Orientation degree

The direction of orientation in HDPE film and the orientation degree can be determined by either the x-ray method, ir polarization spectroscopy, acoustical methods, or birefringence (21,22,120,121). 

Linear N2 molecules adsorbed on graphite show a transition from a high-temperature phase with orientational disorder to a low-temperature phase with herringbone ordering of the orientational degrees of freedom (see Sec. lie and Fig. 11). 

Here the functions g(0) and /(0) are defined in a suitable way to produce the desired phase behavior (see Chapter 14). The amphiphile concentration does not appear expHcitly in this model, but it influences the form of g(0)— in particular, its sign. Other models work with two order parameters, one for the difference between oil and water density and one for the amphiphile density. In addition, a vector order-parameter field sometimes accounts for the orientional degrees of freedom of the amphiphiles [1]. 

In order to provide a more general description of ternary mixtures of oil, water, and surfactant, we introduce an extended model in which the degrees of freedom of the amphiphiles, contrary to the basic model, are explicitly taken into account. Because of the amphiphilic nature of the surfactant particles, in addition to the translational degrees of freedom, leading to the scalar OP, also the orientational degrees of freedom are important. These orientational degrees of freedom lead to another OP which has the form of the vector field. 

In ternary mixtures of oil, water, and surfactant the ordering properties of the system follow from the vectorial character of the interactions of the surfactant molecules with both the oil and the water molecules. The typical size of the ordered domains, much larger than the molecular size, justifies the application of the mesoscopic Landau-Ginzburg approach to the ordering. In the simplest approach of Gompper and Schick [3,12], which we call here the basic Landau-Ginzburg model, the orientational degrees of free-... 

For molecules the radial distribution function can be extended with orientational degrees of freedom to characterize the angular distribution. 

Z n + DJ (where D and DL stand for optical density when tp = 0° and

high orientation degrees. The fact that the absorption of plane-polarized light is maximal only if the polarization plane... 

Lso is the commutator with the electron spin Zeeman Hamiltonian (assuming isotropic g tensor, Hso = gS- Bo), Lrs = Lzfs (the sub-script RS stands for coupling of the rotational and spin parts of the composite lattice) is the commutator with the ZFS Hamiltonian and Lr = —ir, where is a stationary Markov operator describing the conditional probability distribution, P(QolQ, t), of the orientational degrees of freedom through ... 

There are many further issues that can be addressed by the model of the kind described here. Clearly, the HA model is amenable to a number of generalizations that allow one to study more sophisticated features of amphiphilic copolymers, including, for instance, backbone stiffness, orientational degrees of freedom, or additional structural constraints such as the saturation of monomer-monomer interactions [98], which are crucial, e.g., for the folding of RNA. Also, it is easy to introduce dipole moments for side H - P bonds and specific directional interactions (like hydrogen bonds) for some of the chain units. These additional factors can result in the formation of intramolecular secondary structures and lead to an increase in the stability of globules formed by such polymers. 

Fig. 12. Pair distribution functions j hhM and ft (/) for the plastic and annealed (A) and quenched phases (Q) of methane. Only the orientational degrees of freedom were considered in the calculation.

In Eq. (7-43) the last term on the right hand side accounts forthe energy spent to polarize the orientational degrees of freedom of the solvent and V(t) is the potential that would generate the orientational part of the PCM charges (P(r = 0) = VGS and V (t = +oo) = VK). We note that the function 5k (0 satisfies the following conditions ... 

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