Onsager Samaras

The image forces (Wagner-Onsager-Samaras theory). 67... 

The image forces (Wagner—Onsager—Samaras theory)... 

The Onsager-Samaras theory fails at electrolyte concentrations above approximately 0.2 M. One of the reasons is the assumption that the screening length X does not depend on the distance to the interface. In reality, the screening in the ion-depleted region near the surface is smaller than in the bulk. Only when X is large compared to the thickness of the depleted layer, the above approximation is accurate. Other reasons for the inaccuracy (additional interactions and surface charge) will be examined later in the paper. 

However, a few years after the Onsager-Samaras theory, experiments performed by Jones and Ray [33] indicated that the surface tension at the water/air interface is decreased by the addition of small amounts of KC1 and exhibits a minimum at approximately cE=0.001 M. Because the relative changes in surface tension are of... 

However, the additional interactions AW are not known, and there is no consensus about their microscopic origin. One natural candidate for this additional interaction is the screened image force (Wagner-Onsager-Samaras)2... 

Treating the fluctuation potential, we will depart a bit from the scheme used for the (unary) electrostatic potential. As a zero iteration the modified Onsager-Samaras approximation will be taken [25], that preserves a proper asymptotic behavior of this potential along the p-axis (see for details elsewhere [24]). 

Onsager and Samaras inspired by success of the Debye-Hiickel theory refined this argument and developed a limiting law which holds for diluted electrolyte solutions [5]. The Onsager-Samaras theory derives, subject to certain simplifying assumptions on the nature of the screening length, an analytical expression for the surface tension of the electrolytes. It predicts identical... 

Onsager-Samaras theory was believed to capture the relevant physical interactirMis even though some shortcomings were obvious from the very beginning. The surface tension isotherms reveal an ion specificity that cannot be accounted for within the framework of pure electrostatics. The measured surface tension depends on the nature of the electrolyte For instance, sodium fluoride shows a stronger increase in the surface tension than an equimolar solution of... 

The surface tension is important for the calculation of mass transfer coefficients and the specific contact area (see Section 9.4.4). Depending on the availability of necessary parameters, the surface tension for a molecular species can be determined either with the simplest method of Hakim-Steinberg-Stiel or with a more complex DIPPR-method (see Ref. [52]). The mixture surface tension can be obtained via a mixing rule. A further extension to cover electrolyte mixtures is realized by the method of Onsager and Samaras (see Ref. [44]). The latter uses an additive term which can be estimated using the dielectric constant of the mixture and molar volumes of electrolytes. 

This is a repulsive force which increases as 1/x as the ion gets closer to the interface. A model based on these concepts was developed by Onsager and Samaras [6] to estimate values of Fg for electrolyte solutions. This model is reasonably successful for dilute electrolyte solutions. 

Onsager, L., Samaras, N.N.T. The surface tension of Debye-Hiickel electrolytes. J. Chem. 

Ions in solution, apart from interacting with each other, also feel repulsion from the interface due to image-charge effects, as discussed by Onsager and Samaras [25]. It can be shown, however, that these effects become negligible as soon as the surface coverage exceeds about 2% [12]. 

Onsager L, Samaras NNT (1934) The surface tension of Debye-Hckel electrolytes. J Chem Phys 2 528-536... 

The electrostatic theory connected with these effects was first treated by Wagner (1924) and by Onsager and Samaras (1934). 

The electrostatic image treatment of Wagner (1924) was improved by Onsager and Samaras (1934), taking account of Debye-Huckel screening effects (the K parameter) in the ion distribution resulting from repulsive image interactions. They derived the relation for the relative ion... 

The previous calculation applies to a particular situation of the ion at the surface. It is evident, however, that a distribution of ions will be generated (cf., Onsager and Samaras, 1934) near the surface according as becomes smaller with increasing 1 as 1 > r. The net... 

Solutions to the Poisson—Boltzmann equation in which the exponential charge distribution around a solute ion is not linearized [15] have shown additional terms, some of which are positive in value, not present in the linear Poisson—Boltzmann equation [28, 29]. From the form of Eq. (62) one can see that whenever the work, q yfy - yfy), of creating the electrostatic screening potential around an ion becomes positive, values in excess of unity are possible for the activity coefficient. Other methods that have been developed to extend the applicable concentration range of the Debye—Hiickel theory include mathematical modifications of the Debye—Hiickel equation [15, 26, 28, 29] and treating solution complexities such as (1) ionic association as proposed by Bjerrum [15,25], and(2) quadrupole and second-order dipole effects estimated by Onsager and Samaras [30], etc. 

The electrostatic potential for a siuface site ion at the primitive interace is taken from a model first derived by Wagner [33] and Onsager and Samaras [30] using the method of electrical images. An electrical point charge, e, is positioned in a solution a distance, x, above an interface, and an image charge is placed in the solid a distance, -x, below the interface, as shown in Fig. 3. 

Equation (68) gives the electrostatic potential at the surface of a solute ion in a pure dielectric solvent. To find the electrostatic potential, Tg, for electrostatic charge, e, in a dielectric solution requires that, Tg, be a solution of the Poisson— Boltzmann equation [21, 25]. Owing to the spherical and planar geometry of a charge in an interfacial system, Onsager and Samaras chose cylindrical co-ordinates (, X) for the Poisson—Boltzmann equation. 

In order to solve Eq. (69) explicitly, Onsager and Samaras [30] found two approximations necessary (1) the dielectric strength of the solid was set equal to zero, 0 and (2) the dependence of K on distance from the interface K was omitted... 

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