# Surface van der Waals Forces in a Nutshell

## TL;DR

This paper presents a simple, unified equation that accurately describes surface van der Waals forces across all distances, capturing the transition from non-retarded to retarded interactions and their effects at nanometer scales.

## Contribution

It introduces a single, tractable formula for surface van der Waals forces that includes retardation effects and polarization, improving upon the traditional Hamaker approximation.

## Key findings

- Retardation effects significantly alter force behavior at nanometer distances.
- The new model captures the crossover from London to Casimir regimes.
- The approach uses standard material properties and matches conventional accuracy.

## Abstract

Most often in chemical physics, long range van der Waals surface interactions are approximated by the exact asymptotic result at vanishing distance, the well known additive approximation of London dispersion forces due to Hamaker. However, the description of retardation effects that is known since the time of Casimir is completely neglected for lack of a tractable expression. Here we show that it is possible to describe surface van der Waals forces at arbitrary distances in one single simple equation. The result captures the long sought crossover from non-retarded (London) to retarded (Casimir) interactions, the effect of polarization in condensed media and the full suppression of retarded interactions at large distance. This is achieved with similar accuracy and the same material properties that are used to approximate the Hamaker constant in conventional applications. The results show that at ambient temperature, retardation effects significantly change the power law exponent of the conventional Hamaker result for distances of just a few nanometers.