Diffusion-limited Behavior Research Articles

Inside Cover: Organic Photovoltaics: Elucidating the Ultra-Fast Exciton Dissociation Mechanism in Disordered Materials (Angew. Chem. Int. Ed. 29/2014)

It has proven difficult to obtain a mechanistic understanding of exciton dissociation in bulk-heterojunction organic solar cells because of confounding factors, such as phase impurity, domain size, and the extent of exciton delocalization. In their Communication on page 7456 ff., T J. Marks, M. A. Ratner et al. present a new exciton dissociation model, which reproduces experimentally verified ultrafast and diffusion-limited behavior by combining initial exciton delocalization with traditional Förster energy transfer.

TEMPO/Viologen Electrochemical Heterojunction for Diffusion-Controlled Redox Mediation: A Highly Rectifying Bilayer-Sandwiched Device Based on Cross-Reaction at the Interface between Dissimilar Redox Polymers

A couple of totally reversible redox-active molecules, which are different in redox potentials, 2,2,6,6-tetramethylpiperidin-1-oxyl (TEMPO) and viologen (V(2+)), were employed to give rise to a rectified redox conduction effect. Single-layer and bilayer devices were fabricated using polymers containing these sites as pendant groups per repeating unit. The devices were obtained by sandwiching the redox polymer layer(s) with indium tin oxide (ITO)/glass and Pt foil electrodes. Electrochemical measurements of the single-layer device composed of polynorbornene-bearing TEMPO (PTNB) exhibited a diffusion-limited current-voltage response based on the TEMPO(+)/TEMPO exchange reaction, which was almost equivalent to a redox gradient through the PTNB layer depending upon the thickness. The bilayer device gave rise to the current rectification because of the thermodynamically favored cross-reaction between TEMPO(+) and V(+) at the polymer/polymer interface. A current-voltage response obtained for the bilayer device demonstrated a two-step diffusion-limited current behavior as a result of the concurrent V(2+)/V(+) and V(+)/V(0) exchange reactions according to the voltage and suggested that the charge transport process through the device was most likely to be rate-determined by a redox gradient in the polymer layer. Current collection experiments revealed a charge transport balance throughout the device, as a result of the electrochemical stability and robustness of the polymers in both redox states.

In Situ Spectroscopic Measurements of Individual Cation and Anion Dynamics in a RuO2 Electrochemical Capacitor

Improving the energy storage capability of electrochemical capacitors is inherently dependent on clarifying our understanding of ion dynamics of advanced electrolytes in a variety of materials. Herein, we apply a new in situ infrared spectroscopy technique to selectively and simultaneously measure both cation and anion dynamics of an ionic liquid (1-ethyl-3-methylimidazolium triflate (EMIm-Tf)) in a functioning RuO2 capacitor. The individual cation and anion dynamics of EMIm-Tf are measured as a function of step voltage input, voltage scan rate, and RuO2 content in the electrode. Results show that cations and anions transport as aggregates and cations are the dominant charge carrying species. Also, the ratio of cations to anions in the cathode during charge storage increases with increasing step voltage input and RuO2 content in the electrode. In addition to changes in the cation to anion distribution, the concentration of both cations and anions increases and the rate of change of cations and anions increases as the porosity of the RuO2 electrode increases, which all correspond to an increase in the volumetric capacitance. Cyclic voltammetry, in conjunction with infrared spectroscopy experimental results, confirm that charge storage, as well as cation and anion transport both follow a diffusion-limited behavior.

Self-assembly mechanisms of silk protein nanostructures on two-dimensional surfaces

Self-assembly processes are ubiquitous in natural systems, and their study can provide insight into the harnessing of unique properties for engineering of new materials from the bottom up. Models for diffusion-limited assembly behavior have shown that structures formed have a characteristic fractal dimensionality that is smaller than the embedding space or the lattice. Typically however, these processes have only been studied via theoretical and computational tools, with relatively few natural systems having been reported to approach the limiting conditions assumed. Sericin, a protein critical to silk macrostructure, displays the remarkable ability to self-assemble through different modes of classical and non-universal diffusion-limited aggregation to produce radially-branched dendritic architectures. We report on the characterization of these assemblies by pure proteins from different species of silkworms in the absence of any charge shielding or modulation by salts. It is shown how physical differences between colloidal systems can yield remarkable changes in branching architectures from proteins that are functionally similar. This represents a novel system for fundamental and applied studies of particle aggregation and the development of biomaterials based on self-similarity at multiple length scales.

