Carboxyl-richness controls organic carbon preservation during coprecipitation with iron (oxyhydr)oxides in the natural environment

The coprecipitation of organic carbon with iron minerals is important for its preservation in soils and sediments, but the mechanisms for carbon-iron interactions and thus the controls on organic carbon cycling are far from understood. Here we coprecipitate carboxylic acids with iron (oxyhydr)oxide ferrihydrite and use near-edge X-ray absorption fine structure spectroscopy and wet chemical treatments to determine the relationship between sequestration mechanism and organic carbon stability against its release and chemical oxidative remineralisation. We show that organic carbon sequestration, stabilisation and persistence increase with an increasing number of carboxyl functional groups. We suggest that carboxyl-richness provides an important control on organic carbon preservation in the natural environment. Our work offers a mechanistic basis for understanding the stability and persistence of organic carbon in soils and sediments, which might be used to develop an overarching relationship between organic functional group-richness, mineral interactions and organic carbon preservation in the Earth system. Organic carbon sequestration, stabilisation and burial through its interaction with iron is enhanced by carboxyl-richness of the organic moiety, according to elemental and microstructure analysis of experimentally produced co-precipitates.

T he sequestration of organic carbon (OC) by iron (oxyhydr) oxides in soils and sediments provides a 'rusty sink' for OC 1,2 that helps generate and maintain soil function 3,4 , mitigate against climate change 5,6 and enhance the burial of OC for regulation of atmospheric CO 2 and O 2 over geological time 2 . Despite the importance of OC-iron (oxyhydr)oxide phases, however, the mechanisms responsible for OC sequestration, stabilisation against remineralisation and persistence with iron (oxyhydr)oxides are poorly understood 1 . At first glance, most OC and iron (oxyhydr)oxides are transient, with OC subject to extensive remineralisation 7 and reactive iron (oxyhydr)oxides reductively dissolved or transformed into more crystalline forms during diagenesis 8 . The sequestration of OC by iron (oxyhydr) oxides, however, results in the persistence of OC-iron phases in both oxic and anoxic soils and sediments over hundreds to thousands of years 2,9 .
The sequestration of OC with iron (oxyhydr)oxides typically occurs through a variety of sequestration processes that remove OC from solution to the solid mineral particles 10 . Sequestration processes can include the surface sorption, or adsorption, of OC to preformed mineral particles and the coprecipitation of OC with neoformed mineral phases, where OC is removed from solution as a consequence of mineral precipitation [11][12][13] . During coprecipitation, OC can become adsorbed at particle surfaces and incorporated into particle interiors 11 . In soils and sediments, OC is often present in the porewaters from which iron (oxyhydr) oxides precipitate, and thus the coprecipitation of OC with these minerals is a common process for OC-iron (oxyhydr)oxide formation [11][12][13][14] that is recently shown to be quantitatively important for OC persistence on a global scale 2,15 .
Despite the importance of the sequestration of OC with iron (oxyhydr)oxides via coprecipitation, relatively little is known about coprecipitation sequestration mechanisms or how these stabilise OC against remineralisation. Coprecipitation with OC can stabilise iron (oxyhydr)oxides because the association of OC with the mineral particles can kinetically retard reductive dissolution [16][17][18][19] and mineral transformation 18,20,21 . Coprecipitated OC in turn might be stabilised by an adsorption and/or incorporation mechanism that limits exposure of the sequestered OC to remineralisation 15 . Such an adsorption mechanism would need to rapidly remove OC from the remineralisable dissolved pool and strongly bind it to mineral particles, so that it undergoes only limited desorption back into the dissolved reservoir 22 . Similarly, an incorporation mechanism must locate OC inside mineral pore spaces for example, where it can become adsorbed and/or is otherwise physically inaccessible to remineralisation 23 .
Previous experimental work on the sequestration of OC during coprecipitation with iron (oxyhydr)oxides indicates that the adsorption of carboxyl functional groups to mineral particles is a dominant coprecipitation sequestration mechanism, involving the formation of outer-sphere 12 or inner-sphere complexes, the latter involving carboxyl ligand exchange between an OH of a carboxyl group and an OH of a mineral site 14 . Previous experimental work on the sequestration of OC during adsorption with preformed iron (oxyhydr)oxides also indicates that carboxyl ligand exchange might result in strongly adsorbed OC 9,24-26 with increased resistance to remineralisation 27 . All these studies, however, use natural organic matter (NOM), which is an extremely complex mixture containing a variety of different organic functional groups 28 . This complexity together with differences between types of NOM in terms of sources, ages and diagenetic histories has therefore precluded a systematic investigation of the relationship between a carboxyl sequestration mechanism and OC stabilisation against remineralisation 29 . Indeed a link between particular binding mechanisms and OC persistence is only presumed and has never been systematically investigated 30 .
Here we take a direct mechanistic approach to determine how carboxyl-rich OC is sequestered during coprecipitation with iron (oxyhydr)oxides, and how this sequestration mechanism controls the stabilisation of OC against its release and chemical oxidative remineralisation. We perform controlled coprecipitation experiments, using a series of simple carboxylic acids as model organic compounds and the iron (oxyhydr)oxide ferrihydrite. We use scanning transmission X-ray microscopy and near-edge X-ray absorption fine structure spectroscopy (STXM NEXAFS) to determine OC sequestration mechanism, and a variety of wet chemical treatments to determine the relationship between OC sequestration mechanism and stabilisation against its release and oxidation. Finally, we apply a kinetic model to our wet chemical data to quantify OC persistence over time. Our work shows that simple carboxylic acids are sequestered during coprecipitation with ferrihydrite via a carboxyl ligand exchange adsorption mechanism occurring predominantly at the ferrihydrite surface. We show that an increasing number of carboxyl groups directly increases OC sequestration via multi-carboxyl ligand exchange. We demonstrate that this multi-carboxyl adsorption mechanism increases the stability of OC against desorption and oxidation and results in a pool of non-desorbable OC that might persist with iron (oxyhydr)oxides in soils and sediments. Our work indicates that OC persistence at least partly depends on its carboxylrichness and the association of this OC fraction with iron (oxyhydr)oxides. Our results also indicate that using the amount of OC and reactive iron to predict OC sequestration is insufficient and rather our work provides a mechanistic platform from which organic functional group-richness might be used as a basis for predicting the stability and persistence of OC in the natural environment.

Results
Establishing a model system for carboxyl-iron (oxyhydr)oxide coprecipitation. To represent carboxyl-rich OC, we chose a selection of saturated aliphatic mono-, di-and tri-carboxylic acids containing only COOH carboxyl and CH methyl groups (Fig. 1). These acids are directly relevant to soil and sediment porewaters where they and other low molecular weight organic acids are prevalent 31,32 . They also serve as model organic compounds for understanding the role of carboxyl groups in the sequestration of more complex dissolved NOM 33 , which is recently shown to comprise a number of universal molecular structures containing predominantly carboxyl and hydroxyl groups 34 . To represent iron (oxyhydr)oxides, we chose ferrihydrite, which is abundant and commonly associated with OC in the natural environment 8 .
