Storage and Distribution of Organic Carbon and Nutrients in Acidic Soils Developed on Sulfidic Sediments: The Roles of Reactive Iron and Macropores.

In a boreal acidic sulfate-rich subsoil (pH 3-4) developing on sulfidic and organic-rich sediments over the past 70 years, extensive brownish-to-yellowish layers have formed on macropores. Our data reveal that these layers ("macropore surfaces") are strongly enriched in 1 M HCl-extractable reactive iron (2-7% dry weight), largely bound to schwertmannite and 2-line ferrihydrite. These reactive iron phases trap large pools of labile organic matter (OM) and HCl-extractable phosphorus, possibly derived from the cultivated layer. Within soil aggregates, the OM is of a different nature from that on the macropore surfaces but similar to that in the underlying sulfidic sediments (C-horizon). This provides evidence that the sedimentary OM in the bulk subsoil has been largely preserved without significant decomposition and/or fractionation, likely due to physiochemical stabilization by the reactive iron phases that also existed abundantly within the aggregates. These findings not only highlight the important yet underappreciated roles of iron oxyhydroxysulfates in OM/nutrient storage and distribution in acidic sulfate-rich and other similar environments but also suggest that boreal acidic sulfate-rich subsoils and other similar soil systems (existing widely on coastal plains worldwide and being increasingly formed in thawing permafrost) may act as global sinks for OM and nutrients in the short run.

Nalidixic Acid and Fe(II)/Cu(II) Coadsorption at Goethite and Akaganéite Surfaces.

Interactions between aqueous Fe(II) and solid Fe(III) oxy(hydr)oxide surfaces play determining roles in the fate of organic contaminants in nature. In this study, the adsorption of nalidixic acid (NA), a representative redox-inactive quinolone antibiotic, on synthetic goethite (α-FeOOH) and akaganéite (ß-FeOOH) was examined under varying conditions of pH and cation type and concentration, by means of adsorption experiments, attenuated total reflectance-Fourier transform infrared spectroscopy, surface complexation modeling (SCM), and powder X-ray diffraction. Batch adsorption experiments showed that Fe(II) had marginal effects on NA adsorption onto akaganéite but enhanced NA adsorption on goethite. This enhancement is attributed to the formation of goethite-Fe(II)-NA ternary complexes, without the need for heterogeneous Fe(II)-Fe(III) electron transfer at low Fe(II) loadings (2 Fe/nm2), as confirmed by SCM. However, higher Fe(II) loadings required a goethite-magnetite composite in the SCM to explain Fe(II)-driven recrystallization and its impact on NA binding. The use of a surface ternary complex by SCM was supported further in experiments involving Cu(II), a prevalent environmental metal incapable of transforming Fe(III) oxy(hydr)oxides, which was observed to enhance NA loadings on goethite. However, Cu(II)-NA aqueous complexation and potential Cu(OH)2 precipitates counteracted the formation of ternary surface complexes, leading to decreased NA loadings on akaganéite. These results have direct implications for the fate of organic contaminants, especially those at oxic-anoxic boundaries.

CO2 Mineralization by MgO Nanocubes in Nanometric Water Films.

Water films formed by the adhesion and condensation of air moisture on minerals can trigger the formation of secondary minerals of great importance to nature and technology. Magnesium carbonate growth on Mg-bearing minerals is not only of great interest for CO2 capture under enhanced weathering scenarios but is also a prime system for advancing key ideas on mineral formation under nanoconfinement. To help advance ideas on water film-mediated CO2 capture, we tracked the growth of amorphous magnesium carbonate (AMC) on MgO nanocubes exposed to moist CO2 gas. AMC was identified by its characteristic vibrational spectral signature and by its lack of long-range structure by X-ray diffraction. We find that AMC (MgCO3·2.3-2.5H2O) grew in sub-monolayer (ML) to 4 ML thick water films, with formation rates and yields scaling with humidity. AMC growth was however slowed down as AMC nanocoatings blocked water films access to the reactive MgO core. Films could however be partially dissolved by exposure to thicker water films, driving AMC growth for several more hours until nanocoatings blocked the reactions again. These findings shed new light on a potentially important bottleneck for the efficient mineralization of CO2 using MgO-bearing products. Notably, this study shows how variations in the air humidity affect CO2 capture by controlling water film coverages on reactive minerals. This process is also of great interest in the study of mineral growth in nanometrically thick water films.

