Sharp Reaction Front Research Articles

Stratiform Host-Rock Replacement via Self-Sustaining Reactions in a Clastic-Dominated (CD-type) Zn Deposit

Abstract Stratiform to stratabound replacement of a mixed siliciclastic-carbonate host rock is a defining characteristic of many sediment-hosted base metal deposits. Mineralized rocks in clastic-dominated (CD-type) Zn-Pb ore deposits, which represent our highest value base metal resources, are generally thin (101 m), laterally extensive (103 m), and stratiform to stratabound in fine-grained siltstone and mudstone facies. At the recently discovered Teena CD-type Zn-Pb deposit (Proterozoic Carpentaria province, Australia), the host rock was undergoing burial diagenesis when altered and mineralized by hydrothermal fluids that moved up to 2 km lateral to the fluid input conduit (growth fault) through intraformational intervals. In much of the deposit, carbonate dissolution was an important reaction permeability control, although significant amounts of mineralization also occur in carbonate-free siliciclastic beds. In this study, transmission electron microscopy (TEM) data has been generated on a drill core sample that preserves a sharp reaction front between mineralized and unmineralized domains of the fine-grained siliciclastic compositional end member (carbonate free). Petrographic and mineralogical data provide evidence that oxidized hydrothermal fluids moved through the protolith via reaction permeability that developed from feldspar dissolution. The nature of reactive fluid flow was determined by reactions that took place at the fluid-mineral interface. Pyrite formation during the earliest stage of the hydrothermal paragenesis increased the mineral reactive surface area in the protolith. Acidity was then generated in situ via self-sustaining reactions involving pyrite oxidation, transient Fe sulfate formation, and sphalerite precipitation, which provided positive feedbacks to enhance porosity creation and further fluid infiltration and mineralization. In the absence of carbonate, however, ore fluid pH was buffered by K-feldspar dissolution (~4.5), thereby ensuring sphalerite precipitation was not inhibited under more acidic conditions. All CD-type deposits in the Carpentaria province are hosted by a protolith comprising carbonate, K-feldspar, pyrite, and organic matter; these phases set the boundary conditions for the development of self-sustaining reactions during ore formation. Importantly, these self-sustaining reactions represent a Goldilocks zone for ore formation that is applicable to other sediment-hosted deposits that formed via replacement of mixed siliciclastic-carbonate host rocks (e.g., stratiform Cu).

Diffusion-controlled annihilation A+B→0: Coalescence, fragmentation, and collapse of nonidentical A-particle islands submerged in the B-particle sea.

We present a systematic analysis of diffusion-controlled interaction and collapse of two nonidentical spatially separated d-dimensional A-particle islands in the B-particle sea at propagation of the sharp reaction front A+B→0 at equal species diffusivities. We show that at a sufficiently large initial distance between the centers of islands 2ℓ and a relatively large initial ratio of island-to-sea concentrations, the evolution dynamics of the island-sea-island system demonstrates remarkable universality and, depending on the system dimension, is determined unambiguously by two dimensionless parameters Λ=N_{0}^{+}/N_{Ω} and q=N_{0}^{-}/N_{0}^{+}, where N_{0}^{+} and N_{0}^{-} are the initial particle numbers in the larger and smaller of the islands, respectively, and N_{Ω} is the initial number of sea particles in the volume Ω=(2ℓ)^{d}. We find that at each fixed 0<q≤1, there are threshold values Λ_{★}(q) and Λ_{s}(q)≥Λ_{★}(q) that depend on the dimension and separate the domains of individual death of each of the islands Λ<Λ_{★}(q), coalescence and subsequent fragmentation (division) of a two-centered island Λ_{★}(q)<Λ<Λ_{s}(q), and collapse of a single-centered island formed by coalescence Λ>Λ_{s}(q). We demonstrate that regardless of d, the trajectories of the island centers are determined unambiguously by the parameter q, and we reveal a detailed picture of the evolution of islands and front trajectories with an increase in Λ, focusing on the scaling laws of evolution at the final collapse stage and in the vicinity of starting coalescence and fragmentation points.