We investigate sequestration, stabilisation and persistence of the acids with respect to the number of carboxyl groups (n) at constant number of total carbon atoms (m) and the number of total carbon atoms (m) at constant number of carboxyl groups (n) (Fig. 1, comparing across (sequentially increasing n) or down columns (sequentially increasing m)). The corresponding coprecipitates are denoted Fh_acidn/m_C:Fe, where Fh is ferrihydrite, acid indicates the first three letters of the systematic IUPAC name followed by n carboxyl groups and m total carbon atoms and C:Fe is the molar C:Fe ratio of the solid phase. In the following sections, the results are described for the entire data set and then for specific data subsets with either increasingn/constantm or constantn/increasingm. Data subset Fh_Pen1/5 -Fh_Pen2/5 -Fh_Eth3/5 (green, blue and purple solid squares, respectively, Fig. 1) is described for all results.  1 Schematic showing mono-, di-and tri-carboxylic acids coprecipitated with iron (oxyhydr)oxide ferrihydrite. Mono-, di-and tri-carboxylic acids, including systematic IUPAC name, common name for reference in parentheses, coprecipitate nomenclature and coprecipitate data symbol; number of carboxyl functional groups (nCOOH); number of total carbon atoms (mTotC); molecular weight (MW); and pK a of the carboxyl functional groups (available at Pubchem 85 or calculated using the ACD/Labs I-Lab 2.0 software (algorithm version: v12.1.0.50374)). For the coprecipitate nomenclature, coprecipitates are denoted Fh_acidn/m, where Fh is ferrihydrite, acid indicates the first three letters of the systematic IUPAC name followed by n carboxyl groups and m total carbon atoms. Individual coprecipitates are denoted Fh_acidn/m_C:Fe where C:Fe is the molar C:Fe ratio of the solid phase. For the coprecipitate data symbol, coprecipitates are represented by a consistent data symbol, where colour indicates the number of carboxyl groups n (green, blue and purple = n 1, 2, 3 carboxyl groups, respectively), and shape indicates the number of total carbon atoms m (crosses, open squares, crossed open squares, half solid squares, solid squares, solid diamonds, solid triangles, solid circles = m 1, 2, 3, 4, 5, 6, 7, 8 total carbon atoms, respectively). Influence of the number of carboxyl groups n at constant number of total carbon atoms m on OC sequestration, stabilisation and persistence is investigated by comparing acids across the columns (sequentially increasing n). Influence of the number of total carbon atoms m at constant number of carboxyl groups n on OC sequestration, stabilisation and persistence is investigated by comparing acids down the columns (sequentially increasing m). sequentially increasing initial carbon and fixed initial iron concentration (see 'Methods').
The consistent increase in the sequestration maximum as a function of the number of carboxyl groups and the total number of carbon atoms suggests that total sequestration is not controlled by the capacity of ferrihydrite to sequester OC but rather by the affinity of OC for ferrihydrite 35 . The capacity of the particles to sequester OC is difficult to evaluate, however, because it is a function of both the adsorption capacity and the amount of OC that can be incorporated into the particle interiors. The adsorption capacity can be equated to the surface coverage, but this can be variably defined because adsorbed OC can exist in both monolayer (or monolayer equivalent 36 ) and multilayer coatings [37][38][39] . The incorporation capacity is similarly complicated because there likely exists a continuum between OC-iron macromolecules and OC-iron (oxyhydr)oxide particles that have highly elevated C:Fe 2,14,15 .
If we define the theoretical adsorption capacity as the surface coverage of a monolayer, however, and we nominally assume that all our OC is adsorbed in a monolayer, then we can compare our theoretical and measured surface coverages to hypothetically determine whether our sequestered OC could be entirely accommodated in a monolayer or whether multilayers and/or incorporation into particle interiors is additionally required to achieve our OC loadings. We consider adsorption scenarios in which either just one COOH group from each acid molecule binds to a FeOH adsorption site (one-carboxyl adsorption) or all COOH groups from each acid molecule each bind to a FeOH adsorption site (two-carboxyl and three-carboxyl adsorption for di-and tri-carboxylic acids, respectively) (see 'Methods', Fig. 2 Sequestration of mono-, di-and tri-carboxylic acids during coprecipitation with iron (oxyhydr)oxide ferrihydrite. Sequestration data for carboxylic acid ferrihydrite coprecipitates plotted as C:Fe molar ratio of initial coprecipitation solution vs. C:Fe molar ratio of resulting coprecipitate: a mono-, di-and tri-carboxylic coprecipitates for comparison, and b inset of mono-, di-and tri-carboxylic coprecipitates at low C:Fe initial solution; c monocarboxylic coprecipitates; d di-carboxylic coprecipitates; e tri-carboxylic coprecipitates. Green, blue and purple colour codes depict mono-, di-and tricarboxylic data, respectively. The coprecipitate nomenclature is given in Fig. 1 Fig. 3 and Supplementary Fig. 4 for extended discussion).
The theoretical adsorption capacities of the mono-, di-and majority of the tri-carboxyl coprecipitates provide between~1 and 99% more sequestration capacity than would be required to accommodate all our OC in a monolayer at the particle surfaces (Supplementary Data 2). The theoretical adsorption capacities for some of the tri-carboxyl coprecipitates with the highest sequestrations, however, provide~17% less sequestration capacity assuming the one-and two-carboxyl scenarios (last data point for Fh_Pen3/8, with C:Fe 2.681, Fig. 2) and~7-76% less sequestration capacity assuming the three-carboxyl scenario (last 2-3 data points for each tri-carboxyl coprecipitate, with C:Fe 0.787-2.681, Fig. 2), than would be required for only monolayer adsorption (Supplementary Data 2). Thus, almost all our acids could theoretically be adsorbed in a monolayer at the particle surfaces, without requiring any extra sequestration capacity that might be provided by adsorption in multilayers and/or incorporation into particle interiors 11,40 . The tri-carboxylic acids with the highest sequestrations, however, are likely also adsorbed in multilayers [37][38][39] and/or are incorporated into OC-iron macromolecules or particle interiors 2,15,23,41 .
Increasing number of carboxyl groups promotes multicarboxyl carbon sequestration. To determine the sequestration mechanisms of the acids with ferrihydrite, we subject our coprecipitates to STXM NEXAFS (see 'Methods'). We chose coprecipitates (Supplementary Data 1) encompassing a range of molar OC (but excluding the tri-carboxylic coprecipitates with the highest sequestrations) and including several data subsets with approximately constant molar OC and either increasingn/ constantm or constantn/increasingm (see 'Methods').
