Paul M. Chaikin

Charge renormalization, osmotic pressure, and bulk modulus of colloidal crystals: Theory

The interactions between charged colloidal particles with sufficient strength to cause crystallization are shown to be describable in terms of the usual Debye–Huckel approximation, but with a renormalized charge. The effective charge in general is smaller than the actual charge. We calculate the relationship between the actual charge and the renormalized charge by solving the Boltzmann–Poisson equation numerically in a spherical Wigner–Seitz cell. We then relate the numerical solutions and the effective charge to the osmotic pressure and the bulk modulus of the crystal. Our calculations also reveal that the renormalization of the added electrolyte concentration is negligible, so that the effective charge computations are useful even in the presence of salts.

Lock and key colloids

New functional materials can in principle be created using colloids that self-assemble into a desired structure by means of a programmable recognition and binding scheme. This idea has been explored by attaching ‘programmed’ DNA strands to nanometre- and micrometre- sized particles and then using DNA hybridization to direct the placement of the particles in the final assembly. Here we demonstrate an alternative recognition mechanism for directing the assembly of composite structures, based on particles with complementary shapes. Our system, which uses Fischer’s lock-and-key principle, employs colloidal spheres as keys and monodisperse colloidal particles with a spherical cavity as locks that bind spontaneously and reversibly via the depletion interaction. The lock-and-key binding is specific because it is controlled by how closely the size of a spherical colloidal key particle matches the radius of the spherical cavity of the lock particle. The strength of the binding can be further tuned by adjusting the solution composition or temperature. The composite assemblies have the unique feature of having flexible bonds, allowing us to produce flexible dimeric, trimeric and tetrameric colloidal molecules as well as more complex colloidal polymers. We expect that this lock-and-key recognition mechanism will find wider use as a means of programming and directing colloidal self-assembly.

Crystallization of hard-sphere colloids in microgravity

The structure of, and transitions between, liquids, crystals and glasses have commonly been studied with the hard-sphere model, in which the atoms are modelled as spheres that interact only through an infinite repulsion on contact. Suspensions of uniform colloidal polymer particles are good approximations to hard spheres, and so provide an experimental model system for investigating hard-sphere phases. They display a crystallization transition driven by entropy alone. Because the particles are much larger than atoms, and the crystals are weakly bound, gravity plays a significant role in the formation and structure of these colloidal crystals. Here we report the results of microgravity experiments performed on the Space Shuttle Columbia to elucidate the effects of gravity on colloidal crystallization. Whereas in normal gravity colloidal crystals grown just above the volume fraction at melting show a mixture of random stacking of hexagonally close-packed planes (r.h.c.p.) and face-centred cubic (f.c.c.) packing if allowed time to settle,, those in microgravity exhibit the r.h.c.p. structure alone, suggesting that the f.c.c. component may be induced by gravity-induced stresses. We also see dendritic growth instabilities that are not evident in normal gravity, presumably because they are disrupted by shear-induced stresses as the crystals settle under gravity. Finally, glassy samples at high volume fraction which fail to crystallize after more than a year on Earth crystallize fully in less than two weeks in microgravity. Clearly gravity masks or alters some of the intrinsic aspects of colloidal crystallization.

Elastic properties of colloidal crystals and glasses

We have measured the shear modulus of lattices of charged polystyrene spheres. We describe a simple apparatus used in this study for determining the frequency of standing shear modes. For the monodisperse lattices, crystals form, stabilized by the repulsive Coulomb interaction, producing a classical ’’Wigner crystal’’ characterized by Bragg scattering and finite rigidity. We studied the rigidity as a function of volume fraction and electrolyte concentration for several particle diameters. Mixtures of colloids with different particle diameters form classical ’’Wigner glasses’’ characterized by the absence of long range order and Bragg scattering but the presence of a finite shear rigidity. We have studied the shear properties of these solids as a function of composition and electrolyte concentration.

