Transitions occurring in nanosystems, such as a chemical reaction or folding of a protein, are greatly affected by friction and thermal noise. Almost 80 years ago, physicist Hendrik Kramers predicted that these transitions are more frequent at an intermediate level of friction, an effect known as Kramers rotation. Now scientists from the Institute of Photonic Sciences (ICFO) and other European centers have measured this effect on a laser-trapped particle, confirming for the first time experimentally the Kramers prediction.
In a study published recently in Nature Nanotechnology, researchers at the Institute of Photonic Sciences (ICFO, in Barcelona), the ETH Zurich Polytechnic (Switzerland) and the University of Vienna have laser-trapped a particle to measure and experimentally confirm a prediction on nanotransitions formulated by the Dutch physicist Hendrik in 1940.
Although this story begins long before. In 1827, the English botanist Robert Brown made an apparently insignificant observation at the time, but would then play a central role in the development of the atomic theory of matter. Looking through his microscope, he noticed that the pollen grains floating in the water were constantly shaking, as if driven by an invisible force, a phenomenon now known as Brownian motion. It was later understood that the irregular motion of the pollen particle is caused by the incessant pounding of the water molecules surrounding the pollen particle. Albert Einstein’s theoretical analysis of this phenomenon provided crucial evidence for the existence of atoms.
Collisions between pollen grains and water molecules have two important effects on grain movement. On the one hand, they generate friction that slows the particle and, on the other hand, its thermal agitation keeps the particle in motion. Brownian motion is the result of the balance of these competing forces.
Friction and thermal movement caused by the environment also greatly affect transitions between long duration states, for example, phase transitions such as freezing or melting. Long lasting states, for example, different phases of a material or different chemical species, are separated by a high energy barrier in the form of choline.
The barrier between the valleys, or wells, prevents the physical system from jumping steadily and rapidly between the two states. As a consequence, the system spends most of its time fluttering in one of the wells and rarely jumps from one well to the other. These transitions are important for many processes in nature and technology, ranging from phase transitions to chemical reactions and protein folding.
UNEXPECTED INFLUENCE OF FRICTION IN THE TRANSITIONS
How often, then, do these rare events occur between wells? This is the question posed by the Dutch physicist Hendrik Kramers at a theoretical level in 1940. Using a simple model system, he mathematically demonstrated that the speed at which transitions occur decreases rapidly with increasing barrier height. And what is more surprising, Kramers predicted that the pace of transition also depends on friction in a very interesting way. For strong friction, the system moves slower, leading to a small transition rate. As the friction decreases, the system moves more freely and the transition rate increases.
However, for a sufficiently low friction, the transition speed begins to decrease again because in this case the system takes a long time to acquire enough energy from the environment to overcome the barrier. The maximum resulting from the transition rate in the intermediate friction is called the rotation of Kramers.
Now, as part of an international collaboration, scientists from ETH Zurich, ICFO and the University of Vienna have been able to directly observe the rotation of Kramers for a levitating nanoparticle. In their experiment and using a laser trap, they were able to maintain a nanoparticle between two wells, separated by an energy barrier.
Like the pollen grain observed by Brown, the nanoparticle constantly collides with surrounding molecules and these random interactions occasionally push the nanoparticle over the barrier.
By monitoring the movement of the nanoparticle over time, scientists determined the speed at which the nanoparticle jumps between the wells for a wide range of frictions, values that can be adjusted precisely by adjusting the gas pressure around the nanoparticle. The transition rate they have obtained from their experiment confirms the prediction made by Kramers almost 80 years ago.