DLVO theory repulsive potential

The force between particles is the sum of a pH-independent van der Waals component, which is always attractive, and a pH-dependent electrostatic component, which can be attractive or repulsive. In Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, the potential is used to calculate the interaction force or energy as a function of the distance between the particles. Atomic force microscopy (AFM) makes it possible to directly measure the force between the particles as a function of the distance, and commercial instruments are available to perform such measurements. Different approaches have been proposed to utilize the results obtained by AFM to determine the pHq. The quantity obtained by AFM corresponds to the lEP rather than the PZC. AFM was used to measure the force between SiO2 (negative potential over the entire studied pH range) and Si,N4 (lEP to be determined) in [681]. The pH at which the force at a distance of 17 nm was equal to zero was identified with the lEP. The van der Waals forces are negligible at such a distance, and the force is governed by an electrostatic interaction. The experimental results were consistent with DLVO theory. 

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 well-known DLVO theory of coUoid stabiUty (10) attributes the state of flocculation to the balance between the van der Waals attractive forces and the repulsive electric double-layer forces at the Hquid—soHd interface. The potential at the double layer, called the zeta potential, is measured indirectly by electrophoretic mobiUty or streaming potential. The bridging flocculation by which polymer molecules are adsorbed on more than one particle results from charge effects, van der Waals forces, or hydrogen bonding (see Colloids). 

The physicochemical forces between colloidal particles are described by the DLVO theory (DLVO refers to Deijaguin and Landau, and Verwey and Overbeek). This theory predicts the potential between spherical particles due to attractive London forces and repulsive forces due to electrical double layers. This potential can be attractive, or both repulsive and attractive. Two minima may be observed The primary minimum characterizes particles that are in close contact and are difficult to disperse, whereas the secondary minimum relates to looser dispersible particles. For more details, see Schowalter (1984). Undoubtedly, real cases may be far more complex Many particles may be present, particles are not always the same size, and particles are rarely spherical. However, the fundamental physics of the problem is similar. The incorporation of all these aspects into a simulation involving tens of thousands of aggregates is daunting and models have resorted to idealized descriptions. 

Fig. 1 Illustration of the DLVO theory interaction of two charged particles as a function of the interparticle distance (attractive energy curve, VA, repulsive energy curve, VR and net or total potential energy curve, Vj).

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 most widely used theory of suspension stability, the DLVO theory, was developed in the 1940s by Derjaguin and landau (1941) in Russia and by Verwey and Overbeek (1948) in Holland. According to this theory, the stability of a suspension of fine particles depends upon the total energy of interaction, Vt, between the particles. Vf has two components, the repulsive, electrostatic potential energy, Vr, and the attractive force, Va, i. e. 

Calculation of Coagulation Rate. Here we discuss an interaction potential of two charged particles in a liquid within a framework of DLVO theory. Following this theory, the overall interaction potential U, of charged spherical particles of the same radius R and surface distance d is a sum of a coulombic repulsive force of charged particles and a van der Waals attractive force given by the equation (28) ... 

The role of electrostatic repulsion in the stability of suspensions of particles in non-aqueous media is not yet clear. In order to attempt to apply theories such as the DLVO theory (to be introduced in Section 5.2) one must know the electrical potential at the surface, the Hamaker constant, and the ionic strength to be used for the non-aqueous medium these are difficult to estimate. The ionic strength will be low so the electric double layer will be thick, the electric potential will vary slowly with separation distance, and so will the net electric potential as the double layers overlap. For this reason the repulsion between particles can be expected to be weak. A summary of work on the applicability or lack of applicability of DLVO theory to non-aqueous media has been given by Morrison [268],... 

A pair of polysaccharide molecules approaching each other in water exerts an interaction potential ( ) that is the algebraic sum of the competing attractive and repulsive forces. integrated over all pairs of molecules, is . This principle is embodied in the Deijaguin-Verwey-Landau-Overbeek (DLVO) theory of colloidal stability (Ross and Morrison, 1988). The equilibrium distance between the molecules is related to c, the volume of the hydrated particles, ionic strength, cosolute, nonsolvent additions, temperature, and shearing. 

The scope of this paper is to demonstrate via Monte Carlo simulations that the conventional Debye-Hiickel screened pair potential, which is based on the DLVO theory and is repulsive at all distances, can explain the experimental observations of Ise et al. Consequently, the pair potential does not have to become attractive at large distances to explain the Ise et al. observations. The simulations have been carried out for a wide range of charges and volume fractions of the particles as well as a few electrolyte concentrations. The paper is organized as follows In Section 2, the model and the Monte Carlo algorithm will be described. In Section 3, the main results will be presented. Section 4 will emphasize the conclusions. 

Most of the water-mediated interactions between surfaces are described in terms of the DLVO theory [1,2]. When a surface is immersed in water containing an electrolyte, a cloud of ions can be formed around it, and if two such surfaces approach each other, the overlap of the ionic clouds generates repulsive interactions. In the traditional Poisson-Boltzmann approach, the ions are assumed to obey Boltzmannian distributions in a mean field potential. In spite of these rather drastic approximations, the Poisson-Boltzmann theory of the double layer interaction, coupled with the van der Waals attractions (the DLVO theory), could explain in most cases, at least qualitatively, and often quantitatively, the colloidal interactions [1,2]. 

The DLVO theory [1,2], which describes the interaction in colloidal dispersions, is widely used now when studying behavior of colloidal systems. According to the theory, the pair interaction potential of a couple of macroscopic particles is calculated on the basis of additivity of the repulsive and attractive components. For truly electrostatic systems, a repulsive part is due to the electrostatic interaction of likely charged macroscopic objects. If colloidal particles are immersed into an electrolyte solution, this repulsive, Coulombic interaction is shielded by counterions, which are forming the diffuse layer around particles. A significant interaction occurs only when two double layers are sufficiently overlapping during approach of those particles. 

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