Spreading pressure, adsorbate

Isotliennal compressibility Spreading pressure, adsorbed plrase Osmotic pressure Nrunber of plrases, plrase rale Joule/Tlromson coefficient Dipole moment Chemical potential, species i Stoiclriometric number, species i Molar or specific deirsity = 1 / V Critical density Reduced density... 

Equation (16-36) with y = 1 provides the basis for the ideal adsorbed-solution theoiy [Myers and Prausnitz, AIChE J., 11, 121 (1965)]. The spreading pressure for a pure component is determined by integrating Eq. (16-35) for a pure component to obtain... 

Thus, contributions include accounting for adsorbent heterogeneity [Valenzuela et al., AIChE J., 34, 397 (1988)] and excluded pore-volume effects [Myers, in Rodrigues et al., gen. refs.]. Several activity coefficient models have been developed to account for nonideal adsorbate-adsorbate interactions including a spreading pressure-dependent activity coefficient model [e.g., Talu and Zwiebel, AIChE h 32> 1263 (1986)] and a vacancy solution theory [Suwanayuen and Danner, AIChE J., 26, 68, 76 (1980)]. 

The spreading pressure defines the lowering of surface tension at the aqueous-solid phase (i. e., adsorbate-solution) interface ... 

The decrease in free energy is equal to ir, the spreading pressure, a quantity which has been widely used in studies at liquid interfaces. As the free energy is reduced, the spreading pressure becomes larger. The pressure of gas above the solid is p, and F is the concentration of adsorbed material. Converting into the experimental variables usually measured, we have... 

The quantity Cr correlates the effects of monolayers, both spread and adsorbed, on K, as in Fig. 11. As one may show quantitatively with talc particles, the eddy velocity at the interface is greatly reduced by the mono-layer. The latter restrains fresh liquid from being swept along the surface, i.e., there is less clearing of the old surface. If now All is the surface pressure resisting the eddy due to its partly clearing an area (Fig. 12) in... 

Langmuir, in 1917, constructed the film balance for the measurement of the surface or spreading pressure. Thus, it became possible to experimentally observe that adsorbed films pass through several states of molecular arrangement. The various states resemble that of a two-dimensional gas, a low-density liquid, and finally a higher density or condensed-liquid state. In the latter case the spreading pressure can be described by the linear relationship,... 

Ideal Adsorbed Solution Theory. Perhaps the most successful general approach to the prediction of multicomponent equilibria from single-component isotherm data is ideal adsorbed solution theory. In essence, the theory is based on the assumption that the adsorbed phase is thermodynamically ideal in the sense that the equilibrium pressure for each component is simply the product of its mole fraction in the adsorbed phase and the equilibrium pressure for the pure component at Ike same spreading pressure. The theoretical basis for this assumption and the details of the calculations required to predict the mixture isotherm are given in standard texts on adsorption. Whereas the theory has been shown to work well for several systems, notably for mixtures of hydrocarbons on carbon adsorbents, there are a number of systems which do not obey this model. Azeotrope formation and selectivity reversal, which are observed quite commonly in real systems, are not consistent with an ideal adsorbed phase and there is no way of knowing a priori whether or not a given system will show ideal behavior. 

A mixture equilibria model which is not based on any specific isotherm model does not have the limitations expressed in the derivation of such a model. The Ideal Adsorbed Solution Theory of Jtyers et al. (3 ) is based on the equivalence of the spreading pressures and does not presuppose any isotherm model. In fact, in the original papers, Glessner and Myers (k) stipulated that the model should only be applied using raw equilibrium data to calculate the spreading pressures. This is a very restrictive covenant and does not permit the use of the model for predictive purposes other than that for which data are available. However various authors have applied the Ideal Adsorbed Solution Theory (IAST) model using isotherm models (5., ) quite satisfactorily. 

The equilibrium thermodynamic functions describing the retention process are essentially related to the net retention volume. For example, the intermolecular adsorption of Gibbs free energy, —AGa, for one mole of solute vapor from a reference gaseous state with the partial pressure, Po, to a reference adsorbed state with the equilibrium spread pressure (or two-dimensional pressure), no, is given as [115]... 

According to second and third observations, it is difficult to appreciate the maximum value of the surface free energy and surface enthalpy of a solid, especially in the case of microporous materials which are widely efficient adsorption properties of the surface (sample V). Therefore, for this material, more works may be needed on the adsorption isotherm, spreading pressure, isosteric heat of adsorption, and even heterogeneities of solid surfaces. They are concerned with the finite concentration technique with increasing amount adsorbed, which will be dealt to some extent in the next section. 

Gibbs 508, 514 (9)] and obtain expressions for the adsorbate spreading pressure. ... 

Furthermore, as with a liquid, the surface tension of the adsorbent is reduced result of physisorption (Hill, 1968). This lowering of the surface tension is called spreading pressure and denoted by 77 so that ... 

Comparison of Equations (2.61) and (2.67) shows that the second term of the right-hand side of Equation (2.67) is due to the spreading pressure, which is related to the interactions between adsorbed molecules, often referred to as the lateral interactions . It is only at very low coverages, where the spreading pressure is negligible, that the integral molar entropy of adsorption is simply dependent on the adsorbate-adsorbent interaction. 

Equation (2.72) is not easy to use in the general case in which the spreading pressure is unknown. But in the particular case of stepwise isotherms where there are two adsorbed phases in equilibrium with the gaseous adsorptive (i.e. in the case of a univariant adsorption system), Larher (1968, 1970) showed that the isosteric method may be used with the transition pressure p" to give integral molar energies un and entropies sn of the quasi-layer ... 

If one pictures the adsorbed monolayer as a two-dimensional imperfect gas, it seems reasonable to assume the applicability of a two-dimensional form of the van der Waals equation in which the gas pressure is replaced by the spreading pressure and the volume by the surface area. By combining this with the Gibbs adsorption equation - Equation (2.34) - de Boer (1968) obtained the equation... 

TABLE 4 Spreading Pressure (in I0 3 N/m) of Adsorbed Films on Solids Measured by Adsorption Experiments... 

Here /j is the fiigacity of component i in the bulk gas phase f°is the standard-state fugacity, i.e. the fiigacity of pure component i at the equilibrium spreading pressure of the mixture, n x, and y-, are the mole fraction of component i in the adsorbed and gas phase,... 

Equation (1) is the central equation of LAST, specifying the equality of chemical potential in the bulk gas and the adsorbed phase (which is assumed to be ideal in the sense of Raoult s law). Equation (2) calculates the spreading pressure from the pure-component isotherm. The total amount adsorbed and the selectivity are given by equations (3) and (4), respectively. 

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