Total energy of interaction

The combination of and G i with G gives the total energy of interaction, Gp (assuming that there is no contribution from any residual electrostatic interaction), that is [6]  

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The total potential energy of adsorption interaction may be subdivided into parts representing contributions of the different types of interactions between adsorbed molecules and adsorbents. Adopting the terminology of Barrer (3), the total energy of interaction is the sum of contributions... 

In equation (2) Rq is the equivalent capillary radius calculated from the bed hydraulic radius (l7), Rp is the particle radius, and the exponential, fxinction contains, in addition the Boltzman constant and temperature, the total energy of interaction between the particle and capillary wall force fields. The particle streamline velocity Vp(r) contains a correction for the wall effect (l8). A similar expression for results with the exception that for the marker the van der Waals attraction and Born repulsion terms as well as the wall effect are considered to be negligible (3 ). 

We return to the complex formation equilibria described in Chapter 2 (Eqs. 2.1 -2.10). The equilibrium constants as given in these equations are essentially intrinsic constants valid for a (hypothetically) uncharged surface. In many cases we can use these constants as apparent constants (in a similar way as non-activity corrected constants are being used) to illustrate some of the principal features of the interdependent variables that affect adsorption. Although it is impossible to separate the chemical and electrical contribution to the total energy of interaction with a surface without making non-thermodynamic assumptions, it is useful to operationally break down the interaction energy into a chemical and a Coulombic part ... 

Schematic forms of the curves of interaction energies (electrostatic repulsion Vr, van der Waals attraction Va, and total (net) interaction Vj) as a function of the distance of surface separation. Summing up repulsive (conventionally considered positive) and attractive energies (considered negative) gives the total energy of interaction. Electrolyte concentration cs is smaller than cj. At very small distances a repulsion between the electronic clouds (Born repulsion) becomes effective. Thus, at the distance of closest approach, a deep potential energy minimum reflecting particle aggregation occurs. A shallow so-called secondary minimum may cause a kind of aggregation that is easily counteracted by stirring.

The results of energy partitioning in Li+... OH2 obtained with a number of different basis sets are listed in Table 3. Since intermolecular overlap is small in these kind of complexes (Table 1), we expect the electrostatic model to be a good approximation for classical contributions to the total energy of interaction. Indeed, ZlE cou is to a good approximation proportional to the dipole moment of the water molecule calculated with the same basis set. This can be seen even more clearly in Table 4 where zIEcou is compared with ion-dipole and ion-quadrupole energies obtained from the classical expression of the multipole expansion series 45,95-97) ... 

The most widely used theory of suspension stability, the DLVO theory, was developed in the 1940s by Derjaguin and landau (1941) in Russia and by Verwey and Overbeek (1948) in Holland. According to this theory, the stability of a suspension of fine particles depends upon the total energy of interaction, Vt, between the particles. Vf has two components, the repulsive, electrostatic potential energy, Vr, and the attractive force, Va, i. e. 

Using this data for the layer thickness, the total energy of interaction was calculated by summing the electrostatic and steric contributions, the latter of which was calculated according to the method of Ottewill. Total interaction energies at three values of interparticle separation are shown in Figure 11 as a function of polymer dose. 

Choosing for the electrons a Fermi distribution with values of p from 0 to pmax, we obtain for the total energy of interaction the following cumbersome expression ... 

The total energy of interaction between the particles in a lyophobic sol is obtained by summation of the electric double layer and van der Waals energies, as illustrated in Figure 8.2. 

By addressing issue 9 of how isoelectronic chemical reactivities enter the total energy of interaction of two disjoint, nonoverlapping systems [50], we show in Sect. 8 how contact can be made between chemical reactivities and the initial segment of, or portal to, the reaction pathway. As by-products, a clear definition of the chemical stimuli which couple to the reactivity indices, the chemical responses, and a clear definition of dynamic as well as static chemical reactivities emerge, resolving issues 7 and 8, respectively. 

Summing die contribution from each effect gives the total energy of Interaction ... 

Fig. 1. Profile of the total energy of interaction between a colloidal particle and the collector surface arising from the double-layer repulsion and London attraction.

The total energy of interaction ( VT ) is obtained from the summation between the electrostatic repulsive energy (i.e., the electrical double layer) and the attractive energy (i.e., van der Waals forces) ... 

A computational procedure for the modeling of chromatographic separation of racemic Co(acac)3 into enantiomers on a dinitrobis(arginine)cobalt(III) complex as a chiral selector was described. Predicted elution order calculated from the differences in total energy of interaction for A and A selectands were found to be in agreement with the experimental results. The predictive power of the method and its possible practical applications in designing efficient chiral stationary phases was demonstrated . ... 

Next there is a lateral interaction term. If left alone (i.e., in the absence of an external field), dipoles will pair up to minimize their total energy of interaction, yielding Z = 0. This opposes the tendency of the field to orient all the dipoles in one direction, making the transition from one orientation to the other even slower. 

The error involved in making this approximation amounts to only a few kcals for the sodium chloride molecule. This is negligible for our present purpose. The total energy of interaction of the ions is then given by,... 

According to DLVO theory, the total energy of interaction between colloidal particles is given by the sum of the attraction (Va) and repulsion (Vr) energies ... 

Fig. 7 Variation of the attraction and repulsion energies and the total energy of interaction between two colloidal particles with interparticle distance.

Approximate Contributions to the Total Energy of Interaction Between Molecules, in kj/mol... 

The central theory for colloidal, and therefore latex, stability is because of the complimentary work of Derjaguin and Landau in Moscow and Verwey and Overbeek in Holland. This has become known as DLVO theory.The idea is to represent a total energy of interaction as the sum of individual attractive and repulsive potentials. Fig. 4 sketches out the van der Waals and electrostatic potentials, as well as the total interaction for a particular particle size, surface potential, and electrolyte concentration. 

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