 98, 11 597-11 609. 

D. Y. Yoon, Polym. Prepr. ACS, Div. Polym. Chem., 30(2j, 71 (1989). Chain Packing and Phase Transition of Cubic-Lattice Polymer Systems with Orientation-Dependent Interactions. 

This conclusion was reached, tentatively, by Frenkel, Shaltyko and Elyashevich A phenomenological analysis presented by Pincus and de Gennes predicted a first-order phase transition even in the absence of cooperativity in the conformational transition. These authors relied on the Maier-Saupe theory for representation of the interactions between rodlike particles. Orientation-dependent interactions of this type are attenuated by dilution in lyotropic systems generally. In the case of a-helical polypeptides they should be negligible owing to the small anisotropy of the polarizability of the peptide unit (cf. seq.). Moreover, the universally important steric interactions between the helices, regarded as hard rods, are not included in the Maier-... 

A theoretical treatment has recently been carried out by the author in collaboration with Matheson along the lines discussed above with appeal only to the spatial requirements of hard rods as represented in the lattice model, orientation-dependent interactions being appropriately ignored. The two transitions, one conformational and the other a cooperative intermolecular transition, are found to be mutually affected each promotes the other as expected. The coil-helix conformational transition is markedly sharpened so that it becomes virtually discrete, and hence may be represented as a transition of first-order. These deductions follow from the steric interactions of hard rods alone intermolecular attractive forces, either orientation-dependent or isotropic, are not required. 

Approximation of the orientation factor Zoriem the partition function according to Eq. (9) of the text provides the key to the earlier version of the lattice theory of rodlike particles not subject to orientation-dependent interactions. Although approximate, this formulation offers advantages of simplicity that for most purposes outweigh the incident errors. The latter are generally small (see Table 1). 

The 1956 approximation is generally inapplicable to systems in which orientation-dependent interactions must be taken into account... 

Indeed, Flory s theory in its initial form considered phase separation on the basis of the determining role of the entropy term of the free energy with no account of the forces acting among the particles. In later works , however, orientation-dependent interactions of particles were taken into account, which increased the probability of the liquid crystalline transition. 

Stanley, H.E. and Teixeira, J. Interpretation of the unusual behavior of H2O and D2O at low temperatures test of a percolation model, /. Chem. Phys., 73, 3404,1980. Truskett, T.M., Debenedetti, P.G., Sastry, S., and Torquato, S. A single-bond approach to orientation-dependent interactions and its implications for liquid water,... 

As explained previously, exchange methods most commonly use chemical shift anisotropy or quadrupole coupling as the molecular orientation-dependent interactions through which molecular re orientation is monitored. However, there are cases in which it would be desirable, or even essential to use dipolar couplings. For instance, if one wishes to measure the motion of 1H spins, dipolar coupling may be more useful than chemical shift anisotropy as the chemical shift anisotropy of H is generally small. 

P. J. Flory and G. Ronca, Mol. Cryst. Liq. Cryst., 54(3-4), 311 (1979). Theory of Sptems of Rodlike Particles. II. Thermotropic Systems with Orientation-Dependent Interactions. M. Vacatello and P. J. Flory, Polym. Commun., 25(9), 258 (1984). Helical Conformations of Isotactic Poly(methyl Methacrylate). Energies Computed with Bond Angle Relaxation. 

Flory PJ, Ronca G (1979) Theory of systems of rodlike particles. II. Thermotropic systems with orientation-dependent interactions. Mol. Cryst. Liq. Cryst. 54 311... 

Flory, P. J. Ronca, G. "Theory of Rod-like Particles - Part II Thermotropic Systems with Orientation-Dependent Interactions", Mol. Cryst. Llq. Cryst., 1979, Vol. 54, pp. 311-330. 

The phase separation of the solution is driven by the entropy of forming a liquid-crystalline phase at a high polymer concentration. However, Maier and Saupe [30] concluded that the formation of a nematic phase arises from orientation-dependent interaction of induced dipoles. From these considerations, it appears that both entropy and enthalpy contribute to the stability of mesophases, although in a different ratio for large and small molecules. Asymmetric at-... 

Further details of the model, including the effect of allowing a small attractive force between the rods through the introduction of a non-zero Flory-Huggins parameter, the prediction of phase diagrams and the effect of introducing an orientation-dependent interaction of the Maier-Saupe form are given in reference (4) of section 12.5. 

A similar analysis may be applied to the partially ordered nematic fluids composed of molecules comprising the mesogenic unit and flexible chain segments. In the LC state, one must consider the orientation-dependent interactions in addition to those of the isotropic nature. As mentioned earlier, the volume dependence (1/V ) incorporated in the Maier-Saupe expression may be replaced by MV. In its modified form, Maier-Saupe potential can easily be accommodated by introducing an additional term in the conventional van der Waals expression ... 

Flory, P. J. Conformational rearrangement in the nematic phase of a polymer comprising rigid and flexible sequences in altemating succession orientation-dependent interactions included, MRSSymp. Proc., (Adams, W. W., Eby, R. K., and McLemore, D. E., Eds.), 134,3-9 (1989). 

Orientation-dependent PMF gives valuable insight into the nature of the orientation-dependent interaction between any two amino acid residues. The orientation-dependent PMF also reveals many unexpected pair interactions which defy the trend given by the hydropathy scale. An example is provided by the Arg-Arg pair interaction, which is found to be surprisingly attractive at short separahon, even though it is one of the most hydrophilic residues. 

In recent years, much progress has been made in understanding the thermal properties of simple liquids and colloidal systems [54]. Studies of these systems are often based on the density functional approach, in which the free energy is written as a sum of two contributions, one describing the hard-core repulsion and thus the steric hindrance of the particles, and a second, the long-range and possibly orientation-dependent interactions between them. 

The 3D-RISM/HNC equations (4.9) and (4.9) appropriately treat the excluded volume of the solute regarded as a whole. However, the imperfectness persists for solvent molecules since their orientation is reduced. Cortis, Rossky, and Friesner [23] proposed to perform explicit orientational averaging of the Boltzmann factor for a short-range repulsive part of the initial orientationally dependent interaction potential. The 3D-HNC closure thus modified to include multi-site correlations between solvent sites around the solute is written as... 

Lin J (1998) Reentrant isotropic transition of pol5 peptide liquid crystal effect of steric and orientation-dependent interactions. Polymer 39 5495-5500... 

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