A low energy electron microscopy study of the initial growth, structure, and thermal stability of 4,4′-biphenyldicarboxylic acid domains on Cu(001)

The growth of 4,4(')-biphenyldicarboxylic acid (BDA) on Cu(001) has been studied using low energy electron microscopy and selective area low energy electron diffraction. The emergence of large islands and hydrogen bonding to perpendicularly oriented, adjacent molecules is confirmed. The two benzene rings of adsorbed BDA are twisted along the molecular axis. Unconventional growth of the domains, followed by a second nucleation stage, is observed at room temperature. This unanticipated feature is attributed to the accumulation of stress in the islands. Ostwald ripening in the films and the decay of BDA domains at 448 K exhibits features that are consistent with diffusion limited behavior.

The Effects of Microvoid Defects on MWIR HgCdTe-Based Diodes

The effects of microvoid defects on the performance of mid-wavelength infrared (MWIR) HgCdTe-based diodes were examined. Molecular beam epitaxy (MBE) was utilized to deposit indium-doped, Hg0.68Cd0.32Te on 2 cm × 3 cm, (211)B-oriented, bulk Cd0.96Zn0.04Te substrates. These epilayers generally exhibited state-of-the-art material properties with a notable exception: high and nonuniform microvoid defect densities (mid 104 cm−2 to low 106 cm−2). Diodes were fabricated by ion implantation of arsenic to form planar p–n junctions. Dark current–voltage (I–V) curves were measured and analyzed as a function of operating temperature. There was an inverse correlation between wafer-level microvoid defect density and device operability. On each wafer, devices with the smallest implants exhibited higher operability than devices with larger implants. By removal of pad metal and examination of defects within each implant area, it was found that the presence of one or more microvoids within the junction usually caused tunneling or other high-current mechanisms. Diodes free from microvoids exhibited diffusion-limited behavior down to 150 K, the test set limit.

Bias Switchable Dual-Band InAs/GaSb Superlattice Detector With pBp Architecture

We report on a dual-band [mid/long-wave infrared (MWIR and LWIR)] InAs/GaSb strained layer superlattice detector with a pBp architecture. Fifty percent cutoff wavelengths of 5 and 9 μm were obtained with diffusion-limited behavior for midwave IR absorber. At 77 K, the peak D* values were equal to 5 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sup> Jones (V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> = +0.1 V, λ = 5 μm) and 2.6 × 1010 Jones (V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> = -0.4 V, λ = 9 μm). The corresponding values of responsivity and quantum efficiency were 1.6 A/W and 39% (MWIR) and 1.3 A/W and 17% (LWIR).

Supramolecular Chirality in Solvent‐Promoted Aggregation of Amphiphilic Porphyrin Derivatives: Kinetic Studies and Comparison between Solution Behavior and Solid‐State Morphology by AFM Topography

The solvent-promoted aggregation behavior of some amphiphilic porphyrin derivatives bearing chiral functionality in the form of a charged L-proline group has been investigated by UV/Vis, resonance light scattering, fluorescence and circular dichroism spectroscopy. The investigated macrocycles give rise to aggregates featuring supramolecular chirality with high ellipticity. Kinetic studies reveal peculiar differences in the fashion of aggregation, depending on the intimate nature of the chiral functionality, namely, cationic (nitrogen-quaternized L-proline, 3H(2)) or anionic (carboxylate residue, 6H(2)) group. Formation of anionic 6H(2) aggregates shows a diffusion-limited kinetic behavior. AFM topography studies show formation of tighter globular structures. On the other hand, the corresponding 3H(2) aggregates are formed by a cooperative, fractal-type decay, and appear as long-fibrous, looser structures. In the templated aggregation of 3H(2) over preformed 6H(2) aggregates, AFM images show formation of globular structures with reduced sizes, as a likely consequence of shorter interchromophore distances, due to favorable Coulombic interactions. The results obtained show an interesting parallelism between the solution behavior and the solid-state aggregate structures, corroborating the sergeant-soldier effect observed in the templated aggregation. The results presented give important insights for understanding the complex mechanisms involved in these issues, which are of key importance for the development of chiral supramolecular materials and stereoselective sensors and devices.

