Square Root Of Time Dependence Research Articles

Case II diffusion of water in Na2O–3SiO2 glass: Constant tensile stress gradient at the diffusion interface

AbstractSome polymers and oxide glasses exhibit unusual diffusion of liquid or gas, with the depth of diffusion exhibiting a linear increase with time, instead of normal square root of time dependence. There have been many models, but very few experimental data that can help clarify the cause of the phenomenon's existence in glass. Residual stress in sodium trisilicate glass (Na2O–3SiO2) samples was characterized following Case II water diffusion at 80°C in a saturated water vapor environment. The surface‐swelled layer of the glass was removed by dissolving it in water, and birefringence of the newly revealed surface layer was measured. The presence of a constant negative tensile stress gradient was revealed by indicating that Case II diffusion in sodium trisilicate glass originates from this stress gradient, which overwhelms the more typical Fick's law concentration‐dependent flux.

Drop impact onto wetted walls: an unsteady analytical solution for modelling crown spreading

An unsteady analytical solution is proposed to predict the spreading rate of the crown generated by an impacting droplet onto wetted walls. The modelling strategy is based on the direct integration of the boundary layer correction into the potential flow solution that leads to the well-established square-root time dependence. The original potential flow has the structure of an unsteady, stagnation point flow with decaying strength. For initial strengths of the potential flow $a_0 \geqslant 100\ {\rm s}^{-1}$, we find that a self-similar solution can also be obtained for the boundary layer in the variables $\left (r \sqrt {a(t)/(\nu t)}, z \sqrt {a(t)/(\nu t)} \right )$. The self-similarity of the solution enables a straightforward estimation of momentum losses during the spreading of the liquid layer along the wall. The proposed modelling approach yields an excellent agreement with experiments during the entire spreading phase. Moreover, it enables a smooth transition from the inertia-driven to the shear-controlled regime of crown propagation. In general, the analysis shows that momentum losses arising from viscous effects cannot be neglected during a significant portion of crown propagation, particularly for thin wall films.

Determining the Diffusion Coefficient of Lithium Insertion Cathodes from GITT measurements: Theoretical Analysis for low Temperatures*.

Accurate knowledge of transport properties of Li‐insertion materials in application‐relevant temperature ranges is of crucial importance for the targeted optimization of Li‐ion batteries (LIBs). Galvanostatic intermittent titration technique (GITT) is a widely applied method to determine Li‐ion diffusion coefficients of electrode materials. The well‐known calculation formulas based on Weppner's and Huggins’ approach, imply a square‐root time dependence of the potential during a GITT pulse. Charging the electrochemical double layer capacitance at the beginning of a GITT pulse usually takes less than one second. However, at lower temperatures down to −40 °C, the double layer charging time strongly increases due to an increase of the charge transfer resistance. The charging time can become comparable with the pulse duration, impeding the conventional GITT diffusion analysis. We propose a model to describe the potential change during a galvanostatic current pulse, which includes an initial, relatively long‐lasting double layer charging, and analyze the accuracy of the lithium diffusion coefficient, derived by using the Weppner‐Huggins method within a suitably chosen time interval of the pulse. Effects leading to an inaccurate determination of the diffusion coefficient are discussed and suggestions to improve GITT analyses at low temperature are derived.

Nanosecond pulsed laser processing turns engineering metal alloys antireflective and superwicking

In this work, superwicking and antireflective properties are achieved on engineering metal surfaces by creating a surface pattern using a high energy nanosecond pulsed laser followed by a chemical immersion treatment. The high-energy nanosecond pulse laser scans the metal surface in air. Subsequently, the laser-textured surface is further treated by immersion in a 3-cyanopropyltricholosilane reagent. As a result of these two processes, microgrooves with micro- and nano-scale surface features are generated on the metal surface. Due to the created surface structure and favorable surface chemistry, water sprints uphill defying the gravity. The fast self-propelling movement of water is due to the supercapillary effect of the surface microchannel and the superhydrophilic surface nitrile group. The wicking effect on the processed surface follows the classical square root of time dependence. The processed surface shows good antireflective properties in the visible and infrared spectrum. Surface features, surface chemistry, wettability, surface reflectivity and wicking behavior are measured on AA6061 and Ti-6Al-4V specimens through Scanning Electron Microscopy (SEM), X-ray Photoelectron Spectroscopy (XPS), contact angle goniometer, UV-VIS-NIR spectrometer and high-speed camera, respectively.

