A novel technique for the calculation of site energy densities from gas adsorption isotherm data

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Abstract
A new method of obtaining the site energy distribution for adsorption of gas molecules on a heterogeneous substrate is presented. The method exploits the Fourier convolution nature of the first-kind Fredholm equation which connects the amount of gas adsorbed (the data function) to the site energy density (the object function)via an assumed form for the local isotherm type. The method is capable of handling a wide variety of local isotherm types including both patchwise and random distributions and the effects of lateral interactions. The ill-posed nature of this inverse problem is clearly demonstrated in this method and the effect of noise in the data function on the accuracy of the inversion is easily understood, although a frequency extrapolation technique is used to minimize the effect of noise on the deconvolution. The method is designed to operate on modern adsorption data which can be obtained over a wide pressure regime and very closely spaced (essentially continuously) using the continuous addition technique. The effect of a wrong choice of local isotherm is discussed briefly.

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