Attraction-repulsion mechanism

In agreement with the attraction-repulsion mechanism described above, the excess modulus of the agglomerate network at any amplitude must be proportional to N, so... 

With respect to the attraction-repulsion mechanism between soft spheres (aggregates), there is an excess modulus due to the agglomerate network at any amplitude that must be proportional to N, i.e. (Ge(Yo)-Gejnf) No=(Geo-Ge nf) N Note here G =Gx G =Ge G"=Gv... 

Thus, the two bosons have an inereased probability density of being at the same point in spaee, while the two fermions have a vanishing probability density of being at the same point. This eonelusion also applies to systems with N identieal partieles. Identical bosons (fermions) behave as though they are under the influence of mutually attractive (repulsive) forces. These apparent forces are called exchange forces, although they are not forces in the mechanical sense, but rather statistical results. 

Adsorption of SOC by activated carbon may involve various combinations of chemical, electrostatic, and physical (i.e. non-specific dispersion forces) interactions [59]. The overall adsorption interactions can be very complex for some SOCs. One good example is the adsorption of phenolic compounds, probably the most widely studied class of adsorbates in the activated carbon literature. Several possible mechanisms have been proposed for phenol adsorption [60-69]. These incluile (i) n-n dispersion interactions between the basal plane of activated carbon and the aromatic ring of the adsorbate, (ii) electrostatic attraction-repulsion interactions, (iii) hydrogen bonding between adsorbate and surface functional groups of activated carbons, (iv) electron acceptor-donor complex formation mechanisms between the carbonyl... 

Type R-depen- dence Attractive/ repulsive Orientation dependence Classical/ quantum mechanical Strength eV Method... 

The theory of adsorption forces was developed by London [87,88], de Boer and Custers [89], Lenel [90] and de Boer [91,92]. The studies by Lennard-Jones [93], who proposed the Lennard-Jones attraction - repulsion (6-12) potential used up till now, were of significant importance. Development of mechanics and quantum chemistry (e.g. [94]) had a great effect on understanding the character of... 

To overcome the aggregation and/or coalescence processes, one must overcome the van der Waals attraction by some repulsive mechanism that will give the system kinetic stability with an adequate shelf-life. Normally one requires a shelf-life of 2-3 years under various storage conditions (e.g. temperature variation). 

As mentioned above disperse systems lack thermodynamic stability and they tend to reduce their surface energy by aggregation and/or coalescence of the particles or droplets. The main driving force for the aggregation process is the universal van der Waals attraction which will be discussed in subsequent sections. To overcome the aggregation and/or coalescence processes, one must overcome the van der Waals attraction by some repulsive mechanism and this will give the system kinetic stability with an adequate shelf life. Normally one requires a shelf life of 2-3 years under various storage conditions (e.g. temperature variation). Several stabilization mechanisms are encountered with disperse systems and these are summarized below. 

At this time, bio-control techniques are particularly effective and used in vegetable crops, fruit arboriculture, vineyard and in large-scale farming (see Chapter 1). They are mostly the fruit of research in chemical ecology and more particularly in the classification of the phenomena of attraction, repulsion or induction, in trophic or non-trophic interactions. Bio-control products, preferring the use of natural mechanisms and interactions, are for commercial reasons classified by nature ... 

Zeta potential test is the measurement of the attraction-repulsion forces (charges) between particles when they are dispersed in a liquid. It gives information about the dispersion mechanism, stability of the colloids, agglomerates, etc., and especially, about the electrostatic processes. There are some types of equipment which are focused on the analysis of nanomaterials, and with which it is possible to measure the zeta potential and also the particle size in liquid dispersion. 

Pirkle phases that form solute-CSP complexes by n electron donor-acceptor mechanism (attractive-repulsive interactions). 

There can be subtle but important non-adiabatic effects [14, ll], due to the non-exactness of the separability of the nuclei and electrons. These are treated elsewhere in this Encyclopedia.) The potential fiinction V(R) is detennined by repeatedly solving the quantum mechanical electronic problem at different values of R. Physically, the variation of V(R) is due to the fact that the electronic cloud adjusts to different values of the intemuclear separation in a subtle interplay of mutual particle attractions and repulsions electron-electron repulsions, nuclear-nuclear repulsions and electron-nuclear attractions. 

Note the stnicPiral similarity between equation (A1.6.72) and equation (Al.6.41). witii and E being replaced by and the BO Hamiltonians governing the quanPim mechanical evolution in electronic states a and b, respectively. These Hamiltonians consist of a nuclear kinetic energy part and a potential energy part which derives from nuclear-electron attraction and nuclear-nuclear repulsion, which differs in the two electronic states. 

Just as for an atom, the hamiltonian H for a diatomic or polyatomic molecule is the sum of the kinetic energy T, or its quantum mechanical equivalent, and the potential energy V, as in Equation (1.20). In a molecule the kinetic energy T consists of contributions and from the motions of the electrons and nuclei, respectively. The potential energy comprises two terms, and F , due to coulombic repulsions between the electrons and between the nuclei, respectively, and a third term Fg , due to attractive forces between the electrons and nuclei, giving... 

---