Why is entropy in detail

On the trail of entropy

Chemical reactions, especially in biological systems, often lead to macromolecules changing their shape - their "configuration" - e.g. through rotation or translational displacement. To find out exactly what increases or inhibits the mobility of the molecules, chemists and physicists use simplified model systems, for example molecules adhering to a surface.

These can be investigated at temperatures of just a few degrees above absolute zero (-273 ° C) with the aid of a scanning tunneling microscope (STM for "scanning tunneling microscope"); STM enable the investigation of numerous physical properties of surfaces at the atomic level.

A popular molecule for this type of study is dibutyl sulfide (DBS), an elongated hydrocarbon with a central sulfur atom that allows the molecule to be absorbed, i.e. attached to, a gold surface. Depending on the temperature, its two “arms” rotate more or less easily around the central sulfur axis.

The freedom of movement of a molecule on a surface is usually described in terms of two physical quantities: the energy barrier that it has to overcome in order to complete the movement - in chemical reactions this barrier is called activation energy - and the so-called test rate, which is understood to mean one is the number of attempts the molecule makes to initiate motion. The higher the temperature, the more the two DBS arms rotate (as the higher the temperature, the greater the likelihood of overcoming the energy barrier).

Examination of a single molecule to the picometer - for two weeks

Such rotating molecules aroused the interest of Empa physicist Hans Josef Hug. Their fluctuation rates can be controlled with the help of temperature. This property makes it an ideal model system to study contactless friction and the resulting energy losses at the atomic level. Unfortunately, contactless molecular friction is not that easy to measure with commercially available instruments.

Hug and his team have therefore developed a complex analysis device based on a low-temperature STM in combination with a scanning force microscope (SFM), which operates at temperatures between 4.5 Kelvin and room temperature in an ultra-high vacuum with precision to the picometer can be. The project in turn spurred PSU researcher Eric Hudson to spend a sabbatical in Hug's group.

As is customary in experimental research, the Empa PSU team first began to understand the STM work of other scientists on this molecule. PhD student Jeffrey Gehrig and postdoc Marcos Penedo subjected the DBS molecule to a thorough test: For two weeks, its rotation rates were recorded on a 50 × 50 picometer square grid at eight different temperatures between five and 15 Kelvin.

When the team evaluated the measured jump rates in order to represent the energy barriers for the DBS rotations as a function of the position of the STM tip, there was no uniform “energy landscape” for the DBS molecule; rather, valleys and mountain ridges appeared in it. In other words: Depending on where exactly the STM tip was positioned, the DBS arms rotated sometimes more, sometimes less frequently - despite the constant temperature, as the team reported in the latest issue of "Nature Communications". "That was completely unexpected," emphasizes Hug. "Because it means that the tip, which was still relatively far away from the molecule and not touching it at all, somehow influenced its mobility."

When nature reveals its secrets

And not only that: when Gehrig and Penedo plotted the trial rates of the molecule, they got a graph that was almost identical to the landscape of the energy barriers. "So I thought: Wait a minute, what is nature trying to tell us here?" Hug remembers. The test rate correlates with the entropy difference (see box) between the ground state of the molecule, i.e. before it tries to rotate, and its excited state on the tip of the energy barrier (or activation energy).

Hug's team was able to show that in the case of the DBS molecule, the differences in entropy are proportional to the energy barriers. Hug: “That means that energy and entropy are fundamentally linked in this system. However, it was extremely difficult to prove this. " Eric Hudson adds: “Entropy is often viewed as a measure of disorder or randomness. In this case, however, it is determined by the number of forms that the molecule could potentially assume, as well as by the number of possibilities that the molecule can meet the energetic requirements to change its configuration. "

The results of the Empa PSU team mean that entropy plays a decisive role in the dynamics of the molecule even at very low temperatures, at which the freedom of the molecule (and thus its configuration entropy) is significantly reduced and it was therefore assumed that entropy does not play a major role. “Entropy has been well researched in thermodynamics. At the same time, it is more difficult to grasp than other physical quantities, ”Hug admits. "Maybe that's because it is less of a 'property' and more of a measure of information." Another reason may be that we generally tend to associate entropy with chaos, the “dark side” of entropy, be it in the nursery or on the desk.

Entropy - the mysterious «force» behind spontaneous processes

Imagine putting a drop of dark blue ink in a glass of water. Over time, the ink mixes with the water until it is uniformly colored, as if an "invisible force" had been at work. Could this process ever reverse itself, so that the ink is again concentrated in a dark blue drop? Of course not. Or as a physicist would say: "Only with a very small probability." Such everyday experiences with what happens spontaneously in isolated systems and what does not can be grasped with the concept of entropy, which in turn has to do with probabilities. Isolated systems, such as the ink placed in the water glass, therefore change over time in order to adopt the most probable of all possible configurations, namely the one with the highest entropy. It is hardly surprising that this is also the one with the greatest disorder.

During the rotation of the DBS molecule investigated by the Empa PSU team (see main article), it was fascinating to observe that with the increase in the energy barrier for the rotation of the molecule - as an obstacle to its mobility - the number of possibilities increased at the same time, to overcome this obstacle. There was thus an increase in entropy. “This knowledge also implies,” as Empa physicist Miguel A. Marioni sums up, “that our internally developed STM-SFM is the perfect instrument for examining the entropy of an individual molecule down to the smallest detail.”

Additional Information:

Prof. Dr. Hans-Josef Hug
Nanoscale Materials Science
Tel. +41 58 765 41 25
[email protected]
Editor / Media contact

Dr. Michael Hagmann
communication
Tel. +41 58 765 45 92
[email protected]

Literature:
Surface single-molecule dynamics controlled by entropy at low temperatures, JC Gehrig, M Penedo, M Parschau, J Schwenk, MA Marioni, EW Hudson, HJ Hug, Nature Communications 8 (2017), doi: 10.1038 / ncomms14404

http://www.empa.ch/de/web/s604/entropy

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