Fractal dimensions from Q-TG data for estimation of surface heterogeneity

Matyjewicz, M.; Staszczuk, P.

doi:10.1023/b:jtan.0000005176.39209.9e

Cited by 7 publications

(2 citation statements)

References 14 publications

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“…The geometry heterogeneity was studied on the basis of calculation of volumetric fractal coefficients [17,22]. Their determination is important for the processes of diffusion and adsorption, as well as for chemical reactions and catalysis [18,23].…”

Section: Estimation Of the Energetic Heterogeneity From Q-tg Datamentioning

confidence: 99%

Studies of modified carbon nanotubes by means of thermogravimetry Q-TG and sorptometry techniques

Staszczuk

Zimmerman-Rysz

2014

J Therm Anal Calorim

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The paper presents the physicochemical (adsorption and porosity) properties of closed carbon nanotubes, opened through the action of an oxidizing acid and modified with metal ions of nickel, cobalt, and iron/ cobalt. The carbon nanotubes were prepared via the oxidation process by means of 65 % nitric acid and/or nickel and cobalt nitrates dissolved with 65 % nitric acid. Using special thermogravimetry Q-TG and sorptometry methods physicochemical properties of pure and modified nanotube surfaces were investigated. A numerical and analytical procedure for the evaluation of heterogeneous properties (adsorption capacity, statistical number of adsorbed liquid layers, desorption energy distribution functions) on the basis of liquid thermodesorption Q-TG from the sample surfaces under the quasi-equilibrium conditions are presented. The calculations of the specific surface areas, pore size and volume, and fractal dimensions of carbon nanotubes were made from sorptometry data.

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Section: Estimation Of the Energetic Heterogeneity From Q-tg Datamentioning

confidence: 99%

Studies of modified carbon nanotubes by means of thermogravimetry Q-TG and sorptometry techniques

Staszczuk

Zimmerman-Rysz

2014

J Therm Anal Calorim

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“…Our previous papers present the application of thermogravimetry Q-TG for calculation of fractal coefficients [11,12] as well as studies of adsorption layer properties [13,14], adsorbate-adsorbent interactions [15] and total heterogeneity of solid surfaces [16]. The studies include the process reverse to adsorption, i.e.…”

Section: Studies Of Liquids Diffusion In the Chosen Materials Samples mentioning

confidence: 99%

Studies of liquids diffusion in the chosen material samples

Staszczuk

Płanda-Czyż

Błachnio

et al. 2006

J Therm Anal Calorim

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Adsorption and desorption processes of molecules on the surface of adsorbents on the samples of aluminum oxide and other materials are significantly affected by diffusion of adsorbate molecules towards the surface in the adsorbent pores. The difference of concentration at the gas/solid interface is the direct cause of diffusion. The fractality of the surface has an influence on the diffusion of molecules through porous materials [1,2].Thermal motion of the molecules possessing the kinetic energy of translation is responsible for spontaneous, mutual penetration of various gases and liquids. This phenomenon called diffusion leads to formation of homogeneous mixture of gases or liquids. Its direct cause is the existence of concentration gradient at the contact boundary of two substances. The larger the concentration gradient is, the quicker the diffusion process proceeds. The amount of the substance, dm, diffusing in the time, dt, from one to another layer distant by dx is directly proportional to the surface size S through which transfer takes place and to the concentration gradient dc/dx. This dependence is expressed by the first law of Fick formulated in 1855 [3, 4]:where D is the diffusion coefficient. The analytical solution of Fick's law of diffusion in solids where internal diffusion plays a dominant role is developed for the Henry's region of adsorption isotherm [5]. Its solution for the adsorption in solids possessing the spherical-shaped granules is given by Eqs [3, 4]:where a t and a max -the adsorption at the time t and adsorption capacity (maximal adsorption), K=(π where r -the radius of the intersection of a cylinder, α n -the roots of the equation I 0 (x)=0, and I 0 (x) is the Bassel function of the first kind 0 order and 1≤m<∞.Equations (2) and (3) based on the analytical solution of Fick's law of diffusion were used for the description of physisorption kinetics. The migration of species into the spherical adsorbent can be described by the following form of Fick's second law of diffusion as the first approximation [8]:where r -the distance from the center of the particle, c -the solute concentration in the adsorbent. The migration of species into the cylindrical adsorbent particle can be described by Fick's second law of diffusion in the cylindrical form for D=constant (from Eq. (4) Analysis and Calorimetry, Vol. 86 (2006) 1, 261-265 Institute of Physics, National University in Odessa, Ukraine STUDIES OF LIQUIDS DIFFUSION IN THE CHOSEN MATERIAL SAMPLES Thermogravimetric and Q-TG methodThe new method of diffusion coefficient calculations from thermogravimetry Q-TG data has been presented. Programmed thermodesorption of polar and apolar liquids from aluminium oxide and montmorillonite-Na and -La samples in quasi-isothermal conditions has been made. The result from above method was compared with literature data and good correlation were obtained.

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