Diffusion-limited Kinetics Research Articles

Electrochemical Investigation of Symmetric Aminoquinones

Abstract Quinones have a wide range of valuable properties and potential applications in medicinal chemistry, materials science, optoelectronic devices, and batteries. Molecular redesign using different functional groups, like amines, can optimize their properties and prevent undesired side reactions. However, the synthesis of aminoquinones can be particularly challenging at times, and there is a need for simple and efficient routes to access these compounds without metal catalysts or halogenated starting materials. Here, we demonstrate the synthesis and electrochemical characterization of a series of aminoquinones derived from renewable sources, namely vanillin or 2-methoxyhydroquinone. We employ a series of primary and secondary amines, varying in their electronic situation as well as steric demand. Depending on the type of starting material, either the desired aminoquinone or the related Schiff-base adduct was obtained. The aminoquinones were further explored towards their stability at different pH values. At extreme pH values, the deeply colored aminoquinones decompose, accompanied by decolorization of the solutions within a few minutes (pH 14) or hours (pH 1). At intermediate pH values (3-8) the aminoquinones are stable upon storage in solution, where they feature a quasi-reversible redox chemistry and fast, diffusion limited kinetics.

Nanoimpact Electrochemistry for Unraveling the Reactivity of Diffusion Limited Enzymes

The ultimate challenge of modern electroanalytical chemistry is to reach a single-molecule level of detection. In this framework, nanoimpact electrochemistry (NIE) has been recently developed. It allows studying at high throughput the reactivity of small entities such as nanoparticles, cells, or proteins, that collide on a biased ultramicroelectrode (UME) inside a solution or suspension.1 The collisions cause disturbances in the recorded chronoamperogram such as current spikes or current steps.2 Single enzyme electrochemistry (SEE) can contribute to uncovering effects of dynamics and non-equilibrium behavior of individual enzyme molecules on catalysis, which are hidden in measurements on ensembles due to averaging of the measured parameters over the entire molecular population. However, NIE of smaller entities such as enzymes, is very challenging due to the low sensitivity of the state-of-the-art electrochemical equipment, and most single enzyme techniques are currently based on fluorescence.3 One strategy to overcome this issue is the amplification of the current produced by a single enzyme molecule by fast catalysis: the single enzyme converts several substrate molecules per second consuming several electrons leading measurable current. Some of us reported the implementation of this strategy for the first time, designing a single-entity electrochemical experiment that allowed the detection of catalytic currents from single laccase molecules.4 Soon after the initial SEE report in 2016, a similar approach was applied for investigations of catalase,5 an enzyme that breaks down H2O2 to O2 and H2O with diffusion limited kinetics. However, the unequivocal attribution of current disturbances to the reduction of O2 (produced locally by enzyme) on the electrode during enzyme-electrode collisions remains a challenge. We will address this challenge based on the analysis of SEE experimental data under various conditions, on protein film voltammetry (PFV) studies on rotating disk electrode (RDE), and on simulations. The collected data from the SEE, that is the current spike characteristics in each set of conditions, are statistically analyzed and discussed. PFV studies are used to evaluate basic thermodynamic and kinetic parameters of the system. Finally, we have built a model using Comsol Multiphysics. To the best of our knowledge, this is the first model reported so far that can satisfactorily reproduce the experimental SEE data, using experimentally evaluated parameters as input. The developed methodology is the succesfully implemented to the study of superoxide dismutase.6

Schreibersite oxidation under varied oxygen buffers

Phosphorus is often present in meteorites as the mineral schreibersite, in which P is in a reduced oxidation state as a phosphide. Phosphides such as schreibersite have been proposed to be important to the development of life on the earth and may serve as indicators of metamorphic grade on meteorite parent bodies. Here we investigate how synthetic schreibersite (as the iron end-member, Fe3P) oxidizes into calcium phosphates through reaction with silicates under high temperature conditions, at specific oxygen fugacities, and in the absence of water. We find that schreibersite readily oxidizes to phosphates at temperatures of 750–850 °C over a few weeks depending on the oxygen fugacity of the environment. The rate of this process is best matched by diffusion-limited kinetics. Therefore, the metamorphic heating timescale required to equilibrate phosphorus in meteoritic samples with small schreibersite grains (∼1 μm), such as in the type 3 ordinary chondrites (3.0–3.3), was short (10–100 days).

