How to Measure Molecules

In the late 19th century, physicist Lord Rayleigh calculated the size of a single molecule. He did it, remarkably, using little more than oil and water.

Rayleigh’s experiment is one of the most beautiful in scientific history but has largely been forgotten. It is brilliant not only because of its outcome — Rayleigh showed that a single molecule of olive oil measures 1.6 x 10^-7 centimeters in length, becoming the first person to derive an experimental value for molecular sizes — but also because it shows how simple observations and back-of-the-envelope calculations can be combined to measure otherwise invisible natural phenomena.

Our story does not begin with Rayleigh, however. It starts with Benjamin Franklin, the American statesman and polymath, who published a similar experiment more than a century earlier.

In 1764, Benjamin Franklin had just lost his seat in the Pennsylvania Assembly, so his political allies urged him to travel to London to act “as agent” to the Crown. He agreed and departed for England aboard a fleet of British ships.

Franklin, an astute observer, noticed something strange during his transatlantic voyage. Looking out toward other ships in the fleet, he saw that some of their wakes, or trails, did not cause waves. Franklin asked a sailor on his boat why this was happening, and the sailor replied that a boat’s trails calm when chefs toss greasy kitchen oil out onto the water.

This observation rooted in Franklin’s memory, as he would write several years later:

"I had, when a youth, read and smiled at Pliny’s [a Roman historian who wrote in the 1st century A.D.] account of a practice among the seamen of his time, to still the waves in a storm by pouring oil into the sea; which he mentions, as well as the use made of oil by the divers."

Intrigued, Franklin resolved to follow up on these observations and carry out experiments after arriving in London. But tensions between the Crown and the Colonies ran high in the 1760s, and Franklin quickly got swept up in politics instead.

In February 1765, Great Britain’s prime minister, George Grenville, told Franklin about his plans to enact a “major” tax on the colonies to help pay for their involvement in the Indian Wars. The Stamp Act passed in March 1765, and Franklin spent much of the next year writing letters and organizing meetings to repeal it. He was successful; the Stamp Act was rolled back in early 1766. The following year, though, Parliament passed the Townshend Acts, imposing an additional series of taxes and regulations on the colonies. Once again Franklin responded by waging “an essay war,” ultimately helping to repeal the tax in April 1770. All this left little time for science.

Still, Franklin finally found some spare time in 1770 to perform his oil drop experiments. And so one windy day, the portly man walked over to a pond on Clapham Common. Carrying a small quantity of oil — "not more than a Tea Spoonful," according to his diary — Franklin poured the slick substance onto the wind-blown water. The oil spread rapidly across the surface, covering "perhaps half an Acre" of the pond and rendering its waters "as smooth as a Looking Glass."¹

Franklin repeated his experiment several times, each with the same result. In November 1773, he described his oil experiments in a letter to William Brownrigg, the British scientist who first recognized platinum as an element. Franklin wrote:

"In these experiments, one circumstance struck me with particular surprize. This was the sudden, wide, and forcible spreading of a drop of oil on the face of the water, which I do not know that any body has hitherto considered. If a drop of oil is put on a polished marble table, or on a looking-glass that lies horizontally, the drop remains in place, spreading very little. But when put on water it spreads instantly many feet around, becoming so thin as to produce the prismatic colors, for a considerable space, and beyond them so much thinner as to be invisible, except in its effect of smoothing the waves."

Brownrigg relayed Franklin’s letter to Mr. Farish, a clergyman in Carlisle whose full identity has been lost to history. Upon hearing Franklin’s results, Farish was incredulous. After all, how could such a small amount of olive oil cover half an acre of a pond’s surface? Farish requested a full account of the experiment, which Franklin wrote up and later published in the Royal Society’s journal, Philosophical Transactions, in late 1774. (Franklin’s original paper can still be read on the Royal Society’s website.)

Though Franklin is often described as an “amateur” scientist, our modern notions of the term might under-represent his prowess. In the late 18th century, every scientist could have been called “an amateur” as most did experiments in their basements and living rooms. Franklin was well-versed in mathematics and algebra, repeated his experiments several times, and had a penchant for clear, descriptive prose.