Rate limitations of nano-scale weathering front advance in the slow-eroding Sri Lankan Highlands

In the Sri Lankan Highlands denudation and chemical weathering represent the low-end member in global weathering rates. Here we report on the causes for these low rates in corestones from a highly weathered saprolite profile. By using electron microprobe and transmission electron microscopy (TEM) analyses, we investigated weathering reactions, and derived rates of pyroxene and biotite oxidation. High-resolution TEM analyses on primary minerals showed that the initial weathering products are non-crystalline and that these form the precursors of secondary minerals (kaolinite and smectite). The dissolution of primary minerals is characterised by sharp reaction fronts in the absence of chemical gradients, hence, dissolution can best be described by a dissolution – reprecipitation process. The first observable weathering reaction is the oxidation of structural Fe(II) in pyroxene and biotite. This oxidation is restricted to distinct zones within the minerals without the formation of oxidized layers. While the oxidation is not accompanied by chemical changes, the oxidation of structural Fe(II) in biotite may cause lattice distortion. Pyroxene and biotite oxidation rates were calculated at the corestone-scale by using the gradient of bulk rock Fe(II)/Fetotal ratios, assuming that oxidation is coupled to the weathering front advance rate. At the mineral-scale, oxidation rates were calculated by using gradients of in situ Fe(II)/Fe(III) ratios measured with electron energy-loss spectroscopy (EELS) within the minerals assuming a coupled oxidation-cation diffusion process. The mineral-scale oxidation rates are significantly higher, log Ominin situ = −11 molmin m−2 s−1, than corestone-scale oxidation rates, log Omin = −13 to −15 mol m−2 s−1. We explain the difference to result from the fact that corestone-scale rates average the oxidation over the entire mineral surface. Because at the corestone-scale pyroxene oxidation rates are also similar to dissolution rates, we infer that oxidation preconditions Fe(II)- bearing primary silicate minerals to weathering. However, although oxidation is initiating chemical weathering in this setting and is limited by the supply of O2, overall conversion of bedrock to saprolite is driven by the formation of porosity by fracture formation during this reaction, which allows for fluid transport and subsequent plagioclase weathering. We conclude that in compact bedrock nm- to µm-scale fracture- and porosity generation are the processes that drive weathering in tectonically quiescent regions. They are also the processes at depth that couple the weathering zone with processes at its surface. Finally, the formation of secondary surface layers at the nm-scale is essential in controlling the equilibrium in the local weathering environment and hence mineral dissolution. These layers are likely also those that control isotope fractionation in the weathering zone.

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.

The hydrothermal alkaline alteration of potassium feldspar: A nanometer-scale investigation of the orthoclase interface

