Physicists find gyrations of tiny rod-like viruses induce measurable entropic forces in solution

In an experiment with exquisite sensitivity, physicists at the
University of Pennsylvania have found that fluctuations as fleeting as the bending of
rod-shaped viruses just 880 millionths of a millimeter in length can measurably
increase the entropic forces between other particles in solution. The finding is
reported in the journal Physical Review Letters.

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.

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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.

Contact: Steve Bradt

bradt@pobox.upenn.edu

215-573-6604

University of Pennsylvania