Adsorbed layer phase volume

A typical N2 adsorption measurement versus relative pressure over a solid that has both micropores and mesopores first involves essentially a mono-layer coverage of the surface up to point B shown in isotherm IV (lUPAC classification) in Figure 13.1. Up to and near point B the isotherm is similar to a Langmuir isotherm for which equilibrium is established between molecules adsorbing from the gas phase onto the bare surface and molecules desorbing from the adsorbed layer. The volume of adsorbed N2 that covers a monolayer volume, hence the surface area of N2 can then be determined from the slope of the linearized Langmuir plot when P/V is plotted against P ... 

The study [39] shows that similar equation is valid for adsorption of NH- and NH2-radicaIs, too. There are a lot of experimental data lending support to the validity of the proposed two-phase scheme of free radical chemisorbtion on semiconductor oxides. It is worth noting that the stationary concentration of free radicals during the experiments conducted was around 10 to 10 particles per 1 cm of gas volume, i.e. the number of particle incident on 1 cm of adsorbent surface was only 10 per second. Regarding the number of collisions of molecules of initial substance, it was around 10 for experiments with acetone photolysis or pyrolysis provided that acetone vapour pressure was 0,1 to 0,01 Torr. Thus, adsorbed radicals easily interact at moderate temperatures not only with each other but also with molecules which reduces the stationary concentration of adsorbed radicals to an even greater extent. As we know now [45] this concentration is established due to the competition between the adsorption of radicals and their interaction with each other as well as with molecules of initial substance in the adsorbed layer (ketones, hydrazines, etc.). 

Gas adsorption (physisorption) is one of the most frequently used characterization methods for micro- and mesoporous materials. It provides information on the pore volume, the specific surface area, the pore size distribution, and heat of adsorption of a given material. The basic principle of the methods is simple interaction of molecules in a gas phase (adsorptive) with the surface of a sohd phase (adsorbent). Owing to van der Waals (London) forces, a film of adsorbed molecules (adsorbate) forms on the surface of the solid upon incremental increase of the partial pressure of the gas. The amount of gas molecules that are adsorbed by the solid is detected. This allows the analysis of surface and pore properties. Knowing the space occupied by one adsorbed molecule, Ag, and the number of gas molecules in the adsorbed layer next to the surface of the solid, (monolayer capacity of a given mass of adsorbent) allows for the calculation of the specific surface area, As, of the solid by simply multiplying the number of the adsorbed molecules per weight unit of solid with the space required by one gas molecule ... 

It has been experimentally and theoretically verified that the organic component of the mobile phase adsorbs on the surface of the stationary phase forming a mono- or multi-molecular layer. The volume of the adsorbed layer is not dependent on the length of the alkyl chain [89],... 

In this theory the adsorbed layers are considered to be contained in an adsorption space above the adsorbent surface. The space is composed of equipotential contours, the separation of the contours corresponding to a certain adsorbed volume, as shown in Figure 17.7. The theory was postulated in 1914 by Polanyi(18), who regarded the potential of a point in adsorption space as a measure of the work carried out by surface forces in bringing one mole of adsorbate to that point from infinity, or a point at such a distance from the surface that those forces exert no attraction. The work carried out depends on the phases involved. Polanyi considered three possibilities (a) that the temperature of the system was well below the critical temperature of the adsorbate and the adsorbed phase could be regarded as liquid, (b) that the temperature was just below the critical temperature and the adsorbed phase was a mixture of vapour and liquid, (c) that the temperature was above the critical temperature and the adsorbed phase was a gas. Only the first possibility, the simplest and most common, is considered here. 

The major advantage of protein adsorption studies on high surface area materials is that changes of some extensive properties which accompany the process of adsorption are large enough to be directly measured heat of adsorption through microcalorimetry 141), uptake or release of small ions by a combination of electrokinetic methods and titration 142), thickness of adsorbed layer or an increase of the volume fraction of solid phase by a hydrodynamic method like viscometry 143). Chromatographiclike analysis can also be applied to protein adsorption 144). 