Potassium feldspars (KAlSi3O8) are ubiquitous minerals in the Earth's upper crust. This family of minerals has been the subject of numerous experimental and theoretical investigations concerning their dissolution kinetics and the mechanisms controlling chemical alteration at acid and neutral pH, and at temperatures ranging from ambient to hydrothermal conditions. On the other hand, considerably less research on the dissolution behavior of K-feldspars has been carried out at alkaline conditions, in particular at pH > 9 and elevated temperatures. Filling in this gap in knowledge is the major motivation for this study. More specifically, we wanted to document and understand how the K-feldspar interface structurally and chemically evolves during alteration in order to determine the mechanism of dissolution. In this study we examined interfaces of orthoclase samples that were altered in separate experiments in a Ca(OH)2-H2O solution (pH25°C 12.4) at 190 °C for 24 h. We used a combination of focused ion beam (FIB) milling and advanced analytical transmission electron microscopy (TEM) techniques to investigate the structure and chemistry of the near surface region of post-reaction grains, with particular attention being given to the fluid-solid interface. Even though each grain diminishes in volume due to dissolution, high-resolution TEM imaging indicates that the feldspar structure itself remains completely intact and crystalline, as evidenced by lattice fringes that abruptly terminate at the grain edge. Nanometer-scale chemical composition measurements and mapping by TEM-EDXS (energy dispersive X-ray spectroscopy) and EFTEM (energy filtered TEM) show that the chemistry of the parent feldspar also remains unchanged at the interface. In particular, there is no evidence for the incursion of Ca from the fluid solvent into the structure, either by interdiffusion or by a replacement process. Taken together, the TEM observations point to a sharp chemical reaction front characterized by the congruent (i.e. stoichiometric) release of all elements from the feldspar structure.Nanometer-scale measurements by high resolution analytical TEM also reveal that a surface alteration layer (SAL) of amorphous material forms in situ at the expense of the feldspar structure. The interface demarcates a spatially coincident and nm-sharp chemical and structural discontinuity between the parent feldspar and the amorphous phase. The amorphous SAL has a variable thickness, from under 10 nm up to ~200 nm. This is likely one of the first observed occurrences of a significant surface amorphous layer on feldspar due to alteration in an alkaline solvent. The lack of a gap between the two phases points to an interfacial dissolution-reprecipitation process that continuously operates during hydrothermal alteration, and mostly likely right from the onset of contact with the fluid. After the initial formation of the amorphous layer, a 1–2 μm-thick porous amalgam of secondary crystalline phases comprised of calcite, tobermorite, and hydrogrossular, as well as other minor phases, precipitated over the SAL. These authigenic crystalline minerals formed during the experiment (hydrothermal alteration, followed by fluid loss due to evaporation) by a classical thermodynamically-controlled precipitation process as the reactor bulk fluid became increasingly concentrated.We propose that a coupled interfacial dissolution-reprecipitation (CIDR) mechanism best explains the chemical and structural properties of the interface and the formation of an amorphous surface layer. In fact, many recent studies postulate that a CIDR process controls feldspar dissolution and the formation of SALs at acid and circumneutral pH over a wide range of temperatures. Combining these previous results with our new observations supports the idea that a unique and unifying mechanism likely controls chemical alteration of feldspars in all aqueous fluids.

Diffusion-controlled coalescence, fragmentation, and collapse of d-dimensional A-particle islands in the B-particle sea.

We present a systematic analysis of diffusion-controlled interaction and collapse of two identical spatially separated d-dimensional A-particle islands in the B-particle sea at propagation of the sharp reaction front A+B→0 at equal species diffusivities. We show that at a sufficiently large initial distance between the centers of islands 2ℓ compared to their characteristic initial size and a relatively large initial ratio of island to sea concentrations, the evolution dynamics of the island-sea-island system is determined unambiguously by the dimensionless parameter Λ=N_{0}/N_{Ω}, where N_{0} is the initial particle number in the island and N_{Ω} is the initial number of sea particles in the volume Ω=(2ℓ)^{d}. It is established that (a) there is a d-dependent critical value Λ_{★} above which island coalescence occurs; (b) regardless of d the centers of each of the islands move toward each other along a universal trajectory merging in a united center at the d-dependent critical value Λ_{s}≥Λ_{★}; (c) in one-dimensional systems Λ_{★}=Λ_{s}, therefore, at Λ<Λ_{★} each of the islands dies individually, whereas at Λ>Λ_{★} coalescence is completed by collapse of a single-centered island in the system center; (d) in two- and three-dimensional systems in the range Λ_{★}<Λ<Λ_{s} coalescence is accompanied by subsequent fragmentation of a two-centered island and is completed by individual collapse of each of the islands. We discuss a detailed picture of coalescence, fragmentation, and collapse of islands focusing on evolution of their shape and on behavior of the relative width of the reaction front at the final collapse stage and in the vicinity of starting coalescence and fragmentation points. We demonstrate that in a wide range of parameters, the front remains sharp up to a narrow vicinity of the coalescence, fragmentation, and collapse points.

Numerical investigations of a continuous thermochemical heat storage reactor

Abstract Thermochemical systems are a good alternative to current technologies for long-term heat storage, since the energy is stored as a chemical potential and there is no heat loss during the storage phase. A large number of studies have now been conducted on the development of integrated thermochemical reactors, but fewer studies have investigated separate reactor technologies. The latter present the advantage of dissociating the thermal power and storage capacity of the system, which also increases the energy storage density of the process. This paper investigates the functioning of an open continuous thermochemical reactor with falling solid flow and humid air cross-flow. A 2D model was developed and set up with the finite element simulation software COMSOL Multiphysics to represent heat and mass transfer phenomena in the reactor. This study focuses on the influence of the inlet pressure and vapour fraction of the air on the reaction behaviour and the reactor performance (power, temperature). This study also investigates the influence of the reaction front on the pressure drop in the reactor. It highlights the presence of a sharp reaction front between one part of the reactor (bottom) where the solid is completely hydrated and the other part (top) where the solid has not reacted yet. This sharp front is strongly dependent on the inlet air conditions. Also, there is an inertia phenomenon at the entrance of the unreacted solid, which is influenced by inlet air pressure, creating a particular air velocity field.

