Langmuir s theory

Laboratory. During the period 19191922, Langmuir developed what he called a "deductive chemistry" using the electron-pair theory of valency and the quantum hypothesis. However, physicists rejected the premises and methodology of Langmuir s theory, which proposed the existence of a "quantum force" to counterbalance Coulombic attraction and which used the notion of principal quantum number but deduced positions of equilibrium rather than quantum jumps for electrons. 12... 

The cross-sections of the saturated acids do not vary much, but the length increases with the number of atoms in the carbon chain, as would be expected from Langmuir s theory. The alcohol has a somewhat greater cross-section than the acids. The cross-section of the glycerides is about three times as great as that of the acids from which they are derived, a fact easily explained on the supposition that the three- acidic chains in each case lie side by side, occupying as much area on the water as if they were in separate acid molecules. 

Assuming that monomer can be bound by the template in a similar manner as in the adsorption process we can apply Langmuir s theory to describe this process. 

Langmuir s theory for deriving an isotherm is a kinetic one, assuming the adsorption system is in dynamic equilibrium, where therate of adsorption is equal to that of desorption. The Langmuir isotherm, described by the following equation, is still the most useful for data correlation. 

According to Stem, the charge in the dense part of the EDL can be determined from Langmuir s theory of monomolecular adsorption, discussed in Chapter II. The work required to transfer the z -th ion from the solution bulk to the dense part of the EDL, Wi (x = d) should contain the term - = -(p0 - poS) )/NA, describing the purely adsorption interaction of the ion with the surface (see Chapter 11,2), and the term due to work against electrostatic forces of the interaction of the ion with a charged surface, z,eipd, where (p(/ is the dense layer potential. Thus, the term (p0 - PqS) )/NA in eq. (11.21) should be replaced with O, - z,ebulk concentration, n,(), can be expressed as... 

Macro-Kinetic Aspects of Langmuir s Theory and Its Application to Adsorption Dynamics... 

If we use -p to denote partial pressure and 6 fraction of surface occupied and we use the subscripts H for hydrogen and A for ammonia, then according to Langmuir s theory... 

Adsorption kinetics can be explained on the basis of Langmuir s theory. This theory is based on the following three assumptions (1) a uniform surface with equivalent adsorption sites, (2) single adsorbate per site, and (3) the adsorption energy is independent of occupancy of neighboring sites. 

In Paremuzyan and Aroutiounian (2012a, 2012b), the phenomenon of a reduction in the heat of adsorption was taken into account using the results of Langmuir s theory. The noise for oxygen and other type of gases was calculated. 

The full range of adsorption isotherms under the lUPAC system is shown in Figure 7.46. Brunauer, Emmett and Teller were able to extend Langmuir s theory of monolayer adsorption to obtain an isotherm (the BET equation) which models Type II behaviour, for meso- and macroporous systems. Briefly, in the theory, molecules in one layer act as adsorption sites for molecules in the next layer, so that the adsorbed layer is not of uniform thickness, but rather is made up of a random stack of molecules. The theory has limitations, such as the assumption of liquid-like behaviour in all adsorbed layers but the first however, it has become a... 

Fig. 54. Osmotic pressure p) as a function of the solconccntratibn (/t) according to Langmuir s theory.

The BET theory is an extension of Langmuir s theory of monolayer adsorption to multilayer adsorption with the following hypotheses (i) physical adsorption in layers infinitely, (ii) no interaction between the layers, (iii) Langmuir theory is... 

It should be realized that fitting the Langmuir s model to the experimental data makes sense only if the conditions underlying the Langmuir s theory are fulfilled. These are adsorption equilibrium and identical and independent adsorption sites. It implies localized adsorption and no interaction between the adsorbed molecules. It may be obvious that in particular the last-mentioned condition is often not met in practice. A modification of the theory is discussed later, which takes interaction between adsorbed molecules into account. 

Initial parts of the isotherms (low c) coincide. When more ions are adsorbed, the surface becomes charged and an electrostatic potential is built up. This potential will limit further adsorption of ions, so that the rising part of the isotherm becomes less steep and the saturation value for ion adsorption is lower than for its uncharged analogues, b. Conditions Langmuir s theory ... 

Independent, identical adsorption sites at the surface, such that each molecule adsorbs with the same affinity and with no lateral interaction between adsorbed molecules. Cooperative adsorption implies that adsorption of a molecule promotes the adsorption of a subsequent molecule. For cooperative adsorption, the affinity of an adsorption site is increased by the preadsorbed molecules. The adsorption sites are not independent of each other and therefore Langmuir s theory is not applicable. In case of cooperative adsorption, the affinity increases with T, i.e., T(c)/dc increases with increasing c. The plateau value of the isotherm is reached at a smaller value of c. 

C.R. Bury, Langmuir s Theory of the Arrangement of Electrons in Atoms and Molecules Journal of the American Chemical Society, 43,1602-1609,1921, table from p. 1603. 

The analogy with adsorption from solution is readily demonstrated by considering as a first approximation Langmuir s theory applied to the adsorption of a gas component 1 from a mixture of gases (1 and 2) at a total pressure p chosen so that one of the components (say 2), when adsorbed from the pure... 

Although the previous models well describe the binding of surfactant with the polymer network, they do not explain the issue of the electric field and deformation in the first and third steps. We propose and introduce the adsorption equation based on the Langmuir s theory for the second step. The model of simplicity explains the connection between the first and third steps. The following assumptions have been made to apply the theory to the gel a) the gel is the porous plate made of polymers like activated carbon b) the effective surface of the polymer network is the total area of the fine pores c) the bound molecules do not affect the free molecules once the pore is occupied by a certain numbers of molecules. Accordingly, the polymer network is approximated by a three-dimensional monolayer. 

In the following, we consider the equilibrium and kinetics of adsorption of surfactants at the air-water interface on the basis of Langmuir s theory of adsorption of gases on solids. According to Langmuir s theory, it is assumed that the adsorption surface consists of sites, which can be occupied by adsorbed molecules. These sites correspond to the minimum of surface free energy. At achieving the balance between the adsorbed molecules and molecules of gas, only some parts of the potentially available adsorption sites are occupied by gas molecules. This part is equal to 0, and the total number of molecules Na adsorbed on the surface obeys the ratio... 

Langmuir investigated adsorption phenomena systematically in the early 20th century and proposed the famous monolayer adsorption theory in 1918. Langmuir s theory is the foundation of the kinetics of surface catalytic reaction. Other adsorp>-tion theories basically are the amendment or supplement to Langmuir s adsorption theory. 

Adsorptions not described by Langmuir s theory especially the physical multilayer adsorption of gases on solids can be best described by the BET (Bmnauer-Emmett-Teller) theory discussed next. BET can also be written in a linear form, for reduced pressures (P/Po) up to about 0.4, and yield values of the monolayer coverage and of the specific solid surface area. The BET theory is a very useful tool in describing physical adsorption, although it does... 

Three theories for multicomponent adsorption have been presented, the extension of Langmuir s theory to multicomponent systems, the ideal and real adsorbed solution theories (lAST, RAST) and the multicomponent potential adsorption theory (MPTA). 

With a reference to the well known Langmuir s theory for the equilibrium adsorption-desorption of gas molecules on solid surfaces, Maier and Goritz developed a quantitative model by considering the kinematical aspects of an adsorption-desorption mechanism of rubber chain segments... 

The BET theory is the most accepted for determining the SSAs of materials and it is based on the multilayer adsorption of gas molecules onto the adsorbent. This theory is an extension of Langmuir s theory and it involves the following assumptions (Brunauer et al. 1938 Fagerlund 1973) ... 

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