Potential Energy of Interaction Between Particles and Surfaces

Potential Energy of Interaction Between Particles and Surfaces 

1 Similarities and Differences Between Intermolecular and Interparticle Forces 

As detailed in Chapter 2, van der Waals interactions consist mainly of three types of long-range interactions, namely Keesom (dipole-dipole angle-averaged orientation, Section 2.4.3), Debye (dipole-induced dipolar, angle-averaged, Section 2.5.7), and London dispersion interactions (Section 2.6.1). However, only orientation-independent London dispersion interactions are important for particle-particle or particle-surface attractions, because Keesom and Debye interactions cancel unless the particle itself has a permanent dipole moment, which can occur only very rarely. Thus, it is important to analyze the London dispersion interactions between macrobodies. Estimation of the value of dispersion attractions has been attempted by two different approaches one based on an extended molecular model by Hamaker (see Sections 7.3.1-7.3.5) and one based on a model of condensed media by Lifshitz (see Section 7.3.7). 

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The Hamaker constants are usually inserted in expressions for the potential energy of interaction between particles and surfaces. For a spherical particle-planar slab surface interaction of the same material, for the ( RSph D) case, if we combine Equations (533) and (536), we have... 

The rate of deposition of particles onto a surface, in the presence of London, double-layer, and gravitational forces, is calculated in terms of the energy of interaction between cell and surface by assuming that Brownian motion over a potential energy barrier is the rate-determining step of the... 

The interaction between particle and surface and the interaction among atoms in the particle are modeled by the Leimard-Jones potential [26]. The parameters of the Leimard-Jones potential are set as follows pp = 0.86 eV, o-pp =2.27 A, eps = 0.43 eV, o-ps=3.0 A. The Tersoff potential [27], a classical model capable of describing a wide range of silicon structure, is employed for the interaction between silicon atoms of the surface. The particle prepared by annealing simulation from 5,000 K to 50 K, is composed of 864 atoms with cohesive energy of 5.77 eV/atom and diameter of 24 A. The silicon surface consists of 45,760 silicon atoms. The crystal orientations of [ 100], [010], [001 ] are set asx,y,z coordinate axes, respectively. So there are 40 atom layers in the z direction with a thickness of 54.3 A. Before collision, the whole system undergoes a relaxation of 5,000 fsat300 K. 

The DLVO theory, with the addition of hydration forces, may be used as a first approximation to explain the preceding experimental results. The potential energy of interaction between spherical particles and a plane surface may be plotted as a function of particle-surface separation distance. The total potential energy, Vt, includes contributions from Van der Waals energy of interaction, the Born repulsion, the electrostatic potential, and the hydration force potential. [Israelachvili (13)]. 

Figure S.3 Potential energies of interaction between two colloidal particles as a function of their distance of separation, for electrical double layers due to surface charge (VolK London-van der Waals dispersion forces (V ), and the total interaction (VT). From Schramm [426], Copyright 2003, Wiley.

The variation of the potential energy of interaction between colloidal particles and sohd surfaces can be also succeeded by the addition of a detergent to the suspending medium, which leads to a decrease in the Hamaker constant and, consequently, in the potential energy of attraction. 

Equations (2)-(4) show that the total potential energy of interaction between two colloidal spherical particles depends on the surface potential of the particles, the effective Hamaker constant, and the ionic strength of the suspending medium. It is known that the addition of an indifferent electrolyte can cause a colloid to undergo aggregation. Furthermore, for a particular salt, a fairly sharply defined concentration, called critical aggregation concentration (CAC), is needed to induce aggregation. 

In order to describe the stability of fine disperse systems stabilized by diffuse ionic layers, one has to use the total free energy of interaction between particles, instead of the energy per unit film area, and compare the barrier height,, to the thermal energy, kT. For us to be able to use the solution derived for the case of plane-parallel surfaces, let us introduce some effective area of particle contact, Se[. Then the potential barrier height for the particles can be expressed as = A5 max St(. When diffuse part of electrical double... 

The presence of surface phenomena in SdFFF, except for being a main source of error in calculating physicochemical quantities, could also be a basis for a new separation method called Potential-Barrier Field-Flow Fractionation, which can separate colloidal particles of different size or of any physicochemical parameter involved in the potential energy of interaction between the particles and the FFF channel wall. ° The same method can be also used for the concentration and analysis of dilute colloidal samples, such as those of natural water, where particles are present in low... 

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