From van der Waals equation to acid-base theory of surfaces: A chemical-mathematical journey

Although occasional observations concerning capillarity, adhesion and cohesion date back to antiquity, the proper scientific investigation of such phenomena began only in the early 19th century, with the fundamental contributions of T. Young and P.S. de Laplace, who provided the basic physical understanding and mathematical description of capillarity. The development of the molecular theory of matter led to the recognition of adhesion/cohesion as a macroscopic manifestation of intermolecular forces (van der Waals) and to their explanation in terms of the electromagnetic theory, with the introduction of the fundamental concepts of Keesom, Debye and London/dispersion interactions. The latter, in particular, relied also on the new ideas of quantum mechanics. Next was the attempt at calculating the adhesion forces between macroscopic bodies as a superposition of interactions between pairs of molecules (Hamaker). The quantum-mechanical approach had two important consequences: on the one hand, through quantum field theory, a completely new interpretation of dispersion forces (Casimir), that allowed to overcome the bimolecular approximation, resulted in the celebrated Lifshitz theory and made possible the first actual prediction of dispersion interactions between macroscopic bodies; on the other hand, through the concept of molecular orbital (particularly HOMO and LUMO), the idea that the ability of molecules to accept or donate electron density may provide an important contribution to intermolecular forces, thus introducing the concept of acid-base interactions. This brief review intends to discuss the main steps that led from van der Waals first insights on intermolecular interactions to the modem acid-base theory, which nowadays constitutes a fundamental paradigm to understand and describe adhesion phenomena.