Isotherm adsorption single layer

Sorption and desorption are usually modeled as one fully reversible process, although hystersis is sometimes observed. Four types of equations are commonly used to describe sorption/desorption processes Langmuir, Freundlich, overall and ion or cation exchange. The Langmuir isotherm model was developed for single layer adsorption and is based on the assumption that maximum adsorption corresponds to a saturated monolayer of solute molecules on the adsorbent surface, that the energy of adsorption is constant, and that there is no transmigration of adsorbate on the surface phase. 

Worked Example 10.1 The following data refer to the adsorption of the red-mauve dye from beetroot juice on porcelain at 25 °C. (1) Show that the data obey the Langmuir adsorption isotherm. (2) Demonstrate that 1.2 x 10 8 mol of dye adsorb to form a mono-layer. (3) Estimate the area of a single dye molecule if the radius of a plate was 17.8 cm (we assume the formation of a complete monolayer). 

In some systems, three stages of adsorption may be discerned. In the activated alumina-air-water vapour system at normal temperature, the isotherm is found to be of Type IV. This consists of two regions which are concave to the gas concentration axis separated by a region which is convex. The concave region that occurs at low gas concentrations is usually associated with the formation of a single layer of adsorbate molecules over the... 

Figure 5.5 shows the variation of the pore size distribution as a function of cycles of surface-modification-based N2 adsorption isotherms. The pore size decreases with the modification cycle number. The reduction of the mesopore size for each cycle should be about twice the single-layer thickness. Accordingly, the effective singlelayer thickness is about 6 to 7 A based on the above BET measurements. This value is close to those estimated from the frequency changes of a quartz crystal balance for ultrathin fihns prepared by the surface sol-gel process on 2-D substrates." " ... 

Typical adsorption and desorption isotherms for a porous soHd are indicated in Fig. 1.13. Following the adsorption branch, the steep initial rise (A) is caused by adsorption in the most energetic regions of the soHd (single layer adsorption). Thereafter, in the flat region (B), gas molecules adsorb on sites already occupied by other molecules (multilayer adsorption). 

Na -loess clay, where batch experiments were analyzed by X-ray diffraction and infrared and far-infrared measurements. The adsorption isotherm (Fig. 8.36) shows that loess clay is selective for cesium cations. The raw material contained a large amount of quartz, and the clay material was a mixture of kaolinite and an interstrati-fied iUite-smectite mineral as a result, equilibrium Cs" adsorption data are not consistent with a single site Langmuir model. Cesium adsorption on this particular soil clay occurs by cation exchange on sites with various cesium affinities. At low concentration, far-infrared spechoscopy shows the presence of very selective adsorption sites that correspond to internal collapsed layers. At high concentration, Cs MAS-NMR shows that cesium essentially is adsorbed to external sites that are not very selective. 

Langmuir Equation. It is probable that adsorbed layers have a thickness of a single molecule because of the rapid decrease in intermolecular forces with distance. The Langmuir adsorption isotherm equation is... 

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 ... 

Step isotherms (type H) are observed with porous materials and characterized by a second inhibition. At low pressure a single layer of molecules adsorbs to the surface as for Langmuir adsorption. At intermediate pressures, multilayers start to form and the pores are filled. The saturation at high pressures is caused by the reduction of effective surface area once the pores have been filled. 

At the plateau the maximum uptake value of the adsorbent is therefore reached. The type I or Langmuir isotherm describes the formation of a single monolayer on the surface of the porous material. No multilayers of hydrogen are formed at 77 K, because the interaction strength between single layers is too weak at temperatures higher than the critical temperature of H2. Therefore a type I isotherm is typically obtained for porous materials at adsorption temperatures higher than the critical temperature of the gas. 

The type II isotherm is associated with solids with no apparent porosity or macropores (pore size > 50 nm). The adsorption phenomenon involved is interpreted in terms of single-layer adsorption up to an inversion point B, followed by a multi-layer type adsorption. The type IV isotherm is characteristic of solids with mesopores (2 nm < pore size < 50 nm). It has a hysteresis loop reflecting a capillary condensation type phenomenon. A phase transition occurs during which, under the eflcct of interactions with the surface of the solid, the gas phase abruptly condenses in the pore, accompanied by the formation of a meniscus at the liquid-gas interface. Modelling of this phenomenon, in the form of semi-empirical equations (BJH, Kelvin), can be used to ascertain the pore size distribution (cf. Paragr. 1.1.3.2). 

Multilayer Adsorption Adsorption in which the adsorption space contains more than a single layer of molecules therefore, not all adsorbed molecules will be in contact with the surface of the adsorbent. See also Brunauer-Emmett-Teller Isotherm, Monolayer Adsorption. 

This implies that a smaller molecule will expel a larger one from the surface when their total concentration is increased at constant Ci/C2. Thus, a two-dimensional solution treatment which expresses the chemical potentials of the surface layer components by means of Eq. (2.7) enables us to derive equations of state and adsorption isotherms at fluid interfaces depending on the system considered (ideal or non-ideal surface layer, single surfactant or mixture of... 

As there is no analogue of Butler s equation for ionised surface layers, the procedure used to derive the equation of state has to be based on the Gibbs adsorption equation and a model adsorption isotherm. The isotherm equation can also be derived from the theoretical analysis of the expressions for electrochemical potentials of ions. For the solution of a single ionic surfactant RX, with the addition of inorganic electrolyte XY, starting from Eqs. (2.2) and (2.21) for the electrochemical potentials, one obtains the adsorption isotherm... 

In the absence of chemical reaction between adsorbed species, it is instructive to analyze adsorption/desorption equilibria via steps 3 and 6. The overall objective here is to develop expressions between the partial pressnie / a of gas A above a solid surface and the fraction of active sites a on the catalyst that are occnpied by this gas when it adsorbs. The phenomenon of chemisorption and the relation between pa and a apply to a unimolecular layer of adsorbed molecnles on the catalytic surface. This is typically referred to as a monolayer, where the intermolecular forces of attraction between adsorbed molecules and active snrface sites are characteristic of chemical bonds. When complete monolayer coverage of the surface exists, subsequent adsorption on this saturated surface corresponds to physisorption, which is analogous to condensation of a gas on a cold snbstrate. The enthalpy change for chemisorption is exothermic with valnes between 10 and 100 kcal/mol. The Langmuir adsorption isotherm, first proposed in 1918 (see Langmuir, 1918), is based on the following reversible elementary step that simulates single site adsorption on a catalytic surface when there is only one adsorbate (i.e., gas A) present ... 

The value of the monolayer parameter, in Eq. 1,4 is determined universally with an adsorption isotherm equation. If it is known from experiment that the adsorption forms no more than a single molecular layer on the surfaces of interest. Xn, is then the x intercept of the line... 

Zie is the charge of the species. Stern assumed the location of the adsorption ion at the outer Helmholtz plane separating the compact and diffuse layer, so that the potential in the work term in Eq. (71) corresponds to the potential difference across the diffuse layer. The combination of Eqs. (70a) and (71) gives Stern s expression for the adsorption isotherm from a binary electrolyte solution for the case of a single ionic species being accumulated in the adsorbed state ... 

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