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Integral equation of adsorption

A novel approach is reported for the accurate evaluation of pore size distributions for mesoporous and microporous silicas from nitrogen adsorption data. The model used is a hybrid combination of statistical mechanical calculations and experimental observations for macroporous silicas and for MCM-41 ordered mesoporous silicas, which are regarded as the best model mesoporous solids currently available. Thus, an accurate reference isotherm has been developed from extensive experimental observations and surface heterogeneity analysis by density functional theory the critical pore filling pressures have been determined as a function of the pore size from adsorption isotherms on MCM-41 materials well characterized by independent X-ray techniques and finally, the important variation of the pore fluid density with pressure and pore size has been accounted for by density functional theory calculations. The pore size distribution for an unknown sample is extracted from its experimental nitrogen isotherm by inversion of the integral equation of adsorption using the hybrid models as the kernel matrix. The approach reported in the current study opens new opportunities in characterization of mesoporous and microporous-mesoporous materials. [Pg.71]

In the following paragraphs we will describe in some detail the mathematical process used to invert the integral equation of adsorption, and the method used to create the model matrix. [Pg.72]

Modeling physical adsorption in confined spaces by Monte Carlo simulation or non-local density functional theory (DFT) has enjoyed increasing popularity as the basis for methods of characterizing porous solids. These methods proceed by first modeling the adsorption behavior of a gas/solid system for a distributed parameter, which may be pore size or adsorptive potential. These models are then used to determine the parameter distribution of a sample by inversion of the integral equation of adsorption, Eq. (1). [Pg.81]

NUMERICAL METHODS OF SOLVING THE INTEGRAL EQUATION OF ADSORPTION... [Pg.418]

Equation (7.9) is therefore the general form for any adsorption isotherm and corresponds to equation IV-4 of Ref [3]. Equation (7.9) is now often referred to as the integral equation of adsorption or the generalized adsorption integral. The function q(p,Uo) is called the kernel function or the local isotherm. The local isotherm can take various forms, depending on the geometry of the system that Eqn (7.9) is being used to describe. [Pg.151]

Solving and Using the Integral Equation of Adsorption 7.2.2.1 Analytic solutions... [Pg.152]

The integral equation of adsorption, Eqn. (7.9), can be rewritten in specific units as... [Pg.154]

While DFT allows us to calculate values for q(p, e), it of course provides no analytic form for the function, and in general the form of f(e) is also unknown. However, by using carefully designed numerical methods, model isotherms calculated by MNLDFT can be used in carrying out the inversion of the discrete form of the integral equation of adsorption. In this way one can determine the effective adsorptive potential distribution of the adsorbent from the experimental adsorption isotherm. The method used can be expressed by... [Pg.155]

B. Solving and using the integral equation of adsorption Application of Density Functional Theory... [Pg.311]

The basie relationship used in the theory of adsorption on heterogeneous solid surfaees is the so-ealled integral equation of adsorption isotherm, whieh ean be written as [21,22]. [Pg.110]


See other pages where Integral equation of adsorption is mentioned: [Pg.246]    [Pg.189]    [Pg.79]    [Pg.81]    [Pg.151]    [Pg.152]    [Pg.311]    [Pg.314]    [Pg.319]    [Pg.332]    [Pg.468]    [Pg.29]    [Pg.2]    [Pg.26]    [Pg.26]    [Pg.52]    [Pg.56]    [Pg.106]   
See also in sourсe #XX -- [ Pg.151 ]




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