For example, Franklin clearly wrote that he had used 2 cc of olive oil in his experiments and that it covered half an acre (or 2,000 m²) of water, “becoming so thin as to produce the prismatic colors.” He never used these values to calculate the actual thickness of the oil layer, however, by dividing the volume of his oil (2 cc) by the area it covered on the pond (2,000 square meters). Had he done so, Franklin would have arrived at a value of about 10^-7 centimeters, which happens to be the size of a single oil molecule.²

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But there was simply no way for Franklin to know that the “prismatic” colors he witnessed actually consisted of a single layer of oil molecules, or that by doing this calculation he would have become the first person to experimentally determine the size of such a molecule. As Charles Tanford writes in Ben Franklin Stilled the Waves:

"Most scientists at the time, including Franklin, accepted the concept of a ‘molecule’ as the smallest particle that retained the attributes of any chemical substance. Newton even stated his belief that these ultimate particles might some day be seen by the eye through a microscope. But no numerical estimates of molecular size existed in 1770 and no one had any idea how small the ultimate particles might be. Father Boscovich and Franklin’s friend [Joseph] Priestley even entertained the notion that molecules might be points, with no extension in space at all."

Perhaps Franklin shared Priestley’s view — namely, that molecules are simply “points” without any physical dimensions — and so didn’t see any value in calculating an oil layer’s thickness. When Franklin sent his experiments to Priestley, for example, Priestley didn’t think to do the calculation, either. Instead, Franklin’s mind turned to “practical” applications, like how much oil the Royal Navy would need to calm a harbor on windy days.

It would take another 120 years — and a radical shift in how scientists thought about small particles — before Lord Rayleigh³ repeated Franklin’s experiment (at a much smaller scale) at his home laboratory in Terling Place, Essex and used the results to calculate the size of a molecule.

An academic at the University of Cambridge and a baron by title, Rayleigh was renowned for his work in physics. The Rayleigh number, a common parameter used to describe the flow of water, is named after him; as is Rayleigh scattering, which explains how photons diffuse through the atmosphere and color the sky blue. Rayleigh also discovered the noble gas, Argon, which earned him a Nobel Prize in Physics in 1904.

At the time of Rayleigh’s experiments in 1890, most scientists believed that molecules not only existed but had physical, measurable dimensions. Unfortunately, nobody actually knew how to measure them. X-rays had not yet been discovered,⁴ and there were no tools sensitive enough to image individual molecules. Physicists at the time estimated molecular sizes based on abstract mathematical equations, rather than experimental observations.

But Rayleigh was familiar with Franklin’s experiment, and, in a leap of true genius, he figured that he could use oil and water to calculate the dimensions of a single molecule, thus putting to rest one of the biggest open questions in physics at the time. While the details surrounding Rayleigh’s idea is not entirely accounted for, he cites Franklin’s 1774 paper in his own letters on the experiment.

First, Rayleigh added some camphor chips to a large bowl of water, measuring about one meter across. Camphor chips wiggle in the absence of oil but abruptly still when exposed to it. Then, “Rayleigh added increasing amounts of oil,” writes Tanford, and “calculated the film thickness from the volume of oil that was ‘about enough’ to ‘very nearly stop’ all movement of the camphor.” After repeating this experiment several times and averaging the results, Rayleigh calculated the thickness of the oil layer at 1.63 x 10^-7 centimeters.

Rayleigh’s full equation is below. Note that the numerator is the volume of oil that Rayleigh added to the water (0.00081 cubic centimeters), and the denominator is the area the oil covered on its surface:

The first time I wrote about these experiments, many readers asked: “How did Rayleigh know that the oil molecules formed a monolayer?” After all, there was no way to directly visualize molecules at the time. If the oil formed a bilayer instead, then Rayleigh’s calculation would have been off by a factor of two.

There are a few explanations. The first is that in 1890, many scientists assumed that molecules were a bit like little jostling balls. If an oil droplet consists of many such balls, then it makes intuitive sense that these balls would “roll over” each other until each of them makes contact with the water’s surface.

As a diligent scientist, though, Rayleigh was not one to rest his conclusions solely upon thought experiments. Two additional pieces of evidence from Rayleigh’s experiment itself also support the idea that olive oil forms a monolayer.

First, other physicists at the time had estimated the “rough” dimensions of molecules using kinetic theory and a hypothesis advanced by an Italian schoolteacher named Amedeo Avogadro, which asserted that “equal volumes of gases under the same conditions of temperature and pressure will contain equal numbers of molecules.” Those physicists estimated that molecules have a dimension on the order of 10^-7 centimeters. Rayleigh’s experiment yielded a result within one order of magnitude, suggesting the oil may have formed a monolayer.

