Surfaces, nonideal

The equations get more complicated as the ideal surface assumptions are relaxed, but the Langmuir isotherm is adequate for most engineering purposes. Surface nonideality is discussed, among others, by Boudart and Djeja Mariadasseu (1984), Thomas and Thomas (1999), and Doraiswamy... 

A number of isotherms that dispense with assumptions (1) and (2) have been proposed (see Doraiswamy, 1991). Some studies (e.g., Kiperman et al., 1989) indicate that it may not be possible to model certain reactions without invoking the role of surface nonideality. Fortuitously, the use of more rigorous isotherms does not materially affect the companion problem of the diffusion-reaction behavior of systems (Shendye et al., 1993)—a topic considered in the next section. 

It is possible to extend the analysis for the surface nonidealities. For example, a surface can be composed of patches, each of which has a uniform site energy distribution such that the Langmuir adsorption isotherm... 

In contrast to the methylated surface/air case, in this system, the equilibrium state in the contact can t be estimated, along with the possibility of an incomplete screening of the nondispersion forces and a possible surface nonideality. It makes no difference whether the residual film is modeled as a saturated monolayer, a unsaturated monolayer, or a polylayer of a liquid phase. Consequently, the value of Of is low, not because the contact is ideal, but because the value of o is low. 

In general, one should allow for nonideality in the adsorbed phase (as well as in solution), and various authors have developed this topic [5,137,145-149]. Also, the adsorbent surface may be heterogeneous, and Sircar [150] has pointed out that a given set of data may equally well be represented by nonideality of the adsorbed layer on a uniform surface or by an ideal adsorbed layer on a heterogeneous surface. 

The matter of surface mobility has come up at several points in the preceding material. The subject has been a source of confusion—see Ref. 112. Actually, two kinds of concepts seem to have been invoked. The first is that invoked in the discussion of physical adsorption, which has to do with whether the adsorbate can move on the surface so freely that its state is essentially that of a two-dimensional nonideal gas. For an adsorbate to be mobile in this sense, surface barriers must be small compared to kT. This type of mobile adsorbed layer seems unlikely to be involved in chemisorption. 

The major artifacts contributing to uncertainties in PDCE results stem from effects caused by bombardment of nonideal specimens, particularly thick specimens. The ideal thick specimen would be a homogeneous, smooth electrical conductor that does not change during bombardment. Except for rather simple, well-defined layered structures (e.g., surface oxide layers), specimens having compositional variations with depth yield spectra whose analyses can have large inaccuracies. 

There are few systematic guidelines which can be used to predict the properties of AB2 metal hydride electrodes. Alloy formulation is primarily an empirical process where the composition is designed to provide a bulk hydride-forming phase (or phases) which form, in situ, a corrosion— resistance surface of semipassivating oxide (hydroxide) layers. Lattice expansion is usually reduced relative to the ABS hydrides because of a lower VH. Pressure-composition isotherms of complex AB2 electrode materials indicate nonideal behaviour. 

Experimental determination of the surface composition in nonideal systems, in which the gradients extend over several layers inwards the crystal is as difficult as the exact calculations. Therefore, one has to make again rather unpleasant assumptions. 

In addition to the effect of the nonideality of the metal on the electrolyte phase, one must consider the influence of the electrolyte phase on the metal. This requires a model for the interaction between conduction electrons and electrolyte species. Indeed, this interaction is what determines the position of electrolyte species relative to the metal in the interface. Some of the work described below is concerned with investigating models for the electrolyte-electron interaction. Although we shall not discuss it, the penetration of water molecules between the atoms of the metal surface may be related3 to the different values of the free-charge or ionic contribution to the inner-layer capacitance found for different crystal faces of solid metals. Rough calculations have been done to... 

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. 

L. Lee, Molecular Thermodynamics of Nonideal Fluids, Bntterworth, Boston, 1988. 1. N. Israelachvili, Intermolecular and Surfaces Forces, Academic Press, London, 1992 Watanabe, A. M. Brodsky, andW. P. Reinhardt,/. Phys. Chem. 95 (1991) 4593. 

Counterion Binding. The fractional counterion binding on charged mixed micelles is of fundamental interest because it gives an indication of surface charge density which is related to the mechanism of mixing nonidealities in ionic/nonionic micelles. It is also a necessary... 

A generalized nonideal mixed monolayer model based on the pseudo-phase separation approach is presented. This extends the model developed earlier for mixed micelles (J. Phys. Chem. 1983 87, 1984) to the treatment of nonideal surfactant mixtures at interfaces. The approach explicity takes surface pressures and molecular areas into account and results in a nonideal analog of Butler s equation applicable to micellar solutions. Measured values of the surface tension of nonideal mixed micellar solutions are also reported and compared with those predicted by the model. 

In mixed surfactant systems, physical properties such as the critical micelle concentration (cmc) and interfacial tensions are often substantially lower than would be expected based on the properties of the pure components. Such nonideal behavior is of both theoretical interest and industrial importance. For example, mixtures of different classes of surfactants often exhibit synergism (1-3) and this behavior can be utilized in practical applications ( ).In addition, commercial surfactant preparations usually contain mixtures of various species (e.g. different isomers and chain lengths) and often include surface active impurities which affect the critical micelle concentration and other properties. 

Using this approach, a model can be developed by considering the chemical potentials of the individual surfactant components. Here, we consider only the region where the adsorbed monolayer is "saturated" with surfactant (for example, at or above the cmc) and where no "bulk-like" water is present at the interface. Under these conditions the sum of the surface mole fractions of surfactant is assumed to equal unity. This approach diverges from standard treatments of adsorption at interfaces (see ref 28) in that the solvent is not explicitly Included in the treatment. While the "residual" solvent at the interface can clearly effect the surface free energy of the system, we now consider these effects to be accounted for in the standard chemical potentials at the surface and in the nonideal net interaction parameter in the mixed pseudo-phase. 

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