Interaction energy primary maximum

The values of the interaction energy at the maximum and at the secondary minimum are proportional with the radius a ofthe particle or droplet and depend strongly on the Hamaker constant AH and on the hydration repulsion. As shown in the previous section, small modifications in the ratio (pje ) (and hence in the hydration repulsion) can lead to a large increase in the potential barrier between the primary and secondary minima, thus affecting the stability of the system. 

In general, the electrostatic repulsion is evident at a shorter distance than the steric interaction as long as the adsorbed molecules do not desorb from the particle surface. When three interactions (i.e., electrostatic, van der Waals, and steric) are combined, a primary maximum energy at a large distance results. 

FIGURE 12.4 Examples of the colloidal interaction energy VT (in units of knT) as a function of interparticle distance h, calculated according to the DLVO theory for spherical particles in an aqueous phase. Illustrated are the effects of the magnitude of (a) the Hamaker constant A (b) surface potential i//0 (c) ionic strength 7 and (d) particle radius R. Unless indicated otherwise, A — I.25k i7 i// = 15mV 7= 10 mmolar R — I pm. x, y, and z denote the maximum, the primary minimum, and the secondary minimum in FT, respectively. 

Figure 49. A schematic diagram of the total interaction energy of two bodies. U refers to the energy due to the van der Waals attractive force between two interacting bodies, V refers to the energy due to the electrostatic interaction (repulsive) force, is the short-range repulsive interaction energy. R is the distance between the two bodies. The total interaction energy = L/r + 1/ + V (dotted curves). Curves A and B are the cases where there is a maximum (primary maximum) between two areas of minimum (primary minimum and secondary minimum). Curve C is the case where there is no maximum (no barrier) so that the two bodies could come in close contact with each other at the primary minimum region.

When both attractive and repulsive terms are taken into account, the interaction curve for particles resembles that shown in Figure 10.3, curve 3. In terms of colloidal stability, the key element in such a curve is the height of the so-called primary maximum indicated as AG ax on the curve. Later we will see from whence comes that energy maximum. 

There are, at least, three reasons responsible for diminution of the hemolytic effect on interaction of RBCs with TMS/A-300 (i) strong aggregation of partially hydrophobic silica particles and diminution of the amounts of individual primary silica nanoparticles, which are maximum bioactive, that causes diminution of the total contact area between RBCs and silica (per gram of silica) and a decrease of local interaction of solid particles with membrane proteins, (ii) changes in interaction energy between modified silica surface and the membrane structures due to a decrease in... 

Figure 1 Pair-wise-interaction energy between spherical particles i and j in an electrostatically-stabilized dispersion. The potential Ujj(r) is plotted agairtst rja, where r is the centre-to-centre separation and a is the particle radius. Three regions of the potential are identified primary minimum (A), primary maximum (B), (height u J, and secondary minimum (C). The dotted line represents an effective hard-sphere potential...

An important consideration is the effect of filler and its degree of interaction with the polymer matrix. Under strain, a weak bond at the binder-filler interface often leads to dewetting of the binder from the solid particles to formation of voids and deterioration of mechanical properties. The primary objective is, therefore, to enhance the particle-matrix interaction or increase debond fracture energy. A most desirable property is a narrow gap between the maximum (e ) and ultimate elongation ch) on the stress-strain curve. The ratio, e , eh, may be considered as the interface efficiency, a ratio of unity implying perfect efficiency at the interfacial Junction. 

The solubility of solids in liquids is an important process for the analyst, who frequently uses dissolution as a primary step in an analysis or uses precipitation as a separation procedure. The dissolution of a solid in a liquid is favoured by the entropy change as explained by the principle of maximum disorder discussed earlier. However it is necessary to supply energy in order to break up the lattice and for ionic solids this may be several hundred kilojoules per mole. Even so many of these compounds are soluble in water. After break up of the lattice the solute species are dispersed within the solvent, requiring further energy and producing some weakening of the solvent-solvent interactions. 

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