Partial dissolution of carbonate rock grains during reactive CO2-saturated brine injection under reservoir conditions

One of the major concerns of carbon capture and storage (CCS) projects is the prediction of the long-term storage security of injected CO2. When injected underground in saline aquifers or depleted oil and gas fields, CO2 mixes with the resident brine to form carbonic acid. The carbonic acid can react with the host carbonate rock, and alter the rock structure and flow properties. In this study, we have used X-ray micro-tomography and focused ion beam scanning electron microscopy (FIB-SEM) techniques to investigate the dissolution behavior in wettability-altered carbonate rocks at the nm- to µm-scale, to investigate CO2 storage in depleted oil fields that have oil-wet or mixed-wet conditions. Our novel procedure of injecting oil after reactive transport has revealed previously unidentified (ghost) regions of partially-dissolved rock grains that were difficult to identify in X-ray tomographic images after dissolution from single fluid phase experiments. We show that these ghost regions have a significantly higher porosity and pore sizes that are an order of magnitude larger than that of unreacted grains. The average thickness of the ghost regions as well as the overall rock dissolution decreases with increasing distance from the injection point. During dissolution micro-porous rock retains much of its original fabric. This suggests that considering the solid part of these ghost regions as macro (bulk) pore space can result in the overestimation of porosity and permeability predicted from segmented X-ray tomographic images, or indeed from reactive transport models that assume a uniform, sharp reaction front at the grain surface.

Combined effects of soot load and catalyst activity on the regeneration dynamics of catalytic diesel particulate filters

The combined effects of soot load and catalyst activity on the regeneration dynamics of a catalytic diesel particulate filter have been investigated through transient CFD‐based simulations of soot combustion in a single‐channel configuration. The soot load was changed by varying the amount of soot accumulated as cake layer, while keeping the amount of soot trapped inside the catalytic wall constant. Substantially uniform soot combustion that allows reasonably fast regeneration of the filter under controlled temperature conditions has been simulated only in the absence of cake and at relatively low catalyst activity. Conversely, in the presence of cake, numerical predictions have shown that, regardless of both soot load and catalyst activity, fast regeneration always occurs by propagation of sharp reaction fronts that result in high temperature rises. These findings highlight the importance of avoiding the cake formation, while properly optimizing the catalyst activity, to conduct a safe and effective regeneration of catalytic filters. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1714–1722, 2018

Use of Kissa Software for Accurate Simulation of Electrochemical Problems of Any Compexity

KISSA-software (for 1D and 2D electrode geometry) developed in our group, provides a general framework to treat electrochemical problems (by providing mechanism, rate constant, diffusion coefficients etc.) of any complexity in a user-friendly environment and returns the simulations results without any intervention into numerical part from the user side [1]. The accuracy of the numerical solution is guaranteed in KISSA by employment of a non-uniform and adaptive grid. The latter is constructed on the basis of a kinetic criterion (rather than on a gradient-based one as in other programs) and provides a high dynamic resolution at the acute reaction fronts which are automatically detected and followed by the program [2-5]. The efficiency of this strategy was proved by addressing such sophisticated problems as i) simulation of reaction mechanisms leading to the emission of electrochemiluminescence (ECL) and ii) including the reactive dynamic adsorption. In this context considered ECL systems [6,7] are representative example of systems possessing extremely sharp reaction fronts since some reaction constants are close to the diffusion limit (either cation/anion radicals annihilation reactions or luminophor/co-reactant reaction). More precisely, for the ECL co-reactant system, such as alkyl amines / transition metal(II) complexes, it was shown via simulations with KISSA that changes in ECL intensities emitted by these systems are much more dependent on the relative diffusivities of the two co-reactants than on the range of thermodynamic and kinetic rate constants that are possible to explore and vary. Second example is the competitive reactive adsorption is also involved as an important class of problems covered by KISSA [8-10]. A couple examples of real data imported to KISSA for comparison to simulations for elucidation of mechanism and determination of the parameters are presented.

