In the no man's land of ice crystals
Simulations allow first insights into the crystallization of tiny water droplets
Water that freezes to ice at some point is everyday physics, but even scientists gain new insights into this phenomenon all the time. For example, it is only now that researchers are able to investigate at nanoscale when this crystallization process starts and how quickly it occurs at different temperatures and water drops of different sizes. Researchers at the Max Planck Institute for Polymer Research in Mainz, together with colleagues from the George Washington University in Washington, DC and the University of California at Davis, have developed a model that can simulate the formation of ice in tiny water droplets. They found that the crystallization rate is strongly dependent on the radius of very small droplets. Their results could contribute to an improvement of climate models because crystallization of water plays a key role in cloud formation in the upper layers of the atmosphere.
For their studies, the researchers have considered tiny water droplets with a radius of 2.4 to 6.1 nanometres. "They contain from 2,000 to 32,000 water molecules," said physicist Davide Donadio, who leads the research group Theory of Nanostrucures and Transport at the Max Planck Institute for Polymer Research. "Our simulations are based on a classic model that reproduces the thermodynamics of the water well." This model takes into account a particular property that is characteristic of the behaviour of water: its "density anomaly". In contrast to other liquids, water does not reach the maximum density at the freezing point; it begins with four degrees Celsius. For this reason, ice floats on the water surface and lakes or rivers cannot be completely frozen.
The calculations were carried out by Tianshu Li on a small computer cluster at George Washington University. With their help, the scientists were able to track the movements of every single molecule at temperatures between minus 68 and minus 33 degrees Celsius and watch exactly when the crystallization of water began. "We found that the formation of ice in droplets with a radius of less than five nanometres is strongly dependent on their size," says Tianshu Li. "The smaller the drop, the lower the rate of crystallization at a fixed temperature." At larger radii, the freezing rates on the other hand are barely dependent on the drop size.
In nanodrops, the crystallization rate decreases with their radius
Surface effects are especially responsible for this behaviour: the curvature induces a higher pressure inside the water droplets - a phenomenon called "Laplace pressure" - which become increasingly important with decreasing radius. This is due to the surface tension of the water, the same forces between molecules that ensure that the surface behaves similarly to a film and can carry small loads. This allows, for example, insects to walk across creeks or lakes.
In the tiny drops the Laplace pressure slows ice formation. "The higher pressure in water, the slower the crystallization rates," said Donadio. "The reason is that ice has a lower density, therefore an increase in pressure always leads to a decrease in the freezing point." Just as the simulations showed, the smaller the droplet radius is, the higher rose the Laplace pressure and the smaller was the crystallization rate.
"There is a great debate about the behaviour of water in the temperature region studied by us," said Li. "With the help of our results, other researchers can now interpret the results of experiments better." Such experiments are extremely difficult because the formation of ice in the supercooled drops occurs very quickly and can therefore only be observed with great difficulty - for this reason, scientists also speak of a "no man's land" for experiments. The results of the simulations are also of great importance for atmospheric research: water drops in the clouds scatter sunlight and thereby determine how much radiation on earth matters. The results of Donadio and colleagues Tianshu Li (University of Washington) and Giulia Galli (University of California) will help atmospheric scientists to gain a better understanding of the formation of ice clouds in the stratosphere. They can also improve their climate models, because the scattering of sunlight by clouds can be better calculated.