The NEXAFS spectra exhibit one major peak at~288.6 eV (  Table 1). The exact carboxyl peak position of all the unreacted mono-, di-and tri-carboxylic acid standards occurs at 288.6 ± 0.05, 288.7 ± 0.05 and 288.9 ± 0.05 eV, respectively, and thus appears at slightly higher energy as the number of carboxyl groups increases (Supplementary Table 2). Migration of the carbon 1s-π* transition occurs because the carbon 1s electron is bound more tightly as more electron-withdrawing atoms (such as oxygen in our acids) are added to an organic structure 42 . Compared to their respective standards, the carboxyl peak for all the coprecipitates is reduced in amplitude and broadened indicating that the acids are adsorbed to ferrihydrite via carboxyl ligand exchange between the OH of the carboxyl group and the OH of an adsorption site 14 . It is also apparent, however, that, compared to their respective standards, the peak for these coprecipitates is shifted to lower energy and that this shift becomes increasingly pronounced with increasing number of carboxyl groups (Supplementary Table 2). The shift is remarkably consistent for the mono-, di-and tri-carboxyl coprecipitates over the range of molar OC (average shift from respective standards = −0.1 ± 0, −0.2 ± 0.04 and −0.4 ± 0 eV, respectively) and is therefore corroborated in data subsets with approximately equivalent molar OC and increasingn/constantm (e.g., Fh_Pen1/5_0.044 -Fh_Pen2/5_0.043 -Fh_Eth3/5_0.048 offset Fig. 3 Carbon 1s NEXAFS spectra for mono-, di-and tri-carboxylic acids coprecipitated with iron (oxyhydr)oxide ferrihydrite. Carbon 1s NEXAFS spectra for carboxylic acid standards (dotted lines) and carboxylic acid ferrihydrite coprecipitate samples (solid lines) plotted as energy (eV) vs. normalised absorbance (arbitrary units). Green, blue and purple colour codes depict mono-, di-and tri-carboxylic data, respectively. The coprecipitate nomenclature is given in Fig. 1. Spectra are stacked with an arbitrary offset for clarity. Carboxyl carbon peak positions for the unreacted mono-, di-and tri-carboxylic acid standards are shown with vertical dashed green, blue and purple lines, respectively, and appear at slightly higher energy as the number of carboxyl groups increases. Carboxyl carbon peak positions for the coprecipitate samples are shifted to lower energy compared to their respective standards, and this shift becomes increasingly pronounced with increasing number of carboxyl groups.
A similar carboxyl band shift is observed in Fourier transform infra-red spectra of dissolved NOM coprecipitated with ferrihydrite compared to the unreacted NOM, which becomes increasingly pronounced for coprecipitates with lower molar OC 14 . The carboxylic character of the adsorbing NOM is assumed to be relatively invariant, and thus the shift of the carboxyl band to increasingly lower frequency is interpreted to reflect an increasing number of carboxyl ligand exchange bonds per adsorbing molecule with decreasing OC adsorbed 14 . We have an increasing number of carboxyl groups in our adsorbing OC, and a shift of the carboxyl peak to increasingly lower energy that is independent of OC adsorbed. Our shift is thus indicative of an increasing number of carboxyl ligand exchange bonds per adsorbing acid molecule with increasing number of carboxyl groups.
The NEXAFS spectra also exhibit a broad shoulder feature centred at~287.  Table 1). Compared to their respective standards, the shoulder feature for all the coprecipitates is increased in amplitude but also generally becomes more pronounced in data subsets with constantn/increasingm (e.g. comparing Fh_Met1/ 1_0.033 vs. Fh_Pen1/5_0.044). The aliphatic transition state is specifically attributed to the 1s-σ* C-H /3p state 43 , to mixed 1sπ* CH3,CH2 /3p Rydberg-like excitations of CH groups 44 , or to a number of broad bands associated with the 1s-σ* C-H states on the higher energy side together with some mixture of unresolved 1sπ* transitions on the low energy side 42,43 . Rydberg-like excitations of CH groups can be dampened by Rydberg-valence mixing between the groups, and enhanced by a comparative lack of Rydberg-valence mixing that might occur when the groups are involved in adsorptive interactions 45 . A progressive prominence of the shoulder feature with increasing number of total carbon atoms is therefore indicative of an increasing number of CH adsorptive interactions per adsorbing acid molecule with increasing number of total carbon atoms.
The STXM elemental distribution maps show that carbon and iron are highly spatially correlated, with carbon apparently more concentrated at the particle edges (R 2 = 0.881-0.945, Supplementary Fig. 6). In these samples, the particles are of varying thickness, and the particle edges are likely to be thinner than the interiors. The STXM signal at the edge regions therefore reflects carbon mainly located at the particle surfaces while the signal over the central regions reflects carbon also incorporated throughout the bulk interior. A concentration of carbon at the edges, as opposed to a more uniform distribution over the entire particle, therefore confirms our theoretical adsorption capacity calculations that carbon is mainly adsorbed, without substantial incorporation into the interior (see 'Methods' for extended discussion of thickness-dependent detection bias). It should be noted, however, that carbon appears to be distributed at the particle surfaces in patches ( Supplementary Fig. 6Ac, Bc). While this is consistent with our theoretical adsorption capacity calculations for carbon adsorbed in a monolayer equivalent, the spatial resolution of STXM is not sufficient to distinguish whether the patches are truly monolayer or multilayer 46 . Thus, although all adsorbed OC in these samples can be accommodated as a monolayer equivalent, some patches may form multilayer conglomerations 37,38 . A continuum between monolayer equivalent and multilayer conglomerations is consistent with our theoretical adsorption capacity calculations for our tricarboxylic coprecipitates with the highest sequestrations that require multilayering to achieve their OC loadings and observations of NOM with minerals in sediments 38 .
Increasing number of carboxyl groups promotes stable carbon sequestration. To quantify the stability of the acids with ferrihydrite against release and oxidation, we exposed our coprecipitates to solutions typically used to either desorb or oxidise OC sequestered with iron (oxyhydr)oxides (see 'Methods'). We chose coprecipitates (Supplementary Data 1) encompassing a range of molar OC (excluding tri-carboxylic coprecipitates with the highest sequestrations) and including several data subsets with approximately constant molar OC and either increasingn/constantm or constantn/increasingm (see 'Methods').
In all desorption and oxidation experiments, removal or destruction of the OC is incomplete. The entire data set shows that, as the number of carboxyl groups increases, the percent OC remaining sequestered increases (R 2 = 0.789, Supplementary Fig. 7), with the tri-carboxyl coprecipitates retaining up to~65,~40 and 32% OC after treatment with artificial seawater, sodium hydroxide and sodium hypochlorite, respectively ( Fig. 4 and Supplementary Data 4). Additionally, the percent OC remaining is highest for artificial seawater, which is the least aggressive treatment towards OC release (see 'Methods'). (The coprecipitates were washed with ultrapure water immediately after synthesis, and so essentially all OC remains after further ultrapure water washes, Supplementary  Fig. 8). All data subsets with increasingn/constantm corroborate the above trends (e.g. Fh_Pen1/5_0.044 -Fh_Pen2/5_0.043 -Fh_Eth3/ 5_0.048, R 2 = 0.989 with sodium hydroxide, Supplementary Fig. 7). Unlike the sequestration data, however, neither the entire data set (R 2 = 0.264, Supplementary Fig. 9) nor most of the data subsets with constantn/increasingm show a strong dependence on the number of total carbon atoms (e.g. Fh_Met1/1_0.055 up to Fh_Pen1/5_0.044 at final coprecipitate C:Fe ≈ 0.05, R 2 = 0.120 with sodium hydroxide, Supplementary Fig. 9). This suggests that the adsorptive interactions involving the CH groups identified with NEXAFS are relatively weak 37 , so while they enhance affinity, they offer little resistance to desorption and oxidation. Thus, even for mono-carboxylic acids, a fraction of the OC is very strongly sequestered, and with increasing number of carboxyl groups, the acids are increasingly resistant to desorption and oxidation.