Diffusion-controlled formation and collapse of a d-dimensional A-particle island in the B-particle sea.

We consider diffusion-controlled evolution of a d-dimensional A-particle island in the B-particle sea at propagation of the sharp reaction front A+B→0 at equal species diffusivities. The A-particle island is formed by a localized (point) A-source with a strength λ that acts for a finite time T. We reveal the conditions under which the island collapse time t_{c} becomes much longer than the injection period T (long-living island) and demonstrate that regardless of d the evolution of the long-living island radius r_{f}(t) is described by the universal law ζ_{f}=r_{f}/r_{f}^{M}=sqrt[eτ|lnτ|], where τ=t/t_{c} and r_{f}^{M} is the maximal island expansion radius at the front turning point t_{M}=t_{c}/e. We find that in the long-living island regime the ratio t_{c}/T changes with the increase of the injection period T by the law ∝(λ^{2}T^{2-d})^{1/d}, i.e., increases with the increase of T in the one-dimensional (1D) case, does not change with the increase of T in the 2D case and decreases with the increase of T in the 3D case. We derive the scaling laws for particles death in the long-living island and determine the limits of their applicability. We demonstrate also that these laws describe asymptotically the evolution of the d-dimensional spherical island with a uniform initial particle distribution generalizing the results obtained earlier for the quasi-one-dimensional geometry. As striking results, we present a systematic analysis of the front relative width evolution for fluctuation, logarithmically modified, and mean-field regimes, and we demonstrate that in a wide range of parameters the front remains sharp up to a narrow vicinity of the collapse point.

Oxidative dissolution under the channel leads geomorphological evolution at the Shale Hills catchment

The hydrologic connectivity between hillslopes and streams impacts the geomorphological evolution of catchments. Here, we propose a conceptual model for hydrogeomorphological evolution of the Susquehanna Shale Hills Critical Zone Observatory (SSHCZO), a first-order catchment developed on shale in central Pennsylvania, U.S.A. At SSHCZO, the majority of available water (the difference between incoming meteoric water and outgoing evapotranspiration) flows laterally to the catchment outlet as interflow, while the rest is transported by regional groundwater flow. Interflow, shallow hillslope flow, is limited to the upper 5 to 8 m of highly fractured bedrock, thought to have formed during periglacial conditions in the late Pleistocene. In contrast, groundwater flowpaths are influenced by the primary permeability of the varying stratigraphic units. Both flowpaths respond to weathering-related secondary permeability. O2-rich interflow mixes with deep O2-poor groundwater under the catchment outlet at depths of 5–8 m. Penetration of this oxygenated interflow under the valley results in pyrite oxidation, release of sulfuric acid, dissolution of minerals, and weakening of bedrock. This is hypothesized to enhance channel incision and, in turn, to promote drainage of deep groundwater from the ridges. Drainage subsequently lowers the catchment water table, advancing the cascade of reactions that produce regolith. Weathering in the catchment is characterized by both sharp and diffuse reaction fronts. Relatively sharp fronts (pyrite, carbonate) mark where vertical, unsaturated flow changes to horizontal, saturated flow, while diffuse fronts (illite, chlorite, feldspar) mark where flow is largely vertical and unsaturated. According to this model, catchment morphology reflects subsurface pyrite reactions due to mixing of interflow and groundwater flow under the valley floor that ultimately results in clay weathering and regolith production nearer the land surface.

A similarity solution for reaction front propagation in a fracture-matrix system.

