Surfaces specific Langmuir

Balamumgan, S., Obubuafo, A., Soper, S. A., McCarley, R. L., Spivak, D. A. (2006). Designing highly specific biosensing surfaces using aptamer monolayers on gold. Langmuir 22, 6446-6453. 

Specific surface area from the Langmuir method (0.01 < p/p < 0.05, interval of relative pressure). Specific external surface areas obtained from the t-method. 

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... 

Many adsorption phenomena especially of surfactants, polymers, proteins and the chemical adsorption of gases on solids can be well represented by the Langmuir adsorption isotherm. This equation can be expressed in a suitable linear form and we can obtain the two parameters of the model, of which one is the concentration or volume at maximum (full) coverage or the so-called monolayer coverage. Knowledge of this monolayer coverage and of the specific surface area of the solid can help us estimate the surface area occupied by a molecule at the interface and thus the amount needed for stabilization. The specific solid surface area can be obtained from gas adsorption measurements on the same solid. 

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. 

Dye adsorption from solution may be used to estimate the surface area of a powdered solid. Suppose that if 3.0 g of a bone charcoal is equilibrated with 100 ml of initially 10 Af methylene blue, the final dye concentration is 0.3 x 10 Af, while if 6.0 g of bone charcoal had been used, the final concentration would have been 0.1 x Qr M. Assuming that the dye adsorption obeys the Langmuir equation, calculate the specific surface area of the bone charcoal in square meters per gram. Assume that the molecular area of methylene blue is 197 A. ... 

A variety of experimental data has been found to fit the Langmuir equation reasonably well. Data are generally plotted according to the linear form, Eq. XVn-9, to obtain the constants b and n from the best fitting straight line. The specific surface area, E, can then be obtained from Eq. XVII-10. A widely used practice is to take to be the molecular area of the adsorbate, estimated from liquid or solid adsorbate densities. On the other hand, the Langmuir model is cast around the concept of adsorption sites, whose spacing one would suppose to be characteristic of the adsorbent. See Section XVII-5B for an additional discussion of the problem. 

According to the classical Langmuir model, n is actually equal to the monolayer capacity, and can be converted into the specific surface A of the solid by the standard relation A = n a L (cf. Equation (2.1)). A number of lines of argument would suggest, however, that this interpretation is invalid, and that the value of A arrived at does not represent a true specific surface. 

A large number of potential applications for organized protein monolayers have recently motivated considerable research activity in this field (Boussaad et al. 1998, Kiselyova et al. 1999). Construction of specific interaction-directed, self-assembled protein films has been performed at the air-water interface. The Langmuir-Blodgett (LB) technique has been extensively used to order and immobilize natural proteins on solid surfaces (Tronin et... 

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 Langmuir adsorption isotherm provides a simple mechanistic picture of the adsorption process and gives rise to a relatively simple mathematical expression. It can also be used to obtain a crude estimate of specific surface areas. More important, from the viewpoint of the chemical engineer, it serves as a point of departure for formulating rate expressions for heterogeneous catalytic reactions. 

L. Haussling, H. Ringsdorf, F.J. Schimitt, and W. Knoll, Biotin-functionalized self-assembled monolayers on gold-surface-plasmon optical studies of specific recognition reactions. Langmuir 7, 1837-184 (1991). 

K. Das, J. Penelle, V.M. Rotello, and K. Niisslein, Specific recognition of bacteria by surface-templated polymer films. Langmuir 19, 6226-6229 (2003). 

An HM-HEC monolayer at the air/aqueous interface was formed by adsorption from an aqueous solution of the polymer placed in the Langmuir trough overnight. In "stress-jump" experiments, HM-HEC monolayers were placed under rapid compression to a large degree and surface pressure was measured as a function of time after compression was stopped. (The compressional "jumps" required a minute or two to complete, and in some cases were on the order of the polymer monolayer relaxation times. See later section for discussion). In hysteresis experiments, the adsorbed monolayers were subjected to continuous compression-expansion cycles at a specific speed, while surface pressure was determined as a function of surface area. 

The number of gas molecules can be measured either directly with a balance (gravimetric method) or calculated from the pressure difference of the gas in a fixed volume upon adsorption (manometric method). The most frequently apphed method to derive the monolayer capacity is a method developed by Brunauer, Emmett, and Teller (BET) [1], Starting from the Langmuir equation (monolayer adsorption) they developed a multilayer adsorption model that allows the calculation of the specific surface area of a sohd. The BET equation is typically expressed in its linear form as... 

If the surface complex is the chromophore, then the photochemical reductive dissolution occurs as a unimolecular process alternatively, if the bulk iron(III)(hydr)-oxide is the chromophore, then it is a bimolecular process. Irrespective of whether the surface complex or the bulk iron(IIl)(hydr)oxide acts as the chromophore, the rate of dissolved iron(II) formation depends on the surface concentration of the specifically adsorbed electron donor e.g. compare Eqs. (10.11) and (10.18). It has been shown experimentally with various electron donors that the rate of dissolved iron(II) formation under the influence of light is a Langmuir-type function of the dissolved electron donor concentration (Waite, 1986). 

M.A. Anderson, Control of surface and. potentials on nanoporous Ti02 films by potential-determining and specifically adsorbed ions, Langmuir 16 (2000) 6094-6101. 

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