The increase in the percent OC remaining as a function of the number of carboxyl groups is moderated by the molar OC sequestered. The entire data set shows that as the molar OC sequestered increases the percent OC remaining decreases (R 2 = 0.867 with sodium hydroxide; Supplementary Fig. 10). All data subsets corroborate the above trend, with the percent OC remaining decreasing with increasing molar OC for all those with increasingn/constantm (e.g. Fh_Pen2/5_0.043 -FhEth3/5_0.048 = 26/40% OC remaining vs. Fh_Pen2/5_0.756 -FhEth3/5_0.787 = 11/17% OC remaining with sodium hydroxide) and constantn/ increasingm (i.e. Fh_Pen2/5_0.043 vs. Fh_Pen2/5_0.756 =~26 vs. 11% OC remaining with sodium hydroxide). This suggests that, although the acids are adsorbed via a common carboxyl ligand exchange adsorption mechanism as a function of the number of carboxyl groups, binding strength heterogeneities in their local adsorption environment, caused by electrostatic repulsion and/or steric hindrance between more closely packed molecules and/or accumulation of molecules in multilayer conglomerations that extend away from the mineral surface 37,38 , render molecules adsorbed at high C:Fe less strongly bound and thus more susceptible to desorption and oxidation 24 . The scatter within the entire data set is highest, and thus the relationship between molar OC sequestered and percent OC remaining is weakest, for artificial seawater (R 2 = 0.583, Supplementary Fig. 10a). This suggests that binding strength heterogeneities are more pronounced during desorption with the least aggressive treatment.
Increasing number of carboxyl groups promotes persistent carbon sequestration. To quantify the persistence of the acids with ferrihydrite, we exposed our coprecipitates to sodium hydroxide and modelled desorption over time (see Methods). We chose only specific data subsets with approximately constant molar OC and increasingn/constantm, and increasing molar OC with constantn/constantm (see 'Methods').
All data subsets corroborate the stability experiments, where as the number of carboxyl groups or molar OC increases, the percent OC remaining increases or decreases, respectively. The subsets also show however, that the percent OC remaining decreases with time, in an apparently two-step desorption process, with up to~70% of the OC removed within 1 h, followed by up to~97% within 96 h (Fig. 5). The trends in the experimental data may be described using a two-or three-pool first-order kinetic model 47 . The two-pool model assumes one pool of desorbable carbon and a pool of non-desorbable carbon, while the three-pool model assumes two pools of desorbable carbon and a pool of non-desorbable carbon. In both models, the non-desorbable pool approaches an asymptote representing a fraction of OC that remains sequestered over the experimental timescale, similar to the G-model approach used to represent OC persistence in soils and sediments [47][48][49] (see 'Methods' for extended model descriptions and goodness-of-fit evaluation). The two-pool model provides adequate fits to the data but the non-desorbable pool is overestimated (R 2 ≥ 0.960; model selection criteria average 2.85 ± 0.66; Supplementary Data 5 and Supplementary Fig. 11). This is likely because a two-pool model does not allow for sufficient binding strength heterogeneity in the local adsorption environment and thus in the apparent desorption rate of the desorbable pool 47 . The three-pool model provides better fits to the data by allowing for a slower desorption rate of one of the desorbable pools (R 2 ≥ 0.999; model selection criteria average 6.06 ± 1.03; Supplementary Data 5 and Supplementary Fig. 11).
Thus, over our experimental timescale, even for mono-carboxylic acids, a small fraction of OC persists with ferrihydrite (~2% for Fh_Pen1/5_0.044), and this fraction increases with an increasing number of carboxyl groups (up to~11% for Fh_Eth3/5_0.054; 8% for Fh_Eth3/5_0.547).  4 Desorption and chemical stability of mono-, di-and tri-carboxylic acids coprecipitated with iron (oxyhydr)oxide ferrihydrite. Desorption and chemical oxidation data for carboxylic acid ferrihydrite coprecipitates plotted as C:Fe molar ratio coprecipitate vs. percent C remaining after treatment: a exposure to artificial seawater, b exposure to 0.1 M NaOH, and c oxidation with 1 M NaOCl. Green, blue and purple colour codes depict mono-, di-and tricarboxylic data, respectively. The coprecipitate nomenclature is given in Fig. 1 5 Time series desorption of mono-, di-and tri-carboxylic acids coprecipitated with iron (oxyhydr)oxide ferrihydrite. Time series desorption data for carboxylic acid ferrihydrite coprecipitates plotted as time (h) vs. percent C remaining after exposure to 0.1 M NaOH. Green, blue and purple colour codes depict mono-, di-and tri-carboxylic data, respectively. The coprecipitate nomenclature is given in Fig. 1. Symbols are as follows: solid square: Fh_Pen1/5, Fh_Pen2/5 and Fh_Eth3/5 at 0.05 C:Fe; crossed solid square: Fh_Pen2/5 and Fh_Eth3/5 at~0.5 C:Fe. Data points and error bars represent the mean and one standard error of the mean (1 SEM) for duplicate coprecipitates each desorbed in duplicate and measured in duplicate. Errors are propagated through all calculations using standard error propagation rules.

Discussion
The importance of OC coprecipitation and adsorption processes for regulating the global carbon cycle has been discussed for several decades 2,6,7,50 . A direct relationship between particular sequestration mechanisms and sequestration, stabilisation and persistence has not been established for coprecipitation or adsorption processes, however 30 , and the controls on OC preservation remain poorly understood 51 . We investigate the role of carboxyl groups in the sequestration, stabilisation and persistence of OC during its coprecipitation with ferrihydrite. We show that simple carboxylic acids as model organic compounds are sequestered via an adsorption mechanism, in which carboxyl functional groups undergo ligand exchange with mineral hydroxyls. We show that an increasing number of carboxyl groups per acid molecule increases the number of carboxyl ligand exchange bonds formed between each molecule and the ferrihydrite particles. We conclude that this multi-carboxyl adsorption mechanism controls the enhanced sequestration, stability and persistence observed in our experiments. By extension, we propose that carboxyl-richness plays an important role in the sequestration, stability and persistence of more complex but typically carboxylrich NOM 34 during coprecipitation with and adsorption to iron (oxyhydr)oxides in soils and sediments.
