Forces Coulomb

Furthermore, the actual Coulomb forces are also important. If the molecules have polar substituents or a permanent dipole moment, or if they are electrically charged in a heteropolar fashion, i.e. the crystals are salts, then the intermolecular interactions are naturally also determined by the static monopole, dipole, and Coulomb forces with their long range. This of course also influences the crystal structures 

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Debye-Hiickel theory The activity coefficient of an electrolyte depends markedly upon concentration. Jn dilute solutions, due to the Coulombic forces of attraction and repulsion, the ions tend to surround themselves with an atmosphere of oppositely charged ions. Debye and Hiickel showed that it was possible to explain the abnormal activity coefficients at least for very dilute solutions of electrolytes. 

The discrepancy is not large and the last term is zero for a system without net charge. Thus we see that the use of a shifted Coulomb force is equivalent to a tin-foil reaction field and almost equivalent to a tin-foil Born condition. 

In the context of molecular simulation, particularly biomolecular modelling, a critical aspect for numerical simulation is the presence of long-range Coulombic forces which render the force computations much more costly... 

The forces which bring about adsorption always include dispersion forces, which are attractive, together with short-range repulsive forces. In addition, there will be electrostatic (coulombic) forces if either the solid or the gas is polar in nature. Dispersion forces derive their name from the close connection between their origin and the cause of optical dispersion. First... 

RBS is based on collisions between atomic nuclei and derives its name from Lord Ernest Rutherford who first presented the concept of atoms having nuclei. When a sample is bombarded with a beam of high-energy particles, the vast majority of particles are implanted into the material and do not escape. This is because the diameter of an atomic nucleus is on the order of 10 A while the spacing between nuclei is on the order of 1 A. A small fraction of the incident particles do undergo a direct collision with a nucleus of one of the atoms in the upper few pm of the sample. This collision actually is due to the Coulombic force present between two nuclei in close proximity to each other, but can be modeled as an elastic collision using classical physics. 

The Orientation of Water Molecules Adjacent to an Ion. Order and Disorder in the Vicinity of Solute Particles. Coulomb Attraction and Repulsion between Ions. Activity Coefficients. The Distance of Closest Approach. Activity Coefficients of Various Solutes. Forces Superimposed on the Coulomb Forces. 

In Fig. 69 we have been considering a pair of solute particles in pure solvent. We shall postpone further discussion of this question until later. In the meantime we shall review the Coulomb forces in very dilute ionic solutions as they are treated in the Debye-Hiickel theory. 

Since we have reason to believe that the order-disorder situation in ionic co-spheres, overlapping and merging as in Fig. 69, could give rise to forces of attraction or repulsion, superimposed on the Coulomb forces, we may inquire whether the observed facts as to activity coefficients may be correlated with the known behavior of the ions as regards viscosity and entropy. 

Forces Superimposed on the Coulomb Forces. The discussion has been based on the idea that, superimposed on the electrostatic forces between a pair of ions, there are rather short-range forces of other origin, which may be attractive or repulsive. Consider now what the situation will be if these forces cause the mutual potential energy to fall at short distances, below the value — e2/er that is assumed in the Debye-Hlickel theory. In Fig. 74 let the broken curve be a plot of — e2/er, while the full curve gives the actual potential energy between a certain pair of... 

Now lei us turn to the problem of how the composition of a nucleus affects its stability. The forces that exist between the particles in the nucleus are very large. The most familiar of ihe intranuclear forces is the coulomb force of repulsion which the protons must exert on one another. In order to appreciate the magnitude of this repulsive force, let us compare the force between two protons when they are separated by 10 8 cm, as they are in the hydrogen molecule, with the force between two protons separated by 10-18 cm, as they are in a helium nucleus. In the first case we have... 

Copper (continued) properties, 400. 408 Core, of earth, 440 Corrosion, 405 Coulomb, 241 Coulombic forces, 416 Coulson, C A., 252 Covalent bonds, 274, 277, 288 elements that form solids using, 302... 

Conductivity curves (A versus c ) of salts in solvents of low-permittivity commonly show a weakly temperature-dependent minimum around 0.02 molL-1 followed by a strongly temperature-dependent maximum at about 1 mol L 1. According to Fuoss and Kraus [101,102] the increase of conductivity behind the minimum is due to the formation of new charge carriers from the ion pairs. They assume that coulombic forces suffice to form bilateral cationic [C+A-C+] and anionic [A C+A ] triple ions in solvents of low-permittivity ( <15) if the ions have approximately equal radii. 

In the derivation of the Boltzmann equation, it was noted that the distribution function must not change significantly in times of the order of a collision time, nor in distances of the order of the maximum range of the interparticle force. For the usual interatomic force laws (but not the Coulomb force, which is of importance in ionized gases), this distance is less than about 10 T cm the corresponding collision times, which are of the order of the force range divided by a characteristic particle velocity (of the order of 10 cm/sec for hydrogen at 300° C), is about 10 12 seconds. 

The inner layer (closest to the electrode), known as the inner Helmholtz plane (IHP), contains solvent molecules and specifically adsorbed ions (which are not hilly solvated). It is defined by the locus of points for the specifically adsorbed ions. The next layer, the outer Helmholtz plane (OHP), reflects the imaginary plane passing through the center of solvated ions at then closest approach to the surface. The solvated ions are nonspecifically adsorbed and are attracted to the surface by long-range coulombic forces. Both Helmholtz layers represent the compact layer. Such a compact layer of charges is strongly held by the electrode and can survive even when the electrode is pulled out of the solution. The Helmholtz model does not take into account the thermal motion of ions, which loosens them from the compact layer. 

The most frequent type of interaction between solid and species in solution would be electrostatic adsorption (ion exchange), due to the action of attractive coulomb forces between charged particles in solution and the solid surfaces. This process would also be concentration dependent. 

Neglecting for simplicity the long-range character of the Coulomb force, the above summations yield (31) a bounded result (x) when extended to infinity. Bielectron integrals can thus be regarded as scaling like Nq", either in the thermodynamic limit (Nq °°), or (31) in the dissociation limit (aQ °°). 

Electrical or Coulomb force results from the interactions between charged particles. For two charges and q2... 

The acidity of a bimacrocydic phenol [50] has also been measured and has been compared with analogues (Czech et al., 1988). Values of pK are given in Table 23. In the bimacrocydic phenol, no diversion from the expected pKa values could be found. The observed acidities were comparable to those of the analogues [1], [6] and [49], although a comparison is difficult due to the fact that, again, Coulomb forces probably play an important role. 

In the previous Sections, the properties of acids and bases in macrocycles and other concave structures have been compared. A number of factors have been recognized which influence the acidity or basicity of an acid or base (i) hydrogen bonds, (ii) hindered solvation (exclusion of solvent), (iii) formation of tight ion pairs (high microacidity but low overall acidity), and (iv) Coulomb forces when poly anions are formed. A fifth influence, (v) steric hindrance, still has to be discussed. 

The coulombic force is proportional to the square of the effective charge on the polyion, i.e. n], (The effective charge is equivalent to the number of free counterions, ,.) When the charge along the polyion, Q, is small the extensive forces involved are those of purely coulombic repulsion. 

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