Specific interaction energy

A selection of polar liquids is required for a systematic study of the surface chemistry. In the early work of Zettlemoyer and Chessick (1974), liquids of different dipole moment were used with the aim of obtaining a linear relation between the energy of immersion and the specific interaction of the dipole and the surface electrostatic field. Differences in the non-specific interaction energies were minimized by maintaining a constant hydrocarbon moiety (e.g. by comparing the energies of immersion of n-butylamine and n-butanol). 

Table I. Heat of Adsorption, Q, and Contribution of the Specific Interaction Energy, AQgpecific for NaX Zeolite, Kcal/Mole...

Jahne et al. (1987) also investigated isotopic specific diffusion coefficients for He and the change in 5C (C02) during diffusive gas loss from water. The increase in He diffusivity for the He compared to Tie was in agreement with the ratio of the square-root of their masses. This result provides further supporting evidence that the diffusion coefficients for individual isotopic noble gas species can reasonably be determined as a function of mass from Table 5 for variable temperatures. This is in contrast with the results for the study of 5C (C02), which showed a fractionation factor far lower than the value predicted from the square root of the reduced mass. This discrepancy indicates that in the case of active gases the difference is not just an effect of mass but of the isotope specific interaction energy with the water molecules. 

TABLE 2.6. Heats of Adsorption and Specific Interaction Energies (kcal/mole) for Sorption of Various Species on NaX Zeolite... 

Anion Adsorption, Tx 10 °mol/sm Work of adsorption, kJ/mol Specific interaction energy ... 

One can evaluate f, k, and analytically for the simple shape of the specific interaction energy profile. For example, in the case when energy distributions around the primary minimum and the barrier region can be approximated by a parabolic distribution, these constants are given by [115]... 

The specific interaction energies eaiPj in Eqs. 44a-44c are the adjustable parameters of the theory, but, as shown below for the PS-b-PnAMA systems, not aU are independent. The factor C in Eq. 43 again ensures that x is normalized as a traditional monomer-monomer interaction parameter. Equations 43 and 44 can readily be extended to systems in which one component is a copolymer, and the details are given in [ 114],... 

The idea that unsymmetrical molecules will orient at an interface is now so well accepted that it hardly needs to be argued, but it is of interest to outline some of the history of the concept. Hardy [74] and Harkins [75] devoted a good deal of attention to the idea of force fields around molecules, more or less intense depending on the polarity and specific details of the structure. Orientation was treated in terms of a principle of least abrupt change in force fields, that is, that molecules should be oriented at an interface so as to provide the most gradual transition from one phase to the other. If we read interaction energy instead of force field, the principle could be reworded on the very reasonable basis that molecules will be oriented so that their mutual interaction energy will be a maximum. 

Mark, A. E., van Gunsteren, W. F. Decomposition of the free energy of a system in terms of specific interactions. Implications for theoretical and experimental studies. J. Mol. Biol. 240 (1994) 167-176... 

The Tersoff potential was designed specifically for the group 14 elements and extends the basic empirical bond-order model by including an angular term. The interaction energy between two atoms i and j using this potential is ... 

Boresch S and M Karplus 1995. The Meaning of Component Analysis Decomposition of the Free Energy in Terms of Specific Interactions. Journal of Molecular Biology 254 801-807. 

A second way of dealing with the relationship between aj and the experimental concentration requires the use of a statistical model. We assume that the system consists of Nj molecules of type 1 and N2 molecules of type 2. In addition, it is assumed that the molecules, while distinguishable, are identical to one another in size and interaction energy. That is, we can replace a molecule of type 1 in the mixture by one of type 2 and both AV and AH are zero for the process. Now we consider the placement of these molecules in the Nj + N2 = N sites of a three-dimensional lattice. The total number of arrangements of the N molecules is given by N , but since interchanging any of the I s or 2 s makes no difference, we divide by the number of ways of doing the latter—Ni and N2 , respectively—to obtain the total number of different ways the system can come about. This is called the thermodynamic probabilty 2 of the system, and we saw in Sec. 3.3 that 2 is the basis for the statistical calculation of entropy. For this specific model... 

The equations we have written until now in this section impose no restrictions on the species they describe or on the origin of the interaction energy. Volume and entropy effects associated with reaction (8.A) will be less if x is not too large. Aside from this consideration, any of the intermolecular forces listed above could be responsible for the specific value of x- The relationships for ASj in the last section are based on a specific model and are subject to whatever limitations that imposes. There is nothing in the formalism for AH that we have developed until now that is obviously inapplicable to certain specific systems. In the next section we shall introduce another approximation... 

Activated diffusion of the adsorbate is of interest in many cases. As the size of the diffusing molecule approaches that of the zeohte channels, the interaction energy becomes increasingly important. If the aperture is small relative to the molecular size, then the repulsive interaction is dominant and the diffusing species needs a specific activation energy to pass through the aperture. Similar shape-selective effects are shown in both catalysis and ion exchange, two important appHcations of these materials (21). 

Because of the high cohesive energy density and their crystalline state the polymers are soluble only in a few liquids of similar high solubility parameter and which are capable of specific interaction with the polymers. 

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