Transcript Brandeis MRSEC 0820492 twisted ribbons.ppt

Theory of Chiral Smectic A Twisted Ribbons
C. N. Kaplan1, H. Tu2, R. A. Pelcovits2 and R. B. Meyer1
1
The Martin Fisher School of Physics, Brandeis University
2 Department of Physics, Brown University
Supported by Brandeis MRSEC 0820492
Rodlike fd viruses in an aqueous solution, along with
polymers that produce an attractive force between the
virus particles, have been observed in laboratory
experiments to self-assemble into a variety of geometric
structures including twisted ribbons (see the schematic
illustration and microscope picture to the right). We have
developed a theoretical model which explains the
properties of these ribbons on the basis of very general
features of the fd rods. The theory yields predictions in
good agreement with experiment, namely, (a) a phase
diagram with a first-order transition from flat membranes
to twisted ribbons, (b) the ratio of the ribbon’s pitch to
width, (c) the tilt angle of the rods at the edge of the
ribbon. The theory has also demonstrated the importance
of molecular chirality (“twisting-handedness”) in the
formation of the ribbons, as well as the tendency of fd
rods to assemble into structures with negative Gaussian
curvature (as in a saddle shape).