Led by graduate student Keng-hui Lin, scientists in the laboratory of Penn physicist Arjun G. Yodh measured the entropic forces exerted by rod-like viruses on particles in water. Their research revealed anticipated entropic forces associated with shifts in position and rotation of the rigid nanorods; to their surprise, it also revealed tiny additional entropic effects of rod flexibility.
Entropy is a measure of the disorder of a system, with systems generally evolving to maximize entropy.
"Entropy in these systems is largely a function of the amount of space components have for moving about," said Yodh, a professor of physics. "It turns out that simply by bending, the rod-like virus can effectively occupy a little more space and thus entropically drive rearrangements of the system."
Yodh’s team captured these minuscule shifts in entropy using "laser tweezers" to manipulate inert, one-micron spheres floating in a microscopic tank full of rod-shaped viruses 880 nanometers long and 7 nanometers in diameter.
"The effects were quite subtle, but our experiments showed that the slight flexibility of the viruses strengthened the attraction between the spheres, driving them more strongly toward each other," Yodh said. "When the rods become a little more flexible, they occupy more space when they spin. The smidgen of additional space occupied by a bent virus compared to a straight virus was enough to increase the attractions between spheres that nearly touch one another."
In the mixture of rods and spheres, the rods seek to maximize their own freedom of motion, and therefore the mixture’s entropic energy, by avoiding the space between the spheres. The net effect of the rods’ preference not to be sandwiched between the spheres is manifested as a slight attraction between the larger particles.
Yodh and his colleagues measured the slight attractive force the viruses impart by partially immobilizing the spheres with laser tweezers. While trapped in the laser beam line trap, the spheres were able to move in only one dimension. By continuously photographing the positions of the spheres in a tank both with and without the rods, the team was able to discern these entropic attractions. The spheres’ attraction is accompanied by an overall increase in the system’s entropy.
The work of the Penn team tested detailed theoretical predictions by Portuguese theorist Carlos Marques and collaborators, demonstrating entropic forces associated with nanorod central position and rotation. These orientational degrees of freedom are, in fact, responsible for the rich variety of liquid crystalline phases exhibited by rods. The measured deviations from theory were due to rod flexibility.
Yodh and Lin were joined on the Physical Review Letters paper by John C. Crocker of the California Institute of Technology and Ana C. Zeri of the University of California, San Diego. Their work was funded by the National Science Foundation and NASA.
Journal
Physical Review Letters