Better adhesion than previously thought in van der Waals force

The quantum mechanical description of the force between uncharged atoms and molecules demonstrated in real structures

They ensure that gases below a certain temperature condense into liquids. They give glue its adhesive force and enable geckos to hang upside down on a wall. The 'they' in question: van der Waals forces. Researchers at the Berlin-based Fritz Haber Institute of the Max Planck Society, together with colleagues in Italy and the USA, have succeeded in describing, more accurately than they were previously able to, the forces of attraction that operate between uncharged nanostructures. For the first time ever, they have successfully applied the concept to real molecular structures. The researchers can now envisage that practice-oriented material scientists, process designers and even drug researchers will one day benefit from the better understanding of van der Waals forces. It could, for example, then be possible to systematically modulate the forces.

The forces of attraction between atoms or molecules, which the Dutch physicist Johannes Diderik van der Waals discovered almost 150 years ago, are admittedly much weaker than the forces between ions or between two atoms that are linked by a genuine chemical bond. But they still exert a major impact. And that is not just because they hold together the particles in liquids. In biochemistry, they turn out to be almost vital, as they determine how enzymes interact with other biomolecules. The importance of van der Waals forces should increase even further as advances are made in nanotechnology. After all, they are the dominant forces between uncharged nanostructures and they ultimately decide what functionality nanostructures can provide.

By virtue of their origin, van der Waals forces are electrostatic forces. They operate not only between polar molecules but also between electrically neutral atoms and molecules. This is because the movement of electrons in the outer shell of the atoms temporarily leads to charge displacements – and to so-called polarization. Charged areas with different signs are then attracted to one another – and therefore ensure an attraction between two atoms, even if these are electrically neutral overall.

Paradigm change in the description of van der Waals forces

Even though scientists have known about the forces for a long time, their physical and mathematical description is still insufficient. There is a classical model, dating back to the physicist Fritz London in the 1930s. According to this model, individual atoms interact with one another in pairs in van der Waals forces. In the mathematical description of the forces, physicists assumed that these forces decrease with the seventh power of the distance between the atoms. Thus, they should have a range of just one nanometre (one billionth of a metre) or less.

However, thanks to today's leading-edge technologies, the measurements that physicists can now perform even on the tiniest structures contradict this mathematical description. And the theoretical calculations that researchers from the Fritz Haber Institute of the Max Planck Society in Berlin have conducted with colleagues in Italy and the USA also contradict this model. Their calculations are based on a quantum mechanical model. "All electrons orbit the atomic nuclei and we describe this complete movement of electrons in a molecule or structure as a wave function", says Alexandre Tkatchenko, Research Group Leader in the Theory Department at the Berlin-based Fritz Haber Institute and Professor of Condensed Matter Physics at the University of Luxembourg, explaining the process. The physicist sees an analogy here with surface plasmons, as they are known – the oscillations of external electrons on metal particles. "If you bring two molecules or nanostructures close together, the waves, meaning the respective electron oscillations, interact with one another", says Tkatchenko. The result of this interaction is the van der Waals force.

The attraction operates at distances of up to 100 nanometres

Based on the assumptions made, it was then possible for the scientists to calculate the energetic status of two neighbouring molecules or two nanostructures – and thus to infer the force that is operating between them. They did this calculation for many distances. They determined among other things that, with increasing distance, the van der Waals force decreased much slower than previously assumed. Its range is therefore much larger than was previously inferred from the conventional model. "This attraction operates up to a distance of 100 nanometres", according to Alexandre Tkatchenko. The researchers also discovered that the rate of decrease, known as the exponent, is in no way constant, but instead varies with the distance. Tkatchenko calls it a paradigm change in the description of the van der Waals interaction. And it clearly leads to a good reproduction of reality. In any case, the scientists' calculations align well with the experimental findings of other researchers in the recent past.

Tkatchenko emphasizes that this is the first time ever that the underlying concept has been successfully applied to real molecular structures with which chemists or biologists work on a daily basis. Among other things, the researchers had calculated the forces that operate between two layers of graphene. The researchers also determined how strongly carbon nanotubes are attracted to one another. In one case, they also calculated the attraction between a fictitious chain of carbon atoms and a protein molecule.

Significance for materials engineers and drug developers

Van der Waals forces are around ten times weaker than the force that exists between differently charged ions, for example. Nevertheless, they are interesting not only for theorists like Tkatchenko and his team but are also highly relevant for application-oriented researchers. One example would be those who research innovative adhesives. Another would be materials engineers. "Take an airplane", says Tkatchenko. "These days, its components are based increasingly on polymer materials. How the individual polymer molecules line up next to one another when they solidify is largely determined by the van der Waals forces operating between them." Understanding these better and being able to count on them will also be of interest to such fields of application.

A better description of van der Waals forces could also be helpful for drug developers in the pharmaceutical industry, for example. Ultimately, it is these forces in particular that will determine how well a drug molecule will bind to a target structure in the organism, frequently a protein. Now that the team has successfully applied the new calculation approach to the interactions between real molecules, physicist Alexandre Tkatchenko hopes that future biologists and chemist will identify the benefits for their respective areas of work. 

KH