Claiming Einstein for chemistry

Was Albert Einstein a chemist at heart? Today he is depicted as the archetypal theoretical physicist, filling the blackboard with arcane and semi-legible equations about the nature of space and time. But Einstein’s early work was largely concerned with the molecular nature of matter and was firmly rooted in the tangible and the mundane. Not only physicists but chemists too should be celebrating ’Einstein Year’, the centenary of his most dramatic discoveries.

Indeed, when Einstein unveiled his theory of special relativity in 1905, his contemporaries might have been most surprised not at its revolutionary claims but at the fact that this astonishing piece of modern physics had come from someone who appeared to be embarking on a promising career in physical chemistry.

A physical chemistry thesis?

Einstein submitted his doctoral thesis to the University of Zürich, Switzerland, only that July, in which he presented a new way to calculate Avogadro’s number and the size of molecules. In the same month he published a paper showing that tiny particles observable under a microscope should undergo wild, erratic motions in a liquid, caused by the impacts of the solvent molecules - the phenomenon known as Brownian motion.

And in the only paper published in that miraculous year that Einstein himself actually considered revolutionary, he sought to explain how metals interact with light by introducing the idea of quanta - discrete packets of energy. All in all, it was a year’s work of which any physical chemist would have been proud.

Now that Einstein’s theories of relativity have led to such grand and mind-boggling notions as black holes and time travel through wormholes, while quantum theory has introduced ideas such as infinitely branching parallel universes and foamy spacetime, it is hard to remember how seemingly prosaic the origins of these theories were.

Relativity was stimulated by difficulties in making James Clerk Maxwell’s theory of electromagnetism work when bodies were in motion, and Einstein begins his 1905 paper on the subject by talking about magnets and wires.

But the main reason for proposing (even if somewhat with tongue in cheek) that Einstein was a chemist goes still deeper than this. Einstein did his seminal work at a time when boundaries had not yet been defined between physics and chemistry - those territories were in fact only then being contended, as physicists and chemists both strove to claim for themselves the exciting new fields of radioactivity and nuclear science.

Scientists debated hotly whether John Dalton’s atoms and molecules truly existed as more than a pedagogical convenience, and the periodic table, chemists’ central organising principle, was still awaiting the explanation that later emerged from quantum theory.

Cross-discipline research

But Einstein himself - likeMichael Faraday 100 years earlier, and James Clerk Maxwell, who bridged the two men both temporally and intellectually - was unconcerned about disciplinary borders.

Einstein’s quest in his later life for a unified theory of the fundamental forces was simply an extension of his earliest work on liquids and intermolecular forces, which drew on the Newtonian model of a kinetic theory of matter.

Newton had speculated that a force might operate on the microscopic scale between atoms just as it did on the cosmic scale between stars and planets. In his first two published papers in 1901 and 1902, Einstein took up this idea by looking for a common origin of gravitational and intermolecular forces. ’It is a wonderful feeling’, he wrote in 1901, aged 21, ’to realize the unity of a complex of phenomena which, to immediate sensory perception, appear to be totally separate things’.

So it should be no surprise to find that, while Einstein was fascinated from an early age by Maxwell’s theory of electromagnetism, his first academic work followed up the other major contribution that Maxwell made to physical science: the kinetic theory of gases.

Johann Diderik van der Waals in the Netherlands extended this theory in 1879 to embrace liquids, and Einstein’s 1901 paper in the Annalen der Physik pursued the same theme that had motivated van der Waals: the role of molecular forces in capillary action. Einstein hoped to develop this work into a doctoral thesis at Zürich; but it led him nowhere, and in April 1901 he accepted a job at the Swiss patent office in Berne. It is significant that Einstein’s father, worried about his son’s prospects at this time, chose to seek support from the famous physical chemist Wilhelm Ostwald.

This was the intellectual strand that led to Einstein’s 1905 dissertation on molecular dimensions. Several methods already existed for determining the size of molecules. The most reliable of these were based on the kinetic theory of gases.