A correlation for burn time of aluminum particles in the transition regime

A study of the combustion times for aluminum particles in the size range of 3–11 μm with oxygen, carbon dioxide, and water vapor oxidizers at high temperatures (>2400 K), high pressures (4–25 atm), and oxidizer composition (15–70% by volume in inert diluent) in a heterogeneous shock tube has generated a correlation valid in the transition regime. The deviation from diffusion limited behavior and burn times that could otherwise be accurately predicted by the widely accepted Beckstead correlation is seen, for example, in particles below 20 μm, and is evidenced by the lowering of the diameter dependence on the burn time, a dependence on pressure, and a reversal of the relative oxidizer strengths of carbon dioxide and water vapor. The strong dependence on temperature of burn time that is seen in nano-Al is not observed in these micron-sized particles. The burning rates of aluminum in these oxidizers can be added to predict an overall mixture burnout time adequately. This correlation should extend the ability of modelers to predict combustion rates of particles in solid rocket motor environments down to particle diameters of a few microns.

Effect of stabilizer on scission and crosslinking rate changes during photo-oxidation of polypropylene

Chain scission and crosslinking rates have been derived from molecular mass distributions obtained by gel permeation chromatography at different stages during photodegradation of polypropylene samples exposed to ultraviolet irradiation (UV). Results for rubber-toughened polypropylene (PP) containing no photostabilizer are compared with those for the same polymer stabilized using a commercial photostabilizing package (PPS). The samples were in the form of 3 mm thick bars and measurements were obtained at various depths from the exposed surface after different exposure times. The depth profiles for PP and PPS were very different. Reaction rates in the interior of PP showed oxygen diffusion limited behaviour and after prolonged exposure, the rates in the interior of PPS were higher than those in PP. The ratio of scission rate/crosslink rate fell when reaction rate increased. Crosslinking became relatively more likely when reaction rates were low. The low degradation rates obtained with stabilized polymer coupled with the sensitivity of the method of analysis enabled detection of inhibition of photodegradation attributed to residual moulding stresses in the samples.

Critical terrace width for step flow growth: Effect of attachment-detachment asymmetry and step permeability

A general expression for the critical terrace width for step flow growth accounting for both the step permeability and the asymmetric incorporation of atoms to ascending and descending steps is derived. It covers both cases of diffusion and attachment-detachment limited regimes of growth at high and low temperatures. It is found that when at least one of the excess step-edge barriers is equal to zero, only diffusion-limited behavior regime is allowed. The step permeability does not affect both limiting cases at high and low temperatures. Comparing the theory with experimental data for the Si11177 surface leads to the conclusion that the nucleation process in the interval 700‐850 K takes place in an attachment-detachment limited regime with critical nuclei consisting of one and three atoms below and above 750 K, respectively. The values of 0.525 and 0.535 eV have been estimated for the energy barriers for incorporation of adatoms into descending and ascending steps, respectively, thus demonstrating an inverse Ehrlich-Schwoebel effect J. Chem. Phys. 44, 1039 1966. A binding energy of 1.65 eV for three-atom nucleus has been evaluated.

Reaction of O2 with the Hydrogen Atom in Water up to 350 °C

The reaction of the H* atom with O2, giving the hydroperoxyl HO2* radical, has been investigated in pressurized water up to 350 degrees C using pulse radiolysis and deep-UV transient absorption spectroscopy. The reaction rate behavior is highly non-Arrhenius, with near diffusion-limited behavior at room temperature, increasing to a near constant limiting value of approximately 5 x 10(10) M(-1) s(-1) above 250 degrees C. The high-temperature rate constant is in near-perfect agreement with experimental extrapolations and ab initio calculations of the gas-phase high-pressure limiting rate. As part of the study, reaction of the OH* radical with H2 has been reevaluated at 350 degrees C, giving a rate constant of (6.0 +/- 0.5) x 10(8) M(-1) s(-1). The mechanism of the H* atom reaction with the HO2* radical is also investigated and discussed.