Water Film-Driven Brucite Nanosheet Growth and Stacking.

Thin water films that form by the adhesion and condensation of air moisture on minerals can initiate phase transformation reactions with broad implications in nature and technology. We here show important effects of water film coverages on reaction rates and products during the transformation of periclase (MgO) nanocubes to brucite [Mg(OH)2] nanosheets. Using vibrational spectroscopy, we found that the first minutes to hours of Mg(OH)2 growth followed first-order kinetics, with rates scaling with water loadings. Growth was tightly linked to periclase surface hydration and to the formation of a brucite precursor solid, akin to poorly stacked/dislocated nanosheets. These nanosheets were the predominant forms of Mg(OH)2 growth in the 2D-like hydration environments of sub-monolayer water films, which formed below ∼50% relative humidity (RH). From molecular simulations, we infer that reactions may have been facilitated near surface defects where sub-monolayer films preferentially accumulated. In contrast, the 3D-like hydration environment of multilayered water films promoted brucite nanoparticle formation by enhancing Mg(OH)2 nanosheet growth and stacking rates and yields. From the structural similarity of periclase and brucite to other metal (hydr)oxide minerals, this concept of contrasting nanosheet growth should even be applicable for explaining water film-driven mineralogical transformations on other related nanominerals.

Temperature-resolved nanoscale hydration of a layered manganese oxide.

Water films captured in the interlayer region of birnessite (MnO2) nanosheets can play important roles in biogeochemical cycling, catalysis, energy storage, and even atmospheric water harvesting. Understanding the temperature-dependent loadings and properties of these interlayer films is crucial to comprehend birnessite reactivity when exposed to moist air and temperature gradients. Using vibrational spectroscopy we show that birnessite intercalates one water (1W) monolayer at up to ∼40 °C, but that loadings decrease by half at up to 85 °C. Our results also show that the vibrational properties of intercalated water are unaffected by temperature, implying that the hydrogen bonding network of water remains intact. Using molecular simulations, we found that the lowered water storage capacity at high temperatures cannot be explained by variations in hydrogen bond numbers or in the solvation environments of interlayer K+ ions initially present in the interlayer region. It can instead be explained by the compounded effects of larger evolved heat, as inferred from immersion energies, and by the larger temperature-driven mobility of water over that of K+ ions, which are electrostatically bound to birnessite basal oxygens. By shedding new light on the temperature-driven intercalation of water in a nanolayered mineral, this study can guide future efforts to understand the (geo)chemical reactivity of related materials in natural and technological settings.

MgO nanocube hydroxylation by nanometric water films.

Hydrophilic nanosized minerals exposed to air moisture host thin water films that are key drivers of reactions of interest in nature and technology. Water films can trigger irreversible mineralogical transformations, and control chemical fluxes across networks of aggregated nanomaterials. Using X-ray diffraction, vibrational spectroscopy, electron microscopy, and (micro)gravimetry, we tracked water film-driven transformations of periclase (MgO) nanocubes to brucite (Mg(OH)2) nanosheets. We show that three monolayer-thick water films first triggered the nucleation-limited growth of brucite, and that water film loadings continuously increased as newly-formed brucite nanosheets captured air moisture. Small (8 nm-wide) nanocubes were completely converted to brucite under this regime while growth on larger (32 nm-wide) nanocubes transitioned to a diffusion-limited regime when (∼0.9 nm-thick) brucite nanocoatings began hampering the flux of reactive species. We also show that intra- and inter-particle microporosity hosted a hydration network that sustained GPa-level crystallization pressures, compressing interlayer brucite spacing during growth. This was prevalent in aggregated 8 nm wide nanocubes, which formed a maze-like network of slit-shaped pores. By resolving the impact of nanocube size and microporosity on reaction yields and crystallization pressures, this work provides new insight into the study of mineralogical transformations induced by nanometric water films. Our findings can be applied to structurally related minerals important to nature and technology, as well as to advance ideas on crystal growth under nanoconfinement.

Mineral Nanoparticle Aggregation Alters Contaminant Transport under Flow.

