If a person pushes a broken-down car alone, there is a certain effect. If another person helps, the result is the sum of their efforts. If two micro-particles are pushing another microparticle, however, the resulting effect may not necessarily be the sum their efforts. A recent study published in Nature Communications, measured this odd effect that scientists call “many body.”
In the microscopic world, where the modern miniaturized machines at the new frontiers of technology operate, as long as we are in the presence of two particles, things are relatively simple. When other particles are added, however, the situation becomes more complicated than common sense would suggest. Imagine there are two people pushing a broken-down car: the total force is the sum of their forces. Similarly, if there are three people, it would be the sum of the force of three people, and so on. Now imagine a solid particle of a few thousandths of a millimeter, a colloid, immersed in fluid. Just ahead there is a similar particle. If there are “critical” thermal fluctuations in the fluid that separates them, they will either repel or attract each other without even touching: the fluctuations are responsible for it. In other words, an interaction force, or "critical Casimir" force emerges, as if the particles were connected by an invisible spring. To obtain critical fluctuations, we only need one of many transparent liquids composed of a mixture of two fluids which gradually separate like oil and water when their temperature is raised.
What happens when a third colloid comes in? “Something counterintuitive,” explains SISSA professor, Andrea Gambassi, one of the authors of the study and long-standing collaborator of Prof. Siegfried Dietrich, Director at the Max Planck Institute for Intelligent Systems (MPI-IS) in Stuttgart, “the total force that one of the particles ‘perceives’ is different from the sum of the interactions with the other two when they are present separately.”
For Dietrich and Gambassi critical Casimir forces are nothing new: in 2008, they published together a study in Nature, where these forces, which had been predicted theoretically since 1978, were directly measured for the first time in collaboration with the experimental group of Prof. Clemens Bechinger, Head of the 2nd Institute of Physics at the University of Stuttgart and Max Planck fellow at the MPI-IS. “In simple words” Gambassi continues, “the forces do not add up linearly like they do in our daily life. Here we are dealing with what physicists call a many-body effect, which is typical of fluctuation-induced forces.”
The new study measured this effect for the first time in a system made up of glass (silica) microspheres immersed in fluid. By reconstructing critical Casimir forces with only two particles and then with three, the researchers demonstrated the nonadditivity of these forces. “The knowledge of these effects is very important from the point of view of both fundamental and applied research, especially for scientists who design micro-machines to perform a variety of tasks. Each micro-machine is made up of several mechanical components in relative motion and in order to understand how the different ‘gears’ interact with each other, the knowledge of many-body interaction is crucial, especially in the presence of fluids,” explains Gambassi.
Laser beams, optical tweezers, and critical mixtures
The experiment, conducted by the group led by Professor Giovanni Volpe at the University of Bilkent in Turkey, starts with colloids immersed in a mixture of water and lutidine (an oily substance). Below 34°C, this mixture is similar to water, but when the temperature is raised, a transition occurs: first the fluid becomes opaque because of the effects of critical fluctuations, after which the oil begins to separate, floating on the water. “It is around this phase transition that we observe the many-body effects,” ex-plains Volpe.
The colloids immersed in fluid, however, move randomly and diffuse with Brownian motion, the typical movement of microscopic objects immersed in a liquid, as explained theoretically by Einstein. In order to “confine” them, the fluid was illuminated by thin laser beams focussed on one point: when the particles entered the beam, they tended to stay where the light was most
intense. In this way, the laser acted as a sort of optical tweezers. By keeping two colloids close together using two laser beams, it was possible to accurately measure their random motions with a video taken from the microscope. Then, using statistical methods, the forces at play were reconstructed. With the help of another optical tweezers, the researchers then added a third particle.
“On approaching the phase transition, when comparing the experiment with two and three colloids, we observed that there was no linear addition of the forces and that many-body effects were present,” explains Dietrich. “Of course, if we added more colloids, the situation would become even more complicated and interesting.” And Volpe concludes: “In this way we demonstrated that the many-body effect is real and we succeeded in measuring it with unexpected accuracy, especially when we consider that we are dealing with forces of one-thousandth of a millionth of a gram. Now we would like to use them to design and develop new micro-machines.”
Colloids confined by laser beams
Illustration: Soft Matter Lab @ Bilkent University