Associated perturbed anisotropic

The Associated-Perturbed-Anisotropic-Chain-Theory and the Gradient Theory... 

In this section, we present the results that have been obtained by the implementation of the Associated-Perturbed-Anisotropic-Chain-Theoiy (APACT) into the gradient theory of van der Waals. Not all details and equations of the APACT will be shown, because they are described in detail elsewhere [19,20,21]. 

In the present section we treat the interfaces of mixtures in which there may be one or more associating component(s). For this purpose, the gradient theory is combined with the Associating Perturbed Anisotropic Chain Theory (APACT) which takes into account the possibility of association. In this section only association due to hydogen bonding is considered. The results are also compared with the results obtained with the gradient theory combined with the PR equation of state. 

As was pointed out earlier, the gradient theory can be linked easily to a semi-empirical equation of state. The equations of state applied in this study are the Peng-Robinson equation of state and the Associated-Perturbed-Anisotropic-Chain-Theory (APACT). The only effect on the interfacial tensions of pure fluids that is strongly influenced by the selected equation of state is the behavioitr in the near-critical region, since other differences are completely annulled by the fitting procerdure that is applied for the influence parameter. 

Ikonomou, G.D., and Donohue, M.D. (1986) Thermodynamics of hydrogen-bonded molecules the associated perturbed anisotropic chain theory, AJChEJ. 32, 1716-1725. 

The first models used to describe hydrogen bonding fluids were developed using a chemical approach, where each associated cluster is treated as a distinct species created from the reaction of monomers and smaller associated clusters [8,9]. The reactions are governed by equilibrium constants that must be obtained empirically. This type of approach has been incorporated into various equations of state including a van-der-Waals-type equation of state [10], the perturbed anisotropic chain theory equation of state (APACT) [11], and the Sanchez-Lacombe [12] equation of state. 

One possibility for this was demonstrated in Chapter 3. If impact theory is still valid in a moderately dense fluid where non-model stochastic perturbation theory has been already found applicable, then evidently the continuation of the theory to liquid densities is justified. This simplest opportunity of unified description of nitrogen isotropic Q-branch from rarefied gas to liquid is validated due to the small enough frequency scale of rotation-vibration interaction. The frequency scales corresponding to IR and anisotropic Raman spectra are much larger. So the common applicability region for perturbation and impact theories hardly exists. The analysis of numerous experimental data proves that in simple (non-associated) systems there are three different scenarios of linear rotator spectral transformation. The IR spectrum in rarefied gas is a P-R doublet with either resolved or unresolved rotational structure. In the process of condensation the following may happen. 

The solutions to the anisotropic diffusion equation can be written as a series expansion, each term of which can be associated with a particular relaxation time. For a harmonic perturbation of the rotational distribution function, as occurs in a dielectric relaxation experiment with an ac electric field, it was found that a single relaxation time was sufficient to describe the relaxation of p, and this could be expressed in terms of the relaxation time Xq) for in the absence of a nematic potential by ... 

Mz is the quantum number associated with this perturbation. If, on the other hand, the Zeeman interaction is anisotropic, the Hamiltonian in Equation 1.35 should be rewritten as... 

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