Amorphous materials, such as glasses and gels, are characterized by a plethora of available configurations that look much the same. With a single low-energy ordered configuration off limits—either because it doesn’t exist or because it’s kinetically inaccessible—their energy landscapes are rugged labyrinths with many local minima, each corresponding to a specific disordered arrangement of the constituent particles.

That disorder can carry more information than meets the eye. Amorphous solids are eternally out of equilibrium, and a hallmark of nonequilibrium thermodynamics is that systems retain information about their history. (For more about how that history dependence is exploited in glass physics, see the article by Ludovic Berthier and Mark Ediger, Physics Today, January 2016, page 40.) Put another way, two configurations that are virtually identical in their bulk properties (such as density and energy) and microscopic measures (such as autocorrelation functions) are nevertheless distinct states, and they may be distinguishable by properties we don’t yet know how to measure.

Now Srimayee Mukherji, her master’s thesis adviser Rajesh Ganapathy, and their colleagues Ajay Sood and Neelima Kandula at the Jawaharlal Nehru Centre for Advanced Scientific Research in Bangalore, India, have shown experimentally1 that they can manipulate the information contained in a raft of soap bubbles like the one shown in figure 1.

Figure 1.

A bubble raft in a Couette cell. Although the disordered arrangement of bubbles appears random, it contains information about shearing amplitudes the raft has experienced. (Courtesy of Rajesh Ganapathy.)

Figure 1.

A bubble raft in a Couette cell. Although the disordered arrangement of bubbles appears random, it contains information about shearing amplitudes the raft has experienced. (Courtesy of Rajesh Ganapathy.)

Close modal

The bubbles’ size distribution is chosen so that they can’t settle into a configuration of crystalline order, and the system behaves like a soft glass. The researchers “train” the raft by applying shear oscillations at a particular strain amplitude γt. Shearing rearranges the bubbles in a way that seems to be random: No visible feature distinguishes a trained raft from an untrained one. Nevertheless, a suitable readout protocol can extract the value of γt several minutes or more after training. A single raft can even hold simultaneous memories of two different γt values—and in principle, more than that.

The memory appears to be related to the bubble raft’s yielding transition. Below a shear strain γy = 0.06, the raft behaves like an elastic solid; for larger strains, it deforms plastically. Surprisingly, the system can remember γt values both greater and less than γy, and the closer γt is to γy, the stronger the memory signature. Although yielding behavior is found in many everyday materials, including whipped cream and solid cooking fats (see the Quick Study by Braulio Macias Rodriguez and Alejandro Marangoni, Physics Today, January 2018, page 70), a rigorous theory of the transition is still elusive.2 The connection between memory and yielding has the potential to shed new light on both.

Many condensed-matter systems exhibit memory of past conditions. In addition to all the systems used and explored for practical data storage, material memories include any system that exhibits hysteresis or is sensitive to its preparation pathway. Recent years have seen a push for a more unified view of memory phenomena, to draw connections among the behaviors of disparate systems.3 For example, dilute colloidal suspensions under cyclic shear can remember their history in a way that bears a striking resemblance to how charge-density-wave solids remember the durations of electrical pulses (for an overview of the latter, see the article by Robert Thorne, Physics Today, May 1996, page 42).

Five years ago, at about the same time as the experiments on sheared suspensions, a trio of theorists predicted a similar yet distinct memory behavior in sheared amorphous solids.4 Ganapathy and his group, who had experience working with granular and colloidal systems under shear, decided to take a look. They opted to use bubble rafts rather than a system of solid particles, because the bubbles interact frictionlessly. The challenge was keeping the bubbles from bursting or coalescing during the experiment.

It’s been known for a century that soap bubbles made by the right recipe can be kept stable for hours or longer; James Dewar, among his other achievements, was a pioneer of soap film research (see the article by Robert Soulen, Physics Today, March 1996, page 32). But the bubbles in that early work weren’t subjected to constant shearing and squeezing. Says Ganapathy, “We tried a whole bunch of different surfactants before we converged on one that worked”—a mixture of toy bubble solution and sodium stearate bar soap.

The bubbles are placed in a Couette cell, the 4-cm-wide annular region between an inner disk (visible at the left of figure 1) and an outer ring (not shown). Rotating the disk alternately clockwise and counterclockwise applies an oscillating shear strain whose amplitude the raft remembers. A typical training protocol comprises 17 oscillations with period 10 seconds.

