Fractional Hoppinglike Motion in Columnar Mesophases of Semiflexible Rodlike Particles

Saber Naderi, Emilie Pouget, Pierre Ballesta, Paul van der Schoot, M. Paul Lettinga, and Eric Grelet

Phys. Rev. Lett. 111, 037801 – Published 16 July 2013

Abstract

We report on single-particle dynamics of strongly interacting filamentous fd virus particles in the liquid-crystalline columnar state in aqueous solution. From fluorescence microscopy, we find that rare, discrete events take place, in which individual particles engage in sudden, jumplike motion along the main rod axis. The jump length distribution is bimodal and centered at half- and full-particle lengths. Our Brownian dynamics simulations of hard semiflexible particles mimic our experiments and indicate that full-length jumps must be due to collective dynamics in which particles move in stringlike fashion in and between neighboring columns, while half jumps arise as a result of particles moving into defects. We find that the finite domain structure of the columnar phase strongly influences the observed dynamics.

Received 8 March 2013

DOI:https://doi.org/10.1103/PhysRevLett.111.037801

Authors & Affiliations

Saber Naderi^1,5, Emilie Pouget^2,3, Pierre Ballesta³, Paul van der Schoot^1,4,†, M. Paul Lettinga^3,6, and Eric Grelet^2,*

¹Faculteit Technische Natuurkunde, Technische Universiteit Eindhoven, Postbus 513, 5600 MB Eindhoven, The Netherlands
²Université de Bordeaux et CNRS, Centre de Recherche Paul-Pascal, 115 Avenue Schweitzer, F-33600 Pessac, France
³ICS-3, Institut Weiche Materie, Forschungszentrum Jülich, D-52425 Jülich, Germany
⁴Instituut voor Theoretische Fysica, Universiteit Utrecht, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands
⁵Dutch Polymer Institute, Post Office Box 902, 5600 AX Eindhoven, The Netherlands
⁶Department of Physics and Astronomy, Laboratory for Acoustics and Thermal Physics, Katholieke Universiteit Leuven, Celestijnenlaan 200D, Leuven B-3001, Belgium

^*grelet@crpp-bordeaux.cnrs.fr
^†p.vanderschoot@phys.tue.nl

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Issue

Vol. 111, Iss. 3 — 19 July 2013

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Images

Figure 1
Hoppinglike motion of filamentous fd virus particles in the hexatic columnar mesophase. (a) In most cases, the particle only jumps, but (b) in some others, they also reorient and eventually bend. Fluorescence images show the raw data where the dashed red line is drawn perpendicular to the long axis of the labeled particle and indicates its position at the initial time. The corresponding traces present the dimensionless displacements along ( $z$ , blue line) and perpendicular ( $x$ , red line) to the long axis (director). Displacements are normalized by the particle length $L$ . The green lines indicate the relative orientation change of the particles in radians (right vertical axes). The experimental uncertainties in determining the position and orientation of the particles are the origin of the noise in the traces.Reuse & Permissions
Figure 2
Experimental distribution of jumps in the columnar mesophase of fd virus particles in aqueous solution. (a) Rotation angle in radians after a jump event. Shown in white is the distribution of jump angles larger than twice the decay angle obtained by an exponential fit (green line). (b) Histogram of the jump length normalized by the rod length $L$ . The green line is a sum of two Gaussian functions centered at $Δ z = L / 2$ and $L$ .Reuse & Permissions
Figure 3
(a) Three snapshots of a simulation, where a particle (red circles) is removed from the middle of a quasi-one-dimensional system and the remaining particles reequilibrate. Displacement of the two neighbors (blue circles) of the removed particle is measured after the particle is removed. (b) Probability distribution of displacement $Δ z$ of the two neighbors after reequilibration. Here, each elongated particle consists of five beads with an equivalent aspect ratio of 5.8.Reuse & Permissions
Figure 4
(a) Displacement of a rodlike particle of length $L$ and diameter $σ$ along ( $z$ , solid black line) and perpendicular to ( $x$ , dashed red line) the main axis of a column. Simulations are performed with reflecting boundary conditions and 100 columns with an overall packing fraction of 28%. In each column, there are $N = 12$ particles corresponding to a linear fraction of $ψ = 0.95$ . Each elongated particle consists of nine beads with an equivalent $L / P = 0.31$ . (b) Distribution of the jump length $Δ z$ . (c) Snapshots of two columns at three different times. The particles are colored orange and white according to their initial position. The images show a circular-type movement with inter- and intra- (particles marked by a green bead) columnar jumps. The gray particles are not involved in this movement.Reuse & Permissions

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