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Structure of disordered matter

In the first part of the cum laude PhD thesis of Ilian Pihlajamaa, he considers the basic but non-trivial question: How should one describe the structure of a disordered material?

He tested various theories for representative liquid materials classes and found that, to his surprise that one of the most popular theories is in fact rather poor. Furthermore, he challenged the status quo that two-particle correlations are sufficient to describe the structure of most liquids.

Pihlajamaa then measured higher-order structural correlations in a simple liquid and discovered that intricate four-particle correlations emerge upon approaching the glass transition. An important implication of this finding is that a successful description of the structure-dynamics link in glass forming materials should incorporate many-body correlations beyond the two-particle level.

Complex dynamics

The second part of Pihlajamaa’s thesis focused on the complex dynamics of glass forming liquids. He capitalized on a recent methodological breakthrough in the field by studying a three-dimensional model liquid extremely close to the glass transition point.

He found that the dynamics of this state-of-the-art model is in fact strongly confounded by polydispersity effects: upon approaching the glass transition, the smallest and largest particles start to lead increasingly distinct dynamical lives.

This ‘dynamical decoupling’ has direct consequences for the proposed mechanisms of glass formation, and it implies that caution is warranted when generalizing results from these specific polydisperse models to other materials.

Taking this a step further, Pihlajamaa studied the same model in two dimensions, and found fundamental differences across dimensions. This work, which also resolves contradictions in recent literature, demonstrated how certain material-specific properties (polydispersity, dimension) can lead to fundamentally different relaxation mechanisms, and challenges the conventional belief that two- and three-dimensional glass formers exhibit the same behavior.

New perspective on failure

Lastly, Pihlajamaa offered an entirely new perspective on one of the most popular, but imperfect, theories to elucidate the structure-dynamics link in glass forming matter.

Instead of trying to improve this theory in an ad-hoc manner (as has been done abundantly, largely fruitlessly, in the last few decades), Pihlajamaa asked the question: why does this theory fail in the first place?

He provided the first direct measurement of each (uncontrolled) approximation in the theory. Surprisingly, he discovered that some often-criticized approximations were remarkably accurate, while the opposite was true for others. This provides the first detailed picture of the theory’s intrinsic ‘anatomy’ and yields much-needed insights to guide further theory development.

Overall, Pihlajamaa's work deepens our understanding of glass formation by shedding new light on the structure, dynamics, and structure-dynamics relation in glass forming materials.

Beyond fundamental physics, these insights could ultimately impact materials science and industry, from designing better amorphous materials to optimizing glass-like substances in technology and manufacturing.