Diffusion-limited Kinetics Research Articles

Role of chemical potential in relaxation of faceted crystal structure.

Below the roughening transition, crystal surfaces have macroscopic plateaus, facets, whose evolution is driven by the microscale dynamics of steps. A long-standing puzzle was how to reconcile discrete effects in facet motion with fully continuum approaches. We propose a resolution of this issue via connecting, through a jump condition, the continuum-scale surface chemical potential away from the facet, characterized by variations of the continuum surface free energy, with a chemical potential originating from the decay of atomic steps on top of the facet. The proposed condition accounts for step flow inside a discrete boundary layer near the facet. To validate this approach, we implement in a radial geometry a hybrid discrete-continuum scheme in which the continuum theory is coupled with only a few, minimally three, steps in diffusion-limited kinetics with conical initial data.

A continuum model for hierarchical fibril assembly

Most of the biological polymers that make up our cells and tissues are hierarchically structured. For biopolymers ranging from collagen, to actin, to fibrin and amyloid fibrils this hierarchy provides vitally important versatility. The structural hierarchy must be encoded in the self-assembly process, from the earliest stages onward, in order to produce the appropriate substructures. In this letter, we explore the kinetics of multistage self-assembly processes in a model system which allows comparison to bulk probes such as light scattering. We apply our model to recent turbidimetry data on the self-assembly of collagen fibrils. Our analysis suggests a connection between diffusion-limited aggregation kinetics and fibril growth, supported by slow, power-law growth at very long time scales.

Reaction instabilities in Co/Al nanolaminates due to chemical kinetics variation over micron-scales

The reaction front dynamics of Co/Al reactive nanolaminates were studied as a function of the initial temperature of the unreacted material. Sample geometries that exhibit stable reaction fronts as well as geometries that present “spinning” reaction front instabilities were investigated at initial temperatures ranging from room temperature to 200 °C. It was found that reactions in samples with small reactant periodicities (<66.4 nm) were stable at all temperatures, reaction in large periodicity samples (≥100 nm) were unstable at all temperatures, and reactions in samples with intermediate periodicities transitioned from unstable behavior to stable behavior with increasing initial temperature. The results suggest that behaviors typical of two types of reaction kinetics are present in unstable reaction fronts: slow, diffusion-limited kinetics in the regions between transverse reaction bands, and a faster mechanism at the leading edge of the transverse bands.

The water vapour sorption behaviour of acetylated birch wood: how acetylation affects the sorption isotherm and accessible hydroxyl content

The water vapour sorption isotherms and sorption kinetics of birch (Betula pendula L) acetylated to different levels have been determined using a dynamic vapour sorption (DVS) apparatus. A DVS instrument was also used to determine the accessible hydroxyl content in the wood samples using deuterium exchange. The results are reported in terms of the reduced equilibrium moisture content (EMCR), in which the moisture content per unit mass of wood substance is used for the calculation. As the level of acetylation of the wood samples increased there was a corresponding reduction in EMCR of the wood samples, which was accompanied by a decrease in hysteresis in the same order. The sorption kinetics were also determined using the DVS and analysed using the parallel exponential kinetics model, in which the sorption kinetics curve is composed of two processes (labelled fast and slow). Using this analysis, it is possible to calculate two pseudo-isotherms associated with the two processes. The sorption isotherm is a composite of the sorption isotherms associated with the fast process water and the slow process water and there are significant differences in behaviour between the two. It is suggested in this paper that the fast process is related to diffusion limited kinetics, whereas the slow process is a relaxation-limited phenomenon. The reduction in accessible OH content due to acetylation was well correlated with the weight gain due to acetylation, although the relationship did not exactly correspond with that theoretically determined.

Measurement of a Reaction-Diffusion Crossover in Exciton-Exciton Recombination inside Carbon Nanotubes Using Femtosecond Optical Absorption

Exciton-exciton recombination in isolated semiconducting single-walled carbon nanotubes was studied using femtosecond transient absorption. Under sufficient excitation to saturate the optical absorption, we observed an abrupt transition between reaction- and diffusion-limited kinetics, arising from reactions between incoherent localized excitons with a finite probability of ~0.2 per encounter. This represents the first experimental observation of a crossover between classical and critical kinetics in a 1D coalescing random walk, which is a paradigm for the study of nonequilibrium systems.