The researchers characterized the response to shear oscillations by filming the raft and calculating how far each bubble moved from the beginning of one cycle to the beginning of the next. For training amplitudes γt much less than γy, the mean-square bubble displacement was always essentially zero: The raft deformed elastically, and each bubble returned to its original position. For larger values of γt, but still less than γy, the first few shear cycles rearranged some bubbles, but after that, the raft settled into a state of purely elastic deformation. For γt > γy, the mean-square displacement started high and decreased but plateaued at a nonzero value: No matter how much the raft is trained in the plastic regime, each new cycle always rearranges some bubbles.

In the readout protocol, the researchers applied a series of shear oscillations of gradually increasing amplitude γo, and they measured the raft response in terms of either the mean-square displacement or the fraction of bubbles displaced by more than a tenth of their diameters. Attempting to read an untrained raft (black data in figure 2a) shows nothing out of the ordinary: The deformation starts out elastic at low amplitudes and becomes gradually more plastic as γo is increased.

Figure 2.

Signatures of memory in a bubble raft’s response to an increasing shear strain amplitude γo. (a) When a raft is trained by shear oscillations at γt = 0.056, its response (purple) looks much like that of an untrained raft (black) except for a sharp drop at γt. (b) A raft trained at two amplitudes, γt1 = 0.042 and γt2 = 0.053, remembers them both. (Adapted from ref. 1.)

Figure 2.

Signatures of memory in a bubble raft’s response to an increasing shear strain amplitude γo. (a) When a raft is trained by shear oscillations at γt = 0.056, its response (purple) looks much like that of an untrained raft (black) except for a sharp drop at γt. (b) A raft trained at two amplitudes, γt1 = 0.042 and γt2 = 0.053, remembers them both. (Adapted from ref. 1.)

Close modal

The readout of a trained raft (purple data in figure 2a) looks similar, except at γt, where the mean-square displacement drops by up to two orders of magnitude. Figure 2b shows the readout of a raft trained on two amplitudes, γt1 and γt2; it simultaneously remembers them both. For each raft, to better measure the sharpness of the memory signals, the researchers scanned γo more slowly in the vicinity of the known training amplitudes. But the memory doesn’t depend on that aspect of the readout protocol—they could just as easily have scanned γo at a constant rate to detect an unknown γt.

Curiously, trained rafts behave like untrained rafts even for γo < γt (or γt1 for the two-memory raft). That means not only that training at γt has no effect on the raft response at γo < γt, but that shearing at γo < γt—which rearranges some of the bubbles—doesn’t disrupt the memory of γt. Both of those features remain to be fully understood.

“We expected to see memory in this system,” says Ganapathy. “But personally, I expected to see a clear memory signature only beyond the yield point, because that is where the system has been reconfigured enough to be subsequently read out.” In fact, the memory works equally well for γt just above and just below γy: All three of the memory signatures shown in figure 2 are for strains less than γy. On the other hand, the memory works poorly for values far from γy in either direction.

That unexpected behavior offers a new path to exploring the nature of the yielding transition itself. Deforming a material at or above the yield strain doesn’t make all of it yield uniformly; some parts flow freely while others remain rigid. Previous experiments from Ganapathy’s group5 showed that at γy, spatial correlations between the flowing and rigid regions are maximized, and the system’s relaxation time diverges, just like at the critical point of a second-order phase transition. And recent simulations have shown that shearing a model glass at γy helps it find its way into an ultrastable, low-energy (but still disordered) configuration.6 

There’s something about γy, it seems, that efficiently rearranges particles and explores the space of possible configurations. What that has to do with memory depends on where and how the memory is stored in the system. If, for example, memory of each γt value is encoded at a particular length scale, that could help explain how the system can remember multiple γt values at the same time and why shearing at γy, which accesses all length scales, strengthens the memory signature.

But that’s all speculation for now, because it’s still not clear what makes a trained raft structurally different from an untrained one. So far, the only known way to tell them apart is by performing the readout protocol. Despite their best efforts, the researchers haven’t found a way to tell the two apart based on the positions of the bubbles alone. An audience member at one of Ganapathy’s talks once asked if the effect might somehow be exploited in cryptography. “I don’t know the answer,” he says, “but there might be advantages to this form of memory.”

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