Polymerization of pyrrole onto “track-etch” membranes

Poly(ethylene terephthalate) (PETP) “track-etch” membranes were used as a matrix for graft polymerization of pyrrole. Diaphragmatic method was utilized. Kinetics studies demonstrated a diffusion-limited behavior of pyrrole polymerization. Permeation properties of modified membranes were tested. New membrane material was prepared by decomposition of a matrix membrane. It comprises two support layers arranged one above the other forming a space between them for the flow of a first fluid, and a plurality of tubules joining two support layers. The flow of a second fluid can be organized through the microtubules. The membrane material characteristics calculated are close to that of natural biological systems. The possible method of mounting a filtration module based on the material is described.

Decay of silicon mounds: scaling laws and description with continuum step parameters

The decay of mounds about a dozen layers high on the Si(111)7×7 surface [Surf. Sci. Rep. 34 (1999) 171] has been measured quantitatively by scanning tunneling microscopy and compared with analytic predictions for the power-law dependence on time predicted for a step-mediated decay mechanism [Mater. Res. Soc. Symp. Proc. 528 (1998) 237]. In accordance with these predictions, we find [Phys. Rev. Lett. 84 (2000) 3662] an exponent 1/4 associated with the (3D) decay of the mound height and exponent 1/3 associated with the (2D) decay of top-layer islands, appropriate to diffusion-limited behavior. The detailed effects of atomic-scale behavior at the step edges enter as the product of step stiffness and mobility; the measured value is consistent with earlier observations [http://www] of decay of single-layer structures. Using parameters from a continuum step model [Phys. Rev. Lett. 80 (1998) 552], we capture the essence of the kinetics. Qualitative features distinguish these mounds from multi-layer islands found on metals such as Cu(111).

Electrical and optical characteristics of two color mid wave HgCdTe infrared detectors

Two-color mid wave triple-layer heterojunction HgCdTe detectors were studied using temperature-dependent current–voltage (I–V) measurements, temperature-dependent spectral response measurements, and temperature-dependent noise measurements. The reverse biased dark current shows diffusion-limited behavior for T&amp;gt;125 K. The same data show evidence for generation-recombination-type behavior for the longer wavelength junction at temperatures between 100 and 125 K. For temperatures less than 100 K, the measurements are background limited by photon flux, even though these measurements are performed at nominal zero background. The upper junction shows soft reverse breakdown voltages on the order of about 250 mV, while the bottom junction shows no breakdown for V&amp;lt;500 mV. At 80 K, the R0A product is in excess of 1×106 Ω cm2. In forward bias, the current–voltage characteristics of the lower junction are diffusion limited for all temperatures, while at lower temperatures, the upper junction showed generation-recombination behavior. Optical measurements found a cutoff wavelength of about 4 μm for the lower junction and about 4.5 μm for the upper junction. The spectral crosstalk was less than 3%. At 80 K, the frequency-dependent noise of the shorter wavelength junction showed no dependence on bias, while for the longer wavelength junction, the noise at lower frequencies increased with bias. There is no difference in the noise characteristics when either the photon flux or the temperature is increased.

Illustration of important mechanisms controlling mass transfer in supercritical fluid extraction

Supercritical fluid extraction profiles are presented for various model systems. The purpose is to illustrate some mechanisms encountered in supercritical fluid extraction by using simplified systems and also to give examples of how pre-extraction steps can be utilized to improve the mass-transfer rate. Extraction of clevidipine (a calcium antagonist) from different, allegedly inert materials, showed significant differences in extraction efficiency. Extraction from stainless-steel beads gave complete recovery with pure carbon dioxide, whereas the extraction from filter paper required the addition of 4% methanol. This indicates that interactions between matrix and analyte can be strong and that a modifier can be used, not only to increase solubility in the carbon dioxide, but also to break analyte/matrix bindings. Recovery of oil applied on an inert material was constant in terms of recovery per volume of extraction fluid for different flow rates, illustrating a solubility-limited behavior. Metal rods with drilled orifices filled with lubricating oil were used in experiments designed to reveal the influence of matrix characteristics on the extraction profile. The plots obtained showed a decreased recovery at higher flow rates, demonstrating diffusion limited behavior due to slow mass transfer through stagnant regions of the supercritical fluid. Bad recovery can sometimes be improved by changing the matrix in a pre-extraction step thus making the analytes more accessible to the extraction fluid. Static pre-extraction improved the extraction efficiency for target compounds from fat samples. Also recovery of clevidipine from a fat containing emulsion was considerably increased when water was removed in a dynamic pre-drying step.