The Effect of a Secondary Process on the Analysis of Isothermal Crystallisation Kinetics by Differential Scanning Calorimetry.

This paper demonstrates the application of a modified Avrami equation in the analysis of crystallisation curves obtained using differential scanning calorimetry (DSC). The model incorporates a square root of time dependence of the secondary process into the conventional Avrami equation and, although previously validated using laser flash analysis and infrared spectroscopy, is not currently transferable to DSC. Application of the model to calorimetric data required long-duration isotherms and a series of data treatments. Once implemented, the square root of time dependence of the secondary process was once again observed. After separation of the secondary process from the primary, a mechanistic n value of 3 was obtained for the primary process. Kinetic parameters obtained from the analysis were used in the model to regenerate the fractional crystallinity curves. Comparison of the model with experimental data generated R2 values in excess of 0.995. Poly(3-hydroxybutyrate-co-3-hydroxyvalerate) was used as model polymer due to the prominent secondary crystallisation behaviour that this polymer is known to display.

Nanosecond Pulsed Laser Processing Turns Engineering Metal Alloys Antireflective and Superwicking

Abstract In this work, superwicking and antireflective properties are achieved on engineering metal surfaces by creating surface pattern using a high pulse energy nanosecond laser followed by a chemical immersion treatment. The high-energy nanosecond pulse laser scans the metal surface in air. Subsequently, the laser-textured surface is further treated by immersion in a 3-cyanopropyltricholosilane reagent. As a result of these two processes, microgrooves with micro- and nano-scale surface features are generated on the metal surface. Due to the created surface structure and favorable surface chemistry, water sprints uphill defying the gravity. The fast self-propelling movement of water is due to the supercapillary effect of the surface microchannel and the superhydrophilic surface nitrile group. The wicking effect on the processed surface follows the classical square root of time dependence. The processed surface shows good antireflective properties in visible and infrared spectrum. Surface features, surface chemistry, surface wettability, surface reflectivity and surface wicking behavior are measured on AA6061 and Ti-6Al-4V specimens through Scanning Electron Microscopy (SEM), X-ray Photoelectron Spectroscopy (XPS), contact angle goniometer, UV-VIS-NIR spectrometer and high-speed camera.

Plasma treatment of silicone oil- infused surfaces switches impact of water droplets from bouncing to tanner-like spreading

Bouncing of water droplets on cold-plasma-treated and non-treated silicone-oil-infused microporous surfaces is reported. Cold plasma treatment of oil-infused surfaces switches the quasi-elastic bouncing to a two-stage spreading. At the first stage, spreading was governed by the square-root time dependence of the contact radius; whereas at the final stage, the kinetics of spreading conformed with the Tanner-like law. Water droplets placed on the pristine silicone-oil infused surfaces are eventually coated with the silicone oil; in contrast water droplets spread on the plasma-treated oil remained uncoated, due to the increase of the specific energy of the silicon oil induced by the plasma treatment. The semi-qualitative analysis of bouncing is introduced.

Impact of Surface Roughness on Capillary Trapping Using 2D-Micromodel Visualization Experiments

According to experimental observations, capillary trapping is strongly dependent on the roughness of the pore–solid interface. We performed imbibition experiments in the range of capillary numbers (Ca) from $$10^{-6}$$ to $$5\times 10^{-5}$$ using 2D-micromodels, which exhibit a rough surface. The microstructure comprises a double-porosity structure with pronounced macropores. The dynamics of precursor thin-film flow and its importance for capillary trapping are studied. The experimental data for thin-film flow advancement show a square-root time dependence. Based on the experimental data, we conducted inverse modeling to investigate the influence of surface roughness on the dynamic contact angle of precursor thin-film flow. Our experimental results show that trapped gas saturation decreases logarithmically with an increasing capillary number. Cluster analysis shows that the morphology and number of trapped clusters change with capillary number. We demonstrate that capillary trapping shows significant differences for vertical flow and horizontal flow. We found that our experimental results agree with theoretical results of percolation theory for $$Ca =10^{-6}$$ : (i) a universal power-like cluster size distribution, (ii) the linear surface–volume relationship of trapped clusters, and (iii) the existence of the cutoff correlation length for the maximal cluster height. The good agreement is a strong argument that the experimental cluster size distribution is caused by a percolation-like trapping process (ordinary percolation). For the first time, it is demonstrated experimentally that the transition zone model proposed by Wilkinson (Phys Rev A 30:520–531, 1984) can be applied to 2D-micromodels, if bicontinuity is generalized such that it holds for the thin-film water phase and the bulk gas phase.

