The Potential Energy of Interaction Between Particles

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 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)]. 

The pair potential of colloidal particles, i.e. the potential energy of interaction between a pair of colloidal particles as a function of separation distance, is calculated from the linear superposition of the individual energy curves. When this was done using the attractive potential calculated from London dispersion forces, Fa, and electrostatic repulsion, Ve, the theory was called the DLVO Theory (from Derjaguin, Landau, Verwey and Overbeek). Here we will use the term to include other potentials, such as those arising from depletion interactions, Kd, and steric repulsion, Vs, and so we may write the total potential energy of interaction as... 

The potential energy of interaction between a system of charged particles and the electric field (3.24) is [Equation (1.285)]... 

When Of a, the potential energy of interaction between an elementary particle and a hoc is equivalent to the potcntiul energy 4(h) between a particle and a fiat plate thus 4(h) used by Huckenstcin and Prieve (1976) still applies. Furthermore, if the conditions necessary for Equation (13) of that paper apply, then (berate constants for reversible flocculation inay be calculated as K/ = 4 / Kf and Kr — Aoaf K where X/ and K, are given by Equation (13). 

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. 

In PBFFF, the variation of the potential energy of interaction between the colloidal particles and the channel wall can be succeeded, except for the variation of the ionic strength, by changing also the pH and the nature of the suspending medium. Polydisperse, irregular supramicron colloidal particles of the mixed sulfides Cuj,Zni j,S (0 < x < 1) were used as model samples to verify the applicability of the potential barrier gravitational field-flow fractionation (PBGFFF), based on the variation of the above parameters, to fractionate colloidal particles. 

The potential energy of interaction between two particles containing z and zi charges (including sign) whose centers are separated by a distance r is... 

The hydrogen atom contains two particles, the proton and the electron. For a system of two particles 1 and 2 with coordinates Zi) and X2,y2, z-, the potential energy of interaction between the particles is usually a function of only the relative coordinates X2 Xi,y2 y, and Z2 Zi of the particles. In this case the two-particle problem can be simplified to two separate one-particle problems, as we now prove. 

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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