The first experimental evidence to validate a newly published universal law
that provides insights into the complex energy states for liquids has been
found using an advanced nuclear technique at ANSTO.
The work has just been published in the Journal of Physical Chemistry
Letters as the editor's choice and featured on the front cover of the
journal.
The equation for the vibrational density of states formulated by Alessio
Zaccone and Matteo Bagglioli was published in a paper in PNAS in 2021,
providing an answer to a question that has been elusive for at least a
century.
The elegant mathematical theory has solved the problem of obtaining the
distribution of these complex energy states for liquids.
"One of the most important quantities in the physics of matter is the
distribution of the frequencies or vibrational energies of the waves that
propagate in the material. It is particularly important as it is the
starting point for calculating and understanding some fundamental properties
of matter, such as specific heat and thermal conductivity, and the
light-matter interaction, "said Prof Zaccone on the University of Milan
website.
"The big problem with liquids is that, in addition to acoustic waves, there
are other types of vibrational excitations related to low energies of the
disordered motion of atoms and molecules— excitations that are almost absent
in solids. These excitations are typically short-lived and are linked to the
dynamic chaos of molecular motions but are nevertheless very numerous and
important, especially at low energies. Mathematically, these excitations,
known as 'instantaneous normal modes' or INMs in the specialized literature
are very difficult to deal with as they correspond to energy states
described by imaginary numbers."
The time-of-flight neutron spectrometer Pelican at ANSTO's Center for
Neutron Scattering has been used to measure the vibrational densities of
states for several liquid systems including water, liquid metal, and polymer
liquids. The Pelican instrument has the extreme sensitivity to measure
rotational and translational vibrations over short time intervals and at low
energies.
The experiments at ANSTO confirmed the linear relationship of the
vibrational density of states with frequency at low energies as predicted by
Alessio Zaccone and Matteo Bagglioli, as shown in the figure below.
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| Confirmation of the universal law with experimental VDOS measured by inelastic neutron scattering on real liquid systems including water, liquid metal, and polymer liquids. Credit: The Journal of Physical Chemistry Letters (2022). DOI: 10.1021/acs.jpclett.2c00297 |
With the COVID lockdown, no accessibility to instruments, the small team
that included University of Wollongong Ph.D. candidate Caleb Stamper, Dr.
Cortie and Dr. Yu decided to focus on re-analyzing past experimental data
from a new perspective, to validate the new law, inspired by the theoretical
work from Alessio Zaccone and Matteo Bagglioli.
"The exercise not only achieves such a great outcome but also provides a
good introduction of neutron spectroscopy to Caleb, who has done an
excellent job," said Dr. Yu as Caleb's ANSTO supervisor and the
corresponding author of the paper.
The work would also help them address questions relating to phase
transitions in superionic liquids in their work on thermoelectric materials.
"Major challenges arise because liquids are not mechanically stable, as the
atoms in a liquid diffuse and the liquid as a whole will flow," explained
Dr. Cortie.
The universal law is based on a theoretical framework, known as
instantaneous normal modes, as described by Prof Zaccone above, which
prescribe a set of instantaneous forces, frequencies, and velocities as
quantities.
A complication in deriving a theory to predict the vibrational density of
states in liquids arose because of the presence of a small fraction of
"imaginary modes."
"Imaginary modes are important because they represent the fact that a liquid
is not stable. The atoms in a liquid are strongly interacting with one
another all the time but not in the same way a solid does. The relationship
is not 'harmonic' meaning that the atoms are not going to be restored to the
same configuration after an interaction. The atoms will continue to diffuse
quickly and slide past each other," said Stamper.
"The imaginary modes reflect the negative curvature on the potential energy
surface of a liquid. It is a very complex energy landscape but if you think
of the analogy of a surfer on an ocean wave. The atoms in the liquid follow
the curves of the wave itself (see the front cover of the journal). But the
atoms can be in a position on the crest, under the surfboard or in the
trough, always moving," said Dr. Yu.
"The law will play, for liquids, the same pivotal role that the Debye law
plays for solids. It will serve as the foundation for the whole research
field involving liquids and beyond."
Reference:
Caleb Stamper et al, Experimental Confirmation of the Universal Law for the
Vibrational Density of States of Liquids, The Journal of Physical Chemistry
Letters (2022).
DOI: 10.1021/acs.jpclett.2c00297
Alessio Zaccone et al, Universal law for the vibrational density of states
of liquids, Proceedings of the National Academy of Sciences (2021).
DOI: 10.1073/pnas.2022303118
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Physics