Repulsion of molecules

The hydrodynamic repulsion of molecules in solution has already been discussed (see Chap. 8, Sect. 2.5) and is analysed in much more detail in Sect. 3 of this chapter. It appears to be a very significant complication, yet it can be analysed relatively straightforwardly. The basic effect arises when one molecule approaches another. Solvent molecules between these two molecules have to be squeezed out in a direction approximately perpendicular to the motion of the approaching molecules. Their approach (and similarly their separation) is impeded and the effective diffusion coefficient is less than that when the molecules are more widely separated. 

Turning to the detonation of condensed EM we note that in this case the study of the equation of state of a dense gas in which repulsion of molecules is more important than their thermal motion turned out to be non-trivial (see the fundamental work by L. D. Landau and K. P. Stanyukovich).29 Water-filled EM were studied by Yu. B. Khariton.30 At present A. N. Dremin is developing ideas on the specific influence of a shock wave on the kinetics of reaction in an EM.31 For gas-dispersion systems the structure of detonation waves has become the subject of numerous studies related to explosions of coal dust husks in grain elevators, gas suspensions of dust in wood processing, etc.32,33 34 5 Works on gas suspensions have also been published abroad.36,37 In gas suspensions we may expect that the reaction rate is determined by diffusion and depends weakly on the temperature. 

Forr, = 70, 100, 150, and 200 pm, the calculated coordination numbers obtained on such a basis are shown in Tables 2.21 and 2.22. Real values should be less, because of lateral repulsion of molecules. 

Single-Exchange A contribution to the exchange interaction (valence repulsion of molecules) non-additivity effect coming from the interaction of the Pauli deformation of the electron cloud due to two interacting molecules with the electric field created by the third molecule. 

Here total means that g(r) pertains to all the diffracting atoms. Application of x-ray diffraction results in the structure of liquid water, in terms of g(Ow-Ow, r), since only the oxygen atoms, but not the hydrogen atoms, diffract x-rays. This function resembles to some extent that of liquid argon, a non-structured liquid by aU accounts (Fisenko et al. 2008), as demonstrated by Marcus (1996). There is, thus, more in the notion of the structure of water than what is measurable by g(r), which is dominated by the strong repulsion of molecules that are too closely packed together. 

Adsorption in external nanospaces. Basically, there are three kinds of interactions in external nanospaces of solids or liquids — adsorption at surface elements, adsorption at line elements, and adsorption at point elements. All these processes present attraction or repulsion of molecules, ions, or particles, influenced by physical forces. Positive adsorption (attraction) is a reversible process and, in the case of noncondensed gasses, only monomolecular layer is adsorbed. This is happening probably because attraction forces over adsorbed molecules are negligible. 

If we would like to discuss a non-ideal dense gas of interacting hard spheres of a finite size, we should introduce a concept of excluded volume to take into account the repulsion of molecules at short intermolecular distances and write the energy of attraction between molecules at large distances. Then the partition function of type (6.48) will include two additional contributions and becomes quite cumbersome. Nevertheless it allows the discussion of the Van der Waals equation of state... 

As for the legitimacy of the principle of tension. Young relies simply on capillary phenomena being able to be attributed to mutual attractions of only the surface particles hquid surfaces must be made up of curves of the nature of the catenary, which are supposed to be the result of a uniform tension in a surface which resists the pressure of a fluid. Finahy he tries to show that one can hnd a cause of normal pressures and tractions only in the play of attractions and repulsions of molecules, and he leaves thus in doubt if the tension acmally exists, or if, by normal forces, the things occur as under the influence from a tension. 

Section 1 10 The shapes of molecules can often be predicted on the basis of valence shell electron pair repulsions A tetrahedral arrangement gives the max imum separation of four electron pairs (left) a trigonal planar arrange ment is best for three electron pairs (center) and a linear arrangement for two electron pairs (right)... 

Many problems with MNDO involve cases where the NDO approximation electron-electron repulsion is most important. AMI is an improvement over MNDO, even though it uses the same basic approximation. It is generally the most accurate semi-empirical method in HyperChem and is the method of choice for most problems. Altering part of the theoretical framework (the function describing repulsion between atomic cores) and assigning new parameters improves the performance of AMI. It deals with hydrogen bonds properly, produces accurate predictions of activation barriers for many reactions, and predicts heats of formation of molecules with an error that is about 40 percent smaller than with MNDO. 

The collision diameter is at the value of s(r) equal to zero, and die maximum interaction of the molecules is where s(r) is a minimum. The interaction of molecules is thus a balance between a rapidly-varying repulsive interaction at small internuclear distances, and a more slowly varying attractive interaction as a function of r (Figure 3.7). 

Several years ago Makino et al. 86) studied the influence of anions on the conformation of poly-[L-methionine-S-methylsulfonium] salts in solution. They found that especially perchlorate will induce a-helix formation whereas Cl- and Br do not. Since then several authors 87 92) have found a similar a-helix inducing effect in the case of poly-L-lysine (Lys) and other BPAA at low pH-values where the polymer molecules usually attain an extended conformation due to the electrostatic repulsion of the ammonium groups. Therefore, the a-helix inducing effect is obviously an... 

Although it is rather certain that electrostatic interactions of polar groups, steric hindrance, and partial double bond character due to conjugation will all be of importance in selected molecules, the explanation of the barrier in ethane probably requires something else. Though far from being proven and certainly not now useful for prediction, the idea that the ethane barrier arises from repulsion of C—H bond orbitals on the carbons, due to their being more concentrated than sp hybrids, seems the most plausible picture available. 

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