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 ofthe 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.