In 1865, for example, the Bohemian chemist Josef Loschmidt presented a method based on a comparison of the densities of various liquids and gases, concluding that the diameter of an ’air molecule’ is about one nanometre. This enabled Loschmidt to calculate Avogadro’s number - the number of molecules in one mole of a substance - which in German-speaking countries was long known as Loschmidt’s number.

Einstein, in contrast, devised an accurate method for calculating molecular sizes that relied only on the properties of liquids. Van der Waals had already established that molecular size was important in understanding the behaviour of liquids: it was partly by taking account of sizes that he had enabled the kinetic theory of gases to embrace the liquid state too.

Particular motions

But Einstein’s dissertation work considered the motion of these particles. It is intimately connected to his interest in molecular diffusion, pioneered by the German chemist Walther Nernst, which led also to his paper on Brownian motion in the same year.

Einstein derived an equation for the coefficient of diffusion of a solute molecule in a solvent based on Stokes’ law, which relates the speed of a particle moving through a fluid to the fluid’s viscosity. Einstein’s equation contained both Avogadro’s number and the radius of the solute particle, and to solve it he used hydrodynamic theory to calculate how the viscosity of a liquid changes when a solute is dissolved in it.

Using experimental data for sugar solutions, he calculated that a sugar molecule has a radius of a nanometre, while the value he obtained for Avogadro’s number was 2.1 x 10²³ per mole. It wasn’t until 1909 that the French physicist Jean Perrin measured Avogadro’s number accurately enough to show that Einstein’s value was too small, forcing Einstein to check his calculations.

He could see nothing wrong with them, but he asked his student Ludwig Hopf to double check, allowing Hopf the inestimable distinction of being one of the few people to find an error in Einstein’s maths. With a faulty equation patched up, Einstein’s method produced a value of 6.56 x 10²³ per mole, which fitted Perrin’s results and is close to the accepted modern value of 6.02 x 10²³.

Proving the existence of atoms

Einstein’s interest in measuring molecular size had a deeper agenda. He was aware that some eminent scientists, among them Wilhelm Ostwald and Ernst Mach, questioned whether atoms and molecules existed at all. It is tempting now to see these anti-atomists as perverse, but at the turn of the century there was not a single piece of direct evidence for the atomic theory of matter. Most physicists and chemists took this theory for granted, and it was a central assumption of the kinetic theory of gases; but Mach pointed out that it was poor science to postulate the existence of entities that could not be perceived. Einstein believed in atoms, but he wanted some form of proof: evidence, as he said, ’which would guarantee as much as possible the existence of atoms of definite finite size’.

He saw that such evidence might be provided by the phenomenon of Brownian motion - or rather, by the random movements of microscopic particles suspended in a liquid, which were first suggested might be related to the motions observed in 1828 by the botanist Robert Brown.

When Brown noticed that pollen grains in water seem to dance erratically, he thought at first this was some manifestation of the ’vital force’ with which organic matter was then still thought by many to be imbued. But he soon discovered ’dead’ particles do the same thing, and his observations led to all kinds of theories in the 19th century, invoking influences such as convection and electricity. Yet none of them seemed satisfactory.

Random molecular motion

Einstein’s approach to the problem drew on the idea, established via the kinetic theory of gases, that heat was the result of random molecular motions. It had previously been supposed that, even though these motions were thought to involve very high velocities, suspended particles like dust or pollen were so much more massive than individual molecules that the effect of molecules impacting on the larger particles would be negligible - it would be like meteorites hitting the Earth.

But Einstein showed that a statistical imbalance in the number of molecules striking a micrometre-sized particle from different directions should indeed make the particle move, and that these erratic movements due to the thermal motions of the molecules should be large enough to be seen under a microscope.

The randomness of this motion causes the particle to diffuse through the liquid: if you follow it over a period of time, it will end up somewhere different from where it began. He calculated this so-called mean-square displacement as a function of time, predicting that a 1mm particle in water would travel about 6mm in one minute.

