A reaction that ticks like a clock

Mix a few clear chemicals in a beaker and stir. The liquid turns yellow, then fades to colourless, then turns yellow again, over and over, with no one touching it. It keeps time like a pendulum. For years, most chemists who heard about it assumed someone had made a mistake.

What happens in the beaker

The Soviet chemist Boris Belousov found the effect around 1950. He was trying to build a test-tube model of a cycle of reactions that living cells use to burn fuel. His mixture was citric acid dissolved in water, bromate in acid as the oxidant, and cerium ions as the catalyst. A. T. Winfree tells what happened next: it “turned colorless and returned to yellow periodically for as long as an hour (at room temperature) while effervescing carbon dioxide!” The colour is the cerium itself. Cerium that has lost four electrons, written Ce⁴⁺, is yellow. Cerium that has lost three, Ce³⁺, is colourless.

A. M. Zhabotinsky later swapped the citric acid for malonic acid, and that version became the standard one. It is now called the Belousov–Zhabotinsky, or BZ, reaction. The catalyst can be swapped too. With ferroin, an iron compound, it is the iron that flips back and forth, between Fe(II) and its oxidised form Fe(III), and the colour change is a different one.

Why it was hard to believe

A reaction normally runs downhill to equilibrium, the resting state where nothing more changes. Near equilibrium, a rule called detailed balance forbids oscillation. Zhabotinsky explains that most chemists took this much further, as “forbidding oscillations in all homogeneous, closed chemical systems”. So “the unfortunate custom prevailed until the mid-1960s” of blaming any rhythm seen in a flask on hidden surface effects or on technical errors.

The BZ reaction breaks no law. It starts far from equilibrium, and the overall reaction still runs downhill the whole time. What goes back and forth is the catalyst and a few short-lived intermediates. A closed beaker can give up to several thousand cycles, but it is spending fuel as it ticks. Belousov found that it stops when either the bromate or the citric acid runs out, and starts again when the missing ingredient is added back.

How it ticks

Zhabotinsky splits the reaction into two parts that take turns. In the fast part, bromate strips an electron from Ce³⁺, turning it into yellow Ce⁴⁺. This step is autocatalytic: one of its products, which Zhabotinsky identified as probably bromous acid (HBrO₂), speeds up the step that makes it, so once it starts it runs away. In the slow part, malonic acid and bromomalonic acid hand electrons back to Ce⁴⁺, and this releases bromide ions, Br⁻.

Bromide is the brake. While there is plenty of it, the fast step is shut off, and the yellow slowly fades as Ce⁴⁺ is used up. As Ce⁴⁺ falls, less bromide is made. When Ce⁴⁺ reaches a lower threshold, bromide “drops abruptly”, the brake comes off, and the runaway step snaps the solution back to yellow. At an upper threshold bromide jumps, the brake goes on, and the cycle repeats. A switch that flips at one level and flips back at another has no resting point, so it swings for as long as the fuel lasts.

How fast it ticks

Zhabotinsky calls the reaction’s time scale “dozens of seconds”. Adamatzky and colleagues measured one closely. In a drop of the ferroin recipe, coated in a plastic powder, they recorded an average period of about 44 seconds at room temperature. Cooled to −1 °C, the “average period of oscillations … doubles from 44 s to 92 s”. As a frequency that is about 23 millihertz warm and 11 cold. Belousov had already seen the same trend: warmer mixtures tick faster. In a dish that is not stirred, a thin layer of the ferroin reaction goes further. Rings of reaction spread outward from small centres, and a broken ring curls up into a spiral.

How the story is usually misremembered

Belousov worked on applied toxicology and radiation medicine at the Institute of Biophysics of the USSR Ministry of Public Health. According to the earlier accounts Pechenkin reviews, two Soviet chemistry journals rejected his paper, in 1951 and 1955. Winfree reports that the first editor called the “supposedly discovered discovery” “quite impossible”. That was disbelief from editors, not a ban by the state, and neither historian describes political suppression. Belousov, by then 64, decided not to publish at all. His only publication on the reaction in his lifetime was a two-page abstract in a collection on radiation medicine. The collection came out in 1959, although the series dates it 1958.

Meanwhile the recipe passed from hand to hand in Moscow and Pushchino. At the end of 1961 Zhabotinsky, a graduate student, was given “a citric acid recipe of unknown origin” by his supervisor, S. E. Schnoll. So Zhabotinsky did not discover it independently. His first paper on it appeared in 1964. The two men wrote to each other, but, Winfree says, “they never met”. In 1980 the Lenin Prize went to Belousov, Zhabotinsky, V. I. Krinsky and G. R. Ivanitsky. Belousov was no longer alive to receive it: he died in 1976, according to Pechenkin’s biography, which is based on the archives (Winfree’s source said 1970). His full 1951 paper finally appeared in Russian in 1981 and in English in 1985, thirty years after it was written (our arithmetic).

In short

The BZ reaction swings back and forth because two steps take turns. A runaway step oxidises the catalyst, turning cerium yellow. A slow step turns it back, and while it does so it makes bromide, which holds the runaway step off until the bromide runs low. The mixture is always running downhill overall, so nothing is being violated. It simply passes through the same states again and again, about every 44 seconds in the drop that was measured.