In our coprecipitation experiments, we attribute the relationship between carboxyl-richness (increasingn/constantm), affinity, stability and persistence to a multi-carboxyl adsorption mechanism. The spectroscopic adsorption configuration of carboxylic acids with iron (oxyhydr)oxides is described in only a few studies, however, and the results are contradictory 52 ; moreover, none evaluate the relationship between carboxyl-richness, stability and persistence. Adsorption of our mono-, di-and tricarboxylic acids via an increasing number of carboxyl ligand exchange bonds per acid molecule is consistent with previous work in which mono-, di-and tri-carboxylic acids adsorb via one 53 , two 54 or three 55 of their carboxyl groups, respectively ( Supplementary Fig. 2). Di-carboxylic But2/4 (succinic) and Hex2/6 (adipic), however, may adsorb via just one of their carboxyl groups, possibly due to steric constraint on formation of a bidentate mononuclear structure 54 , while tri-carboxylic Pro3/6 might adsorb via two carboxyl groups, although the exact adsorption configuration is unknown 56 . Both mono-and polycarboxylic acids may also form outer-sphere complexes (particularly at basic pH) 57,58 . Since our π* C=O carboxyl carbon peak shift is constant for the mono-(−0.1 ± 0.0 eV), di-(−0.2 ± 0.04 eV) and tri-carboxylic acids (−0.4 ± 0.0 eV) ( Fig. 3 and Supplementary Table 2), our results do not suggest substantial variation in the configuration of our molecules within each acid grouping, although we cannot rule out differences in configurations that result in unresolvable changes to the peak position.
In our coprecipitation experiments, we also observe a secondary affinity related to the number of total carbon atoms (constantn/increasingm), which enhances sequestration but does not significantly enhance stability or persistence. Enhanced sequestration of carboxylic acids with more acidic (pK a < 3) carboxyl groups occurs during their adsorption on metal oxides 59 . Our acids however, have similar acidity (pK a1 , pK a2 and pK a3 all >3, except Eth2/2 and Pro2/3 pK a1 < 3) and do not become more acidic with increasing number of total carbon atoms (Fig. 1). Instead we attribute this secondary affinity to an increasing number of total carbon atoms and thus an increasing number of CH interactions per acid molecule occurring between the molecules and the ferrihydrite particles. These can involve either hydrogen bonding between CH groups and FeOH adsorption sites 60 and/or hydrophobic interactions between the CH groups of multiple OC moieties 37,61 . A reduction in our 1s-σ* C-H /3p/1s-π* CH3,CH2 /3p aliphatic carbon peak amplitudes for the mono-, diand tri-carboxylic acids (Fig. 3) is consistent with increasing CH adsorptive interactions within each acid grouping. These interactions can also result in aliphatic hydrocarbons 62 , polycarboxylic NOM analogues 25 and NOM 19 aligning parallel with iron (oxyhydr)oxide surfaces during adsorption, thus favouring formation of an increasing number of carboxyl ligand exchange bonds between the surfaces and increasingly carboxyl-rich molecules. Compared to carboxyl ligand exchange, however, CH interactions are relatively weak 37 , so while they enhance sequestration, they do not enhance stability or persistence.
While we focus on an experimental coprecipitation system using simple carboxylic acids, by studying this system we determine a direct relationship between carboxyl-richness and sequestration, stability and persistence that we propose extends to NOM sequestration during coprecipitation processes with iron (oxyhydr)oxides in soils and sediments. At first glance, our experiments might not capture the breadth of coprecipitation processes occurring in natural environments. We use simple OC with few carboxyl groups and generate organominerals with relatively low C:Fe (<3 with those <1 subject to STXM NEXAFS and wet chemical treatments) in which OC is sequestered via a multi-carboxyl ligand exchange adsorption mechanism and predominantly located at particle surfaces in a monolayer equivalent. By comparison, NOM is extremely complex 28 , with many carboxyl groups 34 , and previous work indicates that hydroxyl groups, particularly those associated with carbon rings and in vicinal configuration, also play an important role in NOM sequestration 26 . As a likely consequence, experimental coprecipitation of NOM with iron (oxyhydr)oxides and also observations of NOM-iron (oxyhydr)oxide associations in the environment report equivalent 11 or often higher C:Fe, likely involving a combination of adsorption in monolayers and/or multilayers and incorporation into OC-Fe macromolecules and particle interiors 2,14,23,63 . In these studies, however, NOM sequestration is at least partly attributable to a carboxyl adsorption mechanism that tethers NOM to the mineral particles 14,63,64 . Moreover, carboxyl adsorption is suggested as the initially dominant process during organomineral microaggregate formation, rather than incorporation of OC into intraparticle pore spaces 63 . Furthermore, our theoretical adsorption capacity calculations and STXM NEXAFS indicate that, as we increase C:Fe in our tri-carboxylic coprecipitates, some multilayers of OC form, but these are still tethered to the particles via our multi-carboxyl adsorption mechanism. Thus, while multilayer interactions may enhance sequestration 14 and/or OC may become incorporated into macromolecules and particle interiors 23,63 , we suggest that our multicarboxyl adsorption mechanism plays a fundamental role in instigating OC uptake during natural coprecipitation processes.
Our results might also be extended to NOM sequestration during adsorption to preformed iron (oxyhydr)oxides in soils and sediments. At relatively low C:Fe (<1), the sequestration mechanism and spatial distribution of OC in our coprecipitation experiments and those with NOM 11 mirrors that seen in true adsorption experiments, where organics are also sequestered predominantly via a carboxyl adsorption mechanism at particle surfaces 14,25,26,65 . In these studies, O-rich groups, and in particular carboxyl groups attached to aromatic rings, are recently shown to be the first groups to adsorb to iron (oxyhydr)oxides and form a tether for subsequent multilayer interactions 66 . On the other hand, coprecipitation and adsorption processes might result in different chemical distributions of particular organic fractions between mineral and solution. Work on the chemical fractionation of NOM with iron (oxyhydr)oxides during coprecipitation and adsorption is limited and the results are contradictory, although fractionation may depend on NOM chemical composition 14 . Using carboxyl-rich NOM, preferential sequestration of the carboxyl-rich component via carboxyl adsorption leads to an enrichment of the carboxyl fraction with the mineral, and the coprecipitated and adsorbed NOM have very similar chemical composition 14 . Using carboxyl-poor polysacchariderich NOM, preferential sequestration of the polysaccharide component occurs with a greater degree of enrichment during adsorption, and a non-uniform fractionation of individual sugar monomers occurs during the two sequestration processes 12 . Despite the differential sequestration of monosaccharides, however, the dominant sequestration mechanism is the same during coprecipitation and adsorption and predominantly involves carboxyl adsorption 12 . Given that these studies investigating adsorption 25,26,65,66 or both coprecipitation and adsorption 12,14 using a variety of different types of NOM all observe the predominance of a carboxyl adsorption mechanism, we suggest that our multi-carboxyl adsorption mechanism provides a mechanistic basis for understanding the chemical fractionation of NOM in the environment. Overall, although it is unlikely that all NOM carboxyl groups interact with iron (oxyhydr)oxide particles 18,19 , their ubiquity in NOM and dominant involvement in NOM sequestration during both coprecipitation and adsorption processes strongly suggests that carboxyl-richness exerts an important control on NOM sequestration and chemical fractionation with these minerals in soils and sediments.
In soil environments, a carboxyl control on NOM preservation may contribute to observations that the relative proportion of carboxyl-rich NOM increases in mineral aggregates and with soil depth, and thus in the aged soil fraction 63,67 . While this is related to the enrichment of the carboxylic fraction during oxidative degradation 68 , it is also consistent with an enhanced sequestration, stability and persistence of carboxyl-rich NOM with iron (oxyhydr)oxides. Similarly, our results offer mechanistic insight into frequently reported but apparently contradictory observations, where some mineral soils are enriched in aliphatic 69,70 while others contain a predominance of aromatic carbon 71,72 . Our work indicates that NOM preservation in soils is not necessarily related to these fractions, because carboxyl groups can be associated with both these components; rather NOM preservation will at least partly depend on its carboxyl-richness and the association of the carboxyl-rich fraction with iron (oxyhydr) oxides.