Iron oxyhydroxide nanoparticle reactivity has been widely investigated, yet little is still known on how particle aggregation controls the mobility and transport of environmental compounds. Here, we examine how aggregates of goethite (α-FeOOH) nanoparticle deposited on 100-300 µm quartz particles (GagCS) alter the transport of two emerging contaminants and two naturally occurring inorganic ligands-silicates and phosphates. Bromide tracer experiments showed no water fractionation into mobile and immobile water zones in an individual goethite-coated sand (GCS) column, whereas around 10% of the total water was immobile in a GagCS column. Reactive compounds were, in contrast, considerably more mobile and affected by diffusion-limited processes. A new simulation approach coupling the mobile-immobile equation with surface complexation reactions to surface reactive sites suggests that ∼90% of the binding sites were likely within the intra-aggregate zones, and that the mass transfer between mobile and immobile fractions was the rate-limited step. The diffusion-controlled processes also affected synergetic and competitive binding, which have otherwise been observed for organic and inorganic compounds at goethite surfaces. These results thereby call for more attention on transport studies, where tracer or conservative tests are often used to describe the reactive transport of environmentally relevant molecules.

Fate and Transport of Pharmaceuticals in Iron and Manganese Binary Oxide Coated Sand Columns.

Predicting the fate and transport of pharmaceuticals in terrestrial environments requires knowledge of their interactions with complex mineral assemblages. To advance knowledge along this front, we examined the reactivity of pipemidic acid (PIP), a typical quinolone antibiotic, with quartz particles coated with a mixture of manganese oxide (MnO2) and goethite (α-FeOOH) under static and dynamic flow conditions. Batch and dynamic column experiments showed that PIP binding to MnO2 proceeded through a heterogeneous redox reaction, while binding to goethite was not redox-reactive. Mixed columns of aggregated goethite-manganese particles however enhanced redox reactivity because (i) goethite facilitated the transport of dissolved Mn(II) ion and increased the retention of PIP oxidation products, and (ii) MnO2 was protected from passivation. This mobility behavior was predicted using transport models accounting for adsorption and transformation kinetics of PIP on both goethite and MnO2. This work sheds new light on reactivity changes of mixtures of Fe and Mn oxides under flow-through conditions and will have important implications in predicting the fate and transport of redox-active organic compounds as well as development of new geomedia filters for environmental remediation.

Phosphorus release from hydrothermally carbonized digested sewage sludge using organic acids.

Hydrothermal carbonization (HTC) is a treatment technique with great potential for sanitizing digested sewage sludge (SS) and converting it into valuable products. In particular, phosphorus (P) recovery from hydrothermally carbonized SS has attracted special attention in recent years. This work aims to examine the leaching efficiency of P and the consequent release of metals and heavy metals from SS hydrochars (at 180, 215 and 250 °C) using organic acids (oxalate and citrate) over a range of pH values (0-4) and extraction times (5 min-24 h). Both organic acids triggered P extraction efficiencies exceeding 75 % at the lowest pH, but only oxalate reached a nearly complete P release from hydrochars at pH > 0 and for all carbonization temperatures. Low HTC temperature (180 °C) and short extraction time (5 min) were the optimal conditions treatment for P recovery when reacted in oxalate solutions of maximal pH buffering capacity (pH = 1.4). However, oxalate leaching also transferred metals/heavy metals into the P-leachate, with the exception of Ca being retained in the solid residue from HTC as Ca-oxalate precipitate. Different characterization methods confirmed the presence of this precipitate, and provided information about the surface and morphological changes of the SS hydrochars following acid treatment. The results suggest that HTC not only a promising technique to sanitize and reduce the volume of SS, but also an efficient means for P recovery using oxalic acid, thus contributing to the circular economy of P.

Silicate surface coverage controls quinolone transport in saturated porous media.

Although silicates are the most common anions in aquatic systems, little is known on the roles they play on the transport of emerging contaminants, such as antibiotics. Using dynamic column experiments, we revealed the controls of Si loadings on goethite (α-FeOOH) coated sands on the transport of a widely used quinolone antibiotic, here focusing on Nalidixic Acid (NA). We find that dynamic flow-through conditions (Darcy velocities of 2.98 cm/h and 14.92 cm/h) sustain monomeric Si species with loadings of up to ~ 0.8 Si/nm2 but that oligomeric species can form at the goethite surfaces under static (batch, no-flow conditions). While these monomeric species occupy no more than ~ 22% of the reactive OH groups on goethite, they can effectively suppress NA binding, and therefore enhance NA mobility in dynamic conditions. NA can also bind on goethite when it is simultaneously injected with high concentrations of Si (2000 µM), yet it becomes progressively replaced by Si over time. Combining kinetics and surface complexation modeling, we present a new transport model to account for the stepwise polymerization of Si on goethite and NA transport. Our findings show that dissolved Si, common to natural surface waters, can play a determining role on the surface speciation and transport of antibiotics in the environment.

