Repulsion between molecules

For the ideal gas, we know that attractions and repulsions between molecules... 

CO/Rh(100) shows a very strong repulsion for CO molecules at nearest-neighbor positions and much weaker repulsion between molecules farther apart. The occurrence of different lateral interactions is typical for real systems and leads to complicated order-disorder phenomena, especially if there are different types of adsorbates. Thermal motion of the adsorbates may overcome some lateral interactions but not others. The phase diagram can be quite complex even if there is only one type of adsorbate, and the effect on the kinetics can be profound. 

The last entry in Table 10.1 is the least well defined of those listed. This is of little importance to us, however, since our interest is in attraction, and the final entry in Table 10.1 always corresponds to repulsion. The reader may recall that so-called hard-sphere models for molecules involve a potential energy of repulsion that sets in and rises vertically when the distance of closest approach of the centers equals the diameter of the spheres. A more realistic potential energy function would have a finite (though steep) slope. An inverse power law with an exponent in the range 9 to 15 meets this requirement. For reasons of mathematical convenience, an inverse 12th-power dependence on the separation is frequently postulated for the repulsion between molecules. 

Intermolecular forces are the forces of attraction and repulsion between molecules. These forces change as the distance between molecules changes. The attractive force increases as the distance between the molecules decreases until the molecules get so close together that their electronic fields overlap. Any further decrease of the distance between the molecules will cause a repulsive force between them. This repulsive force will increase as the molecules are forced closer together. 

Intermolecular forces are the attractions and repulsions between molecules. All molecules attract one another when they are a few molecular diameters apart. However, they repel one another as soon as their electron clouds come into contact. Figure 4.29 shows how the potential energy of a molecule varies with its distance from a second molecule. At moderate separations, its potential energy is lower than when it is infinitely far away attractions always lower the potential energy of an object. As the molecules come into contact, the potential energy starts to rise, because repulsions always increase the potential energy of an object. 

How do we know there are attractions and repulsions between molecules First, gases condense to liquids when cooled or compressed, so their molecules must attract one another. Second, liquids are very difficult to compress, so there must be powerful forces opposing molecules being squashed together into a tiny volume. 

The repulsion between molecules having oily or aqueous properties is the basis for membrane construction. The lipids found in membranes are mostly based on glyceryl phosphate and normally contain three different side chains—one saturated, one unsaturated, and one very polar. 

But just as an underestimation of such problems could cause a chemical engineer s career to falter, so would an overestimation that caused unnecessary expenditure. Therefore, the chemical engineer must also be aware that an estimate, such as the one given above, is based on the assumption that each molecule of gas occupies a volume as though it were all alone in the world. In actuality, there are attractions and repulsions between the molecules. The attractions between molecules are why gases can be made to condense to liquids. The repulsions between molecules are what make materials more and more difficult to compact as the volume becomes smaller and smaller. These attractions and repulsions, collectively called the intermolecular forces, have to be taken into account by the chemical engineer. These intermolecular forces are also the basis for many other intriguing observed properties of materials, which is what we explore next. 

The quantitative comparisons with the available experimental data are less favorable in this case. The transition state and product in water appear to be shifted up in energy by about 15 kcal/mol. The computed curves are more in line with experimental data for ketones, where formation of hydrates is far less favorable than for formaldehyde. The discrepancy likely comes from an overly exothermic hydration energy for the charge-localized hydroxide ion, which lowers the reactant end of the pmfs. This results from the use of two-body potential functions, that is, the TIP4P water molecules are not polarized by the ion, so water-water repulsions between molecules in the first solvent shell are underestimated. Until the polarization can be explicitly treated, ions that have attractive interactions with single water molecules greater than about 18-20 kcal/mol should probably be avoided. For example, CN would be less problematic since its single molecule hydration enthalpy is only 14 kcal/mol, versus 25 for... 

The forces of attraction and repulsion between molecules must be considered for a more accurate and rigorous representation of the gas flow. Chapman and Enskog proposed a well-known theory in which they use a distribution function, the Boltzmann equation, instead of the mean free path. Using this approach, for a pair of non-polar molecules, an intermolecular potential, V (r), is given in the potential function proposed by the Lennard-Jones potential ... 

