The influence of surface heterogeneity on thermodynamics of adsorption. Hard rods on a line

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Abstract
A system of hard rods on a line in an inhomogeneous external field is considered. This is a model of adsorption on a heterogeneous surface or, more closely, adsorption at a heterogeneous step on a surface. The external field (adsorption potential) is a Gaussian distribution of energy corresponding to a single adsorption site. A numerical method of calculation of the microdensity and its derivatives with respect to chemical potential and temperature from the Percus integral equation is described. These derivatives make it possible to calculate the differential entropy and energy (heat) of adsorption. The phenomenon of redistribution of adsorbate with increase of chemical potential is discussed. It is shown that adsorbed phase local density decreases on some parts of the interval and increases on other parts as the total adsorption increases. The differential heat of adsorption is close to the inverse cumulative energy distribution of adsorbate. It is also shown that the variation of the differential entropy of adsorption is suppressed in comparison to adsorption in an uniform external field.