Water
vapor from ambient air will spontaneously condense inside porous materials or
between touching surfaces. But with the liquid layer being only a few molecules
thick this ubiquitous and important phenomenon has lacked understanding, until
now.
Researchers
at The University of Manchester led by Nobel Laureate Andre Geim — who, with
Kostya Novoselov, was awarded the Nobel Prize for Physics 10 years ago this
month — have made artificial capillaries small enough for water vapor to
condense inside them under normal, ambient conditions.
The
Manchester study is entitled ‘Capillary condensation under atomic-scale
confinement’ and will be published in Nature. The research provides a solution
for the century-and-half-old puzzle of why capillary condensation, a
fundamentally microscopic phenomenon involving a few molecular layers of water,
can be described reasonably well using macroscopic equations and macroscopic
characteristics of bulk water. Is it a coincidence or a hidden law of nature?
Capillary
condensation, a textbook phenomenon, is omnipresent in the world around us, and
such important properties as friction, adhesion, stiction, lubrication and
corrosion are strongly affected by capillary condensation. This phenomenon is
important in many technological processes used by microelectronics,
pharmaceutical, food and other industries — and even sandcastles could not be
built by children if not for capillary condensation.
Scientifically,
the phenomenon is often described by the 150-year-old Kelvin equation that has
proven to be remarkably accurate even for capillaries as small as 10
nanometres, a thousandth of human hair’s width. Still, for condensation to
occur under normal humidity of say 30% to 50%, capillaries should be much
smaller, of about 1 nm in size. This is comparable with the diameter of water
molecules (about 0.3 nm), so that only a couple of molecular layers of water
can fit inside those pores responsible for common condensation effects.
The
macroscopic Kelvin equation could not be justified for describing properties
involving the molecular scale and, in fact, the equation has little sense at this
scale. For example, it is impossible to define the curvature of a water
meniscus, which enters the equation, if the meniscus is only a couple of
molecules wide. Accordingly, the Kelvin equation has been used as a poor-man’s
approach, for the lack of a proper description. The scientific progress has
been hindered by many experimental problems and, in particular, by surface
roughness that makes it difficult to make and study capillaries with sizes at
the required molecular scale.
To create
such capillaries, the Manchester researchers painstakingly assembled atomically
flat crystals of mica and graphite. They put two such crystals on top of each
other with narrow strips of graphene, another atomically thin and flat crystal,
being placed in between. The strips acted as spacers and could be of different
thickness. This trilayer assembly allowed capillaries of various heights. Some
of them were only one atom high, the smallest possible capillaries, and could
accommodate just one layer of water molecules.
The
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 at this scale and its structure becomes
distinctly discrete and layered.
“This came
as a big surprise. I expected a complete breakdown of conventional physics,”
said Dr. Qian Yang, the lead author of the Nature report. “The old equation turned
out to work well. A bit disappointing but also exciting to finally solve the
century-old mystery.
“So we can
relax, all those numerous condensation effects and related properties are now
backed by hard evidence rather than a hunch that ‘it seems to work so therefore
it should be OK to use the equation’.”
The
Manchester researchers argue that the found agreement, although qualitative, is
also fortuitous. Pressures involved in capillary condensation under ambient
humidity exceed 1,000 bars, more than that at the bottom of the deepest ocean.
Such pressures cause capillaries to adjust their sizes by a fraction of
angstrom, which is sufficient to snugly accommodate only an integer number of
molecular layers inside. These microscopic adjustments suppress commensurability
effects, allowing the Kelvin equation to hold well.
“Good
theory often works beyond its applicability limits,” said Geim.
“Lord
Kelvin was a remarkable scientist, making many discoveries but even he would
surely be surprised to find that his theory — originally considering
millimeter-sized tubes — holds even at the one-atom scale. In fact, in his
seminal paper Kelvin commented about exactly this impossibility.
“So, our
work has proved him both right and wrong, at the same time.”
Lord Kelvin
Sir
William Thomson, later Lord Kelvin (1824-1907), first referenced his famous
equation in an article entitled ‘On the equilibrium of vapour at a curved
surface of liquid’ published in 1871 in the Philosophical Magazine. Kelvin’s
significant contributions to science have included a major role in the
development of the second law of thermodynamics; the absolute temperature scale
(measured in kelvins); the dynamical theory of heat; the mathematical analysis
of electricity and magnetism, including the basic ideas for the electromagnetic
theory of light; plus fundamental work in hydrodynamics.