Determination of energy distribution function from observed adsorption isotherms

Abstract

One of great unsolved problems of physical adsorption is the influence of heterogeneity on adsorptive properties of adsorption systems (1). Many theoretical procedures have been proposed in order to describe the heterogeneity effects (2-10). One of the most widely known and often used procedures is the integral representation for the overall adsorption isotherm Otwhere 01 is the local adsorption isotherm, )~(e) is the differential energy distribution, and Q is the range of possible variation of the adsorption energy e. The most interesting problem here is to solve the eq. [1] with respect to the function Z(e), when Ot and 01 are known as analytical expressions.Hobson and Armstron9 (11) were the first who investigated theoretically the Dubinin-Radushkievieh equation (D -R) as the overall adsorption isotherm. The D -R isotherm firstly proposed, and widely verified for porous adsorbents (12), has been found to hold for many non-porous adsorbents (metals, glasses) in the submonolayer range. The source of this success has been theoretically investigated by Hobson (13), Haul and Gottwald (14), Ricca, Medana and Bellardo (15), Sparnaay (8), and Marsh and Rand (16). Their results suggested that the D -R behaviour is due to a particular structure of the adsorbing surfaces.Most advanced theoretical results are due to Misra (9) and Cerofolini (6). Assuming that 01 corresponds to a Langmuir isotherm 0~(e,p)= 1 + --e x p ~-~[2] P they have pointed out though in different ways, that the D -R isotherm is related to special distribution Z (s), which is probably characteristic for the majority of heterogeneous adsorbents. Constant K is connected with the molecular partition function for molecules from the monolayer.These results has been obtained by Misra (9) by solving the Stieltjes transform, which is obtained from eq. [1], using the Langmuir isotherm for 01 (17) and by Heer (18) on the basic of statistical mechanics.Cerofolini ( Above B and Pm are two characteristic constants in the equation D-R. However, the energy s and the minimal adsorption energy s,. are given by the following relations P --.[5] e = -R T l n -~ and sm= RTIn K PmAs it appears from the eqs.[4] and r5] the form of the distribution function X(s) depends on the

Application of adsorption methods to determine the effect of pH and Cu-stress on the changes in the surface properties of the roots

“…According to the theory of adsorption on heterogeneous surfaces (Jaroniec and Brauer, 1986;Jaroniec et al, 1976;Kowalczyk et al, 2004), the total adsorption at a given pressure p can be expressed as a sum of local adsorptions a i on a given site of energy E i = (E a,i -E c )/RT, where E a,i is adsorption energy of the i-th site:…”

Determination of Energetic and Geometric Properties of Plant Roots Specific Surface from Adsorption/Desorption Ishoterm

“…This function should be estimated from adsorption in the first layer (monolayer), because in next layers the surface adsorption forces are screened by already adsorbed molecules. Various models are used in the literature to find adsorption energy distribution function [4][5][6]. Here the simplest approach based on graphical (or numerical) differentiation of the adsorption in monolayer vs. adsorption energy curve, similarly as this is described in [7] is presented.…”

A theoretical isotherm for adsorption on heterogeneous surface

“…The integral [13] can be numerically computed in a simple way, and the results of the computations for particular choices of parameters will be discussed in the next section.…”