Calculation of the band structure of semiconductor quantum wells using scattering matrices

The transfer-matrix method widely used in the calculation of the band structure of semiconductor quantum wells is found to have limitations due to its intrinsic numerical instability. It is pointed out that the numerical instability arises from free-propagating transfer matrices. A new scattering-matrix method is developed for the multiple-band Kane model within the envelope-function approximation. Compared with the transfer-matrix method, the proposed algorithm is found to be more efficient and stable. A four-band Kane model is used to check the validity of the method and the results are found to be in good agreement with earlier calculations.

A RESONANT RAMAN-STUDY ON PHONONS IN GAINAS/ALINAS MULTIPLE-QUANTUM WELLS

The LO phonon modes in the barrier layers of a GaInAs/AlInAs multiple quantum well structure are investigated by resonance Raman scattering (RRS), the excitation laser photon energy tuned to resonate with the above barrier interband transition energy. The resonance enhancement of LO phonon peaks are shown to be caused by Frohlich electron-phonon interaction. The pressure-dependent profiles for both AlAs-like (LO(2) mode) and InAs-like (LO(1) mode) Raman peak intensities are well fitted by the Gaussian lineshape. The shift between these two profiles can be explained by the outgoing RRS mechanism, providing information on the pressure-induced shift of the excitonic transition energy. The amplitude ratios of the two profiles are close to 1, showing a well defined two-mode behavior and the nearly equal polarizability for Al-As and In-As bonds in AlInAs alloy.

Intrabeam scattering of heavy ions at HIRFL-CSR

Small-angle multiple intrabeam scattering (IBS) is an important effect for heavy-ion storage rings with electron cooling, because the cooling time is determined by the equilibrium between cooling and IBS process. All usually used numerical algorithms of IBS growth rate calculations are based on the model of the collisions proposed by A.Piwinski, but this result is a multidimensional integral. In this paper, the IBS growth rates are simulated for HIRFL-CSR using symmetric elliptic integral method, and compared with several available IBS code results.

An effective hydrothermal route for the synthesis of multiple PDDA-protected noble-metal nanostructures

In this Article, we demonstrate an effective hydrothermal route for the synthesis of multiple PDDA-protected (PDDA = poly(diallyl dimethylammonium) chloride) noble-metal (including silver, platinum, palladium, and gold) nanostructures in the absence of any seeds and surfactants, in which PDDA, an ordinary and water-soluble polyelectrolyte, acts as both a reducing and a stabilizing agent. Under optimal experimental conditions, Ag nanocubes, Pt and Pd nanopolyhedrons, and Au nanoplates can be obtained, which were characterized by transmission electron microscopy, scanning electron microscopy, energy-dispersive spectroscopy, and X-ray diffraction. More importantly, the nanostrucfures synthesized show potential applications in surface-enhanced Raman scattering and electrocatalysis, in which Ag nanocubes and Pt nanopolyhedrons were chosen as the examples, respectively.

Electrochemical deposition of silver in room-temperature ionic liquids and its surface-enhanced Raman scattering effect

The use of room-temperature ionic liquids (RTILs) as media for electrochemical application is very attractive. In this work, the electrochemical deposition of silver was investigated at a glassy carbon electrode in hydrophobic 1-n-butyl-3-methylimidazolium hexafluorophosphate (BMIMPF6) and hydrophilic 1-n-butyl-3-methylimidazolium tetrafluoroborate (BMIMBF4) RTILs and in KNO3 aqueous solution by cyclic voltammetric and potentiostatic transient techniques. The voltammograms showed the presence of reduction and oxidation peaks associated with the deposition and dissolution of silver from AgBF4 in both BMIMPF6 and BMIMBF4, resembling the redox behavior of AgNO3 in KNO3 aqueous solution. A crossover loop was observed in all the cyclic voltammograms of these electrochemical systems, indicating a nucleation process. From the analysis of the experimental current transients, it was shown that the electrochemical deposition process of silver in these media was characteristic of 3D nucleation with diffusion-controlled hemispherical growth, and the silver nucleation closely followed the response predicted for progressive nucleation in BMIMPF6 and instantaneous nucleation in KNO3 aqueous solution, respectively.

Surfactantless synthesis of multiple shapes of gold nanostructures and their shape-dependent SERS spectroscopy

A useful method for the synthesis of various gold nanostructures is presented. The results demonstrated that flowerlike nanoparticle arrays, nanowire networks, nanosheets, and nanoflowers were obtained on the solid substrate under different experimental conditions. In addition, surface-enhanced Raman scattering (SERS) spectra of 4-aminothiophenol (4-ATP) on the as-prepared gold nanostructures of various shapes were measured, and their shape-dependent properties were evaluated. The intensity of the SERS signal was the smallest for the gold nanosheets, and the flowerlike nanoparticle arrays gave the strongest SERS signals.