In order to test the model used here, calculated values of the limiting free polymer concentration 0 at which phase separation occurs are compared with the experimental data [6] on the aqueous dispersions of polystyrene latex particles with adsorbed polyethylene oxide and with polyethylene oxide as the free polymer. Since no information is available regarding the thickness of the adsorbed layer, the values used by Vincent et al. [6] in their theoretical calculations are adopted. Table 1 compares the experimental values of the limiting volume fraction of the free polymer with our calculated values for two different molecular weights of the free polymer. The simple model used here gives reasonably good agreement with the experimental values. 

On the basis of a lattice model, upper and lower bounds have been established for the entropy of dispersion of spherical globules of radius r and volume fraction in the continuous phase (ref. 20). Here r and are the "actual" radius of the globules (including the adsorbed layer of surfactants) and the corresponding... 

A pertinent question is as the volume of the adsorbed phase increases, do we have to take into account the corresponding increase of buoyancy (e.g. the buoyancy doubles after saturation of an adsorbent with 50% porosity). The answer is no, provided we want to assess the surface excess mass m°. As illustrated in Figure 3.22, because of the buoyancy effect, we do not measure the total mass of the adsorbed layer (shaded+hatched areas) but simply a surface excess mass (hatched area only). Thus, adsorption gravimetry and the Gibbs representation are highly compatible (Findenegg, 1997). 

In the derivations of the retention functions so far, the adsorbed phase volume or thickness of the adsorbed layer was not introduced. The adsorbent and column parameters (surface area and void volume) independently measured are not dependent on the eluent type composition. Measurement of the void volume and adsorbent surface area is discussed in the following references 18 and 23. 

An increase of the acetonitrile equilibrium concentration in this region leads to the linear decrease of the excessively adsorbed amount. The adsorbed layer has a finite volume (or finite thickness), and in this region of very high acetonitrile concentration it is possible to assume that the adsorbed phase is completely filled with acetonitrile, and therefore the following expression for only this region on the isotherm could be written ... 

The analysis of experimental excess adsorption isotherms using equation (2-50) had shown unusual results [22]. The adsorbed layer thickness of acetonitrile adsorbed from water on different types of reversed-phase adsorbents calculated as the ratio of adsorbed layer volume and adsorbent surface area appears to be on average equal to 14 A, which is equivalent to approximately five monolayers of acetonitrile molecules adsorbed on the hydrophobic surface. At the same time, the adsorbed layer thickness of methanol adsorbed from water on the same adsorbents is equal to only 2.5 A, which is equivalent to the monolayer-type adsorption. 

The binary eluent adsorption equilibrium is considered to be not disturbed by the injection of a small amount of the analyte (essentially the third component in the system). In an isocratic mode at a fixed eluent composition, the organic adsorbed layer is a stationary phase for the analyte to partition into. The analyte can partition into the adsorbed layer followed by consequent adsorption on the surface of the reversed-phase adsorbent. The overall retention is a superposition of two consecutive processes. Since the eluent component adsorption could be measured independently and adsorbed layer volume could be represented as a function of the mobile phase composition, the analyte retention also could be expressed as a function of the eluent composition. 

Applying this function into the mass-balance equation (2-33) and performing the same conversions [Eqs. (2-34)-(2-39)], the final equation for the analyte retention in binary eluent is obtained. In expression (2-67) the analyte distribution coefficient (Kp) is dependent on the eluent composition. The volume of the acetonitrile adsorbed phase is dependent on the acetonitrile adsorption isotherm, which could be measured separately. The actual volume of the acetonitrile adsorbed layer at any concentration of acetonitrile in the mobile phase could be calculated from equation (2-52) by multiplication of the total adsorbed amount of acetonitrile on its molar volume. Thus, the volume of the adsorbed acetonitrile phase (Vj) can be expressed as a function of the acetonitrile concentration in the mobile phase (V, (Cei)). Substituting these in equation (2-67) and using it as an analyte distribution function for the solution of mass balance equation, we obtain... 

