Formation and Evolution of Singularities in Anisotropic Geometric Continua

Evolutionary PDEs for geometric order parameters that admit propagating singular solutions are introduced and discussed. These singular solutions arise as a result of the competition between nonlinear and nonlocal processes in various familiar vector spaces. Several examples are given. The motivating example is the directed self assembly of a large number of particles for technological purposes such as nano-science processes, in which the particle interactions are anisotropic. This application leads to the derivation and analysis of gradient flow equations on Lie algebras. The Riemann structure of these gradient flow equations is also discussed.Comment: 38 pages, 4 figures. Physica D, submitte

Irreversible reorganization in a supercooled liquid originates from localised soft modes

The transition of a fluid to a rigid glass upon cooling is a common route of transformation from liquid to solid that embodies the most poorly understood features of both phases1,2,3. From the liquid perspective, the puzzle is to understand stress relaxation in the disordered state. From the perspective of solids, the challenge is to extend our description of structure and its mechanical consequences to materials without long range order. Using computer simulations, we show that the localized low frequency normal modes of a configuration in a supercooled liquid are causally correlated to the irreversible structural reorganization of the particles within that configuration. We also demonstrate that the spatial distribution of these soft local modes can persist in spite of significant particle reorganization. The consequence of these two results is that it is now feasible to construct a theory of relaxation length scales in glass-forming liquids without recourse to dynamics and to explicitly relate molecular properties to their collective relaxation.Comment: Published online: 20 July 2008 | doi:10.1038/nphys1025 Available from http://www.nature.com/nphys/journal/v4/n9/abs/nphys1025.htm

Ultrafast supercontinuum spectroscopy of carrier multiplication and biexcitonic effects in excited states of PbS quantum dots

We examine the multiple exciton population dynamics in PbS quantum dots by ultrafast spectrally-resolved supercontinuum transient absorption (SC-TA). We simultaneously probe the first three excitonic transitions over a broad spectral range. Transient spectra show the presence of first order bleach of absorption for the 1S_h-1S_e transition and second order bleach along with photoinduced absorption band for 1P_h-1P_e transition. We also report evidence of the one-photon forbidden 1S_{h,e}-1P_{h,e} transition. We examine signatures of carrier multiplication (multiexcitons for the single absorbed photon) from analysis of the first and second order bleaches, in the limit of low absorbed photon numbers (~ 10^-2), at pump energies from two to four times the semiconductor band gap. The multiexciton generation efficiency is discussed both in terms of a broadband global fit and the ratio between early- to long-time transient absorption signals.. Analysis of population dynamics shows that the bleach peak due to the biexciton population is red-shifted respect the single exciton one, indicating a positive binding energy.Comment: 16 pages, 5 figure

Can impact excitation explain efficient carrier multiplication in carbon nanotube photodiodes?

We address recent experiments (Science 325, 1367 (2009)) reporting on highly efficient multiplication of electron-hole pairs in carbon nanotube photodiodes at photon energies near the carrier multiplication threshold (twice the quasi-particle band gap). This result is surprising in light of recent experimental and theoretical work on multiexciton generation in other confined materials, such as semiconducting nanocrystals. We propose a detailed mechanism based on carrier dynamics and impact excitation resulting in highly efficient multiplication of electron-hole pairs. We discuss the important time and energy scales of the problem and provide analysis of the role of temperature and the length of the diode

Dynamically controlled deposition of colloidal nanoparticles suspension in evaporating drops using laser radiation

Dynamic control of the distribution of polystyrene suspended nanoparticles in evaporating droplets is investigated using a 2.9 μm high power laser. Under laser radiation a droplet is locally heated and fluid flows are induced that overcome the capillary flow, and thus a reversal of the coffee-stain effect is observed. Suspension particles are accumulated in a localised area, one order of magnitude smaller than the original droplet size. By scanning the laser beam over the droplet, particles can be deposited in an arbitrary pattern. This finding raises the possibility for direct laser writing of suspended particles through a liquid layer. Furthermore, a highly uniform coating is possible by manipulating the laser beam diameter and exposure time. The effect is expected to be universally applicable to aqueous solutions independent of solutes (either particles or molecules) and deposited substrates

Distribution of carrier multiplication rates in CdSe and InAs nanocrystals

The distribution of rates of carrier multiplication (CM) following photon absorption is calculated for semiconductor nanocrystals (NCs). The NC electronic structure is described using a screened pseudopotential method known to give reliable description of NC excitons. The rates of biexciton generation are calculated using the Fermi golden rule with all relevant Coulomb matrix elements, taking into account proper selection rules. In CdSe and InAs NCs we find a broad distribution biexciton generation rates depending strongly on the exciton energy and size of the NC. The process becomes inefficient for NC exceeding 3 nm in diameter in the photon energy range of 2-3 times the band gap.Comment: 4 pages 3 fi

Structural diversity in binary nanoparticle superlattices

Assembly of small building blocks such as atoms, molecules and nanoparticles into macroscopic structures - that is, 'bottom up' assembly - is a theme that runs through chemistry, biology and material science. Bacteria(1), macromolecules(2) and nanoparticles(3) can self-assemble, generating ordered structures with a precision that challenges current lithographic techniques. The assembly of nanoparticles of two different materials into a binary nanoparticle superlattice (BNSL)(3-7) can provide a general and inexpensive path to a large variety of materials (metamaterials) with precisely controlled chemical composition and tight placement of the components. Maximization of the nanoparticle packing density has been proposed as the driving force for BNSL formation(3,8,9), and only a few BNSL structures have been predicted to be thermodynamically stable. Recently, colloidal crystals with micrometre-scale lattice spacings have been grown from oppositely charged polymethyl methacrylate spheres(10,11). Here we demonstrate formation of more than 15 different BNSL structures, using combinations of semiconducting, metallic and magnetic nanoparticle building blocks. At least ten of these colloidal crystalline structures have not been reported previously. We demonstrate that electrical charges on sterically stabilized nanoparticles determine BNSL stoichiometry; additional contributions from entropic, van der Waals, steric and dipolar forces stabilize the variety of BNSL structures.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62551/1/nature04414.pd

Drying-mediated patterns in colloid-polymer suspensions

Drying-mediated patterning of colloidal particles is a physical phenomenon that must be understood in inkjet printing technology to obtain crack-free uniform colloidal films. Here we experimentally study the drying-mediated patterns of a model colloid-polymer suspension and specifically observe how the deposit pattern appears after droplet evaporation by varying particle size and polymer concentration. We find that at a high polymer concentration, the ring-like pattern appears in suspensions with large colloids, contrary to suppression of ring formation in suspensions with small colloids thanks to colloidpolymer interactions. We attribute this unexpected reversal behavior to hydrodynamics and size dependence of colloid-polymer interactions. This finding would be very useful in developing control of drying-mediated self-assembly to produce crack-free uniform patterns from colloidal fluids.ope