General Method for Fitting Kinetics from the SECM Images of Reactive Sites on Flat Surfaces.

Scanning electrochemical microscopy (SECM) is a technique for imaging electrochemical reactions at a surface. The interaction between electrochemical reactions occurring at the sample and scanning electrode tip is quite complicated and requires computer modeling to obtain quantitative information from SECM images. Often, existing computer models must be modified, or a new model must be created from scratch to fit kinetic parameters for different reactive features. This work presents a method that can simulate the SECM image of a reactive feature of any shape on a flat surface which is coupled to a computer program which effectuates the automated fitting of kinetic information from these images. This fitting program is evaluated along with several methods for estimating the shapes of reactive features from their SECM images. Estimates of the reactive feature shape from SECM images were not sufficiently accurate and produced median relative errors for the surface rate constant that were >50%. Fortunately, more precise techniques for imaging the reactive features such as optical microscopy can supply sufficiently accurate shapes for the fitting procedure to produce accurate results. Fits of simulated SECM images using the actual shape from the simulation produced median relative errors for the surface rate constant that were <10% for the smallest reactive features tested. This method was applied to the SECM images of aluminum alloy AA7075 which revealed diffusion-limited kinetics for ferrocene methanol reduction over inclusions in the surface of the alloy.

Diffusion-Limited Kinetics in Reactive Systems.

A proper representation of chemical kinetics is vital to understanding, modeling, and optimizing many important chemical processes. In liquid and surface phases, where diffusion is slow, the rate at which the reactants diffuse together limits the overall rate of many elementary reactions. Commonly, the textbook Smoluchowski theory is utilized to estimate effective rate coefficients in the liquid phase. On surfaces, modelers commonly resort to much more complex and expensive Kinetic Monte Carlo (KMC) simulations. Here, we extend the Smoluchowski model to allow the diffusing species to undergo chemical reactions and derive analytical formulas for the diffusion-limited rate coefficients for 3D, 2D, and 2D/3D interface cases. With these equations, we are able to demonstrate that when species react faster than they diffuse they can react orders of magnitude faster than predicted by Smoluchowski theory, through what we term "the reactive transport effect". We validate the derived steady-state equations against particle Monte Carlo (PMC) simulations, KMC simulations, and non-steady-state solutions. Furthermore, using PMC and KMC simulations, we propose corrections that agree with all limits and the computed data for the 2D and 2D/3D interface steady-state equations, accounting for unique limitations in the associated derived equations. Additionally, we derive equations to handle couplings between diffusion-limited rate coefficients in reaction networks. We believe these equations should make it possible to run much more accurate mean-field simulations of liquids, surfaces, and liquid-surface interfaces accounting for diffusion limitations and the reactive transport effect.

Iron(III) Carbene Complexes with Tunable Excited State Energies for Photoredox and Upconversion.

Substituting precious elements in luminophores and photocatalysts by abundant first-row transition metals remains a significant challenge, and iron continues to be particularly attractive owing to its high natural abundance and low cost. Most iron complexes known to date face severe limitations due to undesirably efficient deactivation of luminescent and photoredox-active excited states. Two new iron(III) complexes with structurally simple chelate ligands enable straightforward tuning of ground and excited state properties, contrasting recent examples, in which chemical modification had a minor impact. Crude samples feature two luminescence bands strongly reminiscent of a recent iron(III) complex, in which this observation was attributed to dual luminescence, but in our case, there is clear-cut evidence that the higher-energy luminescence stems from an impurity and only the red photoluminescence from a doublet ligand-to-metal charge transfer (2LMCT) excited state is genuine. Photoinduced oxidative and reductive electron transfer reactions with methyl viologen and 10-methylphenothiazine occur with nearly diffusion-limited kinetics. Photocatalytic reactions not previously reported for this compound class, in particular the C-H arylation of diazonium salts and the aerobic hydroxylation of boronic acids, were achieved with low-energy red light excitation. Doublet-triplet energy transfer (DTET) from the luminescent 2LMCT state to an anthracene annihilator permits the proof of principle for triplet-triplet annihilation upconversion based on a molecular iron photosensitizer. These findings are relevant for the development of iron complexes featuring photophysical and photochemical properties competitive with noble-metal-based compounds.

