Physicists have devised a method to capture information that glassy liquids try to hide.
BY DEBDUTTA PAUL
Window glasses are liquids, according to physicists who study them. Molten pitch and window glasses comprise molecules which flow. However, they flow so slowly that one can hardly notice, so they appear to be solid.
To make glass, first, a mixture of sand and limestone is heated to thousands of degrees Celsius. Then, the mixture is cooled slowly to room temperature. Unlike usual liquids, like water, the properties of glassy liquids change drastically while they are formed. For example, the viscosity of a glassy liquid increases suddenly as the temperature changes over a small range while being cooled from the molten state. “If one looks at the structure of the liquid while decreasing the temperature, it changes very little, remaining like that of a liquid,” said Chandan Dasgupta of ICTS-TIFR. “It doesn’t become like the structure of a crystalline solid.”
Theoretical physicists have been making significant advancements in studying glassy liquids and their transitions. Among them is Suman Dutta, a former postdoctoral researcher at ICTS-TIFR, presently with the National Centre for Biological Sciences, TIFR, and Vinay Vaibhav, a postdoctoral researcher at the University of Milan. Their recent paper was published in Physical Review E.
Random motion: water versus glass
To study liquids, physicists rely on tracking the positions of large particles, like pollen grains, under powerful microscopes.
When such particles are suspended in normal liquids like water, they exhibit a motion called the ‘Brownian motion’.
The nearby water molecules kick them around, so they vibrate randomly.
The apparent random motion of atoms, ions or molecules. Video via Wikimedia Commons.
To quantify this motion, physicists track the displacement of a molecule from its initial position with the evolved time. The displacements of various water molecules follow a particular distribution, called the ‘Gaussian distribution’. The displacements are uniform around a zero net displacement following a precise mathematical formula.
However, in glassy liquids, the particles in different regions behave differently at any instant. In some neighbourhoods within the liquid, the particles move around quickly, whereas in others, they move slowly. As a result, the displacements are not distributed uniformly. Physicists call the phenomenon ‘dynamical heterogeneity’. “The non-Gaussianity is a signature of the coexistence of slow and fast regions within the same system,” said Suman.
Dynamical heterogeneity
Studying the non-Gaussianity can help physicists answer key questions regarding the glassy liquids’ dynamical heterogeneity. For example, if a physicist observes a particular region continuously under a powerful microscope, then at short timescales, its neighbourhood can alternate between fast and slow responses. But, over a long time, all regions appear similar. This observation leads to the question: What is the duration of time for which one can expect the local dynamics to look different?
This duration, known as the lifetime of the dynamical heterogeneity, depends on the glassy liquid’s temperature. At low temperatures, the lifetime is longer. But as the temperature increases, the amount of heterogeneity reduces and the lifetime also decreases.
A new way to capture hidden information
For more than two decades, physicists have been using mathematical quantities to capture the deviation from the Gaussian distribution. But, these quantities lack information on how a few particles deviate extremely from their starting positions over long periods, said Suman.
In their new work, Vinay and Suman have proposed a new mathematical method to measure the deviation from randomness. The new measure uses techniques from information theory and machine learning.
According to Suman, the mathematical prescription they have developed describes the complex behaviour of glassy liquids, going beyond the standard methods that quantify only the non-Gaussianity. Moreover, it can be easily measured in future experiments, he said, paving the way for testing the theory. Chandan, who was not involved in the study, agreed. He added the duo’s study also led them to identify a lifetime of the dynamical heterogeneity in glassy liquids which is different from that of previous studies. But, the timescales from the previous studies and the present one are related. “That’s an important observation of their study,” said Chandan.
However, Chandan added the study does not resolve why dynamical heterogeneity happens in the first place. “Can we write down equations from which we can obtain various characteristics of this heterogeneity? There, more progress is required,” he said.
Current research
Researchers across the globe are studying glassy liquids which cannot be controlled by fluctuations in temperature. For example, ketchup, toothpaste, and mayonnaise are glassy liquids that respond to stretching and pulling. Living cells respond to forces from their surroundings instead of temperature.
Suman and his colleagues are studying glassy transitions in biological systems in response to these environmental stimuli. For example, if cells are packed closely, they can lead to a phenomenon called “jamming” that may be responsible for tumours becoming cancerous.
One thing is certain: deep mysteries of glassy transitions and dynamical heterogeneities have scientists hooked. “It’s a difficult problem,” said Chandan.
The author thanks Suman Dutta and Chandan Dasgupta for discussions.
Amazing phenomenon. Thank you for the post.