The origin of van-der-Waals forces – Fundamental concepts and their consequences
Van-der-Waals forces are weak interactions between neutral particles, such as atoms and molecules, who do not interact classically. Caused by the quantum-mechanical ground-state fluctuations of the electromagnetic field, the particles are polarised for a short time, leading to an induced dipole force typically attracting the particles. If these particles are located in a vacuum and separated by a „medium“ ranged distance d, the resulting interaction potential takes the well-known form. But what is this „medium“ range? And what will happen when the particles are located in a solvent? These questions will be addressed during the lectures.
From the theoretical point of view, van-der-Waals forces, as interactions between two polarisable objects, belong to dispersion forces that further include the Casimir effect between two dielectric objects and the Casimir–Polder force between a polarisable object and a dielectric surface. These interactions are well described within the framework of macroscopic Quantum Optics. In the first part of the lecture, I will introduce these concepts starting from Maxwell’s equations, illustrating linear response theory, and demonstrating the quantisation of the electromagnetic fields. By coupling these fields to free particles, we can derive general expressions for the dispersion forces and, thus, address the validity range of the inversed-six-power law.
In the second part of the lecture, we will explicitly consider the impact of a solvent, leading to the so-called cavity models (often called effective polarisabilities or access polarisabilities). Within the quantum-optical framework, the dispersion forces are interpreted by an exchange of virtual photons. A virtual photon is a quasi-particle, meaning it does not exist but behaves like a real photon. Hence, it can be manipulated at interfaces and in media leading to reflections and absorptions. To this end, all manipulations will influence the dispersion forces. This lecture part is dedicated to effectively modelling these impacts for dissolved particles.