Electrostatic repulsive force between charged particles

Aggregation of liposomes both in vitro and in vivo is one of their main stability problems. According to the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, or theory of colloidal stability, a colloidal system is stable if the electrostatic repulsion forces between two particles are larger than the attraction van der Waals forces. Therefore charged liposomal formulations are highly desirable. Manipulation of... 

The very strong Coulombic forces partially explain the difficulties associated with constructing suitable theories for electrolyte solutions (Prausnitz, Lich-tenthaler and de Azevedo, 1999). They also form the basis of the electrostatic repulsive forces between colloidal particles, which are discussed in Chapte 10, as the colloids are typically charged in aqueous media. 

Electrostatic repulsion forces between equally charged particles support a homogeneous distribution. The ability to maintain a homogeneous distribution of particles in a liquid for a long time is referred to in the colloid chemistry as stability of a colloid system. This concept only applies to liophobic colloids, i.e. colloids insoluble in liquid. 

Simple ions and molecule dispersants are most mainly used in aqueous suspensions. They are inorganic compounds, including salts, acids, and bases, which are also known as electrolytes. Selective adsorption of one type of ions onto the particle surface coupled with the formation of a diffuse layer of the counterions, i.e., ions with opposite charge, provides electrostatic stabilization, due to the repulsion between the double layers. The stability of the suspensions is influenced through control the repulsion force between the particles, by the valence and radius of the counterions. According to the Schulze-Hardy mle, the higher the valence of the counterions, the more effective they will be, while for ions with the same valence, the smaller the ions the more effective the dispersants are. 

Coagulation has been considered to be the result of van der Waals attraction which draws two particles together at the moment of collision, unless opposed by a hydration barrier layer or by the electrostatic repulsion forces between the similarly charged particles, or both. There are therefore two factors that retard coagulation-of silica ... 

The concentration and nature of the electrolyte also has a significant impact on the stability of charged colloid dispersions. This was discussed in Section 3.3.2, where the concept of electric double layers was introduced. The electric double layer results from the atmosphere of counterions around a charged colloid particle. The decay of the potential in an electric double layer is governed by the Debye screening length, which is dependent on electrolyte concentration (Eq. 3.8). In the section that follows, the stability of charged colloids is analysed in terms of the balance between the electrostatic (repulsive) forces between double layers and the (predominantly attractive) van der Waals forces. 

Figure 1.5. Interactions between two negatively charged colloidal particles. The abscissa and ordinate represent the distance of separation between two particles and potential energy barrier against coagulation as a result of the competitive van der Waals attraction force and electrostatic repulsion force between the two interactive particles.

Mixed anionic and nonionic surfactant systems have been widely used in industry to manufacture latex products. Anionic surfactants can provide electrostatic repulsion force between two similarly charged electric double layers. By contrast, nonionic surfactants can impart two approaching latex particles... 

The elastic stress may be external or internal. External stresses are exerted on the chromatin during the cell cycle when the mitotic spindle separates chromosome pairs. The 30-nm fiber should be both highly flexible and extensible to survive these stresses. The in vitro experiments by Cui and Bustamante demonstrated that the 30-nm fiber is indeed very soft [66]. The 30-nm fiber is also exposed to internal stresses. Attractive or repulsive forces between the nucleosomes will deform the linkers connecting the nucleosomes. For instance, electrostatic interactions, either repulsive (due to the net charge of the nucleosome core particles) or attractive (bridging via the lysine-rich core histone tails [49]) could lead to considerable structural rearrangements. 

The crucial importance of the double layer when dealing with colloidal particles dispersed in a solution is due to the repulsion of one particle by another. While overall the particles are neutral, because the diffuse layer can extend into the solution, the unbalanced charge in the diffuse layer of one particle experiences a repulsion by that of another particle. Normally, from the Coulomb law of electrostatics, the force between two equal (in charge and in sign) particles is given by... 

It is important to note that the concept of osmotic pressure is more general than suggested by the above experiment. In particular, one does not have to invoke the presence of a membrane (or even a concentration difference) to define osmotic pressure. The osmotic pressure, being a property of a solution, always exists and serves to counteract the tendency of the chemical potentials to equalize. It is not important how the differences in the chemical potential come about. The differences may arise due to other factors such as an electric field or gravity. For example, we see in Chapter 11 (Section 11.7a) how osmotic pressure plays a major role in giving rise to repulsion between electrical double layers here, the variation of the concentration in the electrical double layers arises from the electrostatic interaction between a charged surface and the ions in the solution. In Chapter 13 (Section 13.6b.3), we provide another example of the role of differences in osmotic pressures of a polymer solution in giving rise to an effective attractive force between colloidal particles suspended in the solution. 

The combined effect of attraction and repulsion forces has been treated by many investigators in terms borrowed from theories of colloidal stability (Weiss, 1972). These theories treat the adhesion of colloidal particles by taking into account three types of forces (a) electrostatic repulsion force (Hogg, Healy Fuerstenau, 1966) (b) London-Van der Waals molecular attraction force (Hamaker, 1937) (c) gravity force. The electrostatic repulsion force is due to the negative charges that exist on the cell membrane and on the deposition surface because of the development of electrostatic double layers when they are in contact with a solution. The London attraction force is due to the time distribution of the movement of electrons in each molecule and, therefore, it exists between each pair of molecules and consequently between each pair of particles. For example, this force is responsible, among other phenomena, for the condensation of vapors to liquids. 

The basic point is that the mass action laws of chemistry ([A][B]/[AB] = constant) do not work for ions in solution. The reason they do not work puzzled ehemists for 40 years before an acceptable theory was found. The answer is based on the effects of electrostatic interaction forces between the ions. The mass aetion laws (in terms of concentrations) work when there are no charges on the partieles and hence no long-range attraction between them. When the particles are charged. Coulomb s law applies and attractive and repulsive forces (dependent on 1/r where r is the distanee between the ions) come in. Now the particles are no longer independent but puU on each other and this impairs the mass action law, the silent assumption of which is that ions are free to act alone. 

Every atom has an extremely dense nucleus that contains most of the atom s mass. The nucleus contains positively charged protons and neutral neutrons, both of which are referred to as nucleons. You may have wondered how protons remain in the densely packed nucleus despite the strong electrostatic repulsion forces produced by the positively charged particles. The answer is that the strong nuclear force, a force that acts only on subatomic particles that are extremely close together, overcomes the electrostatic repulsion between protons. 

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