A mechanistic model for understanding root-induced chemical changes controlling phosphorus availability

doi:10.1093/aob/mcq098

Ann Bot. 2010 June; 105(7): 1183–1197.

Published online 2010 May 22. doi: 10.1093/aob/mcq098

PMCID: PMC2887072

A mechanistic model for understanding root-induced chemical changes controlling phosphorus availability

Nicolas Devau,¹ Edith Le Cadre,² Philippe Hinsinger,¹ and Frédéric Gérard¹^*

¹INRA

²Supagro, UMR 1222 Eco&Sols – Ecologie Fonctionnelle & Biogéochimie des Sols (INRA-IRD-SupAgro), Place Viala, F-34060 Montpellier, France

^*For correspondence. E-mail gerard/at/supagro.inra.fr

Received January 21, 2010; Revised March 23, 2010; Accepted April 19, 2010.

This article has been cited by other articles in PMC.

Abstract

Background and Aims

Plant nutrition models do not properly account for the effects of root-induced chemical changes in the rhizosphere, e.g. pH changes, on the availability of nutrients such as phosphorus (P). As a result, they underestimate the actual P uptake, i.e. P bioavailability to the plant, in low-P soils. The present study aims at simulating root-induced chemical mechanisms controlling P nutrition in a P-limited soil.

Methods

In this work a mechanistic description for the adsorption of cations and anions by soil constituents (1pK-Triple Plane Model, ion-exchange and Nica–Donnan) was used to simulate changes induced by durum wheat (Triticum durum turgidum) in the P availability of the soil, as measured by water and CaCl₂ extraction. Calcium (Ca) availability was also measured and simulated.

Key Results

The simulations were found to be in close agreement with experimental data. In the rhizosphere, the goodness-of-fit required to account for the measured uptake of Ca by plants, in addition to the measured uptake of P and root-induced alkalization, were satisfactory. Calcium uptake significantly increased P availability, as assessed through water extraction, by decreasing the promoting effect of Ca adsorption on P adsorption. The study thus enabled P and Ca availability to be related to their bioavailability for durum wheat under experimental conditions. It was also shown that P was primarily adsorbed onto Fe oxides and clay minerals (kaolinite and illite) depending on soil pH. The major source of P for durum wheat nutrition was P desorbed from goethite and kaolinite.

Conclusions

In addition to confirming the validity of our approach to model P availability, the present investigation suggested that in the studied soil, a novel root-induced chemical process was controlling P nutrition under P-deficient conditions, namely the uptake of Ca.

Keywords: Triticum turgidum durum, rhizosphere, phosphorus, calcium, pH, adsorption, surface complexation model

INTRODUCTION

Phosphorus (P) is the least mobile major nutrient in soils and is frequently the prime limiting factor for plant growth (Hinsinger, 2001; Raghothama and Karthikeyan, 2005). In standard plant nutrition models, the amount of P taken up by plants (i.e. P bioavailability) depends on both (a) the concentration of P in soil that can be taken up by plants, i.e. P availability, and (b) P uptake kinetics, as well as soil transfer and root growth processes (Schenk and Barber, 1979; Silberbush and Barber, 1983; Geelhoed et al., 1999; Dunbabin et al., 2002; Kirk, 2002; Wissuwa, 2003; Mollier et al., 2008). Standard plant nutrition models can predict P bioavailability in soils exhibiting high P availability well but they also invariably underestimate it in soils with low P availability (Barber, 1995; Geelhoed et al., 1997a; Mollier et al., 2008). Silberbush and Barber (1983) and Geelhoed et al. (1997a) suggested that the failure of standard plant nutrition models to simulate P bioavailability under low P availability was due to the method used to simulate P availability. Indeed, Silberbush and Barber (1983) showed with sensitivity analysis that variables describing P availability were the second most important in controlling P bioavailability, after root elongation variables.

