Langmuir theory

BET method. The most commonly used method for determining the specific surface area is the so-called BET method, which obtained its name from three Nobel prize winners Brunauer, Emmett and Teller (1938). It is a modification of the Langmuir theory, which, besides monolayer adsorption, also considers multilayer adsorption. The equation allows easy calculation of the surface area, commonly referred to as the BET surface area ( bet). From the isotherms also pore-radii and pore-volumes can be calculated (from classical equation for condensation in the pores). 

William H. Brock. The Norton History of Chemistry. New York W. W. Norton Co., 1993. Source for Lewis-Langmuir theory early plastics Staudinger controversy available technology carbon dioxide emissions, but relatively clean technology. 

Brunauer, Emmett, and Teller extended the Langmuir theory to multimolecular layer adsorption [8]. They related the condensation rate of gas molecules onto an adsorbed layer and the evaporation rate from that layer for an infinite number of layers. The linear form of the relationship is called the BET equation ... 

Niels Bohr s 1913 hydrogen atom paper demonstrates the traditional interest of some physicists in placing the facts and laws of chemistry within a broader framework of foundational principles laid out by physicists. During the course of the next two decades, a number of physicists who became known as quantum physicists developed physical theories and mathematical techniques that they claimed would create a mathematical and theoretical chemistry. However, few of them had much chemical knowledge beyond a general understanding of the periodic table of the elements and familiarity with the Lewis-Langmuir theory of the electron duplet and octet. 

It should be mentioned that the extension of the Langmuir theory to adsorption from binary adsorbate systems is thermodynamically consistent only in the special case where Q = Q2. However, that thermodynamic consistency is of secondary importance if Eq. (18) provides the correct analytical description of the adsorption phenomena. 

The Frumkin theory with Eqs. 17-18 presents the first improvement of the Szyszkowski-Langmuir theory and is shown in Pig. 1 by the thick line. The Frumkin theory requires input for the surfactant interaction parameter... 

Using the Langmuir theory and equation (4.5) as a starting point to describe the equilibrium between the vapor and the adsorbate in the first layer... 

The classical Langmuir theory for gas adsorption can be applied to adsorption from solution, if the solution is sufficiently dilute 45,46). The surface is considered to consist of sites of about the same area as the projected area of the solute of interest (Fig. 6). 

In Langmuir model, the maximal adsorption is that of a monolayer. Langmuir adsorption isotherms all saturate at high vapor pressures. This is unrealistic for many cases. In order to consider the adsorption of multilayers, Brunauer, Emmett, and Teller extended the Langmuir theory and derived the so-called BET adsorption isotherm [378], The basic idea in the BET theory was to assume a Langmuir adsorption for each of the layers (Fig. 9.8). 

In recent years a radical change has been taking place in the interpretation of the Type I isotherm for porous adsorbents. According to the classical Langmuir theory, the limiting adsorption w (at the plateau) represents completion of the monolayer and may therefore be used for the calculation of the surface area. The alternative view, which is now widely accepted, is that the initial (steep) part of the Type I isotherm represents micropore filling (rather than surface coverage) and that the low slope of the plateau is due to multilayer adsorption on the small external area. 

The experimental isotherm does not provide sufficient information to indicate which one of the two basic assumptions of the Langmuir theory should be rejected. Consequently Vol kenshtein (417) has undertaken the task of deducing the interrelationship between the functions (r) and p(Q) which give rise to the same isotherm 4>(p). 

Since, according to Langmuir theory only a single layer of molecules is adsorbed on the surface of the adsorbent, the fraction 8 gives a measure of the amount of the gas adsorbed per unit mass of the v v... 

Although valency strokes have been customary in chemical formulae for a century, one could not until recently attach to them any real notion about their true nature. On the patient paper one operated with them as with hooks which were undone, rotated etc. at will. Even the Rutherford-Bohr theory of the atom furnished no explanation, not even for the bonding of two hydrogen atoms to form a hydrogen molecule. The successful octet theory and the Lewis and Langmuir theory of the electron-pair bond associated with it was also still purely formal, but later was seen to be essentially correct. 

Everywhere there appears the strong tendency to the formation of complete octets as required by the Lewis-Langmuir theory (see also p. 200), owing to the relative stability of the inert gas configuration. 

Although Lewis originated the idea of the electron-pair bond, much of the credit for its early acceptance must go to Irving Langmuir, who extended it somewhat and enthusiastically popularized it to the extent that it began to be known as the Lewis-Lang-muir theory, and even as the Langmuir theory ... 

Langmufr s work on gas adsorption and insoluble monolayers prepared the way for more progress to be made in the interpretation of adsorption from solution data. In the light of the Langmuir theory, it seemed logical to suppose that the plateau of a solute isotherm represented monolayer completion and that the monolayer capacity could be derived by application of the Langmuir equation. 

Hypervalent molecules and ions are fascinating species, since they appear to violate the traditional Lewis-Langmuir theory of bonding by expanding the valence shell of a main gronp element. Althongh species snch as PCI5,... 

If hypervalent literally means exceeding the lowest chemical valence, then even NH4+ is hypervalent, despite the fact that the Lewis-Langmuir theory easily accounts for its stability. Furthermore, if the definition of hypervalency is restricted to Groups 15-18, then this artificially excludes species such as SiFs and SiFe, which are isoelectronic and isostructural with PF5 and SFe, respectively. The ambiguities in the original definition have led to several changes. Today, no one would regard NH4+ as hypervalent, while those that consider PF5 and SFe hypervalent would classify SiFs" and SiFe in the same way. 

The Langmuir type (L) occurs often, even when the premises of the Langmuir theory are not satisfied. Perhaps type F is the most common it is typical for heterogeneous surfaces. High-qffinity isotherms are characterized by a very steep Initial rise, followed by a (pseudo-) plateau. Whether or not the rise is "infinitely" steep is virtually determined by the sensitivity of the technique used to determine the bulk concentration. Hence, there is no difference of principle between types L and H. 

The atomic and molecular volumes of inorganic liquids were considered from the point of view of the Lewis-Langmuir theory of atomic structure by Pease.2 Tasiro gave the formula log v=[ml /(p+k)]+log Voo, where Vao=sp. vol. at infinite pressure, iw=tangent of the angle between the isotherm and the abscissa axis, fc=an arbitrary constant 2 5651 Voo=b (van der Waals s constant). 

It might be supposed that rate and equilibrium constants for adsorption or desorption could be established from pure-component adsorption data on the components involved. However, such results rarely agree with the values of the constants determined from rate data for the reaction. Interaction effects between components, other inadequacies of the Langmuir theory, and the assumption of a single controlling step, explain the deviation. 

Because of its abstruse character, the potential theory has not attracted attention at the grass roots comparable to that accorded the Langmuir theory. 

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