Atomic Measurements in the 18th Century

In my previous post, I briefly touched on one of the most fascinating properties of nanoscale systems; their incredibly high surface-to-volume ratio. In this post, I want to discuss some of the methods that we use to measure the size of different nanoscale materials. How do scientists go about measuring the diameter of a nanoparticle, the thickness of an atomically thin material, or the size of a single molecule?

Many modern characterization techniques, including transmission electron microscopy, scanning tunneling microscopy, and atomic force microscopy (the inventors of the former two shared the 1986 Nobel Prize in Physics), are incredibly precise instruments; true feats of engineering and testaments to the ingenuity and creativity of their inventors.[1] These powerful pieces of equipment are capable of taking some of the highest resolution images currently possible, able to image single molecules and even single atoms. In 2013, IBM famously released the first atomic scale stop-motion movie, “A Boy And His Atom”, using a scanning tunneling microscope to manipulate individual carbon dioxide molecules.[2] How did we get here? We obviously couldn’t have jumped from simple microscopes to atomic manipulation. Nanoscience, like all science, is an incremental process, each generation building slowly and steadily (or sometimes rapidly, where a Nobel is involved) on the work of those before. Interestingly, we as a species have had the ability to accurately measure the size of single molecules for hundreds of years, we just didn’t know it at the time.

The Knowledge of the Vulgar

In 1757, Benjamin Franklin was on his way to London in order to discuss the minutiae of colonial taxation in the context of the French and Indian War. During his long voyage, he noticed that the wakes trailing a number of the ships appeared smoother than those of the other ships, almost as if some of the ships were gliding on top of the water rather than cutting through it. Upon mentioning his observation to one of the captain of his vessel, he learned that dampened wakes following ships were common occurrences, and generally indicated that the cooks had emptied their oily water overboard. Franklin initially disregarded this as an unlikely explanation, coming, as it were from a non-scientist. But after further consideration he could imagine no other alternative explanation, and conceded that there must be some wisdom to the crude suggestion of the ship captain.[3]

“The learned, too, are apt to slight too much the knowledge of the vulgar”

-Benjamin Franklin

Once he had arrived in London, Franklin set out to test the claim for himself. He visited a pond outside of Clapham on a windy day and, dropping a small amount of oil onto the surface of the water, noticed that “the oil, though not more than a tea spoonful, produced an instant calm over a space several yards square, which spread amazingly, and extended itself gradually till it reached the see side, making all that quarter of the pond, perhaps half an acre as smooth as a looking-glass”. Clearly something interesting was happening here. After this initial success, Franklin always carried a little oil with him in the hollow of his bamboo cane, ready to dazzle friends and acquaintances with his newfound knowledge.

Franklin was not the first to observe this phenomenon. In fact, the smoothing of rough water by oil was mentioned in writing by such notables as Aristotle, Plutarch, and Pliny. In 1886, Lieutenant A.B. Wyckoff of the U.S. Navy published an article in the Proceeding of the American Philosophical Society, outlining the historical basis for the use of oil in calming rough waters by divers in the Mediterranean, fishermen in Norway and Scotland, and sailors in Portugal, all of whom had been using this trick for hundreds of years. In fact, the method of calming water with oil was so effective that Wyckoff predicted that “the time must soon come, when no vessel will leave port without some cheap fish or vegetable oil”.[4]

How Big is a Molecule of Oil?

Ok, so we’re convinced that a drop oil can calm a body of water. Why is this, and what does this have to do with measurements on the nanoscale?

To answer the first question, we need to revisit Franklin’s early experiments. Franklin noticed that “when put on water [the oil] spreads instantly many feet round, becoming so thin as to produce the prismatic colours, for a considerable space, and beyond them so much thinner as to be invisible … It seems as if a mutual repulsion between its particles took place as soon as it touched the water”. While the “prismatic colours” are certainly a result of thin-film interference (I’ll cover this in a later post), it’s important to consider what Franklin is saying here. The oil, as if propelled by some mutual repulsion, is spreading out across the water into a very thin layer. Oil is primarily composed of various fatty acids, molecules which are hydrophilic on one end, and hydrophobic on the other. Dropped on the surface of the water, these molecules will spontaneously arrange to form a molecular single layer (known as a molecular monolayer or a self-assembled monolayer), with their hydrophilic “head” facing the water, and their hydrophobic “tail” interacting with the air. On the formation of waves, Franklin wrote, “air in motion, which is wind, in palling over the smooth surface of water, may rub, as it were, upon that surface, and raise it into wrinkles, which, if the wind continues, are the elements of future waves.” In other words, the friction of the air “tugging” on the water creates the waves. The oil monolayer on the water acts as a lubricant; the hydrophobic “tail” of the molecule interacts more favorably with the air, thus reducing the “tug” of the wind on the surface of the liquid.

How can we use this information to measure the size of an oil molecule? If we know that a drop of oil will form a molecular monolayer on the surface of water, then we can simply measure the width of the oil slick! Let’s consider Franklin’s earlier example. A teaspoon of oil spread to an area of half an acre. One teaspoon is about 2 mL, or 2 * 10–6 m^3. Half an acre is about 2200 m^2. If the oil has truly formed a monolayer, then the area of the oil slick will be exactly one molecule tall everywhere. The total volume of the oil must remain constant, so we can calculate the thickness of the oil molecule by dividing the total volume of oil by the area that the monolayer covers:

(2 * 10–6 m^3)/(2200 m^3) = 9 * 10–10 m = 9 Å = 0.9 nm

So how did we do? For reference, oleic acid, one of the most common fatty acids in many oils, has a molecular length of about 2 nm. Not spot on, but not bad considering our none-too-specific area measurement of “perhaps half an acre”. With more accurate measurements of the size of the oil slick, the error of this calculation can be significantly reduced. Franklin, however, did not think to carry out these calculations. It would be another hundred years before Lord Rayleigh finally used this method to calculate the thickness of an olive oil monolayer.[5]

Our experimental capabilities have exploded over the past hundred years. Measurements that were previously thought impossible are now commonplace. With the advent of electron and scanning probe microscopes, we are able to image the nanoscale world like never before. In modern science, it’s often all too easy to overlook the steady, incremental advances, built up over the preceding centuries, that have enabled the discovery of these new methodologies. I think this particular experimental development is a great representation of the value of a curious nature in general. I do not claim that had Ben Franklin not commented on the differences in the wakes of ships, we would be without electron microscopes today, rather that it’s easy to overlook the incremental nature of science and the value of keeping your eyes open and always being ready to question the world around you. Nanoscience often seems like the exclusive realm of bespectacled doctors with high powered microscopes hiding behind laboratory doors, but in fact it’s all around us in everyday life.


  1. The Nobel Prize in Physics 1986. Nobel Media AB 2018. Thu. 20 Sep 2018. <
  2. “A Boy And His Atom”. IBM Research. May 1, 2013. <;
  3. Franklin, W. Browning, and J. Farish, Of the stilling of waves by means of oil, Phil. Trans. 64, 445–460 (1774).
  4. B. Wyckoff, The use of oil in storms as sea, Proc. Am. Philos. Soc. 23, 383–388 (1886).
  5. Rayleigh, Measurements of the amount of oil necessary in order to check the motions of camphor upon water. Proc. R. Soc. Lond. 47, 364–367 (1890).