In marine environments, our work offers mechanistic insight into the generation and persistence of OC-iron phases in typical continental margin sediments underlain by oxic bottom waters whose molar C:Fe ratios (4.0 ± 2.8) far exceed those expected for monolayer adsorption 2,15 . We show that similarly elevated C:Fe are unlikely to be achieved simply in the presence of more NOM but rather require the presence of more carboxyl-rich NOM. Increasing carboxyl-richness then likely results in a continuum of OC-iron associations, including multilayers ('blebs') of NOM tethered to iron (oxyhydr)oxide surfaces 38 and incorporation of NOM into macromolecules and iron (oxyhydr)oxide particles 2 . Our work might also offer new insight into the enigmatic carboxyl-rich alicyclic molecules (CRAM) component of the dissolved NOM seawater pool 73 . Recent work indicates that marine sediments might be sources of CRAM to both sediment porewaters and the overlying water column 74 , but the mechanism(s) that generate the CRAM signal are unknown 73 . Given the chemical fractionation of NOM with iron (oxyhydr)oxides towards carboxyl-rich components 14,66 and new work showing that OC-Fe colloidal organominerals diffuse out of marine sediments 75 , we suggest that nanoscale OC-Fe colloids, macromolecules and nanoparticles carry a CRAM signal from the sediments into the overlying water column that might be measured as part of the dissolved NOM seawater pool.
Overall our work indicates that NOM sequestration, stability and persistence with iron (oxyhydr)oxides is strongly linked to its carboxyl-richness. A direct extrapolation of our work using iron (oxyhydr)oxides and carboxyl-richness alone to predict NOM persistence, however, is too simplistic. On the one hand, although a substantial proportion of OC is bound to iron (oxyhydr) oxides 2,15 and survives in these OC-iron phases for hundreds to thousands of years 2,9 , clay minerals are also important for OC stabilisation against remineralisation 27 . Additionally, although NOM is carboxyl-rich 34 and associates with iron (oxyhydr)oxides predominantly via carboxyl adsorption 9,14 , NOM is complex 28 and contains a variety of other groups that are also known to interact strongly with these minerals 26 . Instead our results provide a mechanistic framework that can be built upon to predict the affinity, stability and persistence of NOM in soils and sediments. We propose that in future work the link between other mineral sequestration mechanisms and OC persistence is similarly systematically investigated, so that a quantitative relationship between functional group-richness in simple OC moieties can be determined and then extended to more complex NOM. Together with improved understanding of the molecular composition of NOM 34 , a combined molecular level and mechanistic approach might allow us to develop an overarching relationship between organic functional group-richness, mineral interactions and NOM preservation that is required to better understand the controls on the global carbon cycle.

Methods
Ferrihydrite and ferrihydrite carboxylic acid coprecipitate synthesis. Ferrihydrite was synthesised via the rapid hydrolysis of 0.1 M Fe(NO 3 ) 3 .9H 2 O with 1 M KOH at pH~7, under vigorous stirring at room temperature 76 . Carboxylic acid ferrihydrite coprecipitates were synthesised via the rapid hydrolysis of ferrihydrite as above but in the presence of different mono-, di-and tri-carboxylic acids (Fig. 1). Each coprecipitate was synthesised in triplicate and up to 11 different coprecipitate triplicates were generated for each carboxylic acid by sequentially increasing the concentration of C used in the rapid hydrolysis, while keeping the concentration of Fe constant. The initial solution C:Fe molar ratios for most coprecipitates ranged from 0.005 to 10.100, depending on the solubility limit of the carboxylic acid (Supplementary Data 1). Ferrihydrite and coprecipitates were gravitationally separated from the synthesis solution and then washed multiple times with ultrapure water (18.2 MΩ.cm) over a period of 4-5 days until the wash solution was between pH 5 and 7. Ferrihydrite and coprecipitates were stored as wet slurries at 4°C.
Elemental analysis. Total C contents of the ferrihydrite and coprecipitate triplicates were determined on freeze-dried subsamples using a LECO SC-144DR Dual Range Sulphur and Carbon Analyser. Standard medium C and low C soil (no. 502-309, lot no. 1012) were used as analytical standards. Total C content of ferrihydrite was subtracted from total C contents of the coprecipitates to obtain final coprecipitate C contents. Total Fe content of the ferrihydrite and coprecipitate triplicates was determined by inductively coupled plasma mass spectrometry. For complete digestion, 1 mL of 1 M HCl was added to 0.2 mg sample in 10 mL glass vials and then subsequently diluted 10-fold with ultrapure water to obtain 1% (v/v) HCl. All elemental analyses were performed in triplicate.
Surface area analysis. The specific surface area of the ferrihydrite and selected coprecipitate triplicates was determined on freeze-dried subsamples by the multipoint Brunauer-Emmett-Teller method using a Micromeritics Gemini VII 2390a Surface Area Analyser. Samples were degassed at room temperature for 24 h using N 2 (g) (<1 ppm CO 2 (g)) prior to analysis. Graphite was used as an analytical standard. All specific surface area analyses were performed in triplicate.
X-ray diffraction. Mineralogy of the ferrihydrite and selected coprecipitate triplicates was confirmed on freeze-dried subsamples using a Bruker D8 Diffractometer with Cu-Kα radiation (λ ≈ 0.154 nm). Diffractograms were recorded from 2-90°2θ with 0.02°2θ step size and 930 ms acquisition time. Silicon dioxide was used as an analytical standard. Coprecipitate triplicates were homogenised into a single subsample prior to analysis.