Fig. 11-25. 7T5m (k) isoterms in the presence of attraction and repulsion between molecules in adsorption layer... 

The theory describing diffusion in binary gas mixtures at low to moderate pressures has been well developed. Modem versions of the kinetic theory of gases have attempted to account for the forces of attraction and repulsion between molecules. Hirschfelder et al. (1949), using the Lennard-Jones potential to evaluate the influence of intermolecular forces, presented an equation for the diffusion coefficient for gas pairs of nonpolar, nonreacting molecules ... 

Most of the exothermic ion—molecular reactions have no activation energy (Talrose, 1952). Quantum-mechanical repulsion between molecules, which provides the activation barrier even in the exothermic reactions of nentrals, can be suppressed by the charge-dipole attraction in the case of ion-molecular reactions. Thus, rate coefficients of the reactions are very high and often correspond to the Langevin relations (2 8)-(2-50), sometimes partially hmitedby quantum-mechanical factors (Su Bowers, 1975 Virin et al., 1978). The efiect obviously can be apphed to both positive and negative ions. 

The general mean-field results, presented in this section, enable us to clarify this problem. It should be noted that Straley s theory was developed for a system of rigid rods and thus it takes into consideration only a short-range steric repulsion between molecules. On the other hand, in the theory of Helfrich and Petrov and Derzhanski the flexocoefficients are expressed in terms of Frank elastic constants, which, in turn, are determined by both the intermolecular attraction and repulsion. The relation between the two contributions can be clarified using Eqs (1.31) and (1.32), which can be used to obtain the following estimate of the flexoelectric coefficients ... 

A more accurate and rigorous treatment must consider the intermolecular forces of attraction and repulsion between molecules and also the different sizes of molecules A and B. Chapman and Enskog (H3) solved the Boltzmann equation, which does not utilize the mean free path X but uses a distribution function. To solve the equation, a relation between the attractive and repulsive forces between a given pair of molecules must be used. For a pair of nonpolar molecules a reasonable approximation to the forces is the Lennard-Jones function. 

Adsorption Surface phenomenon based on electrostatic attraction and repulsion between molecules, useful in separating pollutants from water prior to discharge into a stream, lake, or sea. 

Unfortunately there is as yet no known way to obtain the repulsion energy from properties of the separate molecules. An attempt has been made to characterise the repulsive surface of a molecule by performing IMPT calculations between the molecule and a suitable test particle, such as a helium atom. Because the helium atom has only one molecular orbital and is spherically symmetrical, such calculations can be done much more easily than calculations involving two ordinary molecules. From the data for the repulsion between molecule A and the test particle, and between B and the test particle, it may be possible to construct a repulsive potential between A and B. Some limited progress has been made with this idea. An alternative approach has been based on the suggestion that the repulsion energy is closely correlated with the overlap between the molecular wavefunctions, but this seems likely to be more useful as a guide to the form of analytic models than as a direct route to accurate potential functions. 

Gavezzotti developed a method for calculating lattice energy by integrating over the molecular electron density in the crystal. The molecular electron density is typically taken from a molecular quantum mechanical calculation, although it is not restricted in this way as the density could come from solid state calculations too. The Coulomb interaction between the molecules is calculated by a numerical integration over the tabulated electron densities. The repulsion between molecules is calculated from the overlap between... 

We can estimate the repulsion between molecules using the general exponential decay seen in the atomic orbitals (Table 3.2) and a rough application of Hartree theory (Eq. 4.26) ... 

The osmotic second virial coefficient represents an experimentally accessible thermodynamic parameter to evaluate colloidal stability. This parameter reflects the overall attraction or repulsion between molecules such that a positive value represents net repulsion and vice versa. measurements have been used extensively in the field of protein crystallization to screen for solution conditions favorable to crystallization. In contrast, good pharmaceutical stability seeks strong protein-solvent interactions (positive 22 values) representing conditions under which protein molecules should be less likely to associate. Measurements of 22 h ve proven helpful in developing formulation conditions to minimize aggregation. However, in cases where aggregation proceeds via the formation of a small fraction of a partially unfolded species, the B measurement is not likely to adequately reflect the aggregation propensity of the system [14]. 

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