Patterning Cylindrical Fibers with Long-Range Electrostatic Forces
- PDF / 349,601 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 4 Downloads / 162 Views
1062-NN05-17
Patterning Cylindrical Fibers with Long-Range Electrostatic Forces Kevin L. Kohlstedt1,2, Graziano Vernizzi2, and Monica Olvera de la Cruz2,3 1 Department of Chemical and Biological Engineering, Northwestern University, 2145 Sheridan Rd., Tech E-136, Evanston, IL, 60208 2 Department of Materials Science and Engineering, Northwestern University, 2220 Campus Drive, Evanston, IL, 60208 3 Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, IL, 60208 ABSTRACT We report our findings with theoretical arguments on chiral symmetry breaking on the surface of charged cylinders. We use a model for periodic patterns of charges constrained over a cylindrical surface. In particular we focus on patterns of oriented lamellar patterns, such as, chiral helices, achiral rings or vertical lamellae, with the constraint of global electroneutrality. We study the dependence of the patterns' size and pitch angle on the radius of the cylinder and salt concentration. We obtain a phase diagram by using numerical and analytic techniques. For pure Coulomb interactions, we find a ring phase for small radii and a chiral helical phase for larger radii. We extend the findings to discrete triangular lattices wrapped over a cylindrical geometry. We find no symmetry breaking chiral helical phase in the discrete wrapping when using just an electrostatic potential and the minimum energy configuration is an achiral lattice matching the six-fold symmetry of triangular lattice. Conversely, with the addition of an elastic potential between the charges on the surface of the cylinder we find a stable chiral configuration. We discuss possible consequences and generalizations of our model. INTRODUCTION From a theoretical vantage point, the electrostatic patterning of a system of charges on cylindrical surfaces is relatively unexplored. Certainly, the effects of longrange electrostatic forces have been widely studied for planar two dimensional systems1; also the behavior of short-range interactions over cylindrical geometries has been addressed, such as the Ising model of spins on the curved surfaces2. We analyze here an intermediate case where charges are confined over a cylindrical surface and interact via long-range and short-range forces. A further issue we consider is whether spherically symmetric electrostatic interactions are capable to break translational, rotational or chiral isometries of the cylinder. Recently, there has been interest to study crystalline systems over constrained geometries such as the surface of spheres, cylinders, and tori3,4,5. The generalization to more general curved substrates shows an interesting, rich behavior6. MODEL We provide the full phase diagram of lamellar charged patterns on a cylinder, as a function of the cylinder radius and screening length. We explicitly show the existence of
a phase where the system spontaneously adopts chiral configurations. We study also its “Coulombic” origin by observing how it disappears when increasing the screening length. Our model is a generalizat
Data Loading...
