A team of researchers reports they have succeeded in disproving a long-held tenet of modern physics–that useful work cannot be obtained from random thermal fluctuations–thanks in part to the unique properties of graphene.
The microscopic motion of particles within a fluid, otherwise known as Brownian motion for its discovery by Scottish scientist Robert Brown, has long been considered an impossible means of attempting to generate useful work.
The idea had been most famously laid to rest decades ago by physicist Richard Feynman, who proposed a thought experiment in May 1962 involving an apparent perpetual motion machine, dubbed a Brownian ratchet.
In theory, this device would consist of a gear and a rachet that vibrates while immersed in a heat bath, allowing motion only in one direction. The premise is that the unidirectional motion would produce a force in the absence of any heat gradient, seemingly defying the second law of thermodynamics. However, Feynman argued that since the machine’s components will also undergo Brownian motion, there will inevitably be faults in the way it functions, thereby canceling out any useful work it might generate.
Now, a team of researchers with the University of Arkansas Department of Physics argues that they have demonstrated thermal fluctuations in freestanding graphene can indeed be used as part of a novel new method that allows the creation of useful work, upending more than a century of conventional thinking in modern physics.
Graphene Ripples as a Brownian Particle
Graphene is a fullerene comprised of a sheet of graphite just one atom in thickness. Due to the rippled structure freestanding graphene possesses, its unique behavior in response to ambient temperature made it ideal for use in the team’s research.
In a paper describing their discovery, the team theoretically considers “a graphene ripple as a Brownian particle,” which is coupled to an energy storage circuit. If the circuit and the Brownian particle remain at a consistent temperature, energy cannot be generated from the particle according to the second law of thermodynamics. This remains true even if a rectifying diode is introduced into the circuit.
“However, when the circuit contains a junction followed by two diodes wired in opposition,” the paper’s authors explain, “the approach to equilibrium may become ultraslow.” More specifically, the balance between these elements is temporarily interrupted as current passes between a pair of diodes, which charges the storage capacitors.
“The energy harvested by each capacitor comes from the thermal bath of the diodes,” the paper’s authors explain, “while the system obeys the first and second laws of thermodynamics.” Hence, although there are no thermodynamic laws being defied, useful work is nonetheless generated from Brownian motion, very much in defiance of Feynman’s decades-old arguments to the contrary.
During the research process, the team, led by University of Arkansas physics professor Paul Thibado, discovered that while larger capacitors produce more stored charge, the use of smaller graphene-based capacitors offered not only a higher rate of charging initially but also discharged over a longer period—a significant factor, since the use of graphene capacitance in this way allows for the storage capacitors to be disconnected from the circuit used to harvest the energy before loss of the net charge.
Solving the Fokker-Planck equation
In an email to The Debrief, Thibado explained that the new source of power he and his colleagues discovered managed to evade physicists for so long because of the limitations researchers faced in the 1960s during early attempts at resolving a partial differential equation that has long perplexed physicists.
“We found this new source of power by solving the Fokker-Planck equation (FPE),” Thibado says.
In the 1960s, around the same time that Feynman presented his arguments about the use of Brownian motion to produce useful work, scientists also made their earliest attempts to resolve the Fokker-Planck equation.
“This is a challenging partial differential equation to solve,” Thibado says, and during attempts that were made in the 1960s, computers were not available to aid in the necessary calculations that were required.
“Even though studies were published in the 1960s mistakes were made,” Thibado told The Debrief. Thibado says the primary issues arose from the diode, which possesses a nonlinear resistance. Because of this, the Fokker-Planck equation must be solved numerically.
According to Thibado, “Most physicists would try to use the ideal diode equation, but we found this equation to be unrealistic.” This is because the current that is generated grows unbounded with voltage.
“As a result, the solution to the Fokker-Planck equation cannot be found,” Thibado told The Debrief. “An improved model uses the ideal diode but in series with a resistor.”
“We used this and it controlled the numerical difficulties,” Thibdo says.
Although a temperature gradient has long been understood to be a requirement to generate thermal power in traditional settings, Thibado told The Debrief that he and his team were able to overcome this because, in the method they developed, the new thermal power is generated by nonlinear resistance of the diode.
“If the diode is replaced with a resistor, then the source of power goes away,” Thibado explained.
“However, it is important to realize that this is a transient effect,” he added. “A lot of scientists will only focus on the final thermodynamic equilibrium state of the system. This was another mistake.”
“We solved for everything,” Thibdao said.
“In addition, we found a special circuit layout that allows ultrafast charging of the storage capacitors, and it also allows ultraslow discharging to thermodynamic equilibrium. This provides time to harvest the energy for an application, and repeat.”
Ultimately, the team’s findings represent the solution to a problem Thibado has spent more than a decade studying. He now plans to construct what he calls a Graphene Energy Harvester (GEH), which employs a negatively charged graphene sheet placed between a pair of metal electrodes that can produce a pulsing DC current, thereby performing work on a load resistor.
The GEH will be developed into commercial products in cooperation with nanotechnology company NTS Innovations.
Thibado and his team’s recent paper, “Charging capacitors from thermal fluctuations using diodes,” was published in Physical Review E on August 16, 2023.