Attractive or Repulsive Interactions

With the aid of (B1.25.4), it is possible to detennine the activation energy of desorption (usually equal to the adsorption energy) and the preexponential factor of desorption [21, 24]. Attractive or repulsive interactions between the adsorbate molecules make the desorption parameters and v dependent on coverage [22]- hr the case of TPRS one obtains infonnation on surface reactions if the latter is rate detennming for the desorption. 

The assumptions made to derive the Langmuir isotherm (Eq. 2.7) are well known Energetic equivalence of all adsorption sites, and no lateral (attractive or repulsive) interactions between the adsorbate molecules on the surface. This is equivalent to a constant, coverage independent, heat (-AH) of adsorption. 

We have already made use of the so-called mean-field approximation by assuming that (1) all adsorbed species are distributed randomly over the surface and (2) there is no interaction betv een the adsorbed species. This is an approximation that is seldom fulfilled. Usually there vill be either an attractive or repulsive interaction... 

Attractive or repulsive interaction between two solid surfaces should play an important role in the interfacial frictional behavior [87,92-95]. From previous theoretical [89] and experimental investigations [87, 95], it was known that the attractive interaction result in a high friction and repulsive interaction results in low friction force. To characterize the interfacial molecular structure between two solids under electrostatic interaction is also important to elucidate the frictional properties of two solids. 

Attractive or repulsive interactions between the adsorbate molecules make the desorption parameters Edes and V dependent on coverage [17],... 

In the previous sections, we saw that, in most cases, a nonbonded attractive or repulsive interaction is enforced by both four electron destabilization and two electron stabilization. Hence, in order to simplify subsequent discussions, we shall adopt the OEMO model with neglect of overlap. Consequently, in the remainder of this work... 

Figure 10 Lateral interaction model on an fcc(lll) lattice. The adsorbed sulfate anion binds to two surface atoms in a bridged fashion (black atoms), making bonding to the first shell of neighboring sites (white) impossible. There is a finite attractive or repulsive interaction with sulfate anions binding to the second neighbor shell (grey)...

Pecul calculated the 1J(3He,3He) coupling in ,154 i.e., one of the weakest bonded van der Waals complexes, using full Cl46 and EOM-CCSD methods.44,155 158 She found that in this complex the FC term of such coupling decreases exponentially with the d(He-He) distance being He, 3He) 22 Hz, for d(He He) = 4 au and falling below 0.1 Hz for d(He-He) = 7 au. Pecul concluded that the main FC coupling pathway is the overlap between the electronic clouds of both helium atoms and that its efficiency does not depend on whether this corresponds to an attractive or repulsive interaction. Similarly, Pecul et al.159 carried out calculations based on... 

Let us consider the various possible types of biopolymer-surfactant interactions. We first note that, because of the amphiphilic nature of both biopolymers and surfactants, it can be envisaged that the mechanistic interpretation could be based on attractive or repulsive interactions acting between the original biopolymer and surfactant molecules/particles or between biopolymer particles modified by the surfactants. For example, attractive interactions could arise from ... 

Two - particle energy correction correction to electron - electron correlation energy due to the phonon field. This non-adiabatic term represents full attractive contribution, and can be compared to the reduced form of Frohlich effective Hamiltonian which maximizes attractive contribution of electron - electron interaction and that can be either attractive or repulsive (interaction term of the BCS theory). For superconducting state transition at the non-adiabatic conditions, the two-particle correction is unimportant - see [2],... 

Electrostatic coulombic interactions Attractive or repulsive interactions... 

Problem 11-5. If there is no significant attractive or repulsive interaction between two radicals, the probability of first encounter at r=d from the initial distance at r=ro is expressed as... 

Broadly speaking, promoters can be divided into structural promoters and electronic promoters. In the former case, they enhance and stabilize the dispersion of the nanoparticle-dispersed active phase on the catalyst support. In the latter case, they enhance the catalytic properties of the active phase itself. This stems from their ability to modify the chemisorptive properties of the catalyst surface and to significantly affect the chemisorptive bond strength of reactants and intermediates. At the molecular level this is the result of direct ( through the vacuum ) and indirect ( through the metal ) interactions. The term through the vacuum denotes direct electrostatic, Stark type, attractive or repulsive interactions between the adsorbed... 

In the simplest case, all equilibrium positions of sorbate molecules in the solid are equivalent, and the state of a sorbed molecule is independent of the presence of other sorbate molecules in the solid. The sorbent is thus considered to be energetically homogeneous with respect to its interaction with the sorbate, and it is assumed that there is no attractive or repulsive interaction between the sorbate molecules. 

The electronic structure of interfacial excitations was recently described by Beljonne, Herz, Friend, and coworkers [38,88]. Static dipoles in the ground state of one polymer chain are considered to modulate the exciton energy on the neighboring polymer chains by Coulomb interactions across the heterojunction. Depending on the relative position of the chains, attractive or repulsive interaction were found, which respectively stabilize or obstruct charge-transfer state formation [88]. This implies that the density of states of interfacial excitons is broader than that for bulk excitons. Indeed, this was experimentally observed by femtosecond time-resolved photoluminescence spectroscopy in the same study [88]. The broader density of states at the heterojunction is consistent with the fast directional motion toward the interface described above (see Section 13.3.1) [87]). Excitons could transfer quickly into lower energy interfacial sites when they approach the interfacial region. 

We note that the boundary conditions chosen in Eqs. (57) to (58) model the particular situation of electrostatic attraction in competition with a short-range (steric) repulsion of nonelectrostatic origin. Possible variations of these boundary conditions include surfaces with a constant surface charge (discussed later) and surfaces with a nonelectrostatic short-range attractive (or repulsive) interaction with the polymer [83, 127]. Far from the surface (jc -> oo), both f and f reach their bulk values and their derivatives vanish f x oo = 0 and f x oo — 6. 

Let us first consider the situation when macromolecules do not exhibit any attractive or repulsive interaction with the porous column packing surface except for the effects caused by the imperviousness of the pore walls. This corresponds to AH=0 in Equation (17) and the sample retention volume is controlled exclusively by the entropy of process. The fictitious retention volume of eluent molecules corresponds to total volume of liquid within column, becanse the small molecules... 

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