Aggregation of nanoparticles and morphology of aggregates in porous media with computations

HypothesisThe main hypothesis is that the aggregation process for nanoparticles (NPs) propagating in porous media is affected by the structure of the flow field as well as by the properties of the primary NPs. If this were true, then the aggregation could be predicted and controlled. However, to obtain reliable results from computations, one needs to account for the interactions between the NPs as well as the details of the fluid velocity, thus making advances over prior efforts that either ignored the aggregation of NPs, or used probabilistic methods to model aggregation. ExperimentsComputational experiments were conducted using the lattice Boltzmann method in conjunction with Lagrangian particle tracking (LPT). The LPT accounted for the physicochemical interaction forces among NPs. Computationally obtained aggregation kinetics and fractal dimensions of Cerium oxide (CeO2) particles, suspended in potassium chloride (KCl) solutions with different concentration, were verified against experimental results. The model was then employed to investigate the effects of ionic strength, fluid velocity, and particle size on the aggregation kinetics and the aggregate morphology, as NPs propagated in the pore space between randomly packed spheres. FindingsThe aim of this study was to develop a computational model to simulate the aggregation of NPs and obtain the morphology of aggregates in confined geometries, based on the physics of NP interactions and the flow field. The most important factor that impacted both the aggregation process and the aggregate structure was found to be the concentration of the electrolyte. The pore velocity influenced the aggregation kinetics and the NP fractal dimension, especially in diffusion-limited aggregation. The primary particle size affected the diffusion-limited aggregation kinetics and the fractal dimension of reaction-limited aggregates noticeably.

Temperature-dependent growth kinetic and crystallization behavior of the supercooled erythritol as a phase change material in long-term heat storage

Along with the development of long-term heat storage, the utilization of sugar alcohol with large supercooling has been valued in recent years. However, the heat release rate is not easy to control, and the supercooling would be easily influenced by accident factors. Different from the research of directly developing the composites to control the heat release rate and keep stable supercooling, this paper investigated the temperature-dependence crystal growth of erythritol coupled with diffusion-limited kinetics to find the mechanism for better understanding the utilization of supercooling upon different heat needs. The mean crystal growth rate (vm) on supercooled erythritol and the thermodynamic parameters were characterized experimentally. A nucleation factor J* was proposed to improve the modern Wilson-Frenkel equation, which enables a more accurate reflection of the nucleation effect on the practical vm. The sensitivity analysis indicates that the diffusion coefficient (D) and liquid–solid interfacial free energy (IFE1) have a great impact on vm, with 62% and 37% correlations. To verify this result, 0.1 wt% PVA was added to erythritol, which resulted in a significant reduction in the vm maximum by 33.3%. An oil seal was added to reduce the liquid–air interfacial free energy (IFE2) of erythritol, which significantly extended the supercooling duration to 5 days with a 12% cumulative crystallization fraction. Moreover, the crystal morphology analysis revealed that the maximum growth rate had preferred orientations of (211), the largest grain boundary size of 9.2 mm, and exhibited three-dimensional growth. This work can aid in the creation of a dependable heat release model for sugar alcohols in long-term heat storage systems.

Selective Electrochromic Regulation for Near-Infrared and Visible Light via Porous Tungsten Oxide Films with Core/Shell Architecture.

Dual-band electrochromic smart windows have become a research hotspot owing to their unique ability to selectively control near-infrared (NIR) and visible (VIS) light. However, the design and exploitation of dual-band electrochromic films are still an extreme challenge due to the scarcity of relevant high-performance materials. To solve this issue, we here proposed a type of porous WO3 film with nanowires/nanoparticles core/shell architecture as a promising candidate, endowing smart windows with a dual-band electrochromic feature. Moreover, the mechanism of the dual-band electrochromism is illustrated by the response of the transmittance spectra in Li+-based or TBA+-based electrolytes to distinguish the electrochemical behavior and the cyclic voltammetry to determine the degree of diffusion-limited kinetics. Our results indicate that the dual-band electrochromic performance is credited to the progressive electrochemical reduction procedure, in which the capacitive charging process gives rise to NIR regulation and the following ion intercalation contributes to VIS light modulation. Furthermore, we develop a dual-band electrochromic energy storage prototype device utilizing the porous WO3 film. This work describes a judicious strategy for designing dual-band electrochromic films, promoting the evolution of dual-band electrochromic technology.

