Theory Langmuir monolayer

Zhang, J., C.J. Slevin, C. Morton, P. Scott, D.J. Walton, and P.J. Unwin. 2001. New approach for measuring lateral diffusion in Langmuir monolayers by scanning electrochemical microscopy (SECM) Theory and application. J. Phys. Chem, B 105 11120-11130. 

It is also unavoidable that sometimes the same symbol is used for different physical quantities, because we wanted to avoid excessive use of subscripts and superscripts. Mostly this does not give rise to problems, but in those places where it might, we have added a caveat. For Instance, cross-sectional areas per molecule have different meanings in lattice theories and in surface pressure Isotherms for Langmuir monolayers we explain this in sections 3.3 and 3.4. 

R. Mendelsohn, J.W. Brauner, and A. Gericke, External Infrared Reflection Absorption Spectrometry of Monolayer Films at the Air-Water Interface, Ann. Rev. Phys. Chem. 46 (1995) 305. (Review theory and practice of IRRAS as applied to Langmuir monolayers determination of conformational states of hydrocarbon tails and H-bonding, ionization states of head groups, and molecular orientation illustrated with experimental results on monolayers of single-chain amphiphiles, phospholipids and proteins.)... 

Brunauer-Emmett-Teller (BET) [20], Langmuir isotherm theory is applied when a monolayer of molecules is sorbed on a homogeneous surface where each site requires the same energy to adsorb molecules. The Freundlich isotherm also assumes a monolayer, but allows for an exponential distribution of adsorption energies. BET isotherms provide for multilayer adsorption. 

In monolayer adsorption, all the adsorbed molecules are in contact with the surface layer of the adsorbent [46]. The adsorbate molecules are thus adsorbed on a fixed number of localized sites, each of which can only hold one adsorbate molecule (the molecules of the adsorbate are not deposited on others already adsorbed, only on the free surface of the adsorbent). The most suitable models describing the monolayer theory are the Langmuir-type ones. They presume that all adsorption sites are energetically equivalent and that there is no interaction between the adsorbed molecules [47]. 

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... 

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... 

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. 

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... 

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 ... 

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). 

The BET surface area equation is based on Langmuir s kinetic theory of monolayer gas adsorption on surfaces [6], Langmuir theorized that the collision... 

Before our theory was fully developed, extensive work by J. Koral in cooperation with R. Ullman (15) confirmed in detail and with considerable accuracy all previously known features. They ascertained, in addition, the particulars of the adsorption isotherms for a number of polymers and dispersed adsorbates and established the remarkable degree to which most isotherms could be approximated by 2-parameter equations, like Langmuir s isotherm for monolayers of small molecules. They found the dependence of the adsorption on MW to be weak and determined the area per adsorbed molecule. 

In 1938, Brunauer, Emmett and Teller(12) and Emmett and de Witt(13) developed what is now known as the BET theory. As in the case in Langmuir s isotherm, the theory is based on the concept of an adsorbed molecule which is not free to move over the surface, and which exerts no lateral forces on adjacent molecules of adsorbate. The BET theory does, however, allow different numbers of adsorbed layers to build up on different parts of the surface, although it assumes that the net amount of surface which is empty or which is associated with a monolayer, bilayer and so on is constant for any particular equilibrium condition. Monolayers are created by adsorption on to empty surface and by desorption from bilayers. Monolayers are lost both through desorption and through the adsorption of additional layers. The rate of adsorption is proportional to the frequency with which molecules strike the surface and the area of that surface. From the kinetic theory of gases, the frequency is proportional to the pressure of the molecules and hence ... 

Using a kinetic approach, Langmuir was able to describe the type I isotherm with the assumption that adsorption was limited to a monolayer. According to the kinetic theory of gases, the number of molecules striking each square centimeter of surface per second is given by... 

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). 

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