Studies Of Energetical And Geometrical Heterogeneity Of Solid Surfaces
studies of energetical and geometrical heterogeneity of solid surfaces
by thermal analysis
V.V. Kutarov2, M. Planda1, P. Staszczuk1,
1Department of Physicochemistry of Solid Surface, Faculty of Chemistry,
Maria Curie-Sklodowska University,
Maria Curie-Sklodowska sq. 3, 20-031 Lublin, Poland
2Physical Research Institute, Odessa I.I. Mechnikov National University, Pastera st. 27, 65026 Odessa, Ukraine
Energetic heterogeneity of sorbents is conditioned by the differences in topology of adsorption centres, dispersion of pore sizes and other factors [1]. The paper describes the method applied for estimation of sorbents energetic heterogeneity making use of the results of programmed thermodesorption of liquids from the solid surface using single Q-TG and Q-DTG curves [2].
In the case of non-associated one-component layers, monomolecular desorption kinetics is described by means of the following equation:
(1)
where: , q – the degree of surface coverage, n – the entropy factor, E– the desorption energy, To i T – the initial and given temperatures of desorption, b – the sample heating rate, t – the time.
Equation (1) holds true when the amount of desorbed substance does not cover the whole surface area uniformly and the basic desorption process takes place in the range of capillary condensation. Using equation (1), one makes also the analysis of desorption from the energetically heterogeneous, multilayer filled solid surface. In this case desorption rate is described by integral equation:
(2)
The shape of element of integration function (3) can be analysed using the analytical method. According to this method, equation of desorption
kinetics (1) for the part of surface characterized by the constant value of desorption energy has the form:
(3)
The desorption kinetics process is given in equation:
(4)
The real form of distribution function jn(E) from single Q-TG and Q-DTG curves (Fig. 1) is obtained by normalization of the function j(E):
(5)
For the correctly calculated distribution function of desorption energy, the equation should satisfy the normalization conditions:
(6)
After calculating the normalized density function jn(E) all size constants reduce reciprocally which makes calculation of the quantity jn(E) much easier:
(7)
The desorption energy distribution function of n-octane on aluminium oxide surface is presented in Fig. 2.
Fig.1.The Q-TG and Q-DTG curves of n-octane desorption from aluminium oxide sample
Fig.2.The desorption energy distribution function of n-octane on aluminium oxide surface
The geometrical heterogeneity of surfaces was estimated as follows. The volume core coefficient Q for cylindrical pores was calculated from equation:
(8)
The Q value changes from 1.95 for p/po = 0.4 to 1.35 for p/po = 0.8. The relationship between pore volume V and pore radius R (Fig.3) is given by equation:
(9)
The pore-size distribution function of the aluminium oxide sample is presented in Fig. 4. This function was calculated on the basis of equation:
(10)
where: fractal surface dimention D = 2.72.
Fig.3.The relationship between pore volume and pore radius of the aluminium oxide sample
Fig.4.The pore size distribution function of n-octane on aluminium oxide sample
References
1. P. Staszczuk, D. Sternik, G.W. Chądzyński, Congress Journal, D.J.Bernhardt Ed., World Chemistry Congress, Brisbane, Australia, 1-6July, 2001, p. 273.
2. P. Staszczuk, D. Sternik, V.V. Kutarov, J. Thermal Anal. & Cal., in press.
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