Accelerated Sulfur Oxidation by Ozone on Surfaces of Single Optically Trapped Aerosol Particles

The sulfur oxidation in mixed sodium thiosulfate/sucrose/aqueous microdroplets by gaseous ozone is studied in this work via aerosol optical tweezers coupled with Raman spectroscopy, which can simultaneously determine various physicochemical properties and the heterogeneous reaction kinetics of single optically trapped microdroplets, allowing for elucidating their complicated interplay. According to the kinetics measurement results at different relative humidities, ozone concentrations, and stoichiometries of inorganic and organic solutes, this work finds that a high aerosol ionic strength can accelerate the ozone oxidation of thiosulfate at air–water interfaces, while a high aerosol viscosity prolongs the reaction time scales due to diffusion-limited kinetics. The kinetic multilayer model of aerosol surface and bulk chemistry (KM-SUB) is utilized to investigate the observed heterogeneous kinetics results and to retrieve the surface reaction rate coefficients. The KM-SUB model fit results indicate that the observed kinetics of sulfur oxidation in binary sodium thiosulfate aqueous microdroplets with high ionic strengths is dominated by interfacial reactions, and the fitted surface reaction rate coefficients increase 1 order of magnitude when the droplet ionic strength increases around 40 M. This work further utilizes the kinetics measurements of ozone dependence to discuss the coupling among properties of ozone gas-interface-bulk partitioning and surface reaction rate in the kinetics model. Finally, this work also exploits the surface reaction of thiosulfate with ozone to retrieve the aerosol viscosity of microdroplets containing ternary aqueous sodium thiosulfate and sucrose mixtures, demonstrating the feasibility of pinning down aerosol viscosities via reaction kinetics.

Complex Mixtures: Array PBPK Modeling of Jet Fuel Components

An array physiologically-based pharmacokinetic (PBPK) model represents a streamlined method to simultaneously quantify dosimetry of multiple compounds. To predict internal dosimetry of jet fuel components simultaneously, an array PBPK model was coded to simulate inhalation exposures to one or more selected compounds: toluene, ethylbenzene, xylenes, n-nonane, n-decane, and naphthalene. The model structure accounts for metabolism of compounds in the lung and liver, as well as kinetics of each compound in multiple tissues, including the cochlea and brain regions associated with auditory signaling (brainstem and temporal lobe). The model can accommodate either diffusion-limited or flow-limited kinetics (or a combination), allowing the same structure to be utilized for compounds with different characteristics. The resulting model satisfactorily simulated blood concentration and tissue dosimetry data from multiple published single chemical rat studies. The model was then utilized to predict tissue kinetics for the jet fuel hearing loss study (JTEH A, 25:1-14). The model was also used to predict rat kinetic comparisons between hypothetical exposures to JP-8 or a Virent Synthesized Aromatic Kerosene (SAK):JP-8 50:50 blend at the occupational exposure limit (200 mg/m3). The array model has proven useful for comparing potential tissue burdens resulting from complex mixture exposures.

Rapid Precipitation of Ionomers for Stabilization of Polymeric Colloids.

Polymeric colloids have shown potential as "building blocks" in applications ranging from formulations of Pickering emulsions and drug delivery systems to advanced materials, including colloidal crystals and composites. However, for applications requiring tunable properties of charged colloids, obstacles in fabrication can arise through limitations in process scalability and chemical versatility. In this work, the capabilities of flash nanoprecipitation (FNP), a scalable nanoparticle (NP) fabrication technology, are expanded to produce charged polystyrene colloids using sulfonated polystyrene ionomers as a new class of NP stabilizers. Through experimental exploration of formulation parameters, increases in the ionomer content are shown to reduce the particle size, mitigating a significant trade-off between the final particle size and inlet concentration; thus, expanding the processable material throughput of FNP. Further, the degree of sulfonation is found to impact stabilization with optimal performance achieved by selecting ionomers with intermediate (2.45-5.2 mol %) sulfonation. Simulations of single ionomer chains and their arrangement in multicomponent NPs provide molecular insights into the assembly and structure of NPs wherein the partitioning of ionomers to the particle surface depends on the polymer molecular weight and degree of sulfonation. By combining the insights from simulations with diffusion-limited growth kinetics and parametric fits to experimental data, a simple design formulation relation is proposed and validated. This work highlights the potential of ionomer-based stabilizers for controllably producing charged NP dispersions in a scalable manner.

