Looking for gold in Langmuir's data: Surface heterogeneity identification through pressure derivatives

Two methods of determining surface heterogeneity from experimental adsorpti on data are suggested in this work. The first one, which is a statistical m ethod involving a diagnostic parameter, has been employed to discriminate b etween the generalized Langmuir model(GLM) and the Langmuir model (LM). For three adsorbate systems, viz. (a) CO2/mica, (b) CH4/mica, and (c) N-2/mica , the method yields a value of -0.5 for the diagnostic parameter, implying that the LM is the correct model. A more sensitive second procedure based o n the concept of a pressure derivative product (PDP), which is the product of surface coverage and its pressure derivative, is employed to identify su rface heterogeneity. This PDP when plotted against the surface coverage giv es a maximum. For the N-2/mica and CH4/mica systems, these values are given by theta(max) = 0.333 and theta(max) = 0.25, respectively. This means that the former surface is homogeneous and the latter is heterogeneous with res pect to the adsorption behavior of these adsorbates. It is also shown that the error variance of the PDP is minimal at its maximum. A thermodynamic in terpretation of the PDP is made. The PDP is shown to be related to the grad ient of the differential molar entropy, and also a qualitative interpretati on is made of the PDP peaking at intermediate surface coverages. This origi nates mainly from the configurational part of the differential molar entrop y.