This image from the Caltech team’s simulations features a cutaway of a 2.0 nm-dia. carbon nanotube, revealing confined water molecules. Image: Caltech/Tod Pascal
Scientists often find strange and unexpected things when
they look at materials at the nanoscale. This holds true even for the most
common materials, such as water.
Case in point: In the last couple of years, researchers
have observed that water spontaneously flows into extremely small tubes of
graphite or graphene, called carbon nanotubes. This unexpected observation is
intriguing because carbon nanotubes hold promise in the emerging fields of
nanofluidics and nanofiltration, where nanotubes might be able to help maintain
tiny flows or separate impurities from water. However, no one has managed to
explain why, at the molecular level, a stable liquid would want to confine
itself to such a small area.
Now, using a novel method to calculate the dynamics of
water molecules, California Institute of Technology (Caltech) researchers
believe they have solved the mystery. It turns out that entropy, a measurement
of disorder, has been the missing key.
“It’s a pretty surprising result,” says William
Goddard, the Charles and Mary Ferkel Professor of Chemistry, Materials Science,
and Applied Physics at Caltech and director of the Materials and Process Simulation Center.
“People normally focus on energy in this problem, not entropy.”
That’s because water forms an extensive network of
hydrogen bonds, which makes it very stable. Breaking those strong interactions
requires energy. And since some bonds have to be broken in order for water to
flow into small nanotubes, it would seem unlikely that water would do so
“What we found is that it’s actually a trade
off,” Goddard says. “You lose some of that good energy stabilization
from the bonding, but in the process you gain in entropy.”
Entropy is one of the driving forces that determine
whether a process will occur spontaneously. It represents the number of ways a
system can exist in a particular state. The more arrangements available to a system,
the greater its disorder and the higher the entropy. And in general, nature
proceeds toward disorder.
When water is ideally bonded, all of the hydrogen bonds
lock the molecules into place, restricting their freedom and keeping water’s
entropy low. What Goddard and postdoctoral scholar Tod Pascal found is that in
the case of some nanotubes, water gains enough entropy by entering the tubes to
outweigh the energy losses incurred by breaking some of its hydrogen bonds.
Therefore, water flows spontaneously into the tubes.
Goddard and Pascal explain their findings in a paper
recently published in the Proceedings of
the National Academy of Sciences (PNAS). They looked at carbon nanotubes with diameters
between 0.8 and 2.7 nm and found three different reasons why water would flow
freely into the tubes, depending on diameter.
For the smallest nanotubes—those between 0.8 and 1.0 nm
in dia.—the tubes are so minuscule that water molecules line up nearly single
file within them and take on a gas-like state. That means the normal bonded
structure of liquid water breaks down, giving the molecules greater freedom of
motion. This increase in entropy draws water into the tubes.
At the next level, where the nanotubes have diameters
between 1.1 and 1.2 nm, confined water molecules arrange themselves in stacked,
ice-like crystals. Goddard and Pascal found such nanotubes to be the perfect size
to accommodate crystallized water. These crystal-bonding interactions, not
entropy, make it favorable for water to flow into the tubes.
On the largest scale studied—involving tubes whose
diameters are still only 1.4 to 2.7 nm wide—the researchers found that the
confined water molecules behave more like liquid water. However, once again,
some of the normal hydrogen bonds are broken, so the molecules exhibit more
freedom of motion within the tubes. And the gains in entropy more than
compensate for the loss in hydrogen bonding energy.
Because the insides of the carbon nanotubes are far too
small for researchers to examine experimentally, Goddard and Pascal studied the
dynamics of the confined water molecules in simulations. Using a new method
developed by Goddard’s group with a supercomputer, they were able to calculate
the entropy for the individual water molecules. In the past, such calculations
have been difficult and extremely time-consuming. But the new approach, dubbed
the two-phase thermodynamic model, has made the determination of entropy values
relatively easy for any system.
“The old methods took eight years of computer
processing time to arrive at the same entropies that we’re now getting in 36
hours,” Goddard says.
The team also ran simulations using an alternative
description of water—one where water had its usual properties of energy,
density, and viscosity, but lacked its characteristic hydrogen bonding. In that
case, water did not want to flow into the nanotubes, providing additional proof
that water’s naturally occurring low entropy due to extensive hydrogen bonding
leads to it spontaneously filling carbon nanotubes when the entropy increases.
Goddard believes that carbon
nanotubes could be used to design supermolecules for water purification. By
incorporating pores with the same diameters as carbon nanotubes, he thinks a
polymer could be made to suck water out of solution. Such a potential application
points to the need for a greater understanding of water transport through