An electrochemical mesoscale tool for modeling the corrosion of structural alloys by molten salt

Understanding the impact of microstructure on corrosion rates can aid the development of corrosion-resistant alloys for molten salt reactors. In this work, we develop an electrochemical phase-field model for capturing the microstructure-dependent corrosion of structural alloys by molten salts. As a demonstration problem, we apply this model to capture the selective depletion of Cr from Ni-Cr grain boundaries during corrosion in molten FLiBe salt. We perform sensitivity analysis and model verification on 1D simulations to confirm that the model predicts diffusion-limited kinetics. The model is validated using 1D, 2D, and 3D simulations against experimental data for Ni-5Cr and Ni-20Cr corrosion in molten FLiBe. The 1D simulations predict the corrosion behavior with reasonable accuracy when using an effective diffusion coefficient that accurately represents the grain boundary diffusion. 2D simulations that represent the grain structure underpredict the corrosion. 3D simulations that represent the grain structure predict the corrosion with reasonable accuracy. The corrosion rate predicted by the 3D simulations is proportional to the average grain size at the alloy/salt interface.

In situ 3D spatiotemporal measurement of soluble biomarkers in spheroid culture

BackgroundAdvanced cell culture techniques such as 3D bioprinting and hydrogel-based cell embedding techniques harbor many new and exciting opportunities to study cells in environments that closely recapitulate in vivo conditions. Researchers often study these environments using fluorescence microscopy to visualize the protein association with objects such as cells within the 3D environment, yet quantification of concentration profiles in the microenvironment has remained elusive.ObjectiveDemonstrate an assay that enables near real-time in situ biomarker detection and spatiotemporal quantification of biomarker concentration in 3D cell culture.MethodsA distributed bead-based immuno-assay was used in 3D cell culture to continuously measure the time-dependent concentration gradient of various biomarkers by sequestering soluble target molecules and concentrating the fluorescence intensity of these tagged proteins. Timelapse confocal microscopy was used to measure the in situ fluorescence intensity profile and a calibration curve was separately generated. Application of a calibration transfer function to in situ data is used to quantify spatiotemporal concentration.ResultsExample assays utilize an osteosarcoma spheroid as a case study for a quantitative single-plexed gel encapsulated assay, and a qualitative multi-plexed 3D-bioprinted assay. In both cases, a time-varying cytokine concentration gradient is measured. An estimation for the production rate of the IL-8 cytokine per second per osteosarcoma cell results from fitting an analytical function for continuous point source diffusion to the measured concentration gradient and reveals that spheroid production approaches nearly 0.18 fg/s of IL-8 after 18 h in culture.ConclusionsTheoretical and experimental demonstration of bead-based immunoassays in diffusion-limited environments such as 3D cell culture is shown, and includes example measurements of various cytokines produced by an osteosarcoma spheroid. Proper calibration and use of this assay is exhaustively explored for the case of diffusion-limited Langmuir kinetics of a spherical adsorber.

All-dry free radical polymerization inside nanopores: Ion-milling-enabled coating thickness profiling revealed “necking” phenomena

Conformal coating of nanopores with functional polymer nanolayers is the key to many emerging technologies such as miniature sensors and membranes for advanced molecular separations. While the polymer coatings are often used to introduce functional moieties, their controlled growth under nanoconfinement could serve as a new approach to manipulate the size and shape of coated nanopores, hence, enabling novel functions like molecular separation. However, precise control of coating thickness in the longitudinal direction of a nanopore is limited by the lack of a characterization method to profile coating thickness within the nanoconfined space. Here, we report an experimental approach that combines ion milling (IM) and high-resolution field emission scanning electron microscopy (FESEM) for acquiring an accurate depth profile of ultrathin (∼20 nm or less) coatings synthesized inside nanopores via initiated chemical vapor deposition (iCVD). The enhanced capability of this approach stems from the excellent x–y resolution achieved by FESEM (i.e., 4.9 nm/pixel), robust depth (z) control enabled by IM (step size as small as 100 nm with R2 = 0.992), and the statistical power afforded by high-throughput sampling (i.e., ∼2000 individual pores). With that capability, we were able to determine with unparalleled accuracy and precision the depth profile of coating thickness and iCVD kinetics along 110-nm-diameter nanopores. That allowed us to uncover an unexpected coating depth profile featuring a maximum rate of polymerization at ∼250 nm underneath the top surface, i.e., down the pores, which we termed “necking.” The necking phenomenon deviates considerably from the conventionally assumed monotonous decrease in thickness along the longitudinal direction into a nanopore, as predicted by the diffusion-limited kinetics model of free radical polymerization. An initiator-centric collision model was then developed, which suggests that under the experimental conditions, the confinement imposed by the nanopores may lead to local amplification of the effective free radical concentration at z ≤ 100 nm and attenuation at z ≥ 500 nm, thus contributing to the observed necking phenomenon. The ion-milling-enabled depth profiling of ultrathin coatings inside nanopores, along with the initiator-mediated coating thickness control in the z-direction, may serve to enhance the performance of size-exclusion filtration membranes and even provide more flexible control of nanopore shape in the z dimension.