Several types of adsorption isotherms are used to simulate P availability in standard plant nutrition models (McGechan and Lewis, 2002) based on the assumption that adsorption is more likely to control P availability in soils (Hinsinger, 2001; McDowell et al., 2003). These adsorption isotherms aim at simulating only the decrease in P availability occurring as a result of plant uptake. However, it is well known that plants have evolved complex strategies to acquire soil P. Indeed, plants can alter P availability by acting through their roots and associated microorganisms on several chemical properties of the soil in their vicinity, i.e. the rhizosphere (Barber, 1995; Hinsinger, 2001; Harmsen et al., 2005; Hinsinger et al., 2009). Chemical properties such as pH, concentration of various organic ligands, CO₂ partial pressure and redox potential can be altered by living plant roots. In addition, carbon exudates released by plant roots coating mineral surfaces (Weng et al., 2008) and mineral dissolution (Bertrand et al., 1999) can occur in the rhizosphere, both altering the adsorption properties of minerals compared with bulk soil. Variations in pH are considered as the root-induced chemical change having the greatest effect on P availability in the rhizosphere of many species (Rengel and Marschner, 2005). Root-induced pH changes can be as much as several units in the rhizosphere and thus can have a dramatic influence on biogeochemical processes controlling P availability (Hinsinger, 2001). Hinsinger and Gilkes (1995) concluded that pH was the main driving force to explain changes in P availability and bioavailability measured for narrow leaf lupin (Lupinus angustifolia) and white lupin (Lupinus albus). Gahoonia et al. (1992) also found that root-induced acidification considerably changed P availability and bioavailability for ryegrass (Lolium perenne) in a Luvisol. Nevertheless, the same authors found in another soil type, an Oxisol, that acidification only slightly affected P availability and bioavailability for ryegrass. This point illustrates the difficulty in capturing the exact nature of the root-induced chemical mechanisms that control P availability and bioavailability (Hinsinger, 2001).

Mechanistic numerical models adapted to the modelling of processes controlling the availability of nutrients have been used in an attempt to understand better root-induced chemical changes and their effects on P availability, especially under limited P supply. This was made by modelling the changes in P availability observed between the rhizosphere and bulk soil, i.e. the soil region not influenced by roots. Geelhoed et al. (1999) developed such a model to assess explicitly citrate–phosphate interactions in the rhizosphere of maize (Zea mays), in an artificial substrate made of quartz sand and goethite. They obtained a poor agreement between measured and simulated P availability, undoubtedly because of an inadequate description of other root-induced mechanisms.

The mechanistic adsorption models used by Geelhoed et al. (1999) have been shown capable of predicting P availability in artificial mineral assemblages made of one or two minerals, which are far from the actual complexity of soils (complex assemblages of minerals, occurrence of natural organic matter, etc.). Gustafsson (2001) failed to simulate P availability in a soil sample using the same type of adsorption models, but he only accounted for P adsorption onto Al- and Fe oxides. He concluded that other reactive mineral surfaces, such as clay minerals, were important to consider when simulating P adsorption process. This finding has been confirmed recently by Devau et al. (2009) who simulated the variations in P availability (as measured by CaCl₂ extraction) in a soil as a function of pH by accounting for P and Ca adsorption onto clay minerals, metal oxides and natural organic matter.

The present study aims at identifying the root-induced chemical mechanisms controlling P nutrition in a P-limited soil. For this purpose, a set of mechanistic adsorption models was used to simulate the P availability measured in the rhizosphere and bulk soil. Also the importance of the variations in the adsorption properties in the rhizosphere was evaluated by considering soil samples brought to different pH values.

MATERIALS AND METHODS

Soil properties

The studied topsoil (0–20 cm depth) was sampled at Cazevieille (Hérault, France; 43 °46′N, 3 °47'E). The soil is classified as a Chromic Cambisol (FAO-UNESCO, 1989). The site corresponds to xerotypic shrubland developed in a humid Mediterranean climate. The soil sample was air dried and sieved to 2 mm prior to chemical analyses. Soil properties have been comprehensively described in Devau et al. (2009).

Briefly, the basic soil properties are the following: pH 6·5 (measured in 0·01 m CaCl₂), 31 g kg⁻¹ of organic C (ISO, 1999), 950 mg kg⁻¹ of total P (sulfuric and perchloric acids digestion method) and 148 mg kg⁻¹ of total adsorbed P (ammonium oxalate method). This soil exhibited a low concentration of P availability (P-Olsen = 5 mg kg⁻¹) and 4·01 g kg⁻¹ of exchangeable Ca (cobaltihexamine chloride method), which constituted 91 % of the cation exchange capacity of the soil material (the rest being constituted by 4 % Mg, 3 % K and traces of Al and Fe).

Devau et al. (2009) also determined that the soil contained two Fe oxides, goethite (30·9 g kg⁻¹) and ferrihydrite (0·3 g kg⁻¹), and some gibbsite (5 g kg⁻¹). These authors identified and quantified also two types of clay minerals, kaolinite (175·6 g kg⁻¹) and illite (199·7 g kg⁻¹).

