Repulsion, adsorbed particles

Fig. 18. The repulsion force from adsorbed particles is greater than the van der Waals force between flocculated emulsion droplets under certain...

Further inspection of Fig. 4.5 demonstrates that the O atoms are surrounded by dark zones. The STM technique probes not only the atomic topography but also the electronic structure, and the dark zones reflect the modification of the local electronic density in the vicinity of the adsorbates, this modification being responsible for the operation of indirect interactions (which may be either repulsive or attractive) between adsorbed particles mediated through the substrate. 

Once nanoparticles have been formed, whether in an early state of growth or in a more or less final size, their fate depends on the forces between the individual particles and between particles and solid surfaces in the solution. While particles initially approach each other by transport in solution due to Brownian motion, convection, or sedimentation, when close enough, interparticle forces will determine their final state. If the dominant forces are repulsive, the particles will remain separate in colloidal form. If attractive, they will aggregate and eventually precipitate. In addition, they may adsorb onto a solid surface (the substrate or the walls of the vessel in which the reaction is carried out). For CD, both attractive particle-sur-... 

Since it seems difficult to decide from the shapes of the adsorption isotherms whether the catalyst surfaces are heterogeneous or homogenous with repulsive interaction operative, statistical mechanics have been applied to the isotherm for such low surface coverings that any interaction of adsorbed particles can be ignored (see Section IV). 

The activity coefficients are affected from differences in size, the short-range lateral interactions among the adsorbed particles and in the case of adsorbed ions from the repulsive Coulombic interactions among these ions. Analytical expressions for the activity coefficients may be obtained either from statistical mechanical models or experiment. Thus, an approximate expression, arising from monolayer models under mean field approximation, is the following [12,13,21] ... 

The substrate is exposed to an ideal gas phase at temperature T and chemical potential jtt. Particles can be adsorbed on the substrate with the restriction of at most one adsorbed particle per site and we consider a nearest neighbor (NN) interaction energy w among them (we use the convention > 0 for repulsive and w <0 ot attractive interactions). Then the adsorbed phase is characterized by the hamiltonian ... 

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