Speciation of Rare-Earth Metal Complexes in Ionic Liquids: A Multiple-Technique Approach

The dissolution process of metal complexes in ionic liquids was investigated by a multiple-technique approach to reveal the solvate species of the metal in solution. The task-specific ionic liquid betainium bis(trifluoromethylsulfonyl)imide ([Hbet][Tf2N]) is able to dissolve stoichiometric amounts of the oxides of the rare-earth elements. The crystal structures of the compounds [Eu-2(bet)(8)(H2O)(4)][Tf2N](6), [Eu-2(bet)(8)(H2O)(2)][Tf2N](6)center dot 2H(2)O, and [Y-2(bet)(6)(H2O)(4)][Tf2N](6) were found to consist of dimers. These rare-earth complexes are well soluble in the ionic liquids [Hbet][Tf2N] and [C(4)mim]- [Tf2N] (C(4)mim = 1-butyl-3-methylimidazolium). The speciation of the metal complexes after dissolution in these ionic liquids was investigated by luminescence spectroscopy, H-1, C-13, and Y-89 NMR spectroscopy, and by the synchrotron techniques EXAFS (extended X-ray absorption fine structure) and HEXS (high-energy X-ray scattering). The combination of these complementary analytical techniques reveals that the cationic dimers decompose into monomers after dissolution of the complexes in the ionic liquids. Deeper insight into the solution processes of metal compounds is desirable for applications of ionic liquids in the field of electrochemistry, catalysis, and materials chemistry.

Extracting S-matrix poles for resonances from numerical scattering data: Type-II Pade reconstruction

We present a FORTRAN 77 code for evaluation of resonance pole positions and residues of a numerical scattering matrix element in the complex energy (CE) as well as in the complex angular momentum (CAM) planes. Analytical continuation of the S-matrix element is performed by constructing a type-II Pade approximant from given physical values (Bessis et al. (1994) [421: Vrinceanu et al. (2000) [24]; Sokolovski and Msezane (2004) [23]). The algorithm involves iterative 'preconditioning' of the numerical data by extracting its rapidly oscillating potential phase component. The code has the capability of adding non-analytical noise to the numerical data in order to select 'true' physical poles, investigate their stability and evaluate the accuracy of the reconstruction. It has an option of employing multiple-precision (MPFUN) package (Bailey (1993) [451) developed by D.H. Bailey wherever double precision calculations fail due to a large number of input partial waves (energies) involved. The code has been successfully tested on several models, as well as the F + H-2 -> HE + H, F + HD : HE + D, Cl + HCI CIH + Cl and H + D-2 -> HD + D reactions. Some detailed examples are given in the text.

Scattering theory of multilevel atoms interacting with arbitrary radiation fields

We present a generic transfer matrix approach for the description of the interaction of atoms possessing multiple ground state and excited state sublevels with light fields. This model allows us to treat multi-level atoms as classical scatterers in light fields modified by, in principle, arbitrarily complex optical components such as mirrors, resonators, dispersive or dichroic elements, or filters. We verify our formalism for two prototypical sub-Doppler cooling mechanisms and show that it agrees with the standard literature.

Surface-Enhanced Raman Scattering from Metallic Nanostructures: Bridging the Gap between the Near-Field and Far-Field Responses

We present here a detailed study of the complex relationship between the electromagnetic near-field and far-field responses of "real" nanostructured metallic surfaces. The near-field and far-field responses are specified in terms of (spectra of) the surface-enhanced Raman-scattering enhancement factor (SERS EF) and optical extinction, respectively. First, it is shown that gold nanorod- and nanotube-array substrates exhibit three distinct localized surface plasmon resonances (LSPRs): a longitudinal, a transverse, and a cavity mode. The cavity mode simultaneously has the largest impact on the near-field behavior (as observed through the SERS EF) and the weakest optical interaction: It has a "near-field-type" character. The transverse and longitudinal modes have a significant impact on the far-field behavior but very little impact on SERS: They have a "far-field-type" character. We confirm the presence of the cavity mode using a combination of SERS EF spectra, electron microscopy, and electromagnetic modeling and thus clearly illustrate and explain the (lack of) correlation between the SERS EF spectra and the optical response in terms of the contrasting character of the three LSPRs. In doing so, we experimentally demonstrate that, for a surface that supports multiple LSPRs, the near-field and far-field properties can in fact be tuned almost independently. It is further demonstrated that small changes in geometrical parameters that tune the spectral location of the LPSRs can also drastically influence the character of these modes, resulting in certain unusual behavior, such as the far-field resonance redshift as the near-field resonance blueshifts. DOI: 10.1103/PhysRevX.3.011001

Gaussian pulse mixing and scattering by finite nonlinear layered structures

Multiple Gaussian pulse interactions and scattering in the nonlinear layered dielectric structures have been examined. The Gaussian pulses with different centre frequencies and lengths are incident at oblique angles on the finite stack of nonlinear dielectric layers. The properties of the reflected and refracted waveforms and the effects of the structure and the incident pulses' parameters on the mixing process are discussed. It is shown that the efficiency of forward emission at the combinatorial frequency can be considerably increased when the wavelengths of interacting pulses are close to the edges of electromagnetic bandgap. © 2012 IEEE.

