Force maximum attractive

This is not the same thing as the maximum attractive force, which we get by maximizing F ... 

The net strength of a molecule s Debye interactions is a function of its polarizability and the number and magnitude of its local dipole moments. Since induced dipoles tend to be aligned for maximum attraction, the energy of interaction resulting from Debye forces is very nearly additive. 

Based on Equations 9.1 and 9.2, colloidal stability (maximum dispersion) depends on maximum R, which describes the maximum repulsive energy between two planar colloidal surfaces. It also appears from these equations that Rf is controlled by or CECV. However, in addition to the repulsive force, there is an attraction force (Af) between soil colloidal particles. The force of attraction (van der Waals force) between two particles separated by a distance of 2d (d = particle diameter) is described by... 

Because most of you are probably too lazy to go and review stuff, we ll briefly mention a couple of pertinent points. First, the interaction between two molecules is described in terms of the potential energy (P.E.). When the molecules are too close they strongly repel, when they are too far apart they don t feel each other. There is some optimum distance apart where their interaction is a maximum, hence P.E. is a minimum, or has the largest negative or attractive value. Second, there are advanced theoretical models that deal with potential functions like this, which we will not consider, but for dispersion and weak polar forces the attractive energy varies as 1/r6, where r is the distance between the molecules. 

If the viscosity curve is convex, the molecules of both components are polar. This increase in viscosity may also be explained by the electrostatic forces of attraction of the dipoles, which result in an increase of the viscosity. The occurrence of a maximum in the convex curve often corresponds to the presence of a definite additive compound of the components, the existence of which may be verified by other physico-chemical methods. 

Consider fluorine (F2), which has an electron configuration of ls 2s 2p. Each fluorine atom has seven valence electrons and must have one additional electron to form an octet. As two fluorine atoms approach each other, as shown in Figure 9-1, two forces become important. A repulsive force occurs between the like-charged electrons and between the like-charged protons of the two atoms. An attractive force also occurs between the protons of one fluorine atom and the electrons of the other atom. As the fluorine atoms move closer, the attraction of both nuclei for the other atom s electrons increases until the maximum attraction is achieved. At the point of maximum attraction, the attractive forces balance the repulsive forces. 

If the two nuclei move even closer, the repulsion between the like-charged nuclei and electron clouds will increase, resulting in repulsive forces that exceed attractive forces. Thus the most stable arrangement of atoms exists at the point of maximum attraction. At that point, the two atoms bond covalently and a molecule forms. Fluorine exists as a diatomic molecule because the sharing of one pair of electrons will give both fluorine atoms stable noble gas configurations. Each fluorine atom in the fluorine molecule has one bonding pair of electrons and three lone pairs, which are unshared pairs of electrons. 

Figure 66. Attraction forces due to different binding mechanisms for the sphere/plane model and contact (a = 0, Zq-OA nm). (a) Influence of the size of roughness peaks with radius r on the attraction force, (b) Influence of the diameter x=2R of smooth spheres on the maximum attraction force...

Now ininiiniim boiling azeotropes are formed when the forces of attraction between unlike molecules are smaller than those between identical molecules in the converse case maximum boiling azeotropes occur. On the basis of data compiled by Lecat [20] and Horsley [51]. Ewell, Harrison and Berg [52] have concluded tliat the forces of interaction concerned are mainly those due to hydrogen bonds, compared to which other forces such as dipolar forces and those due to induction are relatively... 

Figure 8.2 The arrows In this diagram show the net forces of attraction and repulsion acting on two fluorine atoms as they move toward each other. The overall force between two atoms Is the result of electron-electron repulsion, nucleus-nucleus repulsion, and nucleus-electron attraction. At the position of maximum net attraction, a covalent bond forms. Relate How is the stability of the bond related to the forces acting on the atoms ... 

For two charges of the same sign, both w(r) and F will be positive, which means that the interaction will be repulsive for unlike charges they will be attractive. In terms of magnitude, the force (whether attractive or repulsive) is at a maximum when the distance of separation r is a minimum, that is, when the two ions are in contact and r equals the sum of the two ionic radii. For example, for a sodium and a chloride ion in contact, r will be 0.276 nm, and the binding energy will be... 

FIGURE 5.28 An example of foree versus distanee between a siliea probe and a membrane surface. (The attractive forces are negative and the magnitude of the maximum attractive force reached on the retraet eurve [-.-] gives the adhesion value.)... 

The van der Waals force is often modeled with the Lennard-Jones function or by an inverse power relation.The former is based on the two fitting parameters Uij and Cij, representing, respectively, the maximum attraction distance and the strength of the interaction.For ions of different species, the Lennard-Jones parameters are typically calculated by combining the values of the individual species ... 

In huntid systems (with a relative humidity of >60%), capillary condensation of the fluid in the gap between the particles in close contact may take place resulting in an attraction. The maximum attraction is achieved for two smooth spherical particles if the liquid covers the particle surfaces completely. For this case, the liquid bridge attraction force, can be calculated as follows [6] ... 

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