Interactions of Anti-Inflammatory and Antibiotic Drugs at Mineral Surfaces Can Control Environmental Fate and Transport.

Various pharmaceutical compounds often coexist in contaminated soils, yet little is known about how their interactions impact their mobility. We here show that two typical antibiotic and anti-inflammatory agents (nalidixic acid (NA) and niflumic acid (NFA)) commonly form dimers at several representative soil- and sediment-building minerals of contrasting composition and structure. Cobinding occurs in the form of a NFA-NA dimer stabilized by hydrogen bonding and van der Waals interactions. Using dynamic column experiments containing goethite-coated sand, we then demonstrated that presorbed NA effectively captured the otherwise weakly binding NFA from solution. Simultaneously injecting NA and NFA to presorbed NA enhanced even further both NA and NFA loadings, thereby altering their transport under flow-through conditions. We also showed that environmental level amounts of natural organic matter can reduce the overall retention in column experiments, yet it does not suppress dimer formation. These environmentally relevant scenarios can be predicted using a new transport model that accounts for kinetics and cobinding reactions of NFA onto NA bound to goethite through metal-bonded, hydrogen-bonded, and outer-sphere complexes. These findings have important implications on assessing the fate of coexisting pharmaceutical compounds under dynamic flow conditions in contaminated soils.

Sodium hypochlorite as an oxidizing agent for removal of soil organic matter before microplastics analyses.

The omnipresence of microplastics (MPs) across Earth's surface has raised concerns about their environmental impact and created an urgent need for methods to identify them in complex soil and sedimentary matrices. However, detecting MPs in the O horizons of soils is difficult because plastic polymers share many physical and chemical properties with natural soil organic matter (SOM). In this study, we assessed whether sodium hypochlorite (NaOCl), a reagent that can oxidize SOM and simultaneously preserve mineral constituents, can be used for MP analysis and characterization in soil environments. In addition, we scrutinized how factors such as MP size, polymer type, extraction methods, and soil matrix affect the recovery of microplastic particles. We used both hydrophobic and density-dependent separation methods to assess the effects of our oxidation treatment on the recovery of MP. We observed that NaOCl effectively removed SOM without greatly altering the surface properties of resistant MP polymers (polypropylene, polylactic acid, low-density polyethylene, and polyethylene terephthalate), which were characterized using scanning electron microscopy and Fourier-transform infrared spectroscopy after SOM removal. The NaOCl treatment caused some chlorination and formation of additional C-OH bonds on polymer surfaces, which likely contributed to the reduced efficiency of the hydrophobic-based (oil) extraction. We conclude that NaOCl treatment can improve detection of MPs in SOM-rich soil and that recovery of MPs from soils is influenced by MP size, polymer type, extraction method, and soil type, which makes it challenging to develop a universal analytical method.

Competitive Carboxylate-Silicate Binding at Iron Oxyhydroxide Surfaces.

Dissolved silicate ions in wet and dry soils can determine the fate of organic contaminants via competitive binding. While fundamental surface science studies have advanced knowledge of binding in competitive systems, little is still known about the ranges of solution conditions, the time dependence, and the molecular processes controlling competitive silicate-organic binding on minerals. Here we address these issues by describing the competitive adsorption of dissolved silicate and of phthalic acid (PA), a model carboxylate-bearing organic contaminant, onto goethite, a representative natural iron oxyhydroxide nanomineral. Using surface complexation thermodynamic modeling of batch adsorption data and chemometric analyses of vibrational spectra, we find that silicate concentrations representative of natural waters (50-1000 µM) can displace PA bound at goethite surfaces. Below pH ∼8, where PA binds, every bound Si atom removes ∼0.3 PA molecule by competing with reactive singly coordinated hydroxo groups (-OH) on goethite. Long-term (30 days) reaction time and a high silicate concentration (1000 µM) favored silicate polymer formation, and increased silicate while decreasing PA loadings. The multisite complexation model predicted PA and silicate binding in terms of the competition for -OH groups without involving PA/silicate interactions, and in terms of a lowering of outer-Helmholtz potentials of the goethite surface by these anions. The model predicted that silicate binding lowered loadings of PA species, and whose two carboxylate groups are hydrogen- (HB) and metal-bonded (MB) with goethite. Vibrational spectra of dried samples revealed that the loss of water favored greater proportions of MB over HB species, and these coexisted with predominantly monomeric silicate species. These findings underscored the need to develop models for a wider range of organic contaminants in soils exposed to silicate species and undergoing wet-dry cycles.