Temperature induced degradation of InAlGaN multiple-quantum well UV-B LEDs

ABSTRACTThe reliability of InAlGaN multiple quantum well LEDs emitting around 308 nm has been investigated. The UV-B LEDs were stressed at constant current and current density, while the heat sink temperature was varied between 15°C and 80°C. The results reveal two different modes of the decrease of the optical power during aging. First, a fast reduction of the optical power within the first 100 h (mode 1) can be observed, followed by a slower degradation for operation times >100 h (mode 2). Mode 1 can be described as an initial degradation activation process which saturates after a certain time, whereas the second degradation mode can be described by a square-root time dependence of the optical power, suggesting a diffusion process to be involved. Both degradation modes are accompanied by changes of the I-V characteristic, particularly the reverse-bias leakage current and the drive voltage. Furthermore, the degradation behavior is strongly influenced by the temperature. Both, the maximum reduction of the optical power and the increase of the leakage current become stronger at higher temperatures.

Effect of lithium-to-magnesium ratio in metaphosphate glasses on crack-tip condensation and sub-critical crack growth

Corner cracks were initiated in a series of lithium–magnesium-metaphosphate glasses with different Li-to-Mg ratios by performing Vickers indentation under humid conditions (RH=50% and RH=65%) and in dry nitrogen gas atmosphere (RH=0.01%). Propagation of each crack was observed up to 240h. Distinct condensation of water at the crack-tip up to 30μm occurred in humid environments, which led to a decrease in open crack length, while in dry nitrogen gas atmosphere this phenomenon was absent. A square root of time dependence was observed for the crack-tip condensation (CTC) kinetics as well as for weight gain experiments on crack-free glass specimens. Slow crack growth and CTC were dependent on the Li-to-Mg ratio of the glasses and showed a negative deviation from a linear compositional trend. Deviation of CTC was largest for glasses of Li-to-Mg ratio >2:1 indicating a mixed mobile ion effect beyond charge neutrality, while the fatigue resistance exhibited a maximum at concentrations of equal charge. On the other hand a positive deviation from additivity was found for hardness and Young's modulus indicating increased resistance against elastic and plastic deformation for glass compositions of mixed Li+ and Mg2+ ions.

MD simulations of onset of tungsten fuzz formation under helium irradiation

When helium (He) escapes a fusion reactor plasma, a tungsten (W)-based divertor may, under some conditions, form a fuzz-like nano-morphology. This is a highly undesired phenomenon for the divertor, and is not well understood. We performed molecular dynamics simulations of high fluence He and also C-seeded He (He+C) irradiation on W, focusing on the effect of the high fluence, the temperature and the impurities on the onset of the structure formation. We concluded that MD reproduces the experimentally found square root of time dependence of the surface growth. The He atomic density decreases when increasing the number of He atoms in the cell. A higher temperature causes a larger bubble growth and desorption activity, specially for the pure He irradiation cases. It also it leads to W recrystallization for the He+C irradiation cases. Carbon acts as a local He trap for small clusters or single atoms and causes a larger loss of crystallinity of the W surface.