We propose a new composite similarity variable, based on which a similarity solution is derived for reaction front propagation in fracture-matrix systems. The similarity solution neglects diffusion/dispersion within the fracture and assumes the existence of a sharp reaction front in the rock matrix. The reaction front location in the rock matrix is shown to follow a linear decrease with distance along the fracture. The reaction front propagation along the fracture is shown to scale like diffusion (i.e. as the square root of time). The similarity solution using the composite similarity variable appears to be applicable to a broad class of reactive transport problems involving mineral reactions in fracture-matrix systems. It also reproduces the solutions for non-reactive solute and heat transport when diffusion/dispersion/conduction are neglected in the fracture. We compared our similarity solution against numerical simulations for nonlinear reactive transport of an aqueous species with a mineral in the rock matrix. The similarity solutions agree very well with the numerical solutions, especially at later times when diffusion limitations are more pronounced.This article is part of the themed issue 'Energy and the subsurface'.

Removal of hydrogen sulfide by permanganate based sorbents: Experimental investigation and reactor modeling

The removal of hydrogen sulfide from ambient air can be accomplished by porous adsorbents, which are impregnated with potassium permanganate. In this study such adsorbents were prepared by granulation on a pelletizing disk and characterized in breakthrough measurements with hydrogen sulfide. In these experiments different reaction times, pellet sizes, inlet concentrations and residence times were analyzed. To investigate the reaction process inside the pellet, microscopic analyses and REM/EDX element scans of reacted particles after different reaction times were performed. These results indicate that the reaction mainly proceeds at a rather sharp reaction front. As a first approach the shrinking core model was applied for the description of the breakthrough curves, showing already a good agreement with the experimental results. Additionally a volume reaction model was developed, which considers two consecutive reactions occurring in the whole particle volume. In contrast to the shrinking core model, the volume reaction model allows for describing the decrease of the measured position of the reaction zone in good agreement with the optical and elemental analyses of the reacted adsorbent pellets.

Phase-field model for the two-phase lithiation of silicon

As an ideal anode material, silicon has the highest lithium-ion capacity in theory, but the broader application is limited by the huge volumetric strain caused by lithium insertion and extraction. To better understand the physical process and to resolve the related reliability issue, enormous efforts have been made. Recent experiments observed sharp reaction fronts in both crystalline and amorphous silicon during the first lithiation half-cycle. Such a concentration profile indicates that the process is likely to be reaction limited. Based on this postulation, a phase-field model is developed and implemented into a finite-element code to simulate the coupled large inelastic deformation and motion of the reaction front in a silicon electrode. In contrast to most existing models, the model treats both volumetric and deviatoric inelastic deformation in silicon as a direct consequence of the lithiation at the reaction front. The amount of deviatoric deformation is determined by using the recently developed kinetic model of stress-induced anisotropic reaction. By considering the role of stress in the lithiation process, this model successfully recovers the self-limiting phenomenon of silicon electrodes, and relates it to the local geometry of electrodes. The model is also used to evaluate the energy-release rate of the surface crack on a spherical electrode, and the result suggests a critical size of silicon nanoparticles to avert fracture. As examples, the morphology evolution of a silicon disk and a Si nanowire during lithiation are also investigated.

KISSA® : A General User-Friendly Software for Accurate Investigation of Electrochemical Mechanism of Any Complexity

