Response modeling methodology (RMM)—a new approach to model a chemo-response for a monotone convex/concave relationship

Abstract

Modeling the variation of a response in terms of the variation transmitted to it by a related factor (or factors) comprises the bulk of the scientific and engineering research effort. Often, we may reasonably assume that the relationship between the response and the affecting factor (or a linear combination of factors) is monotone convex (concave). To model such a relationship, a new Response Modeling Methodology (RMM) has recently been introduced and shown to represent a natural generalization of many theoretical or empirically-derived models, developed over the years in various scientific and engineering disciplines. In particular, many models of chemistry and chemical engineering fall into this category. In this paper, we demonstrate application of the new methodology to the modeling of a chemical response, and discuss extension to non-monotone relationships. It is shown that some well-known and widely used property correlation equations are indeed special cases of the new model. The allied estimation procedures are applied to some published data sets, related to temperature dependence of vapor pressure and solid heat capacity. We assess the effectiveness of the new approach relative to current models.