Efficient computation of population distribution of microdefects at any location in growing Czochralski silicon single crystals

A computationally efficient model to quantify the distribution of microdefect population at any given location in Czochralski grown silicon crystals is proposed and numerically solved. For this purpose, all microdefects are approximated as spherical clusters and the concentration fields of intrinsic point defects and other intermediate species are evolved using a lumped model which eliminates the requirement to store formation and path histories of the clusters. The formation of all clusters is modeled by the classical nucleation theory, while they grow by diffusion-limited kinetics. The model is validated by comparing its predictions against that of a rigorous model, where actual cluster population distribution is captured on the basis of formation and path histories of the clusters.

Accelerated Surface-Enhanced Raman Spectroscopy (SERS)-Based Immunoassay on a Gold-Plated Membrane

A rapid and simple SERS-based immunoassay has been developed to overcome diffusion-limited binding kinetics that often impedes rapid analysis in conventional heterogeneous immunoassays. This paper describes the development of an antibody-modified membrane as a flow-through capture substrate for a nanoparticle-enabled SERS immunoassay to enhance antibody-antigen binding kinetics. A thin layer of gold is plated onto polycarbonate track-etched nanoporous membranes via electroless deposition. Capture antibody is immobilized onto the surface of a gold-plated membrane via thiolate coupling chemistry to serve as a capture substrate. A syringe is then used to actively transport the analyte and extrinsic Raman labels to the capture substrate. The fabrication of the gold-plated membrane is thoroughly investigated and established as a viable capture substrate for a SERS-based immunoassay in the absence of sample/SERS label flow. A syringe pump is used to systematically investigate the effect of flow rate on antibody-antigen binding kinetics and demonstrate that active transport to the capture membrane surface expedites antibody-antigen binding. Mouse IgG and goat anti-mouse IgG are selected as a model antigen-antibody system to establish proof of principle. It is demonstrated that the assay for mouse IgG is reduced from 24 h to 10 min and a 10-fold improvement in detection limit is achieved with the flow assay developed herein relative to the passive, i.e., no flow, assay. Moreover, mouse serum is directly analyzed and IgG level is determined using the flow assay.

Modeling of precipitation of ultra-fine particles by pressure reduction over CO2-expanded liquids

A mathematical model has been developed to describe the process of precipitation of ultrafine particles by pressure reduction over gas (CO2)-expanded liquids. A rapid pressure reduction over a CO2-expanded organic solution, from 30–70 to 1bar at 303K decreases the solution temperature by 30–80K in a very short span of time (0.5–1.5min), which generates a rapid, high, and uniform supersaturation of the dissolved solute in the solution and facilitates precipitation of ultrafine particles. The model developed in this work estimates the supersaturation attained, nucleation and growth rates obtained during the pressure reduction over CO2-expanded organic solutions, and the particle size distribution of the precipitated particles. Cholesterol has been chosen as a model solute to be precipitated, and acetone has been chosen as a solvent. A new method has been developed for prediction of equilibrium solubility of solute which is affected by a decrease in CO2 mole fraction as well as a simultaneous decrease in solution temperature during pressure reduction. This method combines the semi-empirical approach of using the partial molar volume fraction of solvent in a CO2-solvent binary mixture and solid–liquid equilibrium data for a solute–solvent system. Size distributions of the precipitated particles have been calculated assuming primary nucleation (homogeneous as well as heterogeneous nucleation) and diffusion-limited growth kinetics. The predicted mean average particle sizes are then compared with the size of cholesterol particles precipitated by pressure reduction of a CO2-expanded acetone solution of cholesterol. The particle sizes predicted assuming heterogeneous nucleation are found to be closer to the experimentally observed particle sizes, indicating that the heterogeneous nucleation could be the main mechanism of nucleation, which could occur at the gas–liquid interface of the CO2 bubbling out of CO2-expanded solution during pressure reduction.