Electrochemical measurements involve a vast gamme of phenomena ranging from different types of mass-transport to all kinds of surface and bulk reactivity. The coupling of these phenomena creates very often multiscale problems, in the sense that multiple and completely different time and length scales participate simultaneously in governing an electrochemical response. Accurate treatment of the various and simultaneously acting scales is one of the main difficulties in simulations of electrochemical problems. KISSA®, a software developed in our group, provides a general framework to treat such kind of situations. It requires from a user only to set up an electrochemical problem (by providing mechanism, rate constant, diffusion coefficients etc.) in a user-friendly environment and returns the simulations results without any intervention into numerical part from the user side. The accuracy of the numerical solution is guaranteed in KISSA® by employment of a non-uniform and adaptive grid. The latter is constructed on the basis of a kinetic criterion (rather than on a gradient-based one as in other programs) and provides a high dynamic resolution at the acute reaction fronts which are automatically detected and followed by the program [1-5]. The efficiency of this strategy was proved by addressing such sophisticated problems like electropolymerization [5], competitive adsorption of the benzyl halides at silver electrodes [6], electrogenerated chemiluminescence (ECL) [7, 8] etc. In this context ECL systems are representative example of systems possessing extremely sharp reaction fronts since some reaction constants are close to the diffusion limit (either cation/anion radicals annihilation reactions or luminophor/co-reactant reaction). More precisely, for the ECL co-reactant system, such as alkyl amines / transition metal(II) complexes, it was shown via simulations with KISSA® that changes in ECL intensities emitted by these systems are much more dependent on the relative diffusivities of the two co-reactants than on the range of thermodynamic and kinetic rate constants that are possible to explore and vary. In particular, it establishes that decreasing the diffusion coefficients of the metal complexes species (e.g., by adequate redox or photochemically inert large substituents or by anchoring them to the electrode surface) vs. that of the amine co-reactant leads to a great enhancement of the ECL intensity of the first ECL wave, viz., that observed at the level of the amine oxidation peak. Though investigated using simulations based on the thermodynamic and kinetic constants of the most common tri-n-propylamine (TPrA) / Ru(bpy)3 2+ system, this work conclusions are more general [8]. Competitive adsorbtion is also involved as an important class of problems covered by KISSA® software [5, 6, 9]. Thanks to this functionality (as well as previous collaborative SERS and DFT studies [10, 11]) we were able to rationalize behaviour of benzyl halides at silver electrodes, i.e. explain a drastic shift of 0.5 V to more positive potentials of the reduction wave. Indeed, the cyclic voltammetry (CV) at slow scan rates reveal currents behaving as being apparently under diffusion control. However fast scan CVs showed clear involvement of a pre-adsorbtion of the benzyl chloride and its reduction intermediates prior to or after the first electron transfer (see Fig. 1). Simulations with KISSA® allowed a complete and rigorous reconstruction of the pathways undergone by benzyl chloride and establishing the exceptional catalytic properties of silver cathodes [6]. References C. Amatore, O. Klymenko, I. Svir, Electrochem. Commun., 12, 1170-1173 (2010).C. Amatore, O. Klymenko, I. Svir, Electrochem. Commun., 12, 1165-1169 (2010).O. V. Klymenko, I. Svir, A. I. Oleinick, C. Amatore, ChemPhysChem, 13, 845-859 (2012).C. Amatore, O. Klymenko, I. Svir, Anal. Chem., 84, 2792-2798 (2012).O. V. Klymenko, I. Svir, C. Amatore, J. Electroanal. Chem., 688, 320-327 (2013).O.V. Klymenko, O. Buriez, E. Labbé, D.-P. Zhan, S. Rondinini, Z.-Q. Tian, I. Svir, C. Amatore, ChemElectroChem, 1, 227-240 (2014).O.V. Klymenko, I. Svir, C. Amatore, ChemPhysChem, 14, 2237-2250 (2013).I. Svir, A. Oleinick, O.V. Klymenko, C. Amatore, ChemElectroChem, 2, 811-818 (2015).O. Klymenko, I. Svir, C. Amatore, Mol. Phys., 112, 1273-1283 (2014).A. Wang, Y.-F. Huang, U. K. Sur, D.-Y. Wu, B. Ren, S. Rondinini, C. Amatore, Z.-Q. Tian, J. Am. Chem. Soc., 132, 9534-9536 (2010).Y.-F. Huang, D. Y. Wu, A. Wang, B. Ren, S. Rondinini, Z.-Q. Tian, C. Amatore, J. Am. Chem. Soc., 132, 17199-17210 (2010). Figure 1. (Left) Experimental (black) and simulated current (red) for the reduction of PhCH2Cl at Ag electrode (diam. 2 mm), v = 300 V/s. Green curve corresponds to the reduction PhCH2Cl at GCE (diam. 1 mm) and scaled to the ratio of electrode surface areas. (Right) Decomposition of the simulated current to the Faradaic and adsorbtion components. Figure 1