Plant growth conditions

Plants were grown in a mini-rhizobox device that separates plant roots from soil by a 30-μm polyamide mesh to facilitate the collection of roots and rhizosphere, as described in detail by Li et al. (2008). The plant species used in the experiment was durum wheat (Triticum turgidum durum L. ‘Acalou’).

Briefly, 120 seeds of durum wheat were sterilized with 6 % H₂O₂ for 10 min. and germinated in Petri dishes over filter papers wetted with 600 µm and 2 µm of CaCl₂ and H₃BO₃, respectively. After 1 week, all the seedlings were transferred to 6-dm³ buckets containing a nutrient solution of the following composition (μm): Ca(NO₃)₂, 2000; KNO₃, 2000; MgSO₄, 1000; KH₂PO₄, 50; Na₂FeEDTA, 25; H₃BO₃, 10; MnCl₂, 2; ZnSO₄, 1; CuCl₂.5H₂O, 1; Na₂MoO₄, 0·05.

Meanwhile soil was incubated with the same nutrient solution minus P for 2 weeks in the growth chamber at about 70 % of water-holding capacity. In order to get enough rhizosphere material for measurements of P availability as a function of soil pH, 60 minirhizoboxes (e.g. Li et al., 2008) were used. In each device, one 2-week-old seedling was then transferred between two 10 cm × 20 cm mesh bags filled with 34 g of soil (packed in a 1-mm-thick layer). After transplanting, the cropping devices were supplied with P-free nutrient solution through a filter paper wick connected to a nutrient solution reservoir. Prior to the transfer of plants, the soil moisture was increased up to the water-holding capacity (i.e. field capacity). These conditions were maintained over the whole experiment. At the transplanting stage, the 60 remaining durum wheat plantlets were harvested to serve as reference for plant biomass, P and Ca concentrations. An additional 60 soil-containing mesh bags were prepared without plants and were incubated at the water-holding capacity with a P-free nutrient solution to serve as no-plant control soil (i.e. bulk soil).

After 21 d of contact, plants were harvested and the entire soil in the mesh bag was considered as rhizosphere. The experiment was conducted in a growth chamber with the following conditions (day/night): 16 h/8 h light/dark cycles, 550 µmol photons m⁻² s⁻¹ flux density, 25/20 °C temperature and 75/70 % air relative humidity.

Soil pH adjustments

Immediately after harvest, the 60 replicates of rhizosphere and bulk soil were pooled and mixed to form one homogeneous sample of either rhizosphere or bulk soil. Subsamples of the pooled rhizosphere and bulk soil were acidified or made alkaline by adding 10, 20, 25, 35, 60, 80, 100, 125, 150, 175 mmol of either acid (HCl) or alkali (KOH) per kg of soil (on an air-dried basis). The addition of acid or alkali increased the water-holding capacity of soil samples (<1 %) very little. One sample of the rhizosphere and bulk soil was not adjusted for pH. These samples will be referred to as untreated samples. Each type of soil sample, whether acidified, made alkaline or untreated, was replicated three times. Soil samples were then incubated at 25 °C for 84 h.

Soil and plant analyses

After 84 h of incubation, we extracted soil samples with CaCl₂ (0·01 m) and ultrapure water (simply called water herein) at a soil : extractant ratio of 1 : 5 and centrifuged at 15 500 g for 10 min. These two extractions provide indicators of P availability (Houba et al., 1990; Sonneveld, 1990). It was also assumed that these two extractions provided indicators of Ca availability. After centrifugation, supernatants were filtered through 0·45-μm cellulose acetate membrane filter (VWR international). Phosphorus and Ca concentrations were measured in the CaCl₂ and water extracts with the malachite green method (Ohno and Zibilske, 1991) and by flame atomic adsorption spectrometry (Varian FS-220, Australia), respectively. Phosphorus and Ca availability correspond to measured concentrations expressed per unit of soil mass (kg). The soil pH was measured in each supernatant (water and CaCl₂) using a Metrohm pH-meter. Also the concentration of dissolved organic carbon (DOC) in each supernatant was measured with a total organic carbon analyser (TOC-6000; Shimadzu, Japan).

The concentrations in fulvic and humic acids in the soil organic matter were determined by means of the well-known NaOH extraction (e.g. Lumsdon, 2004) applied to the untreated bulk soil sample. According to this method, the DOC concentration of the supernatant corresponds to fulvic and humic acids. The supernatant was then acidified (pH 2) and left 16 h to allow the humic acids to precipitate. The DOC concentration remaining in the supernatant corresponded to fulvic acids. The concentration of humic acids was estimated from the difference in DOC prior to and after acidification.

