Advanced #70

At low temperatures, self-diffusion increases with rising density and pressure

Counterintuitively, water becomes more mobile at low temperatures under pressure.

Scientific Explanation

Self-diffusion describes how quickly an individual water molecule moves through its surroundings. In most liquids, pressure slows diffusion because the molecules are pushed closer together and have less room to move. Cold water (below about 10 degrees Celsius) shows the opposite: self-diffusion increases with rising pressure. The molecules become more mobile under compression.

As with the viscosity anomaly, the cause lies in the hydrogen bond network. At low temperatures, water forms an extended, cage-like network that confines molecules in their positions. Pressure breaks parts of this network apart, interstitial molecules are inserted, and the rigid ordering gives way to a more dynamic structure. The result is increased mobility of individual molecules.

At higher temperatures (above about 30 degrees Celsius), the network is already sufficiently disrupted by thermal energy that the normal pressure effect dominates, and diffusion decreases with pressure as expected.

Self-Diffusion of Water vs Pressure at Low Temperature Line chart showing that at low temperatures (below about 10 degrees C) the self-diffusion coefficient of water increases with pressure, contrary to most liquids. At higher temperatures the normal behavior of decreasing diffusion is observed. Self-diffusion (10⁻⁵ cm²/s) 3.0 2.0 1.0 0 50 100 150 200 Pressure (MPa) 1 °C 10 °C 40 °C increases (anomalous) decreases (normal) Self-Diffusion vs Pressure
Self-diffusion coefficient of water at different temperatures as a function of pressure.

Everyday Relevance

The enhanced diffusion of cold water under pressure matters for chemical and biological processes in the deep sea. In cold, deep ocean layers, dissolved substances can spread faster than one would expect from the temperature effect alone. This influences the transport of nutrients and dissolved gases, and thus the living conditions of deep-sea organisms. In high-pressure chemistry, where reactions in water are carried out at kilobar pressures, this anomalous diffusion behavior must also be taken into account.