Macroscopic Dissolution Rates Research Articles

Role of Mutual Diffusion in the Dissolution Behavior of One Primary Bulk Gas Nanobubble in Liquid: A Molecular Dynamics Study.

Dissolution of one primary bulk gas nanobubble in an undersaturated liquid constitutes one of the underlying issues of the exceptional stability of bulk gas nanobubble population. In this paper, the mutual diffusion coefficient at the gas-liquid interface of one primary bulk gas nanobubble is investigated via all-atom molecular dynamics simulation, and the applicability of the Epstein-Plesset theory is verified. The mutual diffusion coefficient, different from the self-diffusion coefficient in bulk gas or bulk liquid, is essentially determined by the chemical potential due to its driving role in the mass transfer across the interface. We could ascribe the low-rate dissolution of one primary bulk gas nanobubble in an undersaturated liquid to the slight attenuation of the mutual diffusion coefficient at the interface. The results show that the dissolution process of one primary bulk gas nanobubble in an undersaturated liquid fundamentally obeys the Epstein-Plesset theory and that the macroscopic dissolution rate is intrinsically determined by the gas mutual diffusion coefficient at the interface rather than the self-diffusion coefficient in the bulk phase. The mass transfer viewpoint from the present study might actively promote subsequent studies on the super-stability of bulk gas nanobubble population in liquid.

The Role of pH, Temperature, and NH4+ during Mica Weathering

Phyllosilicates are abundant materials both on Earth and Mars, and the weathering of these minerals is an essential part of a wide variety of geochemical cycles. Alteration mainly takes place at the solution−mineral interface and needs to be fully understood in order to correctly model global water−rock interactions. To directly link the physicochemical solution properties to the dominant surface processes controlling phyllosilicate alteration, we used a custom-built hydrothermal atomic force microscope to study in situ the surface reactivity of biotite, phlogopite, and muscovite in contact with aqueous solutions for a broad range of temperatures and pH values. On the basis of our microscopic observations correlated with previously obtained macroscopic dissolution rates, we have constructed a tentative weathering diagram for mica minerals connecting the dominant surface mechanisms and bulk dissolution behavior to the physicochemical solution properties (pH, T, and speciation). The resulting diagram can be divided into two main areas: low-grade weathering occurring at low temperatures and mildly acidic to neutral pH and highgrade weathering taking place at high temperatures and low pH, separated by a transition zone. Each of these areas is characterized by a series of chemical and physical surface processes, which can be related directly or indirectly to incongruent and congruent bulk dissolution. The transition temperatures and pH values depend on the type of mica, with biotite being the most reactive one and muscovite the least reactive one. It is noteworthy that for close to neutral pH conditions the presence of NH4+ shifts the transitions from low- to high-grade weathering to a significantly lower temperature.

Gypsum Dissolution Rate from Atomic Step Kinetics

The macroscopic dissolution rate of minerals is generally deduced from solution chemistry measurements. A microscopic dissolution rate can also be deduced from the dynamics of molecular events (etch pit growth, atomic step migration, etc.). Both hardly ever agree, even qualitatively, and the elaboration of a general theory linking the kinetics at the two scales is still in progress. We present here microscopic dissolution rates of gypsum, measured by atomic force microscopy (AFM), in quantitative agreement with macroscopic rates. This agreement has been obtained in taking care to neutralize the bias induced by the force applied by the AFM tip on the surface, and to identify clearly the driving molecular mechanism. This result shows that the determination, among the topographic changes during the dissolution of a mineral, of the dominant one, and the measurement of its dynamics, may permit deducing from AFM experiments a reliable macroscopic dissolution rate.

Homogenization of a pore scale model for precipitation and dissolution in porous media

In this article, we employ homogenization techniques to provide a rigorous derivation of the Darcy scale model for precipitation and dissolution in porous media. The starting point is the pore scale model in van Duijn & Pop (2004 ), which is a coupled system of evolution equations, involving a parabolic equation which models ion transport in the fluid phase of a periodic porous medium, coupled to an ordinary differential equations modelling dissolution and precipitation at the grains boundary. The main challenge is in dealing with the dissolution and precipitation rates, which involve a monotone but possibly discontinuous function. In order to pass to the limit in these rate functions at the boundary of the grains, we prove strong two-scale convergence for the concentrations at the microscopic boundary and use refined arguments in order to identify the form of the macroscopic dissolution rate, which is again a discontinuous function. The resulting upscaled model is consistent with the Darcy scale model proposed in Knabner et al . (1995 ).

