Solid surface Langmuir adsorption

In a simple solid, a Langmuir adsorption isotherm (Moore 1950) can be used to obtain the surface area assuming monolayer coverage (where the adsorption of gas molecules is measured at a temperature above its condensation into a liquid... 

Ruths, J., Essler, F., Decher, G., Riegler, H. (2000). Polyelectrolytes I polyanion/polycation multilayers at the air/ monolayer/water interface as elements for quantitative polymer adsorption studies and preparation of hetero-superlattices on solid surfaces. Langmuir 16 8871-8. 

Kubiak K, Mulheran PA Mechanism of hen egg white lysozyme adsorption on a charged solid surface, Langmuir 26AS9SA—1S96S, 2010. 

Reimer, U., Wahab, M., Schiller, R, and Mogel, H.-J. 2005. Monte Carlo study of surfactant adsorption on heterogeneous solid surfaces. Langmuir. 21 1640. 

Langmuir adsorption isotherm A theoretical equation, derived from the kinetic theory of gases, which relates the amount of gas adsorbed at a plane solid surface to the pressure of gas in equilibrium with the surface. In the derivation it is assumed that the adsorption is restricted to a monolayer at the surface, which is considered to be energetically uniform. It is also assumed that there is no interaction between the adsorbed species. The equation shows that at a gas pressure, p, the fraction, 0, of the surface covered by the adsorbate is given by ... 

Various functional forms for / have been proposed either as a result of empirical observation or in terms of specific models. A particularly important example of the latter is that known as the Langmuir adsorption equation [2]. By analogy with the derivation for gas adsorption (see Section XVII-3), the Langmuir model assumes the surface to consist of adsorption sites, each having an area a. All adsorbed species interact only with a site and not with each other, and adsorption is thus limited to a monolayer. Related lattice models reduce to the Langmuir model under these assumptions [3,4]. In the case of adsorption from solution, however, it seems more plausible to consider an alternative phrasing of the model. Adsorption is still limited to a monolayer, but this layer is now regarded as an ideal two-dimensional solution of equal-size solute and solvent molecules of area a. Thus lateral interactions, absent in the site picture, cancel out in the ideal solution however, in the first version is a properly of the solid lattice, while in the second it is a properly of the adsorbed species. Both models attribute differences in adsorption behavior entirely to differences in adsorbate-solid interactions. Both present adsorption as a competition between solute and solvent. 

If the data fit this model, a plot of 1/F0 versus 1/(S0) should be linear with a slope K/Vmax and intercept l/Vmax. It is analogous to that used in determining the constants in the Langmuir equation for adsorption on solid surfaces. Other forms that may be used to prepare linear plots are... 

In general, there is an array of equilibrium-based mathematical models which have been used to describe adsorption on solid surfaces. These include the widely used Freundlich equation, a purely empirical model, and the Langmuir equation as discussed in the following sections. More detailed modeling approaches of sorption mechanisms are discussed in more detail in Chap. 3 of this volume. 

Another widely used sorption model is the Langmuir equation. It was developed by Irving Langmuir [140] to describe the adsorption of gas molecules on a planar surface. It was first applied to soils by Fried and Shapiro [ 141 ] and Olsen and Watanabe [142] to describe phosphate sorption on soils. Since that time, it has been heavily employed in many environmental fields to describe sorption on various solid surfaces [19,65]. The general Langmuir model is... 

The adsorption of a number of organic pollutants on various solid surfaces was found to fit the Langmuir-model isotherm [139,143-145]. 

Brunauer-Emmett-Teller (BET) adsorption describes multi-layer Langmuir adsorption. Multi-layer adsorption occurs in physical or van der Waals bonding of gases or vapors to solid phases. The BET model, originally used to describe this adsorption, has been applied to the description of adsorption from solid solutions. The adsorption of molecules to the surface of particles forms a new surface layer to which additional molecules can adsorb. If it is assumed that the energy of adsorption on all successive layers is equal, the BET adsorption model [36] is expressed as Eq. (6) ... 

