Repulsion force, electrostatic model

For the anionic models, the detailed studies on their interactions with poly-and mononucleotides have not yet been carried out. However, we may say that the interactions of bases between the models and polynucleotides would be faint because of the strong electrostatic repulsive forces between the macroanions. 

The von Smoluchowski equation must be corrected when the partners are ions to account for attractive or repulsive forces. They can be approximated by an electrostatic model. The quantity by which Eq. (9-10) or (9-13) is to be multiplied is... 

While Debye and HUckel recognized the short-range repulsive forces between ions by assuming a hard-core model, the statistical mechanical methods then available did not allow a full treatment of the effects of this hard core. Only the effect on the electrostatic energy was included—not the direct effect of the hard core on thermodynamic properties. 

Electrostatic Model. A simple model that can account for the observed bond angles in a qualitative way comes from a consideration of electrostatic repulsions of electron pairs. Let us consider electron pairs around an atom as concentrations of charge placed on a more or less spherical surface, and let us assume that the electrons can move in pairs. Barring other forces, the most likely arrangement will be the one where the electron pairs exert the minimum repulsion on each other. This will be achieved when the electrons get as far away from each other as possible. Since the electrons are restricted by our assumption to a sphere, the maximum distance of separation corresponds to a maximum angle between their positions and the center of the sphere. 

Support to these assumptions has recently come from the analysis of the coupling between electrostatic and dispersion-repulsion contributions to the solvation of a series of neutral solutes in different solvents [31]. It has been found that the explicit inclusion of both electrostatic and dispersion-repulsion forces have little effect on both the electrostatic component of the solvation free energy and the induced dipole moment, as can be noted from inspection of the data reported in Table 3.1. These results therefore support the separate calculation of electrostatic and dispersion-repulsion components of the solvation free energy, as generally adopted in QM-SCRF continuum models. 

Whereas the coupled equations of the polarization model can be solved analytically in the linear approximation (which is valid only for small potentials), in the general case one must rely on numerical solutions [7.5]. The polarization model can explain the restabilization of protein-stabilized polymer latexes, for which the increase in the repulsive force generated by the surface dipoles more than compensates for the decrease in repulsion caused by the decrease in the surface charge and the increase in the screening of the electrostatic field by the increasing ionic strength [7.5]. 

However, there are reasons to believe that more is involved in hydrogen bonding than simply an exaggerated dipole-dipole interaction. The shortness of hydrogen bonds indicates considerable overlap of van der Waals radii and this should lead to repulsive forces unless otherwise compensated. Also, the existence of symmetrical hydrogen bonds of the type F . .. H F cannot be explained in terms of the electrostatic model. When the X—Y distance is sufficiently short, an overlap of the orbitals of the X—H bond and the electron pair of Y can lead to a covalent interaction. According to Eq. (2-8), this situation can be described by two contributing protomeric structures, which differ only in the position of the proton ... 

Figure 2.1. Ionic model for sodium chloride. This is a face-centered arrangement of chloride ions (white), with sodium ions occupying the octahedral interstitial sites (red). The attractive electrostatic forces, a, between adjacent Na+ and Cl ions, and repulsive forces, r, between Na" " ions are indicated.

The DLVO theory, which was developed independently by Derjaguin and Landau and by Verwey and Overbeek to analyze quantitatively the influence of electrostatic forces on the stability of lyophobic colloidal particles, has been adapted to describe the influence of similar forces on the flocculation and stability of simple model emulsions stabilized by ionic emulsifiers. The charge on the surface of emulsion droplets arises from ionization of the hydrophilic part of the adsorbed surfactant and gives rise to electrical double layers. Theoretical equations, which were originally developed to deal with monodispersed inorganic solids of diameters less than 1 pm, have to be extensively modified when applied to even the simplest of emulsions, because the adsorbed emulsifier is of finite thickness and droplets, unlike solids, can deform and coalesce. Washington has pointed out that in lipid emulsions, an additional repulsive force not considered by the theory due to the solvent at close distances is also important. 

In addition to the short-range interactions between species in all solutions, long-range electrostatic interactions are found in electrolyte solutions. The deviation from ideal solution behavior caused by these electrostatic forces is usually calculated by some variation of the Debye-Huckel theory or the mean spherical approximation (MSA). These theories do not include terms for the short-range attractive and repulsive forces in the mixtures and are therefore usually combined with activity coefficient models or equations of state in order to describe the properties of electrolyte solutions. 

It can be observed that the bubble diameter comes into play in all these forces at power 2 or 3, making the computation very sensitive to this parameter. There are many other forces which could be considered (compressive force due to the liquid, surface tension forces, wake-related forces exerted by neighbouring bubbles, electrostatic repulsion forces between bubbles, etc.). However, these forces were not taken into account in this numerical model. The physical data used for the two phases are shown in Table 1. 

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