Volume of Adsorbed Phases

The set of molecules of a fluid phase, i. e. a gas or a liquid, which is within the field of forces of the atoms or molecules of the external or internal surface of a solid sorbent is called the adsorbate of the fluid on this sorbent material. This set may be considered as a thermodynamic system or phase in the sense of W. Schottky [1.63]. Such a system is defined as set ofbodies or molecules divided from its surroundings by clearly defined boundaries and exchanging with its surroundings only mechanical work, heat and mass. Obviously, any adsorbate is an inhomogeneous phase as - by definition - its molecules are subject to the surface forces of the sorbent atoms. Hence the conditions for local (x = (xi, X2, X3)) thermodynamic equilibrium conditions, derived from the Second Law of thermodynamics, are [1.64] 

Here p, p, T, p. indicate the pressure, mass density, temperature and chemical potential of the adsorbate at location x = (xi, X2, X3). T is the temperature of the sorptive fluid. The quantity O = 0(x) is the potential energy per unit mass at location (x) of the surface forces of the sorbent atoms. As this quantity normally is an unknown function of space coordinates (x), so are the local thermodynamic quantities (p, p,T, p). For given model function of the surface 

Here V = V(A) is the volume filled by the set (A) of all molecules of the adsorbate, i. e. all molecules of the sorptive fluid influenced by or exerted to the surface forces of the sorbent material. Assuming the sorptive fluid far away from the sorbent material to approach an equilibrium state of constant density 

This is basically an energetic criterion deciding whether a molecule from the fluid is adsorbed on the surface of a solid material or not. It can be specified as follows Let the energy (E) of the molecule be 

Here Eiti is the kinetic energy of the translational and possibly internal degrees of freedom of the molecule. Let also (Ep) and (E ) be the potential energies of interaction of the 

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The mass concentration x can be related to the volume of adsorbed phase V by an assumed density of adsorbed phase r ... 

The potential theory postulates a unique relationship between the adsorption potential ep and the volume of adsorbed phase contained between that equipotential surface and the solid. It is convenient to express the adsorbed volume as the corresponding volume in the gas phase. 

Vo total volumetric capacity of adsorbent to adsorb Vs volume of adsorbed phase in equilibrium stage Xi equilibrium mol fraction of i in adsorbed phase Xj equilibrium mol fraction of j in adsorbed phase yi mol fraction of component 1 in the fluid phase... 

From isotherm measurements, usually earried out on small quantities of adsorbent, the methane uptake per unit mass of adsorbent is obtained. Sinee storage in a fixed volnme is dependent on the uptake per unit volume of adsorbent and not on the uptake per unit mass of adsorbent, it is neeessary to eonvert the mass uptake to a volume uptake. In this way an estimate of the possible storage capacity of an adsorbent can be made. To do this, the mass uptake has to be multiplied by the density of the adsorbent. Ihis density, for a powdered or granular material, should be the packing (bulk) density of the adsorbent, or the piece density if the adsorbent is in the form of a monolith. Thus a carbon adsorbent which adsorbs 150 mg methane per gram at 3.5 MPa and has a packed density of 0.50 g/ml, would store 75 g methane per liter plus any methane which is in the gas phase in the void or macropore volume. This can be multiplied by 1.5 to convert to the more popular unit, V/V. 

Specific heat of adsorbed phase at constant volume. 

Therefore, the detailed analysis of concentration of defects in surface-adjacent layer and in the volume of adsorbent as well as assessment of the values of diffusion coefficients of defects and particles of various gases in material of adsorbent are very important for understanding the processes of both reversible and irreversible change in electrophysical characteristics of semiconductor during low temperature (if compared to the temperature of creation of defects) interaction with gaseous phase. 

In its simplest form the competition model assumes the entire adsorbent surface is covered by a monolayer of solute and mobile phase molecules. Under normal chromatographic conditions, the concentration of sample molecules will be small and the adsorbed monolayer will consist mainly of mobile phase molecules. Retention of a solute molecule occurs by displacing a roughly equivalent volume of mobile phase molecules from the monolayer to make the surface accessible to the adsorbed solute aiolecule. For elution of the solute to occur -the above process must be reversible, and can be represented by the equilibrium depicted by equation (4.6)... 

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 ... 

M mass of solute to be separated N number of effective theoretical plates P pressure Q flow rate R resolution S peak capacity Sm specific heat of mobile phase Ss specific heat of adsorbent Sg specific heat of detector cell walls V volume in conventional units Vo system dead volume Vr retention volume V r corrected retention volume Vm volume of mobile phase in the column Vs volume of stationary phase in the column Ve extra column volume... 

Vm volume of mobile phase in the heat of adsorption detector cell Vs volume of adsorbent in the heat of adsorption detector cell Vff volume of the wall of the heat of adsorption detector cell Vc total column volume volume Vsi volume of silica in the column Vp pore volume of the packing Vi sample volume... 

W and V° being the total weight of stationary phase and the volume of mobile phase, respectively. From the above two equations it is easily deduced that the Rf value increases from zero to unity with decrease in the K° value, viz., with decrease in the concentration of adsorbed sample molecules. Further it is obvious that Eqs. (2) and (3) confirm the aforementioned qualitative rule for designing a TLC system appropriate for a given sample, i.e., selection of the developer and adjustment of the adsorbent activity. 

In adsorption, the amount adsorbed on a surface is most fundamentally characterized by the fraction of surface sights, 9,, that are occupied by i adsorbate molecules. Because the surface area is often not well known, adsorption isotherms are often reported as the amount adsorbed on the surface per gram of adsorbent. In gas adsorption, this amount is traditionally given as the volume of adsorbate at standard temperature and pressure (STP), v. This volume depends on temperature and on the pressure of the adsorbate in the gas phase. v(T, P) is an equation of state for the surface and, when reported at a constant T, is known as an adsorption isotherm. 

Volumes of adsorbed and nonsorbed phases, per gram of adsorbent Monolayer uptake (g/g) of solvent B from pure B as mobile phase Molecule of solute X in adsorbed or nonsorbed phases Concentration of X in adsorbed or nonsorbed phase A proton-donor solute... 

Adsorbent nonpermeability is an important condition, since it essentially states that all processes occurs in the liquid phase. Since adsorption is related to the adsorbent surface, it is possible to consider the analyte distribution between the whole liquid phase and the surface. Using surface concentrations and the Gibbs concept of excess adsorption [20], it is possible to describe the adsorption from binary mixtures without the definition of adsorbed phase volume. 

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. 

Equation (2) for the number of particles per unit volume of aqueous phase has one undetermined parameter Af which is the difierence between the surfactant charged and the surfactant adsorbed on the surface of the polymer particles. 

If we assume that the volume of stationary phase, Vg, volume of adsorbed liquid. Fa, then replacing Fj by Fa and substituting into equation (3.2) gives... 

Chromatographers and chemical engineers use different values for the equilibrium constant, K. The definitions are the same in both fields. The equilibrium constant is the ratio of the equilibrium concentrations of the solute under study in the two phases of the system. However, chromatographers generally report concentrations as the mass of solute per unit volume of the phase considered, whether liquid or solid, with the result that the equilibrium constant is dimensionless. By contrast, chemical engineers report liquid phase concentrations as the mass of solute per unit volume of the liquid phase but solid (or rather adsorbed... 

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