Nanoscale Hydration in Layered Manganese Oxides.

Birnessite is a layered MnO2 mineral capable of intercalating nanometric water films in its bulk. With its variable distributions of Mn oxidation states (MnIV, MnIII, and MnII), cationic vacancies, and interlayer cationic populations, birnessite plays key roles in catalysis, energy storage solutions, and environmental (geo)chemistry. We here report the molecular controls driving the nanoscale intercalation of water in potassium-exchanged birnessite nanoparticles. From microgravimetry, vibrational spectroscopy, and X-ray diffraction, we find that birnessite intercalates no more than one monolayer of water per interlayer when exposed to water vapor at 25 °C, even near the dew point. Molecular dynamics showed that a single monolayer is an energetically favorable hydration state that consists of 1.33 water molecules per unit cell. This monolayer is stabilized by concerted potassium-water and direct water-birnessite interactions, and involves negligible water-water interactions. Using our composite adsorption-condensation-intercalation model, we predicted humidity-dependent water loadings in terms of water intercalated in the internal and adsorbed at external basal faces, the proportions of which vary with particle size. The model also accounts for additional populations condensed on and between particles. By describing the nanoscale hydration of birnessite, our work secures a path for understanding the water-driven catalytic chemistry that this important layered manganese oxide mineral can host in natural and technological settings.

A gateway for ion transport on gas bubbles pinned onto solids.

Gas bubbles grown on solids are more than simple vehicles for gas transport. They are charged particles with surfaces populated with exchangeable ions. We here unveil a gateway for alkali metal ion transport between oxygen bubbles and semi-conducting (iron oxide) and conducting (gold) surfaces. This gateway was identified by electrochemical impedance spectroscopy using an ultramicroelectrode in direct contact with bubbles pinned onto these solid surfaces. We show that this gateway is naturally present at open circuit potentials, and that negative electric potentials applied through the solid enhance ion transport. In contrast, positive potentials or contact with an insulator (polytetrafluoroethylene) attenuates transport. We propose that this gateway is generated by overlapping electric double layers of bubbles and surfaces of contrasting (electro)chemical potentials. Knowledge of this ion transfer phenomenon is essential for understanding electric shielding and reaction overpotential caused by bubbles on catalysts. This has especially important ramifications for predicting processes including mineral flotation, microfluidics, pore water geochemistry, and fuel cell technology.

Effects of organic matter-goethite interactions on reactive transport of nalidixic acid: Column study and modeling.

The fractionation of natural organic matter (NOM) and its impact on the binding of quinolones to mineral surfaces and transport behavior under flow-through conditions have been scarcely investigated. In this study, the sorption and transport of a widely used quinolone antibiotic, Nalidixic acid (NA), were investigated in goethite-coated sand (GCS) columns over a wide concentration range (5-50 mg/L) of Leonardite humic acid (LHA), a representative NOM. Simultaneous injection of NA and LHA in GCS columns mutually alter transport of each other, i.e. NA mobility and LHA molecular fractionation. Preloading of GCS column with LHA dramatically facilitated the transport behavior of NA, where nonspecific interactions with LHA-covered goethite surfaces controlled NA mobility. Simulations using a two-site nonequilibrium model showed that a modified sorption rate constant was required to accurately describe the breakthrough curves of NA under these conditions. This altered rate constant suggests that nonspecific interactions of NA on bound LHA may take place as an additional binding mechanism affecting adsorption kinetics. NOM fractionation alters sorption mechanisms and kinetics of quinolone antibiotics, which in turn affect their fractionation. These results may have important implications for an accurate assessment of the fate of these types of antibiotics in aquatic environments.