Roots and shoots of plants in contact with soil as well as plants at transplanting were separated. Shoots and roots used to measure P and Ca concentrations were oven-dried at 105 °C and weighed for dry biomass determination. Shoots and roots were then ground (MM 2000, Retsch) and digested in a microwave oven (Ethos touch Control, Milestone) in concentrated HNO₃ (65 %) at 180 °C and 2 10⁶ Pa. Phosphorus and Ca concentrations in the digests were measured using the vanado-molybdate method (AFNOR, 1999) and by flame atomic absorption spectrometry (Varian FS-220, Australia), respectively. Blanks and reference materials of maize leaves (Zea mays, V 463; Bureau Interprofessionnel d'Etudes Analytiques, France) were included during digestions and analyses to check the accuracy of the measurement procedure.

In the present study, P bioavailability was assumed to be equal to the difference between the total P content (mg plant⁻¹) accumulated in the plant after 21 d of contact with soil and the value observed in plants after 2 weeks of hydroponic pre-culture (control plants). Calcium bioavailability was calculated in the same way.

Models

An additive approach was used to simulate P availability in the rhizosphere and bulk soil set at different pH values. This approach assumes that the adsorption properties of the overall soil are equal to the sum of the adsorption properties of its constituents (Davis et al., 1998, 2004; Gustafsson, 2001; Goldberg et al., 2007). In addition, several studies showed that the adsorption of cations such as Ca must be simulated to assess P adsorption adequately (Stachowicz et al., 2008; Devau et al., 2009; Hiemstra et al., 2010). Therefore we selected models for their ability to cope with multicomponent adsorption and different soil constituents.

Three thermodynamic adsorption models were used: (1) the 1-pK Triple Plane Model (TPM) with charge distribution for the adsorption of anions and cations onto Fe and Al-oxides and clay edge sites (Hiemstra and Van Riemsdijk, 1996); (2) the ion-exchange model for the adsorption of cations onto the permanent negatively charged sites of clay minerals (McBride, 1989); and (3) the Nica–Donnan model for the adsorption of cations onto dissolved and soil organic matter (Kinniburgh et al., 1996).

Model equations are given in the Appendix. In brief, the 1-pK TPM reproduces the fact that clay minerals and oxides have a charged surface that varies because of the protonation and deprotonation of its hydroxyl sites bound to Al or Fe atoms (Hiemstra and Van Riemsdijk, 1996; Kinniburgh et al., 1996). Adsorption of cations or anions, such as P or Ca ions, onto clay minerals or oxides was described to account for either innersphere or outersphere surface complexes. According to the TPM, the electrical charges of the adsorbed ions are distributed in a diffuse double layer represented by three electrostatic planes. The volume defined between the first and the second planes involves the surface sites and innersphere surface complexes. The volume between the second and the third planes concerns outersphere surface complexes (Hiemstra and Van Riemsdijk, 1996). Ion exchanges are equivalent to surface complexation reactions without electrostatic effects. In the model used to cope with the effects of natural organic matter, the distributions of the binding sites for protons and cations of carboxylic and phenolic groups were represented with a continuous function. Electrostatic effects were described by means of a Donnan model (Kinniburgh et al., 1999).

Calculations were performed with the software Visual MINTEQ (Gustafsson, http://www.lwr.kth.se/English/OurSoftware/vminteq/). This geochemical software uses the Newton–Raphson method to solve the set of non-linear equations. The thermodynamic data used for the calculation of the aqueous speciation and of the saturation state of minerals with respect to the extracted solutions came from the MINTEQA2 version 4·0 database (US Environmental Protection Agency, 1999).

Input data

For the simulations of P availability in the bulk soil, the total concentration of P used as model input corresponded to the total adsorbed concentration as measured by ammonium oxalate in the untreated sample. As Ca is by far the most abundant cation in the cation exchange capacity of the soil used in the present experiment, its adsorption was also included in the simulations. In contrast, the influence of the adsorption of other divalent cations such as Mg was ignored, as it is recognized that their adsorption has a much smaller influence on P adsorption (e.g. Violante and Pigna, 2002; Stachowicz et al., 2008). For water extracts, the Ca concentration extracted by cobalthexamine chloride was used as the total concentration adsorbed in the soil. For the simulation of CaCl₂ extracts, the amounts of Ca and Cl brought into the system by the extraction solution were also accounted for.

