Coulombic interaction lattice theories

Fint is the free energy of non-Coulomb interactions of monomer units. Finl can be expressed, for example, in terms of the Flory-Huggins lattice theory [21]. In the general case, when network is immersed in solvent which includes 1 different components some of which can be polymeric with the degree of polymerization Pi(Pi 1, i = L 2,... k), Fim in the Flory-Huggins theory has the following form [21-22] ... 

In what follows, we present in Section IV.A a theory of the effects of weak disorder on the retarded interactions of 2D strong dipolar excitons, and in Section IV.B we analyze the effects of stronger disorders on the coulombic interactions, calculating the density of states and absorption spectra in 2D lattices, in the framework of various approximations of the mean-field theory. 

To conclude, we can draw an analogy between our transition and Anderson s transition to localization the role of extended states is played here by our coherent radiant states. A major difference of our model is that we have long-range interactions (retarded interactions), which make a mean-field theory well suited for the study of coherent radiant states, while for short-range 2D Coulombic interactions mean-field theory has many drawbacks, as will be discussed in Section IV.B. Another point concerns the geometry of our model. The very same analysis applies to ID systems however, the radiative width (A/a)y0 of a ID lattice is too small to be observed in practical experiments. In a 3D lattice no emission can take place, since the photon is always reabsorbed. The 3D polariton picture has then to be used to calculate the dielectric permittivity of the disordered crystal see Section IV.B. 

Recently the coexistence of the 2kp CDW with SDW has been found by a diffuse X-ray scattering study of (TMTSFjjPF [65]. This has been ascribed to a purely electronic CDW involving no lattice distortion. In the conventional model of SDW the charge density should be uniform. Very recently a theory has succeeded to explain the coexistence of the purely electronic 2kp CDW with SDW in terms of the next-nearest-neighbor Coulomb interaction between electrons [66]. It is interesting to find the coexistence also in other materails. 

Our calculation is based on a semiempirical classical theory because we use (15.22) and experimental values for ro and n. A more rigorous theory, however, would not improve the result much. That is because the major part of cohesive energy of ionic compounds is due to the Coulomb interaction of the ions which can be considered as electric charges at lattice sites. 

The theory of phonons in metals involves the interaction of the ions with the conduction electrons strictly speaking, this is outside the scope of this book and therefore only a qualitative discussion will be given. The role of the conduction electrons is to screen out the Coulomb interaction between the positive tons, thereby stabilizing the lattice and reducing considerably the range of interionic forces. It is, therefore, tempting to assume that in a first approximation, the interactions between the screened... 

The Born-Fajans-Haber cycle uses thermodynamic cycles to determine lattice energy. An alternative to the Born-Fajans-Haber method is one based on fundamental principles. Because the dominant interactions in an ionic crystal are Coulomb interactions, we can use the theory of electrostatics to calculate the lattice energy. Kapustinskii used these ideas and proposed the following equation ... 

In the first part of this introductory section, we summarize the main collective phenomena acquired by the dipolar exciton from the lattice-symmetry collectivization of molecular properties. The crystal is considered as an assembly of electrically neutral systems, the molecules, physically separated from each other and in electromagnetic interaction. This /V-body problem will be treated quantum-mechanically in the limit of low exciton densities. We redemonstrate the complete equivalence of this treatment with the theories of Lorentz and Ewald, as well as with the semiclassical approximation. In Section I.A, in a more compact but still gradual way, we establish the model of the rigid lattice of dipoles and the general theory of low-exciton-density systems in interaction with the radiation field. Coulombic excitons, photons,... 

The estimation of lattice energies is based on the calculation of the coulombic (Madelung) energy, which comprises most of the lattice energy, to which an additional bonding energy due to metal-metal attractive interaction—for example, as in some rutile type oxides (26)— is added. The latter may be obtained empirically or by use of ligand field theory (11). 

The theory of the cuprate superconductivity must explain all above experimental facts, and the mechanism of the superconductivity itself. The strong Coulomb repulsion is certainly a very important ingredient as is manifested by the fact that parents compounds are Mott insulators. However, we will show that, in addition to it, strong hole-lattice interactions are also very important. In this review, we will present explanations for some of the above anomalies by including the strong hole-lattice interactions. 

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