Chemical gardens grown in flatland

In 1646 chemist Johann Glauber dropped a crystal of ferrous chloride (FeCl₂) into a solution of potassium silicate (K₂SiO₃) and within minutes saw “philosophical trees,” the name he coined for the plant-like shapes that emerged during the reaction. More than three and a half centuries later, scientists still only qualitatively understand how the mineral scapes, now known as chemical gardens, grow into their rich variety of structures. Making them could hardly be simpler: Precipitates are produced when a metal salt dissolves in an alkaline solution of anions, such as silicate, phosphate, or carbonate. That simplicity makes chemical gardens a popular and dramatic demonstration among high schoolers. The science behind the drama, though, is not so simple.

As the salt crystal dissolves, it becomes enveloped in an insoluble semipermeable membrane of the solid metal silicate. Osmotic pressure pulls water from the outside to the inside and further dissolves the salt. The membrane inflates, eventually ruptures, and releases a buoyant jet of metal-rich inner solution that rises and precipitates a new membrane in the outer solution. The result, once the salt is dissolved, is a self-assembled aggregate of hollow mineral stalks. But their growth, driven by a complex interplay between osmosis, buoyancy, reactions, and diffusion, is highly nonlinear and difficult to reproduce from one experiment to the next.

In 2003, to reduce the reaction’s complexity, Florida State University’s Oliver Steinbock led a study that replaced the solid metal salt and instead injected one liquid solution at a constant rate into a beaker full of another. ¹ The step, which led to the first systematic experiments on the gardens’ tubular growth, not only avoids the erratic effects of dissolution but gives researchers control over the concentration and viscosity of each reagent as the semipermeable membranes repeatedly form and rupture.

Anne De Wit at the Free University of Brussels (ULB) in Belgium, Julyan Cartwright of the Spanish National Research Council, and their colleagues Florence Haudin and Fabian Brau, both also at ULB, have now further constrained the reaction. ² Like Steinbock, they injected one solution into another—specifically, cobalt chloride into a reservoir of sodium silicate or vice versa. But they did so using the quasi-two-dimensional geometry of a Hele–Shaw cell, in which the reservoir sits in the half-millimeter gap between two horizontal acrylic plates. The confinement effectively eliminates the buoyancy force.

Precipitation patterns

The confinement also makes the system mathematically tractable. In particular, the Hele–Shaw cell’s planar geometry allows one to replace the formidable 3D Navier–Stokes equations with a simplified set of linear equations to describe the flow. The geometry confers experimental advantages as well. By mounting a video camera atop the transparent cell and a light pad below it, the researchers monitored the reaction’s progress in situ.

The new approach offers reproducibility among identical experimental conditions. But despite the constraints imposed by their 2D system, the researchers found a surprising plethora of patterns—spirals, lobes, worms, flowers, filaments, and others—when they systematically varied either the injection rate or, as shown in figure 1, the reagent concentrations.

A general trend was for precipitation patterns to become circular if one reagent is much more concentrated than the other. When Na₂SiO₃ is used at its highest concentration, for example, it is an order of magnitude more viscous than CoCl₂ at its lowest concentration, and the precipitate accumulates at the outer rim as the dark petals of a flower. The petals emerge as viscous fingers, the hydrodynamic response to the instability that occurs whenever a less viscous fluid is pumped into a more viscous one (see Physics Today, October 2012, page 15 ). When the concentrations of both reagents are high, the precipitates grow into long, meandering filaments. When the concentrations of both are low, wide lobes emerge instead.

To explore a pattern common to 2D gardens—and discernable in some 3D ones—De Wit and her colleagues analyzed the growth kinetics of 173 curly-shaped precipitates they observed in several experiments (marked S_i in figure 1). The shapes, shown more clearly in the magnified view of S₃ in figure 2, were pervasive throughout a wide range of intermediate concentrations. And all of the curls conformed to the mathematics of a logarithmic spiral—the logarithmic dependence of angle on radius—the same structure found in natural systems such as seashells, snail shells, and the horns of animals. In the case of their experiments, De Wit says, “what matters is to have a solid that is pushed, breaks, and starts to rotate when material is added in a self-similar way at the end of a propagating tip.”

Cartwright adds that so generic a model—independent of chemical details—is merely a first step to quantifying how the 2D system behaves. “We’re hoping to model other features, such as the filaments, which are reminiscent of the stalks, or tubes, in 3D gardens, to further constrain the growth mechanism,” he says. A detailed and quantitative 2D model would surely provide some insight and predictive power over the behavior of 3D gardens and such natural formations as deep-ocean hydrothermal vents, rust tubes emanating from corroded iron or steel, and hollow, briny icicles under Arctic sea ice.

De Wit and her colleagues see another compelling application for their approach: building new complex materials. By turning to a catalog of patterns or phases like the one in figure 1, researchers may be able, De Wit speculates, to control the reaction well enough to produce the desired pattern and complexity. But that’s a goal for the long run. And it may involve other building blocks. A related class of self-assembling mineral aggregates known as silica biomorphs also exploits steep pH gradients like those found in chemical gardens—though using a different mechanism—to assemble leaf-like sheets, helical filaments, and “cauliflowers” (see Physics Today, March 2009, page 17 ). ³

Possibilities abound. It’s intriguing to imagine, for instance, a filament-rich chemical garden, tailor-made using an appropriately tweaked recipe, operating as a microfluidic delivery system or catalytic filter.