Use of CONTIN for Calculation of Adsorption Energy Distribution

Abstract

The CONTIN method for inverting noisy linear operators was used to calculate the adsorption distribution function from both simulated and experimental adsorption isotherms. Simulated isotherms allowed us to estimate the resolving power of the method and the influence of errors on the distribution function, while experimental isotherms enabled us to validate the adsorption model and its parameters. It was shown that calculation within the condensation approximation region gives perfect recovering of the original distribution if sufficient information is inherent in the input data, that is, in the case of a large data set over a wide range of relative pressures. When only a window of data is available on the adsorption isotherm, it is possible to calculate the distribution restricted to the condensation approximation (CA) region. The influence of peaks outside the CA region may be eliminated by introducing the constant background term in the calculation. The level of error on the isotherm does not affect the resulting distribution up to 10% in the case of a large data set and up to 5% in the case of a small data set. On the basis of analysis of the randomness of the residuals of the fit to the data, it was possible to establish a true parameter of the lateral interaction constant. This approach applied to experimental data has led to the value k 1 mob = 5.5−5.6 for the HdB mobile adsorption model and k 1 loc = 3 for the FG localized adsorption model. On the basis of the fact that optimal value of k 1 mob is closer to the theoretical value, the mobile adsorption model is preferred. The CONTIN method applied to graphitized carbon black revealed four peaks on the adsorption energy distribution function. The peak constrained analysis allowed us to confirm the existence of all original peaks. The distributions calculated from standard nitrogen adsorption data showed that although reference carbons are heterogeneous in different ways, they possess common peaks at 4.9, 6.8, and 8.8 kJ/mol characteristic to graphitized carbon black Sterling FT. Analysis of the heterogeneity of synthetic carbons revealed the changes in adsorption energy distributions (AEDs) that occur during CVD from methane.

Evaluation of the Structural and Energetic Heterogeneity of Microporous Carbons by Means of Novel Numerical Methods and Genetic Algorithms

“…This program suit is often applied to solve integral equations of the first kind with respect to effectively continuous distributions of diffusion coefficients, molecular weights, relaxation times, electron densities, adsorption energy distributions (46,(52)(53)(54)(55)(56)(57)(58), pore size distributions (35,52,(55)(56)(57)(58)(59)(60), etc. As mentioned above, in CONTIN the regularization method was used for the stabilization of solution.…”

“…Thus, despite the simplicity of calculation of APDs, the AED curves are more sensitive to the changes in the structure of adsorbents. The interpretation of the position of energy peaks obtained from the method studied was recently studied by Puziy and co-workers (46). It was established that the peak in the range of 8 kJ/mol is attributed to interaction between the nitrogen molecules and the basal planes of graphitic microcrystallites (i.e., the formation of monolayer on the walls of wider micropores).…”

“…The results obtained on the basis of the TOMF are compared with those obtained from density functional theory (DFT) (27)(28)(29)(30)(31) from the Nguyen and Do method (ND) (32)(33)(34)(35) and from the Horvath and Kawazoe procedure (HK) (36)(37)(38)(39)(40)(41)(42). Moreover, the adsorption potential (APD) (43) and adsorption energy (AED) (1,2,4,11,35,(44)(45)(46) distributions are evaluated from experimental low-temperature nitrogen adsorption isotherms.…”

Characterization of Titania/Silica Gel by Means of Low-Pressure Nitrogen Adsorption

“…[2] were estimated at p/ p 0 < 0.5 using a local isotherm approximation (22). The constrained regularization CONTIN procedure was successfully utilized to obtain the pore size and adsorption energy distributions (6,23,24) and computed f (E) distributions (especially at a regularization parameter value of 10 −3 ) similar to those obtained with other methods (8,25).…”

Assessment of the structural evolution of polyimide-derived carbons obtained by phosphoric acid activation using Fourier transform infrared and Raman spectroscopy

“…Proton affinity distributions, F(pK), were calculated from proton-binding isotherms (Q versus pH) by solving the adsorption integral equation using the CONTIN method (Provencher, 1982a(Provencher, , 1982bPuziy et al, 1999Puziy et al, , 2001). …”