Randall D. Kamien

The Geometry of Soft Materials: A Primer

We present an overview of the dieren tial geometry of curves and surfaces using examples from soft matter as illustrations. The presentation requires a background only in vector calculus and is otherwise self-contained.

Why is random close packing reproducible

We link the thermodynamics of colloidal suspensions to the statistics of regular and random packings. Random close packing has defied a rigorous definition yet, in three dimensions, there is near universal agreement on the volume fraction at which it occurs. We conjecture that the common value of phi{rcp} approximately 0.64 arises from a divergence in the rate at which accessible states disappear. We relate this rate to the equation of state for a hard-sphere fluid on a metastable, noncrystalline branch.

Geometric theory of diblock copolymer phases.

We analyze the energetics of spherelike micellar phases in diblock copolymers in terms of well-studied, geometric quantities for their lattices. We argue that the A15 lattice with Pm3;n symmetry should be favored as the blocks become more symmetric and corroborate this through a self-consistent field theory. Because phases with columnar or bicontinuous topologies intervene, the A15 phase, though metastable, is not an equilibrium phase of symmetric diblocks. We investigate the phase diagram of branched diblocks and find that the A15 phase is stable.

Soft spheres make more mesophases

We use both mean-field methods and numerical simulation to study the phase diagram of classical particles interacting with a hard-core and repulsive, soft shoulder. Despite the purely repulsive interaction, this system displays a remarkable array of aggregate phases arising from the competition between the hard-core and shoulder length scales. In the limit of large shoulder width to core size, we argue that this phase diagram has a number of universal features, and classify the set of repulsive shoulders that lead to aggregation at high density. Surprisingly, the phase sequence and aggregate size adjusts so as to keep almost constant inter-aggregate separation.

Soap Froths and Crystal Structures

We propose a physical mechanism to explain the crystal symmetries found in macromolecular and supramolecular micellar materials. We argue that the packing entropy of the hard micellar cores is frustrated by the entropic interaction of their brushlike coronas. The latter interaction is treated as a surface effect between neighboring Voronoi cells. The observed crystal structures correspond to the Kelvin and Weaire-Phelan minimal foams. We show that these structures are stable for reasonable areal entropy densities.

Colloquium: Disclination loops, point defects, and all that in nematic liquid crystals

The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress has been made in controlling and measuring colloidal inclusions in liquid crystalline phases. The topological structure of these systems is quite rich but, at the same time, subtle. Motivated by experiment and the power of topological reasoning, we review and expound upon the classification of defects in uniaxial nematic liquid crystals. Particular attention is paid to the ambiguities that arise in these systems, which have no counterpart in the much-storied XY model or the Heisenberg ferromagnet.

Direct determination of DNA twist-stretch coupling

The symmetries of the DNA double helix require a new term in its linear response to stress: the coupling between twist and stretch. Recent experiments with torsionally constrained single molecules give the first direct measurement of this important material parameter. We extract its value from a recent experiment of Strick et al. (Science, 271 (1996) 1835) and find agreement with an independent experimental estimate recently given by Marko. We also present a very simple microscopic theory predicting a value comparable to the one observed.

Making the cut: lattice kirigami rules.

In this Letter we explore and develop a simple set of rules that apply to cutting, pasting, and folding honeycomb lattices. We consider origami-like structures that are extrinsically flat away from zero-dimensional sources of Gaussian curvature and one-dimensional sources of mean curvature, and our cutting and pasting rules maintain the intrinsic bond lengths on both the lattice and its dual lattice. We find that a small set of rules is allowed providing a framework for exploring and building kirigami—folding, cutting, and pasting the edges of paper.

Microscopic Origin of Cholesteric Pitch

Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104(February 1, 2008)We present a microscopic analysis of the instability of the nematic phase to chirality when molecularchirality is introduced perturbatively. We show that for central force interactions the previouslyneglected short–range biaxial correlations play a crucial role in determining the cholesteric pitch.We propose a pseudoscalar strength which quantifies the chirality of a molecule.PACS numbers: 61.30.Cz, 33.15.Bh, 05.20.-y

Dynamics of Shallow Impact Cratering

We present data for the time dependence of wooden spheres penetrating into a loose noncohesive packing of glass beads. The stopping time is a factor of 3 longer than the time d/v0 needed to travel the total penetration distance d at the impact speed v0. The acceleration decreases monotonically throughout the impact. These kinematics are modeled by a position- and velocity-dependent stopping force that is constrained to reproduce prior observations for the scaling of the penetration depth with the total drop distance.