Sold – Einstein Gives a Primer on the Subject of His 1st Paper: Thermodynamics

In 1900, Einstein was granted a teaching diploma by the Federal Polytechnic Institute. Then, even prior to his days as a clerk in the patent office, he submitted his very first paper for publication to the prestigious Annalen der Physik, which published it. Einstein was well versed and interested in thermodynamics, and the article concerned the capillary forces of a drinking straw, and was entitled “Consequences of the observations of capillarity phenomena". Capillary action, or capillarity, is the ability of a liquid to flow against gravity where liquid spontaneously rises in a narrow space such as a thin tube or straw, or in porous materials such as paper. This effect can cause liquids to flow against the force of gravity or the magnetic field induction, and it occurs because of attractive forces between the liquid and solid surrounding surfaces. In his article, Einstein reasoned: "To each atom corresponds a molecular attraction field that is independent of the temperature and of the way in which the atom is chemically bound to other atoms." Later, Einstein worked on similar fields of phyics with his law on viscosity and in developing the Bose-Einstein Constant.

Hans M. Cassel was a lecturer at the Technical University of Berlin, and is on the list of “Displaced Scholars” who fled Germany for the United States after Hitler took power. He was a bio-chemist interested in liquids, and among his publications were “The Stability of Emulsions.” In the mid-1930s, knowing of Einstein’s work in the field, Cassel engaged in a discussion with him of the problem of the thermodynamic stability of a drop of liquid that forms on the surface of a permeable membrane. This involves finding the relationship between the radius of the drop and the pressure it is under. Think a water balloon under pressure, leaking water.

Typed Letter Signed, on his blind embossed letterhead, Princeton, January 15, 1937, to Cassel, explaining with equations and formulas some of the core thermodynamic principles that govern this aspect of the field. The problem he deals with is: a liquid is interior to a membrane that exerts pressure on the liquid to keep it con?ned. Outside of the membrane, a large amount of the substance exists as a liquid, while a small portion exists as a gas, and these are in equilibrium. When an external surface force is placed on the membrane, the conditions of equilibrium change. Then finding the way to a stable equilibrium is the goal.

Einstein starts out by referring to their previous correspondence and then launches into the steps of his proof. “As regards your recent letter, I am going to make another shy attempt, in the hopes that you adopt my simple arguments. 1.) There is a two-phased system of liquid-vapor here. The molecules of the liquid are surrounded by a permeable membrane. On this membrane we put a surface force. With that, pressure in the vapor phase will increase from Po to P, according to this relationship P – P0 = αp…”?Next, in step 2, Einstein makes a connection to his earliest published work, arguing that the contributions of the membrane can equivalently be replaced by the Young-Laplace pressure exerted on a droplet due to capillarity. In some instances, such as when water is placed on glass, a liquid will spread and evenly coat the surface. However, when water is placed on an oily surface, it will form droplets because of the high surface tension. As another example, water inside of a glass tube will tend to rise at at the points where it touches the glass – despite gravity pulling down on the liquid. This is an example of a capillary force such as Einstein had written about in 1900. Einstein finds that the capillary pressure is larger for smaller droplets than for larger droplets and arrives at the expression P = P0 + 2α σ/r. He writes, “2.) The same relationship is valid if the membrane that is under external pressure is replaced by capillary pressure…”

In step 3, Einstein notes that if the membrane surface is coated with a substance which interacts more favorably with the droplet-forming liquid, that the surface tension σ must decrease. This would amount to removing the oily coating on the surface, thereby increasing the degree to which the water wets the surface. He writes, “3.) If now, in addition, there is a substance present which accumulates on the surface and the consistency of the capillary from the latter is brought to a smaller value, then the same formula for the partial pressure of vapor is valid.” In step 4, Einstein argues that in order for a droplet to be stable, the pressure exerted on it must increase as the droplet radius increases. According to Einstein, if the droplet is to be stable, dP /dr > 0. He concludes that Cassel’s reasoning cannot be correct because it came to a different conclusion." Einstein ends by pointedly saying, “The subject has been reduced to its simplest elements by these suggestions.” We recently obtained this letter when Cassel’s family decided to sell it. Filled with explanations and calculations and relating to his own work , it is one of the most significant scientific letters of Einstein to reach the market in many years. Our last comparable letter was sold 7 years ago.

The specific science discussed in this letter is of great value in research over a broad spectrum. Today its concepts are used in nanotechnology, and will eventually permit drug delivery systems using that technology.