I. Langmuir Derived the concept of monolayer adsorption, formed on energetically homogeneous solid surfaces.Was awarded the Nobel Prize in chemistry in 1932 1918... 

ADSORPTION ON SOLID SURFACES 7.9a The Langmuir Equation Theory... 

An equation of the form of Eq. (2.32) was given by Langmuir (Carberry, 1976) for the treatment of data from the adsorption of gas on a solid surface. If the Michaelis-Menten equation is applicable, the Langmuir plot will result in a straight line, and the slope will be equal to l/rmax. The intercept will be KM/rmax, as shown in Figure 2.5. 

The Langmuir isotherm is used to describe single-layer adsorption based on the concept that a solid surface possesses a finite number of sorption sites. When these active sites are filled, the site will no longer sorb solute from the solution ... 

When the components of a gas mixture compete for the adsorption sites on a solid surface, the Langmuir equation takes the general form... 

The theory of Brunauer, Emmett and Teller167 is an extension of the Langmuir treatment to allow for multilayer adsorption on non-porous solid surfaces. The BET equation is derived by balancing the rates of evaporation and condensation for the various adsorbed molecular layers, and is based on the simplifying assumption that a characteristic heat of adsorption A Hi applies to the first monolayer, while the heat of liquefaction, AHL, of the vapour in question applies to adsorption in the second and subsequent molecular layers. The equation is usually written in the form... 

Solid surfaces are usually heterogeneous therefore, since adsorption at the more active sites is favoured, heats of both monolayer physical adsorption and chemisorption might, in this respect, be expected to become significantly less exothermic as the surface coverage increases, as, for example, shown at low pressures in Figures 5.12a and 5.12b. This, in turn would cause the initial slope of an adsorption isotherm to be steeper than that predicted according to the Langmuir equation or the BET equation. 

A The adsorption of hydrogen cyanide on solid surfaces decreases with rising temperature, according to Langmuire (see Graph 3).352... 

In this work we utilized FTIR methods to examine the SA monolayers on flat, polar solid surfaces prepared from nonpolar solutions. We used ATR and GI FTIR measurements to characterize the material and bonding of the S A monolayers, and used transmission and ATR FTIR to monitor the dynamics of the SA adsorption process. With reference to measurements on standard Langmuir-Blodgett monolayer samples, we were able to quantify the S A kinetic results. We also used fluorescence spectroscopy of incorporated pyrene probes in S A mixed monolayer films as a simple method for the determination of the relative adsorption and thermodynamic constants. 

Setoyama N, Ruike M, Kasu T, Suzuki T, and Kaneko K. Surface characterization of microporous solids with He adsorption and small angle x-ray scattering. Langmuir, 1993 9(10) 2612-2617. 

In general, the adsorption of ionic surfactants follows the Langmuir isotherm, as discussed in Section 4.1. The adsorption of the surfactants onto the solid surfaces is dependent on the orientation and the packing efficiency of the solid surfaces. The onset of the adsorption plateau may occur at the critical micelle concentration (c.m.c.) of the surfactant in water, as shown in Figure 4.28. If the adsorption isotherm... 

When gas molecules hit a solid surface, they may be either reflected, or captured by the surface field of force and condense, to evaporate again later. In Langmuir s adsorption theory the factor a expresses the fraction of the impinging molecules which do condense on the surface. In recent years much information as to the manner of reflection or condensation has been obtained experimentally by the use of molecular rays, and theoretically by wave mechanics. Molecular rays are beams of molecules on which a particular direction has been imposed by slits, moving in a vacuum so high that there are practically no collisions between molecules, and the direction of the beams is maintained for long distances. 

Soviet physicists and chemists have been reporting research on the peculiarities of adsorption on solid surfaces and the apparent deviations from the derived laws expressing adsorption phenomena, e.g., deviations from the Langmuir laws. S. Z. Roginskil has treated the nonuniformity of the surface and adsorption under conditions of limited extent of coverage of the surface in a number of articles. 

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