Vr(csi) is the analyte retention as a function of the eluent concentration, Vo is the total volume of the liquid phase in the column, y Cei) is the volume of adsorbed layer as a function of eluent composition, Kp(cei) is the distribution coefficient of the analyte between the eluent and adsorbed phase, S is the adsorbent surface area, and is the analyte Henry constant for its adsorption from pure organic eluent component (adsorbed layer) on the surface of the bonded phase. 

The analyte molecules are distributed between the mobile phase, the acetonitrile adsorbed layer, and the adsorbent surface. The analyte could be in neutral, ionic, and ion-associated form, assuming that only neutral and ion-paired analyte could partition into the organic adsorbed layer and subsequently be adsorbed on the surface. This discussion is limited to the hypothetical energetically homogeneous surface of the reversed-phase adsorbent where residual silanols are effectively shielded by the alkyl bonded layer with high bonding density. The effect of accessible residual silanols, although much discussed in the literature, has never been estimated quantitatively in direct experiments and thus could not be included in any theoretical considerations. The total amount of analyte in the bulk solution p) is represented as a sum of the concentrations of each form of the analyte multiplied by the mobile-phase volume ... 

All the techniques discussed so far refer to clean surfaces or surfaces with adsorbed molecules. When thicker adsorbed layers are present on the surface, the properties of these layers start to resemble those of the corresponding bulk phases. For Instance, for thin water layers on solid surfaces the dielectric permittivity (bulk water. A more or less gradual transition takes place towards wetting films to which we shall return in Volume III and. as far as multilayer adsorption is concerned, in sec. 1.5 g, h. 

Maximum stability is attained when saturation of the adsorbed surfactant layer is reached. In the case of high-volume fraction at a specific surfactant concentration, if the adsorbed layer is unsaturated, the emulsion stability decreases. In a low-volume fraction case, if the specific surfactant concentration is too high, emulsion stability is also decreased. Therefore, while an increase in surfactant concentration may increase the stability of the internal phase, the absolute stability of the ELM may be decreased [88]. Carrier Concentration Mass transfer rates can be increased by increasing the carrier concentration [41], however, increasing the carrier concentration usually increases swelling and lowers the emulsion stability [33,108]. Other studies have found limits to the carrier concentration where further increases do not lead to an increase in extraction rates as the mobility of the carrier is stifled due to an increase in viscosity [34,41]. 

The molecular structure not only determines the adsorbate-substrate interactions but also the lateral interactions between the adsorbed molecules. Attractive adsorbate-adsorbate interactions, for example, due to van der Waals forces between molecules with long hydrocarbon chains, result in the formation of condensed, often ordered ad-layer phases ( self-assembled monolayers, see Chapter 2.1 in Volume 10), in which the strength of adsorption is increased. Reciprocally, repulsive interactions (e.g. dipole-dipole interactions) weaken the adsorption. 

Great emphasis has been placed on the fact that viscosity and rheological behavior are a function of the effective volume fraction. Solvation is another mechanism that alters ( ), and it occurs when a thick adsorbed layer of continuou,s phase or surfactant develops on the surface of particles. In this sense, may be estimated in two ways. In the first. 

Figure 1 illustrates graphically the interfacial region of a two-phase system for two components A and B, with low concentrations of A,B in the gas phase (2) and also of B dissolved in the solid phase (1). The dividing surface is placed parallel to the interface, such that the excess concentration Fa is zero. The extent of the adsorbed layer is just one monolayer of B in this simple picture, and its actual volume is practically insignificant compared to the volume of either phase (1) or (2). Even if the adsorbed layer would consist of two or three monolayers, this would still be tme. The excess concentration Fb is nonzero and equal to the coverage of B. 

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