Van der Waals attraction potential

The van der Waals attractive potential [27] increases with an increase in nanopartide radius or with a decrease in center-to-center separation distance between nanoparticles ... 

For the case of a pair of spherical particles, the van der Waals attractive potential is given by... 

The expression for the van der Waals attractive potential between two identical colloidal particles with adsorbed layers can be written in terms of a composite Hamaker constant A [17] as... 

Helmholtz free energy of the adsorbed film is given as the sum of the van der Waals attraction potential of all molecules in the film with all atoms in the adsorbent, the vapor-liquid surface free energy and the free energy of all molecules in the bulk liquid. This leads to the following relation between the adsorbed amount Nand the relative pressure p/p0 [100, 101] ... 

The first attempt to compile all the factors contributing to the stability of a microemulsion is due to Ruckenstein and Chi [15], who summarized calculations of enthalpic components (van der Waals attractive potential, electrical double layer repulsive potential, and the interfacial stretching and bending free energy) and entropic contributions from the location of droplets. These calculations as well as those following [16] were useful because they revealed the importance of extremely low interfacial tension. 

According to the DLVO theory, total potential energy between two particles is expressed by the sum of van der Waals attractive potential energy and electrical repulsive potential energy and the dispersion is stable when the total potential energy is higher than 15 kT (4). 

The van der Waals attraction between two water molecules is due to the induced dipole moment in the molecules and permanent dipole moments of the water molecules. The attractive potential energy between two molecules varies as the inverse sixth power of the distance between the molecules. The total van der Waals attractive potential energy of a soap film of thickness, t, due to the sum of the interactions between all the molecules in the film is given approximately by... 

The van der Waals attractive potential derives from a dipole-dipole interaction between the two neutrally charged particle surfaces separated by a distance r (see Section 1.3.1), where U —g- and provides a relatively short-range force. In the absence of any otheir forces, therefore, we should expect all colloidal particles to gradually stick to each other and aggregate over time. In reality, because of the short-range nature of this force, other interactions in the system often tend to dominate, and by controlling the strength of these interactions colloidal suspensions can be stabilized under different conditions. 

Fig. 7.1 Principle of atom reflection from an evanescent laser wave with a repnlsive optical potential at a distance A, which is far away from short-distance van der Waals attractive potential.

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