Repulsive force definition

The molecules of liquids are separated by relatively small distances so the attractive forces between molecules tend to hold firm within a definite volume at fixed temperature. Molecular forces also result in tlie phenomenon of interfacial tension. The repulsive forces between molecules exert a sufficiently powerful influence that volume changes caused by pressure changes can be neglected i.e. liquids are incompressible. 

The effectiveness of these forces differs and, furthermore, they change to a different degree as a function of the interatomic distance. The last-mentioned repulsion force is by far the most effective at short distances, but its range is rather restricted at somewhat bigger distances the other forces dominate. At some definite interatomic distance attractive and repulsive forces are balanced. This equilibrium distance corresponds to the minimum in a graph in which the potential energy is plotted as a function of the atomic distance ( potential curve , cf. Fig. 5.1, p. 42). 

Here we present and discuss an example calculation to make some of the concepts discussed above more definite. We treat a model for methane (CH4) solute at infinite dilution in liquid under conventional conditions. This model would be of interest to conceptual issues of hydrophobic effects, and general hydration effects in molecular biosciences [1,9], but the specific calculation here serves only as an illustration of these methods. An important element of this method is that nothing depends restric-tively on the representation of the mechanical potential energy function. In contrast, the problem of methane dissolved in liquid water would typically be treated from the perspective of the van der Waals model of liquids, adopting a reference system characterized by the pairwise-additive repulsive forces between the methane and water molecules, and then correcting for methane-water molecule attractive interactions. In the present circumstance this should be satisfactory in fact. Nevertheless, the question frequently arises whether the attractive interactions substantially affect the statistical problems [60-62], and the present methods avoid such a limitation. 

See Atomic metallic ion emission Anomalous corrugation theory 31, 142 breakdown 146 graphite, and 31, 144 Apparent barrier height 63,171 anomalously low 171 attractive force, and 49, 209 definition 7 image force, and 72 repulsive force, and 171, 198, 209 square-barrier problem, in 63 Apparent radius of an atomic state 153 Atom charge superposition I 11 analytic form 111 Au(lll), in 138 in atomic beam scattering 111 Atom-beam diffraction 107 apparatus 109... 

Finally, the repulsive forces, that as you said play a large role in the definition of advantageous foldings, do also play a big role in the definition of crystalline structures of organic compounds and of inter-molecular vibration movements. It is very unfortunate that theoretical calculations of repulsive forces are much more difficult than those of attractive forces. 

Adding electrolyte will cause the film to thin by shortening the range of the repulsive force. At smaller distances of separation the van der Waals attraction is definitely increased and should be added (as force area 2) to the pressure before attempting this kind of calculation. Even without added electrolyte, the air masses attract each other neglecting this is another possible source of discrepancy between theory and experiment in this example. ... 

The uncertainties of these numbers ( 3 kcal) are so great that it is difficult to draw such a definite conclusion. For example, the electrostatic energy could be as large as 0 kcal and the delocalization as small as 5 kcal with the stated uncertainties. But the comments which I made in my paper about a possible cancellation of the delocalization and repulsion forces can be regarded (if we wish to do so) as evidence that the electrostatic term is physically the most dominant. 

To explain deviations from the ideal gas law, we must look for characteristics of real gas molecules that are ignored in the kinetic model. That model took the view that molecules are noninteracting, infinitesimal points. So, to improve the model, we need to see how interactions play a role and allow for molecules to have a definite size. Actually, these two features are related, because when we say that a molecule has a definite size, we mean that it exerts repulsive forces. When you touch an object, you feel its size and shape because your fingers cannot penetrate into it. That in turn is due to the repulsive forces its atoms exert on the atoms in your fingers. When you dip your finger into a liquid, your molecules repel the molecules of the liquid and push them aside. 

FIGURE 103 Electrostatic repulsion force, F/njAg T versus separation, h, between two identically charged plates with surface potentials of 25 mV in a 1 1 electrolyte solution at 0.001 Hf according to the exact theory with either constant charge or constant potential boundary conditions. Calculated from F = n Jk T (A - A ) with definitions of Aj given in the text for constant charge and potential boundary conditions. 