And second, when Rayleigh added small amounts of oil to the water, it spread out to cover an area directly proportional to the volume of oil added. In other words, if Rayleigh doubled his volume of oil, the area of water it covered also doubled. As Rayleigh continued adding oil, it eventually reached the outer rim of his water bowl and began clumping up, rather than the layer itself growing thicker. He took this observation to suggest that the oil had spread to cover as much area as possible and thus formed the thinnest possible film upon the water’s surface.

Rayleigh wrote up his results in a paper, “Measurements of the amount of oil necessary in order to check the motions of camphor upon water,” and published them in the Proceedings of the Royal Society of London in 1890.

Today, measurements made using X-rays and advanced microscopy methods reveal that the true length of oleic acid, the primary molecule in olive oil, is about 1.97 nanometers. Results from Rayleigh’s simple experiment, therefore, were off by just 17 percent.

I’m fond of Rayleigh’s experiment because it shows, at least anecdotally, how deep scientific insights can emerge from direct observation, an ecosystem of curious minds, simple experimentation, and a bit of mathematics.

Isaac Newton famously used Johannes Kepler’s measurements of planetary motion, combined with Galileo Galilei’s theory of falling bodies, to derive his law of universal gravitation. And similarly, in 1676, Danish astronomer Ole Rømer became the first to assert that light travels at a finite speed, estimating that it takes 11 minutes to travel from the Sun to Earth. He accomplished this by using a homemade telescope to observe Jupiter’s orbital period, carefully measuring “the time intervals between the eclipse of Jupiter and its moon Io,” according to a 2023 study:

"Through years of research [Rømer] stumbled across something very peculiar: The time intervals between expected eclipses of Io were shorter when Earth was at its closest point to Jupiter and longer when it was at its farthest. Rømer realized that as the Earth traveled farther away from Jupiter, it took light longer to traverse the distance, meaning the speed of light in fact had a finite value."

Each of these scientific discoveries suggest that one doesn’t necessarily need complex, scientific apparatuses for profound insights, but sometimes just simple observations coupled with a personal curiosity. Franklin never could have known that his humble experiments at Clapham Common would play such a pivotal role in physics more than 100 years later. But such simple experiments are still worth doing, even if they don’t lead to acclaim in one’s own time, because they form a substrate for those who follow. As Franklin wrote in a letter to Peter Collinson in 1753:

"If I were merely ambitious of acquiring some Reputation in Philosophy, I ought to keep them by me, ’till corrected and improved by Time and farther Experience. But since even short Hints, and imperfect Experiments in any new Branch of Science, being communicated, have oftentimes a good Effect, in exciting the attention of the Ingenious to the Subject, and so becoming the Occasion of more exact disquisitions (as I before observed) and more compleat Discoveries, you are at Liberty to communicate this Paper to whom you please; it being of more Importance that Knowledge should increase, than that your Friend should be thought an accurate Philosopher."

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This article draws heavily upon Ben Franklin Stilled the Waves, an excellent book by Charles Tanford.

Niko McCarty is founding editor of Asimov Press.

Thanks to Ish Freedman, Maarten Boudry, Andrew Miller and Xander Balwit for reading drafts of this.

Cite: McCarty, Niko. “How to Measure Molecules.” Asimov Press (2024). DOI: https://doi.org/10.62211/96oe-84tt

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Footnotes

1. Franklin documented his observations in great detail; they can be read today on the Clapham Society's website.
2. Franklin had performed similar calculations before. In an earlier letter, he wrote: “In 1739 arrived among us from Ireland the Reverend Mr. Whitefield, who had made himself remarkable there as an itinerant preacher. He was at first permitted to preach in some of our churches; but the clergy, taking a dislike to him, soon refus'd him their pulpits, and he was oblig'd to preach in the fields … He had a loud and clear voice, and articulated his words and sentences so perfectly, that he might be heard and understood at a great distance, especially as his auditories, however numerous, observ'd the most exact silence … I had the curiosity to learn how far he could be heard, by retiring backwards down the street towards the river; and I found his voice distinct till I came near Front-street, when some noise in that street obscur'd it. Imagining then a semi-circle, of which my distance should be the radius, and that it were fill'd with auditors, to each of whom I allow'd two square feet, I computed that he might well be heard by more than thirty thousand.”
3. Real Name: John William Strutt
4. X-rays were discovered by W.C. Röntgen in 1895.