Kinetic Monte Carlo Approach To Study Carbonate Dissolution

Reactive properties of carbonate minerals and rocks attract a significant attention with regard to modern environmental and industrial problems, including geologic carbon sequestration, toxic waste utilization, cement clinker production, and the fate of carbonate shell-bearing organisms in acidifying oceans. Despite the ultimate importance of the problem, the number of studies connecting atomistic-scale models to experimental observations is limited. In this work we employ the Kinetic Monte Carlo (KMC) approach to model carbonate dissolution at the nanometer–micron scale range and to access quantitative relationships between the variety of surface reactive sites and experimentally observed spatiotemporal rate variance. The presented KMC model adequately reproduces experimentally observed dissolution patterns and rates. We examine mechanistic and quantitative relationships between site reactivity, atomic step velocity, etch pit evolution dynamics, and macroscopic dissolution rates. The analysis of reactive...

Dissolution of ZrO2 based pyrochlores in the acid pH range: A macroscopic and electron microscopy study

The dissolution kinetics of ZrO2–Nd2O3 polycrystalline pyrochlore and defect fluorite ceramic powders under acidic conditions were observed following a combined macroscopic and electron microscopic (SEM) approach. Dynamic dissolution experiments were carried out with a variation of temperature and pH as well as the chemical composition within the ZrO2–Nd2O3 system. SEM observations indicate a preferential leaching at the grain boundaries for all experiments. A preferential release of Nd during the initial stages of dissolution, which is several orders of magnitude higher than the Zr release, was measured by ICP-MS. At steady state, the normalised Nd-rate approaches the Zr based dissolution rate within one order of magnitude, becoming congruent for most experiments. Zr-based BET surface area normalised steady state rates at c(H+)=0.1N and 90°C are in the range between 4×10−7 and 3×10−6gm−2d−1, indicating no significant influence of the transition pyrochlore to defect fluorite and the chemical composition on the macroscopic dissolution rate. Based on the different numbers of grain boundaries per surface area in the pyrochlore compared to the defect fluorite, a slightly higher “true” dissolution rate could be assumed for the defect fluorite. The influence of pH and temperature variations to the dissolution rates of defect fluorite and pyrochlore are similar and in the range observed for other multioxide materials.

Defining and measuring development rates for a stochastic resist: a simulation study

Photoresist development rate can be defined microscopically (the development rate at a point) or macroscopically (the propagation rate of an average resist height). In the presence of stochastic noise, these two rates will be different. In order to properly calibrate lithography simulators, the difference between these two definitions of development rate should be quantified. Using theoretical derivations and a stochastic (Monte Carlo) development simulator, the propagation rate of a resist surface is characterized in the presence of stochastic variation in the resist deprotection concentration and a nonlinear development rate response. The resulting propagation rate (macroscopic development rate) can be more than an order of magnitude higher than for the case of no stochastic noise. Correlation in the development rate creates an effective surface inhibition over a depth into the resist proportional to the correlation length, with results that are qualitatively different for two-dimensional versus three-dimensional simulations. The differences between microscopic and macroscopic dissolution rate can have an important effect on how development rate models should be calibrated, depending on their use in continuum or stochastic lithography simulators.

Linking nm-scale measurements of the anisotropy of silicate surface reactivity to macroscopic dissolution rate laws: New insights based on diopside

The interfacial zone between a bulk fluid and a mineral surface is where all exchange of matter and energy occurs during chemical weathering. However, our knowledge is still limited with respect to understanding where and how the rate-determining dissolution reactions take place. A complicating factor is the commonplace formation of amorphous Si-rich surface layers (ASSLs), which may hinder contact between the fluid and the mineral surface. To address the role of ASSL, we investigated the dissolution of a common silicate (diopside), and related the bulk dissolution rate with the nanoscale dissolution rate and surface chemistry of its individual prevalent faces. While ASSL were evidenced on all of the investigated faces, only those formed on (110) and (11¯0) were passivating, thereby controlling the reactivity of the underlying faces. The (110) and (11¯0) faces intersect the highest density of Mg–O–Si and Fe–O–Si bonds, and this specificity may explain the passivating behavior of the corresponding ASSL. Moreover, we evidenced an inverse relation between aqueous silica concentration and the bulk dissolution rate of crushed diopside grains, which suggest that the (110) and (11¯0) faces are predominant in a powder. By considering ASSL as a separate phase that can control silicate dissolution rates, extrapolated laboratory-based rates at conditions relevant to the field can be lowered by up to several orders of magnitude, thereby decreasing the large gap between laboratory and natural rates. This has important implications for more accurately modeling chemical weathering reactions, so important today for the C cycle and CO2 sequestration.