In Situ Quasi-elastic Neutron Scattering Study of the Hydration of Tricalcium Silicate

We report on the novel application of quasi-elastic neutron spectroscopy to study the reaction mechanism between tricalcium silicate and water. The in situ data taken at a series of fixed temperatures varying from 10 to 40 °C show that the amount of free water in the system remains relatively constant for an initial period, ranging from 1 h at 40 °C to 16 h at 10 °C. This is followed by an exponential decrease in the amount of free water that crosses over to a diffusion-limited behavior for later times. Fits to an Avrami type behavior allow us to determine an activation energy for the hydration process on the order of 30 kJ/mol.

Diffusion-limited, but not perfusion-limited, compartmental models describe cerebral nitrous oxide kinetics at high and low cerebral blood flows.

This study aimed to evaluate the relative importance of diffusion-limited vs. perfusion-limited mechanisms in compartmental models of blood-tissue inert gas exchange in the brain. Nitrous oxide concentrations in arterial and brain efferent blood were determined using gas chromatographic analysis during and after 15 min of nitrous oxide inhalation, at separate low and high steady states of cerebral blood flow (CBF) in five sheep under halothane anesthesia. Parameters and model selection criteria of various perfusion- or diffusion-limited structural models of the brain were estimated by simultaneous fitting of the models to the mean observed brain effluent nitrous oxide concentration for both blood flow states. Perfusion-limited models returned precise, credible estimates of apparent brain volume but fit the low CBF data poorly. Diffusion-limited models provided better overall fit of the data, which was best described by exchange of nitrous oxide between a perfusion-limited brain compartment and an unperfused compartment. In individual animals, during the low CBF state, nitrous oxide kinetics displayed either fast, perfusion-limited behavior or slow, diffusion-limited behavior. This variability was exemplified in the different parameter estimates of the diffusion limited models fitted to the individual animal data sets. Results suggest that a diffusion limitation contributes to cerebral nitrous oxide kinetics.

Oxygen transport through La 1− xSr xFeO 3−δ membranes. I. Permeation in air/He gradients

Oxygen permeation measurements in air/He gradients were performed on dense La 1 − x Sr x FeO 3 − δ membranes in the composition range x = 0.1–0.4 and temperature range 1123–1323 K. Pretreatment of the lower oxygen partial pressure side of the membranes in a CO-containing atmosphere for several hours at 1273 K led to higher oxygen fluxes, which were in the range of 0.1–4.5 mmol m −2 s −1. After treatment, the observed oxygen fluxes could be described in terms of bulk diffusion-limited permeation behaviour. Experimental evidence for a bulk-diffusion controlled flux was found from thickness dependence measurements on membranes with thicknesses between 0.5 mm and 2.0 mm. Model calculations, based on Wagner theory in conjunction with data of oxygen nonstoichiometry and vacancy diffusion coefficients from literature, were performed. The experimental flux values deviated from the model calculations with factors up to 2.5. Adjustment of the value of the vacancy diffusion coefficient led to good agreement between the experimental data and the model calculations. The calculated vacancy diffusion coefficients D v 0 were virtually independent of composition and were found to be in the range 5.3–9.3 × 10 −6 cm 2 s −1.

Phosphorus segregation at polysilicon-silicon interfaces from in situ P spike-doped silicon films

Phosphorus diffusion in spike-doped chemical vapour deposited layers and its interfacial segregation at the polysilicon/silicon substrate interface was studied by means of secondary-ion mass spectroscopy and spreading resistance measurements. The time dependence of P segregation indicates a diffusion-limited behaviour except for a short starting period. The influence of a thin interfacial oxide on the segregation behaviour was studied by analysing the binding energy of P atoms, segregated at the interface. It correlates with values from elemental phosphorus, indicating that no chemical interaction takes place with residual interfacial oxide. Homogeneous charge carrier profiles across the polysilicon layer, shallow junction formation (less than 50 nm within the silicon substrate) and realization of steep concentration profiles with a slope of 8 nm decade-1 at low temperatures offer a high potential for applications.