D23 Measurement of van der Waals forces

Topic

On clean, dry surfaces, the van der Waals force is ultimately responsible for the adhesion of insect setae; although these adhesive structures rely on other mechanisms under different conditions, in the absence of water or contamination, it is the van der Waals force—acting at the atomic scale between the seta's surface and the substrate—that maintains the adhesive contact, keeping the seta attached to the surface without the need for moisture or additional adhesive substances.

Directly measuring this van der Waals force requires using a special operating mode of the atomic force microscope known as non-contact mode, in which the cantilever oscillates continuously at its own resonant frequency without touching the surface; the gradient of the van der Waals force acting on the tip causes the resonant frequency to shift in proportion to the gradient's intensity, and it is precisely this frequency shift that is recorded as the measurement signal.

This frequency shift does not always correspond to the same regime of the van der Waals force: at separations of less than ten nanometers, the so-called Hamaker force dominates, whereas at greater separations, electromagnetic retardation effects—described by Casimir-Polder dispersion—begin to appear, causing the force to deviate from the behavior predicted by the Hamaker approximation.

The quantity governing this Hamaker force in the short-separation regime is a fundamental system property known as the Hamaker constant; its value depends on the dielectric properties of the materials in contact, meaning that each material combination yields a distinct Hamaker constant. Calculating this constant as rigorously as possible requires the use of Lifshitz theory, which integrates the full spectrum of electromagnetic fluctuations of both materials rather than treating them as simple bodies. To determine this Hamaker constant experimentally, curves of the resonance frequency shift versus the separation between the tip and the surface are recorded; fitting the Hamaker model to these curves allows for the extraction of a numerical value for the constant based purely on experimental data. When this procedure is applied to cuticular pillars resting on hydrophilic substrates, Hamaker constant values ​​on the order of fifty zeptojoules are obtained—values ​​surprisingly similar to those yielded by a system composed of chitin, water, and glass.

This seemingly tiny Hamaker constant results in an adhesive pressure exceeding one million pascals when the separation between the pillar and the surface is reduced to just one nanometer; it is precisely this intense adhesive pressure that explains how a pillar with a radius of merely one hundred nanometers can generate—thanks to van der Waals forces—adhesion forces on the order of a nanonewton on clean, dry surfaces.

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