Isotherms solid/liquid interface

The determination of adsorption isotherms at liquid-solid interfaces involves a mass balance on the amount of polymer added to the dispersion, which requires the separation of the liquid phase from the particle phase. Centrifugation is often used for this separation, under the assumption that the adsorption-desorption equilibrium does not change during this process. Serum replacement (6) allows the separation of the liquid phase without assumptions as to the configuration of the adsorbed polymer molecules. This method has been used to determine the adsorption isotherms of anionic and nonionic emulsifiers on various types of latex particles (7,8). This paper describes the adsorption of fully and partially hydrolyzed PVA on different-size PS latex particles. PS latex was chosen over polyvinyl acetate (PVAc) latex because of its well-characterized surface PVAc latexes will be studied later. 

In the case of adsorption from solution, the apparent adsorption of a solute at the liquid-solid interface is usually evaluated by measuring the decrease in its concentration when brought into contact with the adsorbent. The adsorption isotherm is then plotted as the apparent adsorption of the solute against the equilibrium concentration. 

When (a) there are no external mass-transfer resistances (such as gas-liquid, liquid solid, etc.), (b) catalysts are all effectively wetted, (< ) there is no radial or axial dispersion in the liquid phase, (d) a gaseous reactant takes part in the reaction and its concentration in the liquid film is uniform and in excess, (e) reaction occurs only at the liquid-solid interface, (/) no condensation or vaporization of the reactant occurs, and (g) the heat effects are negligible, i.e., there is an isothermal operation, then a differential balance on such an ideal plug-flow trickle-bed reactor would give... 

N. L. Ha, J. Ungvaral, and E. Kovats, Adsorption isotherm at the liquid-solid interface and the interpretation of chromatographic data, Anal. Chem. 54 (1982), 2410-2421. 

Gas-solid equilibria have been studied for over 200 years, since Fontana showed that activated charcoal adsorbs gases and vapors at room temperature [1]. A considerable amoxmt of theoretical and experimental literature is available. The Gibbs isotherm [2] and the multilayer adsorption theory of Brunauer, Emmett and Teller [3], provide serious theoretical guidelines and support in understanding the results of experimental studies. Although, gas-sohd isotherms are difficult to predict quantitatively [4], this branch of adsorption thermod3mamics is much easier than liquid-solid adsorption because of the relative simplicity of the gas-sohd interface as compared to the liquid-solid interface. The Gibbs equation relates the amoimt of a compoimd adsorbed per unit surface area of a hquid-gas or a hquid-hquid interface and the surface or interfacial tensions [2]. This relationship provides a useful theoretical framework. 

Many different isotherms have been derived for molecular adsorption at interfaces, including the liquid gas, liquid liquid, and liquid solid interfaces. Some of these isotherms can be shown to be approximate versions of the general isotherm derived here. 

C. Derivation of the Gibbs Equation for Adsorption on Liquid/Solid interfaces. Adsorption isotherms... 

The presence of a liquid phase and a liquid-solid interface in multiphase reactors results in added transport resistances. For instance, the effective diffusivity in liquid-filled pores (of the order of 10 to 10 cmVsec) is much smaller than that in gas-filled pores (of the order of 10 cmVsec). The solubility of the gaseous reactant is an important factor since the gaseous reactant has to be dissolved into the liquid reactant for the reaction to take place on the catalyst surface. As emphasized in Chapter 4, the Biot number for heat is much larger than the Biot number for mass for liquid-solid systems the opposite is true for gas-solid systems. Therefore, the major external resistance lies in the mass transport, and the pellet is not necessarily isothermal. In many cases, however, the equilibrium gas concentration in the liquid is quite low and, thus, the heat evolved is small in spite of high heats of reaction. The pellet can be considered isothermal in such a case,... 

In the last two sections the formal theory of surface thermodynamics is used to describe material characteristics. The effect of interfaces on some important heterogeneous phase equilibria is summarized in Section 6.2. Here the focus is on the effect of the curvature of the interface. In Section 6.3 adsorption is covered. Physical and chemical adsorption and the effect of interface or surface energies on the segregation of chemical species in the interfacial region are covered. Of special importance again are solid-gas or liquid-gas interfaces and adsorption isotherms, and the thermodynamics of physically adsorbed species is here the main focus. 

Until relatively recently, the fact that an experimental isotherm necessarily contained composite information concerning the adsorption of the two components of a binary solution was considered to be a major problem. For a rigorous interpretation it was felt necessary to process the data to obtain the so-called individual adsorption isotherm or separate adsorption isotherm of each component. However, this is not at all straightforward and requires the introduction of a number of assumptions relating to the structure of the adsorbed layer. The main problem is of course to know the composition of the adsorbed layer. One assumption often used in the case of volatile components is that introduced by Williams (1913) the solid will adsorb the same amount of each component from the vapour in equilibrium with the solution as from the solution itself. This of course implies that the adsorbed layer has the same composition at the liquid-solid and gas-solid interfaces and it requires numerous gravimetric measurements from the vapour... 

On a liquid-gas interface, the partial pressure of the adsorbed gas is substituted in Equation 1.59. On the solid-gas and solid-liquid interfaces, only the excess surface concentration can be measured directly, and not the surface tension. The Gibbs adsorption isotherm is suitable for the calculation of the change of surface tension. 

The analysis presented so far has assumed an isothermal operation. In gas-liquid or gas-liquid solid reactions, two types of heat can cause nonisothermal operations. The absorption of gas can generate heat at the gas-liquid interface. This type of heat is commonly known as heat of solution. The reaction (in the... 

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). 

Assumption 5 In the definition of the isotherm, the convention is adopted that the solvent (if pure) or the weak solvent (in a mixed mobile phase) is not adsorbed [8]. Riedo and Kov ts [9] have given a detailed discussion of this problem. They have shown that the retention in liquid-solid i.e., adsorption) chromatography can best be described in terms of the Gibbs excess free energy of adsorption. But it is impossible to define the surface concentration of an adsorbate without defining the interface between the adsorbed layer and the bulk solvent. This in turn requires a convention regarding the adsorption equilibrium [8,9]. The most convenient convention for liquid chromatography is to decide that the mobile phase (if pure) or the weak solvent (if the mobile phase is a mixture) is not adsorbed [8]. Then, the mass balance of the weak solvent disappears. If the additive is not adsorbed itself or is weakly adsorbed, its mass balance may be omitted [30]. 

The adsorption isotherms in Table 5.2 can be applied to both fluid and solid interfaces. The surface tension isotherms in Table 5.2, which relate a and Fj, are usually apphed to fluid interfaces, although they could also be used for sohd-liquid interfaces if a is identified with the Gibbs superficial tension. (The latter is defined as the force per unit length that opposes every increase of the wet area without any deformation of the sohd.)... 

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