Holistic approach to dissolution kinetics: linking direction-specific microscopic fluxes, local mass transport effects and global macroscopic rates from gypsum etch pit analysis

Dissolution processes at single crystal surfaces often involve the initial formation and expansion of localized, characteristic (faceted) etch-pits at defects, in an otherwise comparatively unreactive surface. Using natural gypsum single crystal as an example, a simple but powerful morphological analysis of these characteristic etch pit features is proposed that allows important questions concerning dissolution kinetics to be addressed. Significantly, quantitative mass transport associated with reactive microscale interfaces in quiescent solution (well known in the field of electrochemistry at ultramicroelectrodes) allows the relative importance of diffusion compared to surface kinetics to be assessed. Furthermore, because such mass transport rates are high, much faster surface kinetics can be determined than with existing dissolution methods. For the case of gypsum, surface processes are found to dominate the kinetics at early stages of the dissolution process (small etch pits) on the cleaved (010) surface. However, the contribution from mass transport becomes more important with time due to the increased area of the reactive zones and associated decrease in mass transport rate. Significantly, spatial heterogeneities in both surface kinetics and mass transport effects are identified, and the morphology of the characteristic etch features reveal direction-dependent dissolution kinetics that can be quantified. Effective dissolution velocities normal to the main basal (010) face are determined, along with velocities for the movement of [001] and [100] oriented steps. Inert electrolyte enhances dissolution velocities in all directions (salting in), but a striking new observation is that the effect is direction-dependent. Studies of common ion effects reveal that Ca(2+) has a much greater impact in reducing dissolution rates compared to SO(4)(2-). With this approach, the new microscopic observations can be further analysed to obtain macroscopic dissolution rates, which are found to be wholly consistent with previous bulk measurements. The studies are thus important in bridging the gap between microscopic phenomena and macroscopic measurements.

Sphalerite dissolution kinetics at low hydrothermal conditions

A macroscopic (mixed-flow reactor) and microscopic (hydrothermal atomic force microscopy, HAFM) approach was used to quantify sphalerite (ZnS) dissolution rates and to investigate the stoichiometry of dissolution and leached layer formation. HAFM observations of reacted (110) surfaces at room temperature revealed surface roughening which was likely generated by pit formation, local surface swelling or re-deposition of sulphur compounds, as also evidenced by a decreased hardness of the roughened surface. At 125 °C, appearance of hillocks with three-sided facets was observed on the (110) surface, most likely of the forms {111} or { 1 ¯ 1 ¯ 1 ¯ }. On the facets, terraces were separated by steps. At these steps, preferential release of material took place during dissolution and caused the steps to retreat. Macroscopic dissolution rates measured in mixed-flow reactors at pH 2 and 125, 150 and 200 °C are in reasonable agreement with literature data and yielded an apparent activation energy of Zn-release of 96 ± 4 kJ/mol. Elevated dissolution rates were observed during the initial stage of the experiment. The time necessary to attain steady-state ranged from 110 to 250 h. Measured Zn/S concentration ratios in the reactor effluent were at average 1.1 ± 0.1. These ratios do not indicate extensive leached layer formation and agree with HAFM observations that revealed a morphology transition from {110} to {111} or { 1 ¯ 1 ¯ 1 ¯ }. The addition of FeCl 3 to the solution yielded a strong rate increase with an apparent reaction order with respect to Fe 3+(aq) ranging from 0.41 to 0.48.

Effects of the biologically produced polymer alginic acid on macroscopic and microscopic calcite dissolution rates.

Dissolution of carbonate minerals has significant environmental effects. Microorganisms affect carbonate dissolution rates by producing extracellular metabolites, including complex polysaccharides such as alginic acid. Using a combined atomic force microscopy (AFM)/flowthrough reactor apparatus, we investigated the effects of alginic acid on calcite dissolution. Macroscopic dissolution rates, derived from the aqueous metal ion concentrations, are 10(-5.5) mol m(-2) s(-1) for 5 < pH < 12 in the absence of alginic acid compared to 10(-4.8) mol m(-2) s(-1) in its presence. The AFM images demonstrate that alginic acid preferentially attacks the obtuse steps of dissolution pits on the calcite surface. In pure water, the obtuse and acute steps retreat at similar rates, and the pits are nearly isotropic except under highly acidic conditions. In alginic acid, the acute step retreat rate is nearly unchanged in comparison to water, whereas the obtuse step retreat rate increases with decreasing pH values. As a result, the pits remain rhombohedral but propagate faster in the obtuse direction. To explain these observations, we propose that alginic acid preferentially forms dissolution active surface complexes with calcium atoms on the obtuse step, which results in anisotropic ligand-promoted dissolution.