Burton-Cabrera-Frank theory for surfaces with alternating step types

Burton-Cabrera-Frank (BCF) theory has proven to be a versatile framework to relate surface morphology and dynamics during crystal growth to the underlying mechanisms of adatom diffusion and attachment at steps. For an important class of crystal surfaces, including the basal planes of hexagonal close-packed and related systems, the steps in a sequence on a vicinal surface can exhibit properties that alternate from step to step. Here we develop BCF theory for such surfaces, relating observables such as alternating terrace widths as a function of growth conditions to the kinetic coefficients for adatom attachment at steps. We include the effects of step transparency and step-step repulsion. A general solution is obtained for the dynamics of the terrace widths, assuming quasi-steady-state adatom distributions on the terraces. An explicit simplified analytical solution is obtained under widely applicable approximations. From this we obtain expressions for the full-steady-state terrace fraction as a function of growth rate. Fits of the theoretical predictions to recent experimental determinations of the steady state and dynamics of terrace fractions on GaN (0001) surfaces during organometallic vapor phase epitaxy give values of the kinetic coefficients for this system. In Appendixes, we also connect a model for diffusion between kinks on steps to the model for diffusion between steps on terraces, which quantitatively relates step transparency to the kinetics of atom attachment at kinks, and consider limiting cases of diffusion-limited, attachment-limited, and mixed kinetics.

A thermodynamically consistent gradient theory for diffusion–reaction–deformation in solids: Application to conversion-type electrodes

We develop a thermodynamically consistent phase-field finite strain theory for problems in solids mechanics that couple transport of species into a host material, sharp interface reactions of the species with the host, mechanical deformation and stress. The theory distinguishes between diffusion-limited and reaction-limited kinetics, resolving the manner in which a sharp reaction front can be developed in either case. The phase field formulation has the added benefit of enabling the application of wetting (surface energy) boundary conditions which are critical in reproducing experimentally relevant reaction front morphologies. The theory is fully coupled with diffusion and reaction phenomena impacting mechanical deformation and subsequent stress generation, and conversely these phenomena are coupled to mechanical stress. We derive thermodynamically consistent driving forces for diffusion and reaction through a continuum treatment of these phenomena. Importantly, the resulting formulation makes precise the nature of the material properties driving these thermodynamic forces and in turn makes it amenable to being specialized and calibrated for application.While the framework is quite general, we apply it to modeling conversion electrodes for energy storage using a three-dimensional finite element implementation. We demonstrate the manner in which the theory can be specialized and calibrated in straightforward fashion. Simulations are performed of chemical reactions of FeS2 crystals with lithium and sodium ions, both of which proceed through the formation and propagation of a sharp interface, and are compared to experimental observations of the same system. Our simulations show good qualitative agreement with experimental observations, and elucidate the critical role mechanics plays in determining the morphology of the sharp reaction interface and subsequent stress generation which can lead to mechanical deterioration of these materials. Beyond this application, the theoretical framework should serve useful in a number of engineering problems of relevance in which diffusion and sharp interface reactions occur.

Disparities of Single-Particle Growth Rates in Buried Versus Exposed Ritonavir Crystals within Amorphous Solid Dispersions.

