Free energy of interaction

To obtain isolated polymer chains, a solvent must be present. The solvent might be selectively excluded or imbibed by the coil, depending on the free energy of interaction, and thereby perturb the coil dimensions. 

The Debye-Hiickel formula for the activity coefficient of an ion was developed by a consideration of ion atmosphere effects.10 It starts with an electrostatic expression for the free energy of interaction for one ion with one mole of others ... 

In a poor solvent, where both ki and Ki/rpi generally are positive, also will be positive. At the temperature T = , the chemical potential due to segment-solvent interactions is zero according to Eq. (430- Hence the temperature is that at which the excess chemical potential is zero and deviations from ideality vanish. The free energy of interaction of the segments within a volume element is therefore zero also. 

Binodials calculated by Tompa are shown in Fig. 123,a for the special case of a nonsolvent [l], a solvent [2], and a polymer [3] with Vi = V2, X23 = 0, and xi2 = Xi3 = 1.5. Otherwise stated, the nonsolvent-solvent and the nonsolvent-polymer segment free energies of interaction are taken to be equal, while that for the solvent and polymer is assumed to be zero. It is permissible, then, to take Xi = X2 = l and o 3 = V3/vi. The number of parameters is thus reduced for this special case from five to two. Binodial curves are shown in Fig. 123,a for 0 3 = 10, 100, and 00 tie lines are shown for the intermediate curve only. The critical points for each curve, shown by circles, represent the points at which the tie lines vanish, i.e., where the compositions of the two phases in equilibrium become identical. 

The physical reason for the inherent lack of incentive for mixing in a polymer-polymer system is related to that already cited in explanation of the dissymmetry of the phase diagram for a polymer-solvent binary system. The entropy to be gained by intermixing of the polymer molecules is very small owing to the small numbers of molecules involved. Hence an almost trivial positive free energy of interaction suffices to counteract this small entropy of mixing. 

Surface area around a molecule where optimum free energy of interactions of acceptor atoms with H-bond donor probe is realized [38, 39[... 

Surface area around a molecule where optimum enthalpy of interactions of donor atoms with H-bond acceptor probe is realized [38, 39[ Surface area around a molecule where optimum free energy of interactions of donor atoms with H-bond acceptor probe is realized [38, 39[ Sum of enthalpy values (kcalmof interactions between the acceptor atoms in a molecule and donor probe on OEASA [38, 39[ Sum of enthalpy values (kcalmof interactions between the donor atoms in a molecule and an acceptor probe on OEDSA [38, 39[... 

The affinity of the designed drug molecule for its site is governed by the free energy of interaction AG. AG can be determined experimentally from the equation... 

Since it has been shown that nonideal mixing occurs in the 2.5-15.0 dyn cm 1 range, the excess free energies of interaction were calculated for compressions of each pure component and their mixtures to each of these surface pressures. In addition, these surface pressures are below the ESPs and/or monolayer stability limits so that dynamic processes arising from reorganization, relaxation, or film loss do not contribute significantly to the work of compression. 

Figure 25. The free energy of interaction between two DMPC membranes at various degrees of surface tension as indicated. We note that the indicated surface tension is the tension at large membrane-membrane spacing. The salt bulk volume fraction was cps — 0.002. Redrawn from [85] by permission of the American Chemical Society...

It will be assumed that the free energy of interaction can be expanded as a sum of component potentials... 

Q is the value of Qe when the free energy of interaction between the N2 defects is zero,... 

The problem at hand is the evaluation of the activity coefficient defined in Eq. (76). It will be assumed that only pairwise interactions between the defects need be considered at the low defect concentrations we have in mind. (The theory can be extended to include non-pairwise forces.23) Then the cluster function R(n) previously defined in Eq. (78) is the sum of all multiply connected diagrams, in which each bond represents an /-function, which can be drawn among the set of n vertices, the /-function being defined by Eqs. (66), (56), and (43). The Helmholtz free energy of interaction of two defects appearing in this definition can be written as... 

Minton and Sarof (1974) defined a new quantity, also referred to as the average Gibbs free energy of interaction, by the integral... 

Sab She- Although Ackers et al. provided some reasons why the interaction energies should conform to these assumptions, these are not sufficient for the free energies of interactions (see also the next subsection). Table 5.2 is almost a reproduction of Table I from Senear et aZ. (1986). It is clear from the column headed Operator configuration and footnote a to Table 5.2 that the symbol o denotes... 

On the other hand, if one adopts the molecular approach a great deal can be learned about the dependence of the binding constants and free energies of interaction on the molecular properties of the system—as we have done in this and the previous chapters. 

We stress, however, that these two properties of the free energy of interaction are valid only in very special cases. We have shown in Sections 5.4-5.7, that, in general, the interaction free energies do not conform to this behavior there could be long-range correlations, i.e., [or g(a, c)], that differ from unity, and triplet correlations that differ from the product g(a, b)g(b, c). [There is no known example where the triplet correlation may be written as a sum of pair correlations g a, b) + gib, c), as assumed by Ackers et ai]... 

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