Linear Free Energy Relationships between Dissolution Rates and Molecular Modeling Energies of Rhombohedral Carbonates

Bulk and surface energies are calculated for endmembers of the isostructural rhombohedral carbonate mineral family, including Ca, Cd, Co, Fe, Mg, Mn, Ni, and Zn compositions. The calculations for the bulk agree with the densities, bond distances, bond angles, and lattice enthalpies reported in the literature. The calculated energies also correlate with measured dissolution rates: the lattice energies show a log-linear relationship to the macroscopic dissolution rates at circumneutral pH. Moreover, the energies of ion pairs translated along surface steps are calculated and found to predict experimentally observed microscopic step retreat velocities. Finally, pit formation excess energies decrease with increasing pit size, which is consistent with the nonlinear dissolution kinetics hypothesized for the initial stages of pit formation.

Role of molecular oxygen in the dissolution of siderite and rhodochrosite

The dissolution of siderite (FeCO 3) and rhodochrosite (MnCO 3) under oxic and anoxic conditions is investigated at 298 K. The anoxic dissolution rate of siderite is 10 −8.65 mol m −2 s −1 for 5.5 < pH < 12 and increases as [H +] 0.75 for pH < 5.5. The pH dependence is consistent with parallel proton-promoted and water hydrolysis dissolution pathways. Atomic force microscopy (AFM) reveals a change in pit morphology from rhombohedral pits for pH > 4 to pits elongated at one vertex for pH < 4. Under oxic conditions the dissolution rate decreases to below the detection limit of 10 −10 mol m −2 s −1 for 6.0 < pH < 10.3, and hillock precipitation preferential to steps is observed in concurrent AFM micrographs. X-ray photoelectron spectroscopy (XPS) and thermodynamic analysis identify the precipitate as ferrihydrite. At pH > 10.3, the oxic dissolution rate is as high as 10 −7.5 mol m −2 s −1, which is greater than under the corresponding anoxic conditions. A fast electron transfer reaction between solution O 2 or [Fe 3+(OH) 4] − species and surficial >Fe II hydroxyl groups is hypothesized to explain the dissolution kinetics. AFM micrographs do not show precipitation under these conditions. Anoxic dissolution of rhodochrosite is physically observed as rhombohedral pit expansion for 3.7 < pH < 10.3 and is chemically explained by parallel proton- and water-promoted pathways. The dissolution rate law is 10 −4.93[H +] + 10 −8.45 mol m −2 s −1. For 5.8 < pH < 7.7 under oxic conditions, the AFM micrographs show a tabular precipitate growing by preferential expansion along the a-axis, though the macroscopic dissolution rate is apparently unaffected. For pH > 7.7 under oxic conditions, the dissolution rate decreases from 10 −8.45 to 10 −9.0 mol m −2 s −1. Flattened hillock precipitates grow across the entire surface without apparent morphological influence by the underlying rhodochrosite surface. XPS spectra and thermodynamic calculations implicate the precipitate as bixbyite for 5.8 < pH < 7.7 and MnOOH (possibly feitnkechtite) for pH >7.7.

Surface complexation and dissolution of hematite by C1-C6 dicarboxylic acids at pH = 5.0

Adsorption of organic ligands to the surfaces of minerals is a ubiquitous environmental process that often regulates interfacial aqueous chemistry. In the current work, the infrared spectra of dicarboxylate ligands adsorbed to hematite are collected by attenuated total reflectance (ATR) spectroscopy. For each ligand, spectra are recorded at several concentrations at pH = 5.0. Each series of spectra is analyzed by singular value decomposition constrained to a Langmuir adsorption surface model. Oxalate, malonate, and glutarate form bidentate surface complexation structures, whereas succinate and adipate form monodentate structures. The absence of a linear trend in the qualitative form of the binding structure (e.g., bidentate for n = 0, 1, and 3 and monodentate for n = 2 and 4 where n is the length of the carbon chain between carboxylate groups) is attributed to the variation of strain energies for the geometries of possible surface complexation structures. For the bidentate ligands, a linear relationship between the Langmuir binding constant and the second acidity constant is demonstrated. The ligand-promoted dissolution rates at pH = 5.0 are also determined through batch reactor experiments. For the bidentate surface complexes, the dissolution rate at monolayer ligand surface coverage slows in the order oxalate, glutarate, to malonate. Linear relationships are found between the ligand-promoted dissolution rate constants and both the Langmuir binding constants and the second acidity constants. In contrast, succinate and adipate form monodentate surface structures that dissolve slowly, if at all. In this manner, a connection is established between the macroscopic dissolution rate and the microscopic surface complexation structures.