Iron oxide waste form for stabilizing 99Tc

Crystals of goethite were synthesized with reduced technetium [99Tc(IV)] incorporated within the solid lattice. The presence of 99Tc(IV) as a substituting cation in the matrix and “armoring” by an additional layer of precipitated goethite isolated the reduced 99Tc(IV) from oxidizing agents. These products were used to make monolithic pellets to quantify an effective diffusion coefficient for 99Tc from goethite waste form contacted with a synthetic Hanford IDF (Integrated Disposal Facility) pore water solution (pH=7.2 and I=0.05M) at room temperature for up to 120days in static reactors. XANES analysis of the goethite solids recovered post-run demonstrated that the 99Tc in the goethite crystals remains in the reduced 99Tc(IV) state. The slow release of pertechnetate concentration with time in the static experiments with the monolith followed a square root of time dependence, consistent with diffusion control for 99Tc release. An apparent diffusion coefficient of 6.15×10−11cm2/s was calculated for the 99Tc–goethite pellet sample and the corresponding leaching index (LI) was 10.2. The results of this study indicate that technetium can be immobilized in a stable, low-cost Fe oxide matrix that is easy to fabricate and these findings can be useful in designing long-term solutions for nuclear waste disposal.

APPLYING 1/F NOISE FOR DRIFT ESTIMATION

The work introduces a new 1/f noise theory that focuses on limited signals. Usually, 1/f noise represents drift, because 1/f noise is the spectral power density of the drift. The subjects of the new theory are signals that have limited value and duration. Therefore the basis of the new theory of 1/f noise corresponds to the real properties of any device and signal comprising 1/f noise. On this basis, the standard deviation of 1/f noise was derived, which is the most important parameter of 1/f noise. This standard deviation has good consistency with (a) the widely used Hurst approximation, (b) the square root of time dependence of Brownian motion displacement, and (c) theoretically derived Brownian displacement. Comparison of an existing 1/f noise theory and the new one shows that both theories are incompatible because subjects of the existing 1/f noise theory are limitless signals, which do not exist.

Release of Chlorpheniramine Maleate from Fatty Acid Ester Matrix Disks Prepared by Melt-extrusion

Chlorpheniramine maleate was incorporated into disks consisting of glyceryl fatty acid esters, polyethylene glycol fatty acid esters or a combination of the two. A melt-extrusion process was used to prepare the matrix disks containing the drug. The release of the drug into distilled water, pH 1.2 buffer, and pH 7.5 buffer showed the expected square root of time dependence. An increase in the fatty acid ester hydrophilic-lipophilic balance (HLB) from 1 to 14 resulted in a 10-fold increase in the drug release rate from 0.25 +/- 0.01 to 25.84 +/- 1.29 mg cm-2 h-1/2. The maximum release rate was seen from the fatty acid ester with a melting point of 44 degrees C. The pH of the dissolution medium had a small impact on the rate of drug release, but the rate of agitation had no significant influence on the rate of drug release. By blending a fatty acid ester of a high melting point (64 degrees C) and a low HLB value of 2 with esters of lower melting points (33 to 50 degrees C) or higher HLB values (10 to 14), it was possible to modify the release from 10.0 +/- 0.70 to 21.5 +/- 0.57 mg cm-2 h-1/2.

Investigation of delamination mechanisms in polymer coatings by scanning acoustic microscopy

Scanning acoustic microscopy (SAM) was used to investigate disbonding, delamination and blister formation in polymer coatings for different layer structures and initial defect depths during exposure to a corrosive environment. The time evolution of disbonding and blister initiation and their growth was investigated by analysing the SAM images, taken after defined times of exposure to an electrolyte solution (Harrison solution).From investigations of a model system of coatings on steel substrates, it was possible to differentiate between water and/or ion transport (i) through the coating and (ii) along the coating–steel interface. For samples without clear coat randomly distributed blisters appeared at the coating–steel interface after exposure to the electrolyte solution, irrespective of the location of initial defects. The random distribution of growing blisters is related to diffusion of water and/or ions through the coating and ‘nucleation’ at weak points of the substrate or within the polymer. For samples with clear coat a propagating migration front along the coating–steel interface of 3–4 µm height—starting from initial defects—was detected. The linear propagation of this front cannot be explained by Fickian diffusion. Therefore, it is discussed in terms of an accelerated diffusion or crack growth kinetics. Since blistering starts only at sites, where the migration front has passed, the presence of a thin water layer at the coating–steel interface, the loss of adhesion and the following corrosive processes are prerequisites for the nucleation of blisters. The blister growth shows a square-root time dependence.