STXM/NEXAFS spectroscopy. Coprecipitate triplicates were selected directly from the coprecipitation experiments covering a range of molar OC (from Fh_Met1/1_0.033 to Fh_But3/7_1.943) excluding the tri-carboxylic coprecipitates at their highest surface coverages (i.e. those that exceeded estimated monolayer coverage) and including several data subsets each with approximately constant molar OC and either increasingn/constantm (increasing number of carboxyl groups and constant number of total carbon atoms: Fh_Pen1/5_0.044 vs. Fh_Pen2/ 5_0.043 vs. Fh_Eth3/5_0.048; and Fh_Hex2/6_0.796 vs. Fh_Pro3/6_0.909) or constantn/increasingm (constant number of carboxyl groups and increasing number of total carbon atoms: Fh_Met1/1_0.033 vs. Fh_Pen1/5_0.044; up to Fh_Pro3/6_0.909 vs. Fh_But3/7_1.108). Three coprecipitate triplicates were analysed over a range of molar OC (Fh_Pen2/5_0.043/0.709; Fh_Pro3/6_0.290/0.909; and Fh_But3/7_1.108/1.943). C 1s STXM NEXAFS spectra of the selected coprecipitates were recorded on Beamline I08, Diamond Light Source Ltd, Oxfordshire, UK. Coprecipitate triplicates were homogenised into a single subsample prior to analysis by resuspending~2 mg of each coprecipitate triplicate in~500 μL of ultrapure water and sonicating. An aliquot of~5 μL of suspension was then pipetted onto a Si 3 N 4 membrane window (Silson Ltd) and left to air dry. The membrane windows were glow discharged prior to loading with sample to improve particle distribution. Windows were then inserted into a high vacuum environment (<1 × 10 −5 mBar) and analysed in scanning transmission mode. Stack data sets for C were collected from 275 to 310 eV, using varied energy resolution across different spectral regions of 0.5, 0.1 and 0.2 eV step size for pre-edge, running up to and over the edge, and post-edge, respectively. To maximise spectral resolution, the beamline uses Fresnel zone plates to focus the beam and a collimated plane grating monochromator of SX700-type with an undulator that provides a source size of 300 μm in the horizontal and 50 μm in the vertical plane, which was then refocussed into a secondary source with a 50 μm slit, providing an absolute energy resolution of better than 0.05 eV at the C K-edge. To minimise beam damage on the sample, dwell times were set to 10 ms per energy step following beam damage tests conducted by repeatedly measuring the same area of sacrificial samples. Beam damage manifests as a C NEXAFS peak at an absolute energy of 285.2 eV, attributable to the formation of aromatic C in the beam 77 . Sacrificial spectra with beam damage were discarded but the position of the aromatic C peak was used for absolute energy calibration by shifting all spectra in energy space by the required energy to align the beam damage peak to 285.2 eV. Reference spectra for the unreacted acids were obtained from unmodified acid solids or liquids as applicable. The dark signal was measured routinely by scanning a small area with the sample shutter closed. X-ray absorption stacks were aligned using the Axis2000 software. Spectra were extracted from the edge regions of individual coprecipitate particles and the dark signal was subtracted from the raw data using the Mantis software. Spectra were then exported for baseline correction, alignment, calibration and normalisation using the Athena software 78 . Baseline correction and normalisation avoid spectral dependence on the total C content, and as such, spectral features and peak shifts are indicative of C molecular structure and chemistry and not carbon concentration effects occurring during NEXAFS measurement. Peak identification for the normalised spectra was achieved with reference to literature assignations (Supplementary Table 1).
To show the spatial correlation between C and Fe, C and Fe elemental distribution maps were first created by aligning and then converting C and Fe images to optical density (OD) by using the transmitted flux through the sample (I) and the incident flux measured in an empty region adjacent to the analysed particles (I0) where OD = ln(I0/I). C and Fe distribution maps taken on the same region of interest and with the same number of pixels were then aligned to common reference features and overlapped. To determine the C-Fe correlation coefficients, elemental thickness values on a pixel-by-pixel basis were compared by extracting the OD values using the Axis 2000 software, saved as an ascii file, and then the OD values for both C and Fe stacks were plotted against one another. The energies for obtaining the C and Fe distribution maps were C 1s 282.0-289.0 eV and Fe 2p 705.0-712.0 eV. According to Lambert Beer's law, the OD is directly proportional to the amount (thickness) of the element of interest in the X-ray beam path. It should be noted that, because the lowest energy used for the mapping is for C, and because heavier elements (mainly Fe) in the particles will absorb X-rays, C is not quantitatively mapped for particles with varying thickness. Regions where the particles are relatively thin will appear to be more concentrated in C than regions where the particles are relatively thick. Relative changes in OD across a particle are therefore not necessarily indicative of C distribution. For particles of varying thickness, however, the edge regions are generally thinner than the central regions, and thus the STXM signal at the edge regions reflects C mainly located at the particle surfaces, while the STXM signal in the central regions reflects C located at the particle surfaces and in the particle interiors. If C appears to be more concentrated at the edge regions than the central regions, then the distribution of C across the whole particle is approximately equal to that at the particle surfaces and is not substantially augmented in the central regions by additional C associated with the greater particle volume. In this case then, C distribution can be interpreted to be mainly at the particle surfaces, without substantial sequestration into the particle interior.
Desorption and oxidation. Coprecipitate triplicates were selected directly from the coprecipitation experiments covering a range of molar OC (from Fh_Met1/1_0.055 to Fh_But3/7_1.108) excluding the tri-carboxylic coprecipitates at their highest surface coverages (i.e. those that exceeded estimated monolayer coverage) and including several data subsets each with approximately constant molar OC and either increasingn/constantm (increasing number of carboxyl groups and constant number of total carbon atoms) or constantn/increasingm (constant number of carboxyl groups and increasing number of total carbon atoms). Desorption of OC from the selected coprecipitate triplicates was achieved using artificial seawater (pH 8) and 0.1 M NaOH (pH 12), while chemical stability of OC associated with the selected coprecipitate triplicates was tested via oxidation with NaOCl 24,79 . Use of NaOCl affects Fe (oxyhydr)oxides less strongly than H 2 O 2 * 24,79 . Wet coprecipitate slurry was mixed with either artificial seawater or 0.1 M NaOH at a solid:solution ratio of 5 g dry coprecipitate L −1 , and samples were gently agitated end-over-end for 24 h. Solids were separated by centrifugation and the dilution cycle was repeated for a total of five cycles. After the last cycle, solids were separated and freezedried for elemental analysis. All elemental analyses were performed in triplicate. Wet coprecipitate slurry was mixed with 1 M NaOCl at a solid:solution ratio of 10 g dry coprecipitate L −1 , and samples were gently agitated end-over-end at room temperature for 6 h. Carboxylic acids exhibit a reverse adsorption edge on iron (oxyhydr)oxide particles with desorption beginning >pH 3.5 26 . The pH of the 1 M NaOCl was therefore set to pH 3.5 using a few μL of concentrated HCl to ensure that OC removal was due to reduction-release only. After the designated reaction time, solids were separated and freeze-dried for elemental analysis. All elemental analyses were performed in triplicate. Given the reverse adsorption edge for carboxylic acids on iron (oxyhydr)oxides 26 , the artificial seawater treatment at pH 8 is the least aggressive towards OC release, while the 0.1 M NaOH at pH 12 and the 1 M NaOCl, which chemically oxidises OC, are the most aggressive towards OC release. It should be noted that the selected coprecipitate triplicates were also washed with ultrapure water set at pH 3.5 as described above for artificial seawater and 0.1 M NaOH, although because the samples were washed with ultrapure water immediately after their synthesis this wash was not expected to result in significant desorption.
Desorption of OC from selected coprecipitate duplicates reproduced from the coprecipitation experiments was also performed with 0.1 M NaOH as a function of time in a batch desorption approach, with coprecipitate duplicates chosen and individual experiments set up as above for the first desorption cycle but sacrificed at 1, 24, 48 and 96 h (data subset with approximately constant molar OC and increasingn/constantm Fh_Pen1/5_0.044 vs. Fh_Pen2/5_0.045 vs. Fh_Eth3/ 5_0.054; and data subsets with increasing molar OC with constantn/constantm Fh_Pen2/5_0.045 vs. Fh_Pen2/5_0.550 and Fh_Eth3/5_0.054 vs. Fh_Eth3/ 5_0.547). After the designated desorption time, solids were separated and freezedried for elemental analysis. All elemental analyses were performed in duplicate. In all desorption and oxidation experiments, total OC desorbed or released was calculated as the difference between the initial C content of each coprecipitate and the final C content after desorption or oxidation.