This quantitative prediction was crucial: it provided a means of testing whether Einstein’s theory was right. If it was, then it would be hard for anyone to deny that the molecular picture of matter central to the kinetic theory was correct - in other words, molecules must be real. Einstein concluded his 1905 paper with the hope ’that a researcher will soon succeed in solving the problem presented here’.

Many tried, but the experiments were very difficult, largely because it was hard to ensure a constant, uniform temperature in the liquid. By 1908 no one had managed to find quantitative evidence for Einstein’s theory, and he had begun to despair that it was possible to investigate Brownian motion so precisely. But to his delight, Jean Perrin took up the challenge, and that same year confirmed that the theory gave the right predictions - for which work Perrin was awarded the 1926 Nobel prize in physics.

It is well known that Einstein remained for all his life uncomfortable with some of the fundamental aspects of quantum theory - in particular, with the way it appeared to locate chance and uncertainty at the heart of the behaviour of matter.

In some respects he came to resemble Planck in seeing the quantum description of matter as a convenience that allowed one to understand certain mundane properties of matter, such as the photoelectric effect and the heat capacities of solids, while suspecting that a more fundamental, deterministic theory lay beneath.

The core of quantum chemistry

The quantised nature of light and energy is central to all of chemistry. It explains how matter and light interact - why grass is green and the sky is blue - as well as providing the basis of all the spectroscopic methods that enable us to decode the structures of molecules.

Niels Bohr, Arnold Sommerfeld and Wolfgang Pauli showed how the quantum model of the atom explains the structure of the periodic table and the properties of the elements, while Fritz London, Linus Pauling and others developed a quantum picture of interatomic bonding, accounting for the shapes and properties of molecules.

Today, chemistry is inconceivable without quantum theory, which is used to explain and predict anything from the catalytic behaviour of metals to the stereochemistry of organic syntheses. This aspect of Einstein’s work has had a bigger impact on chemistry than on any other science.

Yet cynics might say that even if Einstein began his work in the guise of a chemist, this is hardly what we remember him for today. Chemists’ quantum theory may have been triggered by his work on the photoelectric effect, but doesn’t it owe more to the subsequent elaborations of Bohr, Schrödinger and Heisenberg than to Einstein’s quantised light? And surely his grandest theory, relativity, has become the language of astrophysicists, not chemists? Well, don’t be so sure.

For relativity is important in chemistry too. The theory of special relativity explained that, when objects move close to the speed of light, they gain mass (as well as, from the point of view of an observer at relative rest, becoming shorter and living longer). It turns out that, in heavy atoms, the intense electrostatic attraction between electrons in inner orbitals and the highly charged nucleus induces such high electron speeds that they begin to experience these relativistic effects: the average velocity of the electrons in the innermost orbital of a uranium atom is about two thirds the speed of light.

Orbiting electrons

These relativistic electrons become more massive, which in turn brings them into even tighter orbit around the nucleus. That increases the extent to which these inner electrons shield the outer electrons from the tug of the nucleus, and so in turn the orbits of the outer electrons expand and their energies are lowered. So relativistic effects retune the energy levels of the atom.

It’s not so exotic, nor so rare, as you might imagine. Were it not for relativistic effects, gold would look like silver; the reddish tint comes from gold’s ability to absorb blue light, owing to a relativistic shift in the energies of the metal’s electronic bands.

This is arguably a more profound manifestation of Einstein’s theory than any amount of cosmic gravitational lensing or slowing of atomic clocks, for this aspect of gold’s appearance accounts for its revered cultural status over thousands of years and for the symbolism that has since ancient times linked this precious metal with the sun.

By the same token, relativistic effects account for mercury’s low melting point, which is not only of immense technological importance but gives this metal its mystical association with water and the moon.

In recent years, relativistic effects in atoms have become even more significant thanks to the synthesis of new, ultra-heavy elements in ion-beam collisions. Element makers are now investigating whether the extreme relativistic modifications of the electronic structures of these atoms might even start to undermine the orderly properties of the periodic table. Even at this forefront of modern chemistry, it’s impossible to ignore Einstein’s legacy.