Quantitative fluorescence loss in photobleaching for analysis of protein transport and aggregation

BackgroundFluorescence loss in photobleaching (FLIP) is a widely used imaging technique, which provides information about protein dynamics in various cellular regions. In FLIP, a small cellular region is repeatedly illuminated by an intense laser pulse, while images are taken with reduced laser power with a time lag between the bleaches. Despite its popularity, tools are lacking for quantitative analysis of FLIP experiments. Typically, the user defines regions of interest (ROIs) for further analysis which is subjective and does not allow for comparing different cells and experimental settings.ResultsWe present two complementary methods to detect and quantify protein transport and aggregation in living cells from FLIP image series. In the first approach, a stretched exponential (StrExp) function is fitted to fluorescence loss (FL) inside and outside the bleached region. We show by reaction–diffusion simulations, that the StrExp function can describe both, binding/barrier–limited and diffusion-limited FL kinetics. By pixel-wise regression of that function to FL kinetics of enhanced green fluorescent protein (eGFP), we determined in a user-unbiased manner from which cellular regions eGFP can be replenished in the bleached area. Spatial variation in the parameters calculated from the StrExp function allow for detecting diffusion barriers for eGFP in the nucleus and cytoplasm of living cells. Polyglutamine (polyQ) disease proteins like mutant huntingtin (mtHtt) can form large aggregates called inclusion bodies (IB’s). The second method combines single particle tracking with multi-compartment modelling of FL kinetics in moving IB’s to determine exchange rates of eGFP-tagged mtHtt protein (eGFP-mtHtt) between aggregates and the cytoplasm. This method is self-calibrating since it relates the FL inside and outside the bleached regions. It makes it therefore possible to compare release kinetics of eGFP-mtHtt between different cells and experiments.ConclusionsWe present two complementary methods for quantitative analysis of FLIP experiments in living cells. They provide spatial maps of exchange dynamics and absolute binding parameters of fluorescent molecules to moving intracellular entities, respectively. Our methods should be of great value for quantitative studies of intracellular transport.

Controlled Nanoparticle Formation by Diffusion Limited Coalescence

Polymeric nanoparticles (NPs) have great application potential in science and technology. Their functionality strongly depends on their size. We present a theory for the size of NPs formed by precipitation of polymers into a bad solvent in the presence of a stabilizing surfactant. The analytical theory is based upon diffusion-limited coalescence kinetics of the polymers. Two relevant time scales, a mixing and a coalescence time, are identified and their ratio is shown to determine the final NP diameter. The size is found to scale in a universal manner and is predominantly sensitive to the mixing time and the polymer concentration if the surfactant concentration is sufficiently high. The model predictions are in good agreement with experimental data. Hence the theory provides a solid framework for tailoring NPs with a priori determined size.

Diffusive release of uranium from contaminated sediments into capillary fringe pore water

Despite remediation efforts at the former nuclear weapons facility, leaching of uranium (U) from contaminated sediments to the ground water persists at the Hanford site 300 Area. Flooding of contaminated capillary fringe sediments due to seasonal changes in the Columbia River stage has been identified as a source for U supply to ground water. We investigated U release from Hanford capillary fringe sediments by packing sediments into reservoirs of centrifugal filter devices and saturating them with Columbia River water for 3 to 84days at varying solution-to-solid ratios. After specified times, samples were centrifuged. Within the first three days, there was an initial rapid release of 6–9% of total U, independent of the solution-to-solid ratio. After 14days of reaction, however, the experiments with the narrowest solution-to-solid ratios showed a decline in dissolved U concentrations. The removal of U from the solution phase was accompanied by removal of Ca and HCO3−. Geochemical modeling indicated that calcite could precipitate in the narrowest solution-to-solid ratio experiment. After the rapid initial release in the first three days for the wide solution-to-solid ratio experiments, there was sustained release of U into the pore water. This sustained release of U from the sediments had diffusion-limited kinetics.