Direct observation of anisotropic growth of water films on minerals driven by defects and surface tension.

Knowledge of the occurrences of water films on minerals is critical for global biogeochemical and atmospheric processes, including element cycling and ice nucleation. The underlying mechanisms controlling water film growth are, however, misunderstood. Using infrared nanospectroscopy, amplitude-modulated atomic force microscopy, and molecular simulations, we show how water films grow from water vapor on hydrophilic mineral nanoparticles. We imaged films with up to four water layers that grow anisotropically over a single face. Growth usually begins from the near edges of a face where defects preferentially capture water vapor. Thicker films produced by condensation cooling completely engulf nanoparticles and form thicker menisci over defects. The high surface tension of water smooths film surfaces and produces films of inhomogeneous thickness. Nanoscale topography and film surface energy thereby control anisotropic distributions and thicknesses of water films on hydrophilic mineral nanoparticles.

Influence of water matrix and hydrochar properties on removal of organic and inorganic contaminants.

The removal of contaminants from water using low-cost adsorbents has been widely studied, yet studies employing a realistic water matrix are still lacking. This study investigated the removal of organic compounds (trimethoprim, fluconazole, and perfluorooctanoic acid (PFOA)) and metals (As, Zn, and Cu) from landfill leachate. Additionally, tests in pure water, humic acid, and ion matrices were carried out to better understand how the water matrix affects adsorption. The hydrochars were produced from four feedstocks at three carbonization temperatures. The results show that the removal efficiencies for organic pollutants were low and metal removal by hydrochars was comparable with commercial activated carbon. The removal of all compounds from pure water was substantially lower. Tests with humic acid and ion-containing matrices could not fully explain the increased removal in the landfill leachate, which may be due to the combination of the water matrix and presence of soluble species from the hydrochars.

The impact of hydrothermal carbonization on the surface functionalities of wet waste materials for water treatment applications.

Hydrothermal carbonization (HTC) is an energy-efficient thermochemical process for converting wet waste products into value added materials for water treatment. Understanding how HTC influences the physicochemical properties of the resultant materials is critical in optimizing the process for water treatment, where surface functionality and surface area play a major role. In this study, we have examined the HTC of four wet waste streams, sewage sludge, biosludge, fiber sludge, and horse manure at three different temperatures (180 °C, 220 °C, and 260 °C). The physicochemical properties of these materials were examined via FTIR, SEM and BET with their adsorption capacity were assessed using methylene blue. The yield of solid material after hydrothermal carbonization (hydrochar) decreased with increasing temperature for all samples, with the largest impact on horse manure and fiber sludge. These materials also lost the highest degree of oxygen, while HTC had minimal impact on biosludge and sewage sludge. The differences here were due to the varying compositions of each waste material, FTIR identified resonances related to cellulose in horse manure and fiber sludge, which were not detected in biosludge and sewage sludge. Adsorption capacities varied between 9.0 and 68 mg g-1 with biosludge HTC at 220 °C adsorbing the highest amount. Adsorption also dropped drastically at the highest temperature (260 °C), indicating a correlation between adsorption capacity and HTC conditions. This was attributed to the loss of oxygen functional groups, which can contribute to adsorption. These results suggest that adsorption properties can be tailored both by selection of HTC temperature and feedstock.

Direct identification of reaction sites on ferrihydrite.

Hydroxyl groups are the cornerstone species driving catalytic reactions on mineral nanoparticles of Earth's crust, water, and atmosphere. Here we directly identify populations of these groups on ferrihydrite, a key yet misunderstood iron oxyhydroxide nanomineral in natural sciences. This is achieved by resolving an enigmatic set of vibrational spectroscopic signatures of reactive hydroxo groups and chemisorbed water molecules embedded in specific chemical environments. We assist these findings by exploring a vast array of configurations of computer-generated nanoparticles. We find that these groups are mainly disposed along rows at edges of sheets of iron octahedra. Molecular dynamics of nanoparticles as large as 10 nm show that the most reactive surface hydroxo groups are predominantly free, yet are hydrogen bond acceptors in an intricate network formed with less reactive groups. The resolved vibrational spectroscopic signatures open new possibilities for tracking catalytic reactions on ferrihydrite, directly from the unique viewpoint of its reactive hydroxyl groups.