Stress-modulated driving force for lithiation reaction in hollow nano-anodes

Lithiation of a crystalline silicon anode proceeds by the movement of an atomically sharp reaction front that separates a pristine crystalline phase and a fully-lithiated amorphous phase. The velocity of the reaction front is limited rather by the reaction rate at the lithiation front than by the diffusivity of lithium ions in the amorphous lithiated phase. Experiments on solid nanoparticle/nanowire silicon anodes show an initial rapid advancing of reaction front at the initial stage of lithiation, followed by an apparent slowing or even halting of the reaction front propagation. Lithiation-induced stresses during lithiation are attributed to alter the driving force of lithiation and thus result in the observed slowing of reaction front. Recent experiments on lithiation of hollow silicon nanowires reveals similar slowing of reaction front, however, quantitative study of the effect of lithiation-associated stress on the driving force of lithiation still lacks so far. Here, through chemo-mechanical modeling and theoretical formulation, we present a comprehensive study on lithiation-induced stress field and its contribution to the driving force of lithiation reaction in hollow silicon nanowire anodes. We show that hollow silicon nano-anodes could be fully lithiated with lower stress-induced energy barrier than solid silicon nano-anodes. As a result, it is expected that the hollow nanowires and nanoparticles may serve as an optimal structural design for high-performance anodes of lithium-ion batteries. Results from the present study shed light on a number of open questions of lithiation kinetics of silicon-based anodes in recent literature and offer insight on developing silicon-based anodes with high charging capacity and high charging rate.

Reaction‐driven fracturing of porous rock

AbstractA 2‐D computer model has been developed to investigate fluid‐mediated transformation processes such as chemical weathering, mineral carbonation, and serpentinization that require transport of H2O and/or CO2 into reacting rock volumes. Hydration and carbonation cause local volume expansion, and the resulting nonuniform stresses may drive fracturing, which increases both the rate of transport and the accessible reactive surface area in the system and thus accelerates the rate of the transformation process. The model couples reactions, fracturing, and fluid transport for systems with a range of initial porosities, assumed constant throughout the process. With low initial porosity, a sharp reaction front between completely reacted material and unreacted material propagates into unaltered rock, while for high porosities, diffuse reaction fronts are formed in which a large fraction of the initial volume is partly reacted. When diffusive transport is rate limiting, the total reaction rate depends on porosity to a power N, where N is in the range 0.45–2. The exponent N increases as the reaction‐generated expansion decreases. In high‐porosity rocks, the total reaction rate is limited by reaction kinetics, and it is thus insensitive to porosity variations. As the volume increasing reaction proceeds, fracturing divides the unreacted porous material into subdomains, which may undergo further subdivision as they are consumed by the reaction. The total reaction rate and progress depend on the initial geometry of a reacting domain, and this significantly affects the weathering profiles for systems that evolve from an initial assembly of blocks with different sizes and shapes.

Fracture initiation during volume increasing reactions in rocks and applications for CO2 sequestration

Volume increasing processes in rocks can induce various types of fractures, such as hierarchical domain division of the unreacted material and spalling of the reacted material. The mechanism responsible for the selection of a particular fracture type is generally not known. We study such deformations and fracture mechanisms in a simplified system with a range of numerical techniques, and find that sharpness of reaction fronts and magnitude of volume increase are the main parameters controlling which fracture type forms. Spalling dominates when there is sharp reaction fronts and large magnitude of volume change, otherwise, we get mainly domain dividing fractures. Increasing reaction front sharpness and magnitude of volume change also increases the fracture density, and we argue that the change in fracture density can be important for the viability of in situ CO2 sequestration in ultramafic rock.

Stability of reaction-fronts in porous media

The stability of reaction-fronts in porous media is studied with analytical and numerical methods. A stability criterion has been derived using linear stability analysis assuming a sharp font. The sharp front assumption is an approximation of the mathematical model in the limit of an infinite rapid reaction. The criterion shows that the stability of a sharp reaction front is dependent on the permeability that develops behind it. The sharp front is unstable for perturbations of any wave-length if the permeability increases behind the front. The criterion shows that short wave-length perturbations are more unstable than long wave-length perturbations. The sharp front is labile when the permeabilities are the same at both sides of the front. This means that the perturbed front moves unchanged forward. Finally, perturbations will die out in case the permeability decreases behind the sharp front. The stability of non-sharp fronts are simulated numerically when dissolution is by first order kinetics, the transport is by convection and diffusion and when the permeability and specific reactive surface depends on the porosity. The numerical experiments behave according to the stability criterion.