Water sprints uphill on glass

As a material, glass has been widely used in traditional fluidic devices and more recently in micro- and nanofluidic devices, and its wetting properties are crucially important in these applications. In this work, by using a high-intensity femtosecond laser structuring technique, we create a unique surface pattern on glass that transfer a regular glass surface to superwicking. As a result, water defies the gravity and sprints vertically uphill along the structured glass surface at an unprecedented velocity of 3.8 cm/sec. Our study shows that the dynamics of this fast self-propelled water flow follows a square root of time dependence.

Laser turns silicon superwicking

Using high-intensity femtosecond laser pulses, we create a novel surface pattern that transforms regular silicon to superwicking. Due to the created surface structure, water sprints vertically uphill in a gravity defying way. Our study of the liquid motion shows that the fast self-propelling motion of water is due to a supercapillary effect from the surface structures we created. The wicking dynamics in the produced surface structure is found to follow the classical square root of time dependence.

Debinding behaviors of injection molded ceramic bodies with nano-sized pore channels during extraction using supercritical carbon dioxide and n-heptane solvent

Debinding behaviors related on changes in capillary pore structure during extraction with supercritical carbon dioxide and n-heptane, respectively were investigated for injection molded ceramic bodies consisting of skeleton pores of 68 nm. For the debinding processes, both debinding curves showed a square root of time dependence but significantly deviated in the middle or end period of debinding because of structural changes with pores during extraction. The debinding bodies experienced capillary changes having a debinding front separating the undebinded region with fluid state into the debinding region with pendular state in the wax-based green bodies. The debinding rate of the supercritical fluid extraction was five times higher than that of the solvent extraction because of a higher interdiffusion diffusivity and a formation of relatively large pore channels. An abrupt change of pore structures between debinded and undebinded region in the green bodies caused severe defects during the solvent extraction even at a low rate of debinding at 313.15 K, while the severity of the capillary changes was overcome during the supercritical fluid extraction and the debinded ceramic bodies were free from defects even at a high rate of debinding at 328.15 K. It is attributed to a reduction of the capillary stress developed on debinding front during the supercritical fluid extraction.

Development of Eco-Debinding Process Using Supercritical Extraction of Low Molecular Organic Binders in Ceramic Bodies with Nano-Sized Capillary Structure

Eco-debinding process using supercritical extraction of low molecular organic binders in nano-porous ceramic bodies was examined. The debinding properties related to structural changes during supercritical extraction and conventional solvent extraction were also compared. The debinding rate of supercritical extraction was significantly enhanced compared to the debinding rate of solvent extraction because of the high diffusivity of the supercritical carbon dioxide for the low molecular weight wax binder in the molded bodies with nano-sized pore structure, although both debinding rates showed same a square root of time dependence. The extraction rates with morphological changes varied depending on the degree of saturation at the end of debinding stages. Both the debinding methods experienced morphological changes with a debinding front separating the pendular state region from the undebinded region with fluid state in low molecular paraffin wax based powder compacts during extraction. The capillary structural changes in the green bodies caused severe defects during extraction and degraded the physical properties. In spite of the abrupt changes of the capillary structure, the debinding defect was significantly alleviated for the supercritical debinded ceramic bodies, compared to the solvent extracted bodies.

InGaN Laser Diode Degradation. Surface and Bulk Processes

AbstractWe discuss main degradation mechanisms present in nitride based laser diodes operating in 400-440 nm spectral range. We can clearly divide the aging processes into these occurring on the exposed facets of the device and into the bulk phenomena. Surface processes are predominantly connected with photochemical reactions on the laser mirrors and manifest by the formation of the carbon deposits. The nature of these photochemical reactions resembles very closely the mechanism known as Package Induced Failure observed previously in case of 980 nm laser diodes. Degradation involving bulk like effects is much less understood. The experimental results by other group are not sufficient for proposing an unambiguous model of the physical effects involved. In particular, it consists in observation related to dopants diffusion and recombination mechanisms. Magnesium diffusion from the p-type layers into the active layer was proposed as a possible degradation path. However, our study of SIMS profiles in the device subjected to over 8 000 h of electrical stress reveals no visible modification in the Mg profile. The same holds for the hydrogen spatial distribution thus substantially limiting candidates for the diffusion processes. Nevertheless, it seems that the diffusion mechanism is involved in bulk degradation. The claim is supported by two facts: well confirmed stability of the extended defects network in nitride emitters and characteristic square-root time-dependence of the degradation rate.