Effect of mutual interactions

In conformity with the significance of the terms employed by investigators of anisotropy (Tsvetkov et al. 1964), the effects associated with the first-order terms in equation (10.6) may be called the effects of intrinsic anisotropy, while the second-order effects may be referred to as the effects of mutual interaction. In the second approximation, the principal axes of the relative permittivity tensor do not coincide, generally speaking, with the principal axes of the orientation tensor. It is readily seen that interesting situations may arise when Aa < 0 in this case, the coefficients of the first- and second-order terms have different signs. 

Fig. 9 SAXS-intensities of polyelectrolyte PPP-2 normalized to the respective volume fractions indicated in the graph [71]. The scattering intensities superimpose for higher q-values but differ at small scattering angles. The latter effect can be traced back to the effect of mutual interaction...

It is also desirable to treat network topology in greater detail that is, to incorporate the functionality of crosslinks, their distribution in space, and loop formation. The effect of mutual interaction between chains in the condensed state appears to be accounted for satisfactorily by the tube model for... 

The study of heterogeneous catalysis with the emphasis on the effects of reactant structure stimulates consideration of the reacting system in terms of mutual interactions. Modification of the catalyst surface by the action of reactants is a part of these interactions. This idea is not new, but hitherto little evidence supported it now it is an inherent component of the accepted mechanism of elimination reactions. In general, the working surface may be quite different from the initial surface. Even the solvent may participate in the mechanism, as the results of the Delft school (125, 161, 162) indicate, by temporally accommodating hydrogen species formed in a reaction step from the reactants or hydrogen molecules on the surface. 

The reliability of TDS is somewhat limited by the fact that the effect on the desorption of mutual interaction energies between adsorbates is probably substantial and poorly understood. 

An impurity atom in a solid induces a variation in the potential acting on the host conduction electrons, which they screen by oscillations in their density. Friedel introduced such oscillations with wave vector 2kp to calculate the conductivity of dilute metallic alloys [10]. In addition to the pronounced effect on the relaxation time of conduction electrons, Friedel oscillations may also be a source of mutual interactions between impurity atoms through the fact that the binding energy of one such atom in the solid depends on the electron density into which it is embedded, and this quantity oscillates around another impurity atom. Lau and Kohn predicted such interactions to depend on distance as cos(2A pr)/r5 [11]. We note that for isotropic Fermi surfaces there is a single kp-value, whereas in the general case one has to insert the Fermi vector pointing into the direction of the interaction [12,13]. The electronic interactions are oscillatory, and their 1 /r5-decay is steeper than the monotonic 1 /r3-decay of elastic interactions [14]. Therefore elastic interactions between bulk impurities dominate the electronic ones from relatively short distances on. 

The NOE is caused by dipole-dipole interaction (through-space) of two nuclear magnets, modulated by the tumbling of the molecule in solution. The NOE is an effect of mutual relaxation (or cross relaxation) of two nuclei. Mutual relaxation can occur in two ways zero-quantum (ZQ) relaxation involves a transition from the aft state (one spin up and one down) to the fta state (one spin down and one up) double-quantum (DQ) relaxation involves a transition from the ft ft state (both spins down) to the aa state (both spins up). These transitions are driven by a population difference out of... 

In the following the review is given on the theoretical studies on the effects of mutual Coulomb interactions under the assumption that the electronic state at each site is properly represented by one molecular orbital. Then the Hamiltonian will be expressed as follows. 

The family of bis(cyclam macrocycles) represented by 32, in which the cyclam subunits are linked through nitrogen atoms by — (CH2) — (n = 2-4), m-xylyl, or p-xylyl groups, has been synthesized (58). The di-Ni(II) and di-Cu(II) complexes of these bis(macrocycles) have been used in an investigation of the effects of mutual electrostatic interaction on the redox behavior of the respective metal centers. 

All atoms and molecules attract each other, even in the absence of charged groups, as a result of mutual interactions related to induced polarization effects. Such polarization is sometimes indicated by symbols 5 and 5 . Attraction results from the uneven distribution of electrons when the positive end of one dipole (polarized bond) is attracted to the negative end of another dipole. This arises from three types of interactions ... 

The effect of hydrodynamic interaction of particles on the factor of mutual diffusion of particles has been studied in paper [22]. It formulated a theoretical basis for the determination of collision frequency of particles in a turbulent flow. The effect of internal viscosity of drops on their collision frequency was studied in [23-26]. It was shown that the correct accounting for hydrodynamic interaction ensures a good agreement between the theory and the experiment. 

Equation 10.26 would be valid if colloidal diffusion processes were exactly analogous to those for individual molecules. However, the interactions between particles in colloidal systems tend to extend over distances much greater than those involved in the formation of atomic or molecular activated complexes (say, 10-100 run vs. O.l-l.O nm). As a result, the effects of those interactions will begin to be felt by the particles well before they approach to the critical distance r. Their mutual diffusion rate will therefore be reduced and the collision frequency will drop accordingly. The collision frequency will also be reduced by the hydrostatic effect mentioned above for rapid coagulation. 

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