Effect of flow dynamics on the growth kinetics of CdS thin films in chemical bath deposition

During chemical bath deposition of CdS thin films, the solution is typically stirred to prevent unnecessary concentration gradient and precipitates sticking onto the film surface. Stirring rate changes the thickness of laminar boundary layer over the substrate, affecting the diffusion length of the reactants toward the substrate. It can also change hydrodynamic condition in the bath between laminar and turbulent flow. Interestingly, effect of stirring rate on the deposition kinetics of CdS thin films reported in the literature is conflicting. In this study, we showed that the diffusion-limited deposition kinetics has created a decreasing profile of film thickness along the sample as a function of boundary layer thickness when the substrate was under laminar flow and deposition temperature was between 45°C and 63°C. On the other hand, the deposition became feed-limited when the substrate was under turbulent flow and the deposition temperature was between 45°C and 63°C. While the hydrodynamic condition changed the deposition rate significantly, all the CdS films deposited showed a cubic crystal structure and the optical bandgap was slightly lower than that of single crystalline cubic CdS. The tensile stress in film probed by Raman spectroscopy can explain the low bandgap.

A Hot-Melt Extruded Intravaginal Ring for the Sustained Delivery of the Antiretroviral Microbicide UC781

Microbicide intravaginal rings (IVRs) are a promising woman-controlled strategy for preventing sexual transmission of human immunodeficiency virus (HIV). An IVR was prepared and developed from polyether urethane (PU) elastomers for the sustained delivery of UC781, a highly potent nonnucleoside reverse transcriptase inhibitor of HIV-1. PU IVRs containing UC781 were fabricated using a hot-melt extrusion process. In vitro release studies of UC781 demonstrated that UC781 release profiles are loading dependent and resemble matrix-type, diffusion-limited kinetics. The in vitro release methods employed over predicted the in vivo release rates of UC781 in rabbits. Accelerated stability studies showed good chemical stability of UC781 in prototype formulations, but surface crystallization of UC781 was observed following long-term storage at higher UC781 loadings, unless formulated with a polyvinylpyrrolidone/glycerol surface coating. Mechanical stability testing of prototype rings showed moderate stiffening upon storage. The PU and UC781 had minimal to no impact on viability, tissue integrity, barrier function, or cytokine expression in the tissue irritation model, and UC781 was shown to be delivered to and permeate through this tissue construct in vitro. Overall, UC781 was formulated in a stable PU IVR and provided controlled release of UC781 both in vitro and in vivo.

Praseodymium-cerium oxide thin film cathodes: Study of oxygen reduction reaction kinetics

Praseodymium-Cerium Oxide (PrxCe1-xO2−δ; PCO), a potential three way catalyst oxygen storage material and solid oxide fuel cell (SOFC) cathode, exhibits surprisingly high levels of oxygen nonstoichiometry, even under oxidizing (e.g. air) conditions, resulting in mixed ionic electronic conductivity (MIEC). In this study we examine the redox kinetics of dense PCO thin films using impedance spectroscopy, for x = 0.01, 0.10 and 0.20, over the temperature range of 550 to 670°C, and the oxygen partial pressure range of 10−4 to 1 atm O2. The electrode impedance was observed to be independent of electrode thickness and inversely proportional to electrode area, pointing to surface exchange rather than bulk diffusion limited kinetics. The large electrode capacitance (10−2F) was found to be consistent with an expected large electrochemically induced change in stoichiometry for x = 0.1 and x = 0.2 PCO. The PCO films showed surprisingly rapid oxygen exchange kinetics, comparable to other high performance SOFC cathode materials, from which values for the surface exchange coefficient, k q , were calculated. This study confirms the suitability of PCO as a model MIEC cathode material compatible with both zirconia and ceria based solid oxide electrolytes.

