Pair interaction enthalpy

A useful measure for the interactions in the system is the pair interaction enthalpy /igj, defined as ... 

Freund and Knobel (62) have found that in addition to F-OH-F complexes, F-OH pair interactions are important. Therefore, a mixed type regular and subregular model of the solid solutions should be more appropriate. To a first approximation, the enthalpy of mixing should then have the form ... 

With a ternary system of type biopolymer/ + biopolymey + solvent, in order to characterize all the different pair interactions, the following heat effects, Q, should be measured in flow mode (Semenova et al., 1991) (i) biopolymer, solution diluted by pure buffer, Q (ii) biopolymey solution diluted by pure buffer, Qp and (iii) mixed (biopolymer, + biopolymey) solution diluted by pure buffer, Qijh. The specific enthalpy of interaction between biopolymer, and biopolymey can then be obtained from... 

From model calculations it became clear that the formation enthalpy of cross-links formed in the solution is of the order of 3 kj/mol only and the conclusion is that pair and pair interactions between two discs only, form the cross-links. 

The heats of vaporization are measures of the work that must be done to overcome interatomic attractive forces. Since there are no ordinary electron-pair interactions between noble gas atoms, these weak forces (of the van der Waals or London type) are proportional to the polarizability and inversely proportional to the ionization enthalpies of the atoms they increase therefore as the size and diffuseness of the electron clouds increase. 

For physical adsorption of apolar molecules this is probably not a bad approximation. The usual picture is that the adsorbate molecules are piled on top of each other, but the model is somewhat less restrictive. The pile does not have to be straight. In fact, the adsorbate-adsorbate enthalpy is commonly identified as the heat of condensation, which does not correspond to a pair interaction but interaction with more molecules. With this interpretation in mind, tlie necessity of piling molecules on top of each other disappears (molecules can even bridge neighboring sites) but at the expense of losing the connection with the premises of the theory (no lateral interaction) and the rigorous notion of adsorbate-adsorbate pair with the premises of the theory (no lateral interaction). At any rate, mathematically the assumption implies that if we denote the molecular partition functions of molecules in contact with the surface by Qj, those in layer 2, 3,. .. are all Identical, say Q2. Hence q(l) = qj, q[2] = q q. q 3) = q q, ... etc. Substitution in [1.5.38] yields... 

Yanson et al. [41] using field-ionization mass spectrometry studied the formation of gas-phase GC, CC, AT and TT pairs. From measurements of temperature dependence of equilibrium constants, an interaction enthalpy for the base pair formation was derived. This technique was sometimes questioned because the determination of enthalpy from the slopes of appropriate van t Hoff curves might not be unambiguous. From Table 6 it is evident that the agreement with the present theoretical values is good, and concerns not only the relative interaction enthalpies but even the absolute values the average absolute error is less than 1.5 kcal/mol. 

It seems likely, therefore, that although the major cause of enthalpy strain observed in the alkaline hydrolysis of sultones arises from angle strain, other factors such as 1,3-lone-pair-lone-pair interactions and possibly conjugative effects also contribute to destabilisation of the five-membered ring. 

In ideal solutions it is assumed for the pair interactions that no energy is released on replacing a unit of group 1 by a unit of group 2, that is, Ae in Equation (6-11) equals zero. Consequently, the enthalpy of mixing of an ideal solution is also equal to zero. 

The interaction of adsorbents with various surface energies with the liquid components studied are adequately characterized by the differences in molar adsorption enthalpies between components 1 and 2, h - (l/r )ft, listed in Table 1. In the case of the adsorption of the methanol-benzene liquid pair, these enthalpy differences in the adsorption layer are decreased by the effect of hydropho-bization. 

Comparing Equation (14.9) with Equation (14.23) show s that the vaporization enthalpy is related to the lattice model pair interaction energy waa through... 

Other electrolytes featured in studies of cosolvents in aqueous solutions, for example Bu NBr with a number of cosolvents as reported by Korolev, Kustov, and coworkeis [19,20] are also shown in Table 6.3. Enthalpic pair interaction parameters for CaCl with MeOH, EtOH, and n-PrOh were reported in Ref. 24 and for NaNOj, KNO3, CaCNOj), and La(N03>3 with MeOH in Ref. 25 by Taniewska-Osinska and coworkers. Many other studies concerned electrolyte interactions with cosolvents in water without reporting pair interaction parameters. Examples are the enthalpy of solvation of NaNO, KSCN, and NH BF in aqueous methanol reported by Manin and Korolev [26] and of NH Br and NH BF in aqueous HMPT reported by Kustov [27], but such studies are too numerous to be presented here. 

If we consider studies of nucleic acids and their components, there is currently only one reliable gas phase experiment (mass-field spectroscopy) on the energetics of nucleic acid base pairs [7a]. This experiment provides interaction enthalpies of several base pairs at rather high temperatures of 350-400K. The experimental technique does not allow for the determination of the geometry of complexes, and it is even not possible to distinguish between H-bonded and stacked structures. Recent state-of-the art theoretical analysis of gas phase thermodynamics of uracil dimer indicates that this pair exists as a mixture of several H-bonded and stacked structures [8]. Furthermore, their relative populations could vary depending on experimental conditions. It is likely that... 

This interaction actually involves both covalent (homopolar) and ionic (heteropolar) factors. Thus, Drago et al. introduced four parameters for the prediction of the enthalpies of the acid-base interactions. For an A-B pair, the enthalpy or molar energy of the adduct formation can be expressed by the following empirical relation ... 

Fm is the metal molar volume, which accounts for the steric effects at the interface, and C is a constant fitted to experimental values. This model takes care of the metal-oxygen and the metal-cation pair interactions through the quantities AHq(M) and AH y Neglecting the entropy variations, a partial mixing enthalpy AH Q may be written as a function of the AA, BB and AB pair interactions eAA. and 6ab and as a function of the mean coordination number Z of an atom A dissolved in B, in the following way ... 

Fig. 10. Enthalpy-entropy compensation plot of several enantiomer pairs interacting with -CD. Reproduced with permission from Ref. [30]. Copyright 2005, Am. Chem. Soc.

The geometrical variations reflect the steric strain caused by axial lone-pair interaction. Structural parameters of the other conformers are listed in the original paper. Twenty out of the expected 30 harmonic vibrational frequencies of the favored conformer are also given. The exothermal decomposition c-NgHa- S N2+3 H2 has an enthalpy of —696 kJ/mol [2]. 

V (the potential) is identified with the enthalpy, i.e. the number n of base pairings (contacts), and T corresponds to the entropy. At each stage in the folding process, as many as possible new favourable intramolecular interactions are fonned, while minimizing the loss of confonnational freedom (the principle of sequential minimization of entropy loss, SMEL). The entropy loss associated with loop closure is (and the rate of loop closure exp... 

The chemistry of Lewis acid-base adducts (electron-pair donor-acceptor complexes) has stimulated the development of measures of the Lewis basicity of solvents. Jensen and Persson have reviewed these. Gutmann defined the donor number (DN) as the negative of the enthalpy change (in kcal moL ) for the interaction of an electron-pair donor with SbCls in a dilute solution in dichloroethane. DN has been widely used to correlate complexing data, but side reactions can lead to inaccurate DN values for some solvents. Maria and Gal measured the enthalpy change of this reaction... 

When equation (9) is applied to the transition state of the biphenyl system, it gives directly the isotopic difference in the activation enthalpy per interacting pair of atoms, provided we make the reasonable assumption that initial-state steric effects are independent of isotopic substitution in the 6- and 6 -positions. Since there are two pairs of interacting atoms in the coplanar transition state, the final expression is... 

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