The science of building sand castles mysteriously explained for 150 years by the “Kelvin Equation” is finally understood

Water vapor from ambient air will condense spontaneously within porous materials or between touch surfaces. But with the liquid layer that only a few molecules are thick, this ubiquitous and important phenomenon has lacked meaning, so far.

Researchers at the University of Manchester led by Nobel Laureate Andre Geim – who, with Kostya Novoselov, was awarded the Nobel Prize in Physics 10 years ago this month – have made artificial capillaries so small that water vapor condenses inside them in normal and environmental conditions. .

The Manchester study is entitled ‘Capillary Condensation Under Isolation at the Atomic Scale’ and will be published in Nature. The research offers a solution to the half-century-old enigma of why capillary condensation, an essentially microscopic phenomenon involving several molecular layers of water, can reasonably be described using macroscopic equations and the macroscopic characteristics of bulk water. Was it a coincidence or a hidden law of nature?

Capillary condensation, a textbook phenomenon, is ubiquitous in the world around us, and important properties such as friction, adhesion, fixation, lubrication, and corrosion are strongly influenced by capillary condensation. This phenomenon is important in many technological processes used by microelectronics, pharmaceuticals, food and other industries – even sand castles cannot be built by children if not for capillary condensation.

Scientifically, the phenomenon is often described by the 150-year-old Kelvin equation which has proven to be extremely accurate even for capillaries as small as 10 nanometers, one-thousandth the width of a human hair. Still, for condensation to occur below normal humidity of 30% to 50%, the capillaries must be much smaller, about 1 nm in size. This is comparable to the diameter of water molecules (about 0.3 nm), so only a few molecular layers of water can be inserted inside those pores responsible for the usual condensation effects.

The Kelvin macroscopic equation cannot be justified for describing properties involving the molecular scale, and, in fact, the equation makes little sense at this scale. For example, it is impossible to determine the curvature of a water meniscus, which enters the equation, if the meniscus is only a few molecules wide. Therefore, the Kelvin equation has been used as a poor man approach, for lack of a proper description. Scientific progress has been hampered by many experimental problems and, in particular, by the roughness of the surface which makes it difficult to make and study large-sized capillaries at the required molecular scale.

To create such capillaries, Manchester researchers diligently collected flat atomic crystals of mica and graphite. They place two such crystals on top of each other in narrow strips Grafen, another thin and atomically flat crystal, being placed in the middle. The strips act as dividers and can have different thicknesses. This three-layer mounting allowed capillaries of different heights. Some of them were just one atom high, the smallest capillaries possible and can accommodate only one layer of water molecules.

Manchester experiments have shown that the Kelvin equation can describe capillary condensation even in the smallest capillaries, at least qualitatively. This is not only surprising but contradicts general expectations as water changes its properties to this degree and its structure becomes noticeably discrete and stratified.

“It came as a big surprise,” he said. “I expected a complete breakdown of conventional physics,” said Dr. Qian Yang, lead author of Nature report. “The old equation turned out to work well. A little disappointing, but also exciting to finally solve the age-old mystery.

“So we can relax, all those many condensation effects and related properties are now supported by solid evidence rather than by a scratch that ‘seems to work, so it should be okay to use the equation.’

Manchester scholars argue that the agreement found, though qualitative, is also coincidental. The pressures involved in capillary condensation under ambient humidity exceed 1,000 bar, more than that at the bottom of the deepest ocean. Such pressures cause the capillaries to adjust their size with a fraction of the angstrom, which is sufficient to accommodate only a full number of molecular layers within. These microscopic adjustments suppress the scalability effects, allowing the Kelvin equation to be well maintained.

“Good theory often works beyond its applicability limits,” Geim said.

“Lord Kelvin was an outstanding scientist, making many discoveries, but he too would surely be surprised to discover that his theory – initially looking at millimeter-sized tubes – also stands on the scale of an atom. In fact, in his speech Kelvin commented on precisely this impossibility.

“So our work has proven it both right and wrong, at the same time.”

Lord Kelvin

Sir William Thomson, later Lord Kelvin (1824-1907), first referred to his famous equation in an article entitled ‘On the equilibrium of vapor on a curved surface of a liquid’ published in 1871 in the Philosophical Journal. Kelvin’s significant contributions to science have played a major role in the development of the second law of thermodynamics; absolute temperature rate (measured in kelvin); dynamic theory of heat; mathematical analysis of electricity and magnetism, including basic ideas for the electromagnetic theory of light; plus basic work in hydrodynamics.

Reference: “Capillary condensation under atomic scale isolation” December 9, 2020, Nature.
DOI: 10.1038 / s41586-020-2978-1

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