Predictive Model for Diffusion-Limited Aggregation Kinetics of Nanocolloids under High Concentration

Smoluchowski's equation for the rate of aggregation of colloidal particles under diffusion-limited conditions has set the basis for the interpretation of kinetics of aggregation phenomena. Nevertheless, its use is limited to sufficiently dilute conditions. In this work we propose a correction to Smoluchowski's equation by using a result derived by Richards ( J. Phys. Chem. 1986 , 85 , 3520 ) within the framework of trapping theory. This corrected aggregation kernel, which accounts for concentration dependence effects, has been implemented in a population-balance equations scheme and used to model the aggregation kinetics of colloidal particles undergoing diffusion-limited aggregation under concentrated conditions (up to a particle volume fraction of 30%). The predictions of population balance calculations have been validated by means of Brownian dynamic simulations. It was found that the corrected kernel can very well reproduce the results from Brownian dynamic simulations for all concentration values investigated, and is also able to accurately predict the time required by a suspension to reach the gel point. On the other hand, classical Smoluchowski's theory substantially underpredicts the rate of aggregation as well as the onset of gelation, with deviations becoming progressively more severe as the particle volume fraction increases.

A reactive transport modeling approach to simulate biogeochemical processes in pore structures with pore-scale heterogeneities

Redox processes, including degradation of organic contaminants, are often controlled by microorganisms residing in natural porous media like soils or aquifers. These environments are characterized by heterogeneities at various scales which influence the transport of chemical species and the spatial distribution of microorganisms. As a result, the accessibility of the chemical species by the resident microbial populations may be limited, altering the efficiency of the biodegradation process. Hence, the biodegradation rate of contaminants at large scales does not only depend on the degradation capacity of the indigenous microbial population but also on the heterogeneities of the hosting media at smaller scales. It is thus important to establish a link between effective reaction rates and various structural features of porous media which can be directly observed or measured. This link is urgently needed because explicit resolution of heterogeneities within large-scale reactive transport models is still limited by the available computational capacities. The present study introduces a reactive transport modeling approach to determine the influence of pore-scale heterogeneities on biogeochemical processes in porous media. For this purpose, a pore network model, which simulates flow and advective–diffusive transport of chemical species in heterogeneous pore networks is developed and coupled to the Biogeochemical Reaction Network Simulator (BRNS). The resulting coupled model (PNBRNS) is able to simulate the reactive transport of solutes in heterogeneous pore assemblies. The PNBRNS model is applied for the simulation of a test case of bioavailability and effective biodegradation rate of a dissolved contaminant in different pore networks, built using a discrete set of geostatistically derived pore-size or biomass distributions. Results show that the heterogeneity of the pore-size distribution has a significant impact on bioavailability while the heterogeneity of the biomass distribution only leads to minor effects. The model also includes intra-pore bioavailability restrictions using diffusion-limited biodegradation kinetics. The results indicate that intra-pore limitations lead to extra constrains on the biodegradation of contaminants, even in the presence of larger-scale structural heterogeneities.

Structure–composition relationships of the traditional balsamic vinegar of Modena close to jamming transition (part II): Threshold control parameters

The Traditional Balsamic Vinegar of Modena (TBVM) is a high-valuable Italian specialty that, for reasons not yet fully explained, may undergo non-equilibrium degrading phenomena involving phase separation and flow arrest caused by solidification with or without crystalline order. TBVM was probed for its microstructure and composition as well as for its flow ability under low- and high shear limits. Results indicated vinegar concentration, temperature and viscosity as three independent variables affecting the extent of solidification in TBVM. Polymer-mediated mechanisms and diffusion-limited kinetics were hypothesized for structure development. Three main experimental evidences offered a convincing proof unifying all solidification phenomena observed in TBVM under the concept of colloidal jamming transition: (i) simultaneous presence of fractal-like aggregated colloids and polydispersed biopolymers; (ii) non-linear shear dependence above a critical level of vinegar concentration; (iii) a modified Krieger–Dougherty model satisfactorily described scaling behavior of relative viscosity accounting for the fractal dimension of jammed structure. Threshold for jamming in TBVM was defined in terms of critical concentration of the overall structure-active constituents (corresponding to 72°Bx and 40% w/w of the main sugars) and maximum resistance to the Newtonian flow (the onset for shear-thinning flow was achieved with a low-shear limiting viscosity of about 0.95Pa·s).