Ordering on multiple lengthscales in a series of side group liquid crystal block copolymers containing a cholesteryl-based mesogen

Hierarchical ordering in a side group liquid crystal block copolymer is investigated by differential scanning calorimetry, polarized optical microscopy, small-angle X-ray and neutron scattering (SAXS and SANS) and transmission electron microscopy (TEM). A series of block copolymers with a range of compositions was prepared by atom transfer radical polymerization, comprising a polystyrene block and a poly(methyl methacrylate) block bearing chiral cholesteryl mesogens. Smectic ordering is observed as well as microphase separation of the block copolymer. Lamellar structures were observed for far larger volume fractions than for coil-coil copolymers (up to a volume fraction of liquid crystal block, f(LC) = 0.8). A sample with f(LC) = 0.86 exhibited a hexagonal-packed cylinder morphology, as confirmed by SAXS and TEM. The matrix comprised the liquid crystal block, with the mesogens forming smectic layers. For the liquid crystal homopolymer and samples with high f(LC), a smectic-smectic phase transition was observed below the clearing point. At low temperature, the smectic phase comprises coexisting domains with monolayer S-A,S-1 coexisting with interdigitated S-A,S-d domains. At high temperature a SA,1 phase is observed. This is the only structure observed for samples with lower f(LC). These unprecedented results point to the influence of block copolymer microphase separation on the smectic ordering.

Multiple sol-gel transitions of PEG-PCL-PEG triblock copolymer aqueous solution

An aqueous solution of a poly(ethylene glycol)-polycaprolactone-poly(ethylene glycol) (PEG-PCL-PEG) with a composition of EG13CL23EG13 undergoes multiple transitions, from sol-to-gel (hard gel)-to-sol-to-gel (soft gel)-to-sol, in the concentration range 20.0∼35.0 wt.-%. Through dynamic mechanical analysis, UV-vis spectrophotometry, small angle X-ray scattering, differential scanning calorimetry, microcalorimetry and 13C NMR spectroscopy, the mechanism of these transitions was investigated. The hard gel and soft gel are distinguished by the crystalline and amorphous state of the PCL. The extent of PEG dehydration and the molecular motion of each block also played a critical role in the multiple transitions. This paper suggests a new mechanism for these multiple transitions driven by temperature changes.

Multiple hydrogen bonds induce formation of nanoparticles with internal microemulsion structure by an amphiphilic copolymer

A particulate microemulsion is generated in a simple two-component system comprising an amphiphilic copolymer (Pluronic P123) in mixtures with tannic acid. This is correlated to complexation between the poly(ethylene oxide) in the Pluronic copolymer and the multiple hydrogen bonding units in tannic acid which leads to the breakup of the ordered structure formed in gels of Pluronic copolymers, and the formation of dispersed nanospheres containing a bicontinuous internal structure. These novel nanoparticles termed ‘‘emulsomes’’ are self-stabilized by a coating layer of Pluronic copolymer. The microemulsion exhibits a pearlescent appearance due to selective light scattering from the emulsion droplets. This simple formulation based on a commercial copolymer and a biofunctional and biodegradable additive is expected to find applications in the fast moving consumer goods sector.

SANS/WANS time-resolving neutron scattering studies of polymer phase transitions using NIMROD

We use new neutron scattering instrumentation to follow in a single quantitative time-resolving experiment, the three key scales of structural development which accompany the crystallisation of synthetic polymers. These length scales span 3 orders of magnitude of the scattering vector. The study of polymer crystallisation dates back to the pioneering experiments of Keller and others who discovered the chain-folded nature of the thin lamellae crystals which are normally found in synthetic polymers. The inherent connectivity of polymers makes their crystallisation a multiscale transformation. Much understanding has developed over the intervening fifty years but the process has remained something of a mystery. There are three key length scales. The chain folded lamellar thickness is ~ 10nm, the crystal unit cell is ~ 1nm and the detail of the chain conformation is ~ 0.1nm. In previous work these length scales have been addressed using different instrumention or were coupled using compromised geometries. More recently researchers have attempted to exploit coupled time-resolved small-angle and wide-angle x-ray experiments. These turned out to be challenging experiments much related to the challenge of placing the scattering intensity on an absolute scale. However, they did stimulate the possibility of new phenomena in the very early stages of crystallisation. Although there is now considerable doubt on such experiments, they drew attention to the basic question as to the process of crystallisation in long chain molecules. We have used NIMROD on the second target station at ISIS to follow all three length scales in a time-resolving manner for poly(e-caprolactone). The technique can provide a single set of data from 0.01 to 100Å-1 on the same vertical scale. We present the results using a multiple scale model of the crystallisation process in polymers to analyse the results.