Advanced #69

Strong decrease of diffusion with decreasing temperature

The self-diffusion of water slows down upon cooling more strongly than for other liquids.

Scientific Explanation

Self-diffusion describes how quickly individual molecules move through a liquid via thermal motion. In most liquids, the diffusion coefficient decreases upon cooling according to the Arrhenius equation in a smooth, predictable manner. In water, the decrease is markedly steeper, especially at low temperatures.

At room temperature (25 degrees Celsius), water’s self-diffusion coefficient is about 2.3 times 10 to the power of minus 5 square centimeters per second. Cooling to 0 degrees Celsius reduces it to about 1.1 — a normal trend, but the slope of the curve increases dramatically with further cooling. In the supercooled regime, the coefficient drops so steeply that it no longer follows a straight line in an Arrhenius plot.

This behavior is caused by the increasing interconnection of hydrogen bonds. At low temperatures, progressively larger connected clusters with ice-like structure form. Molecules become essentially trapped within these networks and can only move through cooperative rearrangements, which strongly retards diffusion.

Self-Diffusion Coefficient vs Temperature Line chart comparing the self-diffusion coefficient of water and a typical simple liquid as temperature decreases. Water shows a much steeper decline, especially below 10 degrees C, compared to the gradual decrease of simple liquids. D (10⁻⁵ cm²/s) Temperature (°C) -20 0 20 40 60 0 1.5 3.0 Steep drop Water Simple liquid Self-Diffusion Coefficient vs. Temperature
The self-diffusion coefficient of water drops more steeply at low temperatures compared to simple liquids.

Everyday Relevance

The slowed diffusion at low temperatures explains why sugar dissolves more slowly in cold water than in hot. The dispersal of pollutants in cold water bodies also proceeds more slowly than in warm ones. In biological systems, diffusion rates influence molecular transport within cells — at cold temperatures, metabolic processes slow down not only because of slower chemical reactions but also because the reactants themselves move more sluggishly through the cellular water.