Chiral colloidal clusters

Chirality is an important element of biology, chemistry and physics. Once symmetry is broken and a handedness is established, biochemical pathways are set. In DNA, the double helix arises from the existence of two competing length scales, one set by the distance between monomers in the sugar backbone, and the other set by the stacking of the base pairs. Here we use a colloidal system to explore a simple forcing route to chiral structures. To do so we have designed magnetic colloids that, depending on both their shape and induced magnetization, self-assemble with controlled helicity. We model the two length scales with asymmetric colloidal dumbbells linked by a magnetic belt at their waist. In the presence of a magnetic field the belts assemble into a chain and the steric constraints imposed by the asymmetric spheres force the chain to coil. We show that if the size ratio between the spheres is large enough, a single helicity is adopted, right or left. The realization of chiral colloidal clusters opens up a new link between colloidal science and chemistry. These colloidal clusters may also find use as mesopolymers, as optical and light-activated structures, and as models for enantiomeric separation.

Dense arrays of ordered GaAs nanostructures by selective area growth on substrates patterned by block copolymer lithography

GaAs has been selectively grown in a hexagonally ordered array of nanometer-scale holes with a density as high as ∼1011/cm2 by metalorganic chemical vapor deposition. This array of holes was created using block copolymer lithography, in which a thin layer of diblock copolymer was used as an etching mask to make dense holes in a 15-nm-thick SiNx film. These selectively grown nanoscale features are estimated to be 23 nm in diameter with narrow lateral size and height distributions as characterized by field-emission scanning electron microscopy and tapping mode atomic force microscopy. The narrow size distribution and uniform spatial position of the nanoscale dots we report offer potential advantages over self-assembled dots grown by the Stranski–Krastanow mode.

Cubic crystals from cubic colloids

We have studied the crystallization behavior of colloidal cubes by means of tunable depletion interactions. The colloidal system consists of novel micron-sized cubic particles prepared by silica deposition on hematite templates and various non-adsorbing watersoluble polymers as depletion agents. We have found that under certain conditions the cubes self-organize into crystals with a simple cubic symmetry, which is set by the size of the depletant. The dynamic of crystal nucleation and growth is investigated, monitoring the samples in time by optical microscopy. Furthermore, by using temperature sensitive microgel particles as depletant it is possible to fine tune depletion interactions to induce crystal melting. Assisting crystallization with an alternating electric field improves the uniformity of the cubic pattern allowing the preparation of macroscopic (almost defect-free) crystals that show visible Bragg colors.

Apparatus for thermopower measurements on organic conductors

An apparatus is described for making transport measurements, especially thermopower, on single crystals of highly conducting organic solids. It is designed specifically for small fragile anisotropic samples such as TCNQ salts. The temperature range is 400−1.2 k. A slow ac technique is used so that stray thermal emfs are eliminated and measurements can be taken with a small (0.5 K) temperature gradient for good temperature resolution in regions where the transport properties are changing quickly.

Unusually Dense Crystal Packings of Ellipsoids

In this Letter, we report on the densest-known packings of congruent ellipsoids. The family of new packings consists of crystal arrangements of spheroids with a wide range of aspect ratios, and with density phi always surpassing that of the densest Bravais lattice packing phi approximately equal to 0.7405. A remarkable maximum density of phi approximately equal to 0.7707 is achieved for maximal aspect ratios larger than sqrt[3], when each ellipsoid has 14 touching neighbors. Our results are directly relevant to understanding the equilibrium behavior of systems of hard ellipsoids, and, in particular, the solid and glassy phases.

An Elastic Analysis of Listeria monocytogenes Propulsion

The bacterium Listeria monocytogenes uses the energy of the actin polymerization to propel itself through infected tissues. In steady state, it continuously adds new polymerized filaments to its surface, pushing on its tail, which is made from previously cross-linked actin filaments. In this paper we introduce an elastic model to describe how the addition of actin filaments to the tail results in the propulsive force on the bacterium. Filament growth on the bacterial surface produces stresses that are relieved at the back of the bacterium as it moves forward. The model leads to a natural competition between growth from the sides and growth from the back of the bacterium, with different velocities and strengths for each. This competition can lead to the periodic motion observed in a Listeria mutant.