Seeded growth rates of ritonavir in copovidone at 75% relative humidity (RH) and 50 °C were evaluated by single-particle tracking second harmonic generation (SHG) microscopy and found to be ∼3-fold slower for crystallites at the surface compared to the bulk. The shelf lives of final dosage forms containing amorphous solid dispersions (ASDs) are often dictated by the rates of active pharmaceutical ingredient crystallization. Upon exposure to elevated RH, the higher anticipated water content near the surfaces of ASDs has the potential to substantially impact nucleation and growth kinetics relative to the bulk. However, quantitative assessment of these differences in growth rates is complicated by challenges associated with discrimination of the two contributions (supersaturation and molecular mobility) in ensemble-averaged measurements. In the present study, "sandwich" materials were prepared, in which sparse populations of ritonavir single-crystalline seeds were pressed between two similar ASD films to assess bulk crystallization rates. These sandwich materials were compared and contrasted with analogously prepared "open-faced" samples, without the capping film, to assess the surface crystallization rates. Single-particle analysis by SHG microscopy time-series during in situ crystallization produced average growth rates of 3.8 μm/h for bulk columnar crystals with a particle-to-particle standard deviation of 0.9 μm/h. In addition, columnar crystal growth rates for surface particles were measured to be 1.3 μm/h and radiating crystal growth rates for surface particles were measured to be 1.0 μm/h, both with a particle-to-particle deviation of 0.4 μm/h. The observed appearance of radiating crystals upon surface seeding is attributed to reduced ritonavir solubility upon water adsorption at the interface, leading to higher defect densities in crystal growth. Despite substantial differences in crystal habit, correction of the surface growth rates by a factor of 4 from geometric effects resulted in relatively minor but statistically significant differences in the growth kinetics for the two local environments. These results are consistent, with viscosity being a relatively weak function of water absorption coupled with primarily diffusion-limited growth kinetics.

Diffusion-Limited Reaction Kinetics of a Reactant with Square Reactive Patches on a Plane

We present a simple reaction model to study the influence of the size, number, and spatial arrangement of reactive patches on a reactant placed on a plane. Specifically, we consider a reactant whose surface has an N × N square grid structure, with each square cell (or patch) being chemically reactive or inert for partner reactant molecules approaching the cell via diffusion. We calculate the rate constant for various cases with different reactive N × N square patterns using the finite element method. For N = 2, 3, we determine the reaction kinetics of all possible reactive patterns in the absence and presence of periodic boundary conditions, and from the analysis, we find that the dependences of the kinetics on the size, number, and spatial arrangement are similar to those observed in reactive patches on a sphere. Furthermore, using square reactant models, we present a method to significantly increase the rate constant by sequentially breaking the patches into smaller patches and arranging them symmetrically. Interestingly, we find that a reactant with a symmetric patch distribution has a power–law relation between the rate constant and the number of reactive patches and show that this works well when the total reactive area is much less than the total surface area of the reactant. Since our N × N discrete models enable us to examine all possible reactive cases completely, they provide a solid understanding of the surface reaction kinetics, which would be helpful for understanding the fundamental aspects of the competitions between reactive patches arising in real applications.

Rapid vertical flow immunoassay on AuNP plasmonic paper for SERS-based point of need diagnostics

SERS based immunoassays for point-of-care diagnostics are a promising tool to facilitate biomarker detection for early disease diagnosis and disease control. The technique is based on a sandwiched system in which antigen is first captured by a selective plasmonic paper substrate and then labeled by an extrinsic Raman label (ERL), consisting of a 60 nm gold nanoparticle (AuNP) functionalized with a mixed monolayer of detection antibody and 4-nitrobenezenethiol (NBT) as a Raman reporter molecule. Here, we report on the use of AuNP modified filter paper as a novel capture membrane in a vertical flow format. This vertical flow configuration affords reproducible flow of sample and label through the capture substrate to overcome diffusion limited kinetics and significantly reduced assay time. The filter paper was selected due to its affordability and availability, while the embedded AuNPs maximized plasmonic coupling with the ERLs and SERS enhancement. Additionally, the embedded AuNP served as a scaffold to immobilize capture antibody to specifically bind antigen. In this work, a SERS-based rapid vertical flow (SERS-RVF) immunoassay for detection of mouse IgG was developed to establish proof-of-principle. Optimization of assay conditions led to a limit of detection of 3 ng/mL, which is comparable to more traditional formats carried out in multi-well plates, and significantly reduced assay time to less than 2 min. Additionally, IgG was accurately quantified in normal mouse serum to validate the SERS-RVF assay for application to the analysis of biological samples. These results highlight the potential advantages of the SERS-RVF platform for point-of-need testing.