Debye model criticisms

The Debye model, first proposed by ADELMAN and DOLL [3.11] in a different context, is useful since it makes connection with the lattice Debye temperature. Equation (3.39) again suggests a "corresponding states" form for involving the ratios nig/ms, results for the energy transfer and critical... 

The dielectric spectroscopy of anisotropic fluids started in the 1970s by the extension of the Debye model from isotropic media (described in Appendix D) to uniaxial systems based on statistical mechanical Kubo formalism/ but no quantitative estimates about the critical frequencies or the susceptibilities were obtained. Quantitative estimates were given first on molecules with dipole moments along the long axis/ then for general dipole directions using the rotational Brownian picture in Maier-Saupe mean-field potential. This theory was subsequently refined in the 1990s.i ... 

Fig,2.11. Dispersion and densities of states for the acoustic and optic modes of the linear NaCl crystal, a) Qualitative behaviour for nearest-neighbour interactions note the Van Hove singularities at the critical points w, o) and a)j . b) Einstein model, c) Debye model, d) Hybride Einstein-Debey model... 

The SPC/E model approximates many-body effects m liquid water and corresponds to a molecular dipole moment of 2.35 Debye (D) compared to the actual dipole moment of 1.85 D for an isolated water molecule. The model reproduces the diflfiision coefficient and themiodynamics properties at ambient temperatures to within a few per cent, and the critical parameters (see below) are predicted to within 15%. The same model potential has been extended to include the interactions between ions and water by fitting the parameters to the hydration energies of small ion-water clusters. The parameters for the ion-water and water-water interactions in the SPC/E model are given in table A2.3.2. 

The theory of Debye and Hiickel has survived much criticism since the appearance of their celebrated paper (I). This is no doubt because of the simplicity and essential correctness of the limiting laws (2,3,4). Nevertheless, many modifications of their treatment have failed to provide a convincing picture of the interionic effects and structure in the concentration range of practical importance (5, 6). The work presented here was stimulated by the difficulties of extrapolation encountered in a mixed-solvent emf study (7), and contradicts current trends suggesting that the inadequacy of the DH theory for all but very dilute solutions springs solely from the crudity of the original model. The authors propose a more realistic model that allows the ions to be polarizable and leads to markedly different results. 

Figure 10. Degree of dissociation a of the RPM as a function of the total ion density along the critical isotherms of Debye-Httckel-Ebeling (or Bjerrum) theory (DHEb), Fisher-Levin theory (FL), and Weiss-Schroer theory (WS) [138]. The asterisks show the critical points of the three models.

As a second example, we consider liquid fluoromethane CH3F, which is a typical strongly absorbing nonassociated liquid. For our study we choose the temperature T 133 K near the triple point, which is equal to 131 K. The relevant experimental data [43] were summarized in Table IV. As we see in Table VIII, which presents the fitted parameters of the model, the angle p is rather small. At this temperature the density p of the liquid, the maximum dielectric loss and the Debye relaxation time rD are substantially larger than they would be, for example, near the critical temperature (at 293 K). At such small (5 the theory given here for the hat-curved model holds. For calculation of the complex permittivity s (v) and absorption a(v), we use the same formulas as for water. 

Table 5 Comparison of the critical radius Rc (in au), n (/cm3) and critical pressure Pc (in atm) between the results obtained by using a Debye-Huckel model and an Ion-Sphere (IS) model. Reprinted with permission from [203] Copyright 2006, John Wiley Sons, Inc.

Changes in moisture content affect charged species in foods that are not part of the chemical equation, but that may impart their own effects upon reaction rate. Reactions that involve proton and electron transport, which include hydrolysis, Maillard browning, oxidation, and almost every critical shelf-life-limiting reaction in foods, will be affected by the presence of ions. This is part of the theory behind the Debye-Hiickel equation. This model describes the effect of ionic strength on the reaction rate constant in dilute solutions ... 

Debye-Hiickel theory that has not been criticized. From this perspective, electrolyte models are simply the best tools available to assess whether the dependence of electron transfer rate constants on ionic strength is sufficiently well behaved to justify use of the Marcus model. For this, and despite their shortcomings, they are indispensable. 

The temperature dependence of the experimental data is usually characterized in terms of critical exponents (JOS) which characterize the deviations of the system from the simple van der Waals model of Debye ... 

The molecular structure of PFOA is indicated in fig. (1) and polymer chain dimensions were derived using both Zimm plots [fig. (la)] and also by fitting the data to a Debye random coil model [9], with good agreement between the two approaches. As the pressure is reduced, the solubility decreases and the PFOA falls out of solution at the critical, "neutron cloud point" (T = 65 300 bar), as indicated [fig. (lb)] by a zero intercept... 

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