Theoretical adsorption capacity. To define the theoretical adsorption capacity, we considered the surface coverage of a monolayer, in which either just one COOH group from each acid molecule binds to a FeOH adsorption site (referred to here as one-carboxyl adsorption and resulting in the maximum monolayer OC loading for the number of adsorption sites) or all COOH groups from each acid molecule each bind to a FeOH adsorption site (resulting in two-and three-carboxyl adsorption for di-and tri-carboxylic acids, respectively, and the minimum monolayer OC loading for the number of adsorption sites). We neglected any steric or electrostatic hindrance resulting from the close packing of the acid molecules in the one-, two-and three-carboxyl scenarios and assumed that carboxyl binding can occur using every FeOH adsorption site. Spectroscopic evidence indicates that, in a one-carboxyl scenario, the mono-, di-and tri-carboxylic acids could adsorb using only one carboxyl group per adsorbing acid molecule, and this carboxyl group binds to one FeOH adsorption site, in either a single-bonded or twice-bonded configuration 53,54 ( Supplementary Fig. 3a). In theory, the one-carboxyl twice-bonded configuration is the 'worst case scenario' for one-carboxyl adsorption because, compared to the single-bonded configuration, it tethers one carboxyl group to the surface but requires two FeOH adsorption sites, while the single-bonded configuration similarly tethers one carboxyl group but requires only one FeOH adsorption site. Spectroscopic evidence indicates that, in a two-carboxyl scenario, the di-and tricarboxylic acids could adsorb using two carboxyl groups per adsorbing acid molecule, and these carboxyl groups bind to either one FeOH site (bidentate mononuclear) or two FeOH sites (bidentate binuclear) 54 (Supplementary Fig. 3b). In theory, the bidentate binuclear configuration provides the 'worst case scenario' for two-carboxyl adsorption because, compared to the bidentate mononuclear configuration, it tethers two carboxyl groups to the particle surface but requires two FeOH sites, while the bidentate mononuclear configuration similarly tethers two carboxyl groups to the particle surface but requires only one FeOH site. Spectroscopic evidence indicates that, in a three-carboxyl scenario, the tri-carboxylic acids could adsorb using three carboxyl groups per adsorbing acid molecule, and these carboxyl groups bind to three FeOH sites (tridentate trinuclear) 55 ( Supplementary  Fig. 3c). To calculate the theoretical adsorption capacity, we then used the fact that there are 5.8 FeOH adsorption sites nm −2 as recently determined from an analysis of the ferrihydrite surface structure 80 . It should be noted that, in the one-carboxyl single-bonded scenario (where the acids adsorb via one carboxyl group per adsorbing acid molecule to one FeOH site), with 5.8 sites nm −2 and 1 COOH group/site, each COOH group occupies~0.17 nm 2 , which is comparable to 0.205 nm 2 estimated for the adsorption of a COOH group to hydrous γAl 2 O 3 * 59 .
To calculate the measured surface adsorption (mg C m −2 ), we nominally assumed that all our measured OC (mg C g −1 ) is adsorbed in a monolayer at the particle surfaces (m 2 g −1 ). The specific surface area for the pure ferrihydrite and the ferrihydrite coprecipitates are 333 ± 14.8 m 2 g −1 and between~327 ± 17.0 and 202 ± 9.1 m 2 g −1 , respectively (Supplementary Data 1), and show that, in the presence of the carboxylic acids, ferrihydrite appears to possess a significantly lower specific surface area and thus a larger particle size. X-ray diffraction of the coprecipitates, however, shows that, as the number of carboxyl groups increases, the crystallinity of the ferrihydrite decreases ( Supplementary Fig. 4). This counterintuitive effect is likely because the ferrihydrite surface is somewhat masked by the adsorbed carboxylic acid, and OC molecules have a comparatively much lower specific surface area 11,81 . In keeping with previous work on the sorption of OC to iron (oxyhydr)oxides 11 we therefore assumed that the ferrihydrite fraction of the coprecipitates has at least the same specific surface area as the pure ferrihydrite, i.e. 333 m 2 g −1 .
In the main text, the theoretical adsorption capacities of the coprecipitates for the 'worst case scenarios' for one-, two-and three-carboxyl adsorption (i.e. onecarboxyl twice-bonded, bidentate binuclear and tridentate trinuclear configurations, respectively) are compared to the OC loading.
Kinetic desorption experiment modelling. The kinetics of desorption can be described as a first-order expression as follows 82 : where θ is the concentration of sorbate, t is time (h) and k is the apparent desorption constant (h −1 ). Considering two pools of OC, one for desorbable carbon and one for non-desorbable carbon, the above equation can be solved as 47 : where θ t is the total concentration of carbon associated with the ferrihydrite particles, θ 0 is the concentration of desorbable carbon at time zero, θ ∞ is the concentration of non-desorbable carbon where the modelled carbon approaches an asymptote and, as above, k is the apparent desorption rate (h −1 ) and t is time (h). Similar to the concept of the multi-G model 49,83 for the degradation of organic matter, a three-pool model may also be considered, with two pools of desorbable carbon and a pool of non-desorbable carbon as follows 47 : where θ t is the total concentration of carbon associated with the ferrihydrite particles, θ 01 is the concentration of highly desorbable carbon at time zero, θ 02 is the concentration of less desorbable carbon at time zero, θ ∞ is the concentration of nondesorbable carbon where the modelled carbon approaches an asymptote, k 1 and k 2 are the apparent desorption rates of the highly and less desorbable carbon (h −1 ), respectively, and as above, t is time (h).
To determine the preferred model, we calculated the R 2 and the model selection criteria, the latter of which allows comparison between models with a different number of fitting parameters and where a higher value signifies a better goodness of fit for a smaller number of parameters 84 .
The two-pool model provides adequate fits to the data (R 2 ≥ 0.960 in all cases; model selection criteria average over all cases 2.85 ± 0.66; Supplementary Data 5 and Supplementary Fig. 11). Commensurate with the stability experiments, the desorbable pool and apparent desorption rate decrease with increasing number of carboxyl groups and increase with increasing molar OC sequestered. The nondesorbable pool increases with increasing number of carboxyl groups and decreases with increasing molar OC sequestered, but it is overestimated in all cases. The three-pool model provides better fits to the data (R 2 ≥ 0.999 in all cases; model selection criteria average over all cases 6.06 ± 1.03; Supplementary Data 5 and Supplementary Fig. 11) by allowing for a slower desorption rate of one of the desorbable pools. This results in a highly desorbable pool and apparent desorption rate that decrease with increasing number of carboxyl groups and increase with increasing molar OC sequestered but a less desorbable pool with a lower desorption rate that increases with increasing number of carboxyl groups and decreases with increasing molar OC sequestered. In agreement with the two-pool model, the non-desorbable pool increases with increasing number of carboxyl groups and decreases with increasing molar OC sequestered but without overestimation.