The Supercritical Smoke

Samuel Kistler's Jelly Wager and the Knudsen Effect in Nanoporous Silica

At the College of the Pacific in Stockton, California, in 1931, chemistry professor Samuel Stephens Kistler made a laboratory wager with his colleague Charles Learned. Both chemists were studying wet hydrogels—substances like fruit jelly or coagulated sodium-silicate gel. These gels bounce like solid rubber on a plate despite consisting of more than ninety-five percent liquid water by volume. The bet was simple. Could either chemist remove all the liquid trapped inside a wet jelly and replace it with gas without causing the solid network to shrink or collapse?

Leave a wet silica hydrogel sitting on a counter to dry by ordinary evaporation, and you lose the wager every time. As water evaporates from the exterior of the gel, the liquid level retreats inward into the nanometer-wide pores of the amorphous silica skeleton. Wherever a liquid meets a gas inside a narrow wettable tube, intermolecular attraction pulls the liquid surface into a curved concave meniscus. Across that curved boundary, surface tension generates a crushing inward suction governed by the Young-Laplace capillary pressure equation:

Here $\Delta P$ is the capillary pressure pulling the pore walls inward, $\gamma$ is the liquid surface tension ($0.072\text{ N/m}$ for water at room temperature), $\theta$ is the wetting contact angle against the silica wall ($\cos\theta \approx 1$), and $r$ is the pore radius. Because pore radius $r$ sits in the denominator, shrinking the pore down to the nanoscale causes capillary pressure to explode. Inside a wet silica gel whose pores have a radius of $r = 5\text{ nanometers}$, the receding water meniscus exerts an inward stress of nearly $30\text{ megapascals}$—three hundred atmospheres of pressure. Under that immense capillary vice, the fragile chains of silica nanoparticles snap and collapse inward. The gel shrinks to one-tenth of its original volume and dries into a hard pebble called a xerogel.

Kistler realized that the Young-Laplace equation offered only one thermodynamic escape hatch. If he could eliminate the curved meniscus between liquid and gas, surface tension $\gamma$ would drop strictly to zero ($\gamma = 0 \implies \Delta P = 0$). Instead of evaporating the liquid across the boiling phase boundary, he walked around the top of the phase diagram into the supercritical region.

Because supercritical water at $374^\circ\text{C}$ dissolves silica directly, Kistler first soaked his water-filled silica gel in alcohol baths until methanol replaced the water inside the pores, forming an alcogel. Next, he sealed the wet alcogel inside a steel pressure autoclave and heated the vessel above the critical point of methanol ($239^\circ\text{C}$ and $8.1\text{ megapascals}$ of pressure). Modern plants substitute liquid carbon dioxide, whose critical point sits at a gentle $31.1^\circ\text{C}$ and $7.38\text{ megapascals}$.

Once the temperature and pressure inside the autoclave crossed the critical point, the physical distinction between liquid and gas vanished. No boiling occurred, no vapor bubbles formed, and no receding meniscus ever touched the silica walls. When Kistler vented the supercritical fluid out of the hot valve and cooled the chamber, he pulled out a translucent blue block of silica aerogel (published in Nature in May 1931). The block kept the exact dimensions of the wet jelly while consisting of up to $99.8\text{ percent}$ air by volume.

Built from dendritic chains of two-nanometer fused silica spheres surrounding twenty-nanometer air pockets, silica aerogel exhibits a counterintuitive thermal property. Even though it is almost entirely filled with open air, a block of aerogel insulates against heat transfer twice as effectively as still air itself ($0.013\text{ W/m}\cdot\text{K}$ versus $0.026\text{ W/m}\cdot\text{K}$ for stagnant air). That thermal barrier relies on the Knudsen effect. At sea-level atmospheric pressure, nitrogen and oxygen molecules travel an average distance—their mean free path $\ell$—of $68\text{ nanometers}$ before colliding with another gas molecule to pass along kinetic heat. Because the nanopores inside silica aerogel measure only $20\text{ nanometers}$ across, trapped gas molecules collide repeatedly with the insulating silica walls before they can strike a neighbor. In January 2006, NASA's Stardust capsule parachuted into the Utah desert carrying thousand-cell blocks of silica aerogel that had decelerated comet Wild 2 dust grains from 6.1 kilometers per second to a dead stop within millimeters without melting a single mineral crystal.