Isosurfaces of electron density are obtained from the probability density isosurfaces for molecules described in Chapter 6. These are surfaces in three-dimensional space that include all the points at which has a particular value. The value of electron density chosen to define the isosurface is selected by some definite, though arbitrary, criterion. There is broad acceptance of a standard density of 0.002 el ao), where is the Bohr radius. This value is thought to best represent the sizes and shapes of molecules because it corresponds to the van der Waals atomic radii discussed earlier in the context of repulsive forces. These are the same dimensions depicted in space-filling models of molecules. 

To understand perfume behaviour on these surfaces and/or matrices, we must consider the range of attractive or repulsive forces between the perfume components and the surface itself. The situation is complicated by the way in which perfume is delivered to the surface. For example, for a perfume ingredient in a soap bar to be substantive it must first be efficiently delivered to the skin during washing, it must then survive rinsing and, finally, it must be retained for some time on the skin. Definitions of substantivity and of retention vary, but here retention is used to indicate the affinity a perfume has for a substrate when delivered to it, whilst substantivity also includes delivery barriers. 

When the Hamaker constant is positive, it corresponds to attraction between molecules, and when it is negative, it corresponds to repulsion. By definition, 3 = 1 and n3 = 1 for a vacuum. As we know from McLachlan s equation (Equation (92)), the presence of a solvent medium (3) rather than a free space considerably reduces the magnitude of van der Waals interactions. However, the interaction between identical molecules in a solvent is always attractive due to the square factor in Equation (567). On the other hand, the interaction between two dissimilar molecules can be attractive or repulsive depending on dielectric constant and refractive index values. Repulsive van der Waals interactions occur when n is intermediate between nx and n2 in Equation (566). If two bodies interact across a vacuum (or practically in a gas such as air at low pressure), the van der Waals forces are also attractive. When repulsive forces are present within a liquid film on a surface, the thickness of the film increases, thus favoring its spread on the solid. However, if the attractive forces are present within this film, the thickness decreases and favors contraction as a liquid drop on the solid (see Chapter 9). 

Basically, the term refers to what we might call a balance of forces . In the case of mechanical equilibrium, this is its literal definition. A book sitting on a table top remains at rest because the downward force exerted by the earth s gravity acting on the book s mass (this is what is meant by the weight of the book) is exactly balanced by the repulsive force between... 

In the collision theory reactant species are represented as hard spheres with definite radii, similar to snooker balls. Thus, the theory abandons any attempt to take into account the chemical structure of reactants. Furthermore, all attractive forces between species are ignored and a very large repulsive force is assumed to exist between them when they collide that is, the hard spheres do not deform in any way. Figure 7.2 illustrates a typical collision. The assumptions are no doubt drastic but have the advantage that the mathematics becomes tractable. 

The connection between molecular mechanics and crystal structures came about in the attempt to quantify the non-bonded interactions. These were first taken oyer from intermolecular interaction potentials of rare-gas-type molecules. They start from the premise, contained in the van der Waals equation of state for real gases, that atoms are not localized at points, i.e. not at their respective nuclei. They occupy a volume of space and can be assigned, at least as a first step, more or less definite radii, by custom called van der Waals radii, which were initially estimated for many types of atom mainly from packing radii in crystals. Mutual approach of non-bonded atoms to distances less than the sum of these radii leads to strong repulsive forces. The empirical atom-atom potentials that were introduced to describe the balance between atom-atom attractions and repulsions were assumed to be characteristic of the atom types and independent of the molecules they are embedded in. They were assumed to hold equally for interactions between non-bonded atoms in... 

When two molecules approach each other, the electron clouds surrounding each molecule would be expected to interact and create a repulsive force tending to push them apart. This repulsive force would arise from simple coulombic repulsion of charges. However, because of the differences in shape and size of molecules, no definite theoretical treatment of this short-range repulsion force has been established. This repulsive interaction has been described by the following general formula ... 

It follows from the aforesaid that, when T > 0 (for definiteness, take systems with an UCST), the repulsion forces between chain-distant segments predominate over the attraction ones. 

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