A new type of poly(vinyl alcohol)/nitrocellulose/granular activated carbon/KNO3 composite bead used as a biofilter material

A new type of poly(vinyl alcohol)/nitrocellulose/granular activated carbon/KNO3 composite bead was prepared and shown to be suitable for use as a filter material in the biofiltration process. This composite bead was a porous spherical particle with a diameter of 2.4–6.0 mm and a density of 1.125 g/cm3. The amount of water-soluble nitrogen dissolved out of this composite bead was 145.5 mg N/g dry composite bead. The biochemical kinetic behaviors of n-butyl acetate in a spherical poly(vinyl alcohol) (PVA)/nitrocellulose (NC)/granular activated carbon (GAC)/KNO3 composite bead biofilter (NC biofilter) and a spherical PVA/peat/GAC/KNO3 composite bead biofilter (peat biofilter) were investigated. The values of the half-saturation constant K s for the NC biofilter and the peat biofilter were 33.55 and 35.54 ppm, respectively. The values of the maximum reaction rate V m for the NC biofilter and the peat biofilter were 23.83 and 22.46 ppm/s, respectively. Diffusion-limited zero-order kinetics were regarded as the most adequate biochemical reaction model for the two biofilters. The microbial growth rates and biochemical reaction rates for the two biofilters were inhibited at higher inlet concentrations. The biochemical kinetic behaviors of the two biofilters were similar. The maximum elimination capacities of the NC biofilter and the peat biofilter were 170.72 and 174.51 g C/h m3 bed volume, respectively. The PVA/nitrocellulose/GAC/KNO3 composite bead made it easier for the microbes to adjust to their new environment and secrete exocellular enzymes to break down the substrate.

Evolution of morphology and composition in three-dimensional fully faceted strained alloy crystals

Alloy structures such as core-shell particles, heteroepitaxial multilayers and nanowires have received a lot of attention in recent years due to their applications in logic, energy storage and optoelectronics. In typical growth conditions, the surfaces of these structures are usually faceted i.e. they adopt low-energy singular crystalline orientations. For alloy systems, the growth law for a fully faceted structure requires the specification of the normal velocity of each facet, the incorporation rate of each alloy component on the surface, and the exchange of surface atoms with the bulk. The latter process requires consideration of both surface segregation and possibly bulk material transport. By using only fundamental concepts of thermodynamics, we derive the governing equations for the growth of strained and fully faceted two-component crystals in regimes where surface material transport may be governed by surface-attachment limited kinetics or surface diffusion limited kinetics. In both cases we derive a very compact form for the surface mass fluxes from chemical potentials that account for the constraint stemming from the fact that while the growth rate of each alloy component can vary along the surface (as governed by the individual chemical potentials), their sum should remain constant along the facet and should be equal to the growth velocity of the facet. Within our approach, the dynamics of surface segregation and other important features of faceted crystal growth that lead to compositional patterning such as a kinetic barrier for exchange of alloy components between different facets emerge in a very natural fashion.

Micromechanics of colloidal aggregates at the oil–water interface

The micromechanics of two-dimensional (2D) colloidal aggregates at the oil–water interface are measured using optical tweezers. Aggregates form from stable 2D suspensions after introducing either 0.25 M NaCl/0.1 mM SDS in the aqueous sub-phase or 25 μM sorbitan monooleate (SPAN 80) in the oil super-phase. Aggregates formed with NaCl/SDS have strong bond bending rigidities due to tangential forces between particles, leading to an average aggregate rigidity κa = 4.9 ± 3.1 mN m−1. Rigid aggregates are consistent with previously reported open microstructures and irreversible, diffusion-limited cluster aggregation kinetics. In contrast, aggregates formed by SPAN 80 exhibit weak bond rigidities (κa = 0.28 ± 0.31 mN m−1), enabling particle rearrangements that lead to a denser microstructure. The micromechanical properties of aggregates that constitute the macrocolloidal structure of 2D suspensions provide a critical link between their colloidal interactions and interfacial rheology.