Three scenarios for the modelling of P availability in the rhizosphere were considered. In the first scenario (S1), P uptake by durum wheat was the sole root-induced chemical mechanism included in the model, whereas the pH and total dissolved Ca concentration were set to their values measured in the bulk soil. In the second scenario (S2), the effect of root-induced pH variations to P uptake was added. Devau et al. (2009) showed in the same soil that the presence of Ca can dramatically influence P adsorption. Hence as the third scenario (S3), the uptake of Ca by durum wheat was added on top of P uptake and pH changes.

Since the present modelling investigation was performed under equilibrium conditions, the temporal dynamics of the soil–root interactions, such as can be represented by Michaelis–Menten kinetics to simulate nutrient uptake, were ignored (e.g. Nowack et al., 2006; Gérard et al., 2008; Szegedi et al., 2008). Therefore, in the three aforementioned scenarios, the uptake of P and Ca by durum wheat was taken into account by removing the measured values of P and Ca bioavailability from the concentrations set as model input for the simulations in the bulk soil.

Variations in soil pH, either induced naturally by the activity of roots or artificially by the addition of alkali or acid, were simulated by using the measured values as the model inputs.

Model parameters

Model parameters were assumed identical in both bulk soil and rhizosphere. Parameters used in: (a) the 1-pK TPM to describe the adsorption/desorption of protons, P, Ca and Cl ions onto the five mineral surfaces occurring in the studied soil (goethite, ferrihydrite, gibbsite, kaolinite and illite); (b) the ion-exchange model for the adsorption of Ca ions onto permanent negatively charged sites of clay minerals; (c) the Nica–Donnan model for the adsorption of Ca ions and protons onto organic matter, are given in the Appendix (Table A3). Their origin has been discussed recently in Devau et al. (2009).

To sum up, the occurrence of three types of P innersphere surface complexes (monodentate, bidentate and protonated bidentate), which were deduced from infrared spectroscopy (Tejedor-Tejedor and Anderson, 1990) were considered. These surface complexes have the same reaction stoichiometry for the five soil minerals but their equilibrium constants change according to the mineral. For the modelling of CaCl₂ extraction, Cl was assumed to be adsorbed as an outersphere complex by all the minerals (Rahnemaie et al., 2005a). Calcium adsorption onto goethite and ferrihydrite occurred as innersphere monodentate surface complexes (Rahnemaie et al., 2005b). For gibbsite, Ca adsorption was described by means of three innersphere complexes. Their formation reaction differs by the number of protons released from the mineral surface (ranging from 0 to 2). The adsorption of Ca onto the edge sites of kaolinite was controlled by the formation of an innersphere bidentate surface complex and an outersphere bidentate surface complex associated with the release of two protons. The adsorption of Ca onto illite was simulated by accounting for the formation of a single outersphere monodentate surface complex and two bidentate surface complexes (outersphere and innersphere complexes). Exchange reactions between Ca and two protons onto the permanent negatively charged sites of clay minerals were also considered.

Concerning the adsorption of Ca and protons onto natural organic matter, it was assumed that dissolved and soil organic matter behave like generic humic and fulvic acids in terms of acid/base and metal binding properties (Milne et al., 2001, 2003). The proportion of humic acids versus fulvic acids in the soil organic matter was determined from the results of the NaOH extraction. The common assumption that the whole DOC behaves like the generic fulvic acid was made (e.g. Dudal and Gérard, 2004).

Statistics

The statistical analyses were performed with R software (CRAN, 2006). The variations in P or Ca availability between the bulk soil and rhizosphere as a function of pH or extraction method were tested by means of a two-way, non-parametric analysis of variance (Friedman test). The same statistical test was applied to study the influence of root activity on the soil pH, as measured by CaCl₂ and water extraction.

With respect to plant variables, the difference after 21 d of growth in dry biomass, P and Ca concentrations in plant tissues and total P and Ca contents in plants were tested with a standard one-way ANOVA.

The goodness-of-fit for the simulations of P and Ca availability on untreated samples and over a range of soil pH in both rhizosphere and bulk soil was estimated by two statistical criteria. The first is the root mean square error (RMSE):

A mathematical equation, expression, or formula.
Object name is mcq098eqn1.jpg

where n is the number of samples, corresponding to different soil pH values, X_o,i are the measured P concentrations and X_c,i is the concentration calculated by the model.

This RMSE is a measure of the scatter around the observed mean between measured and calculated values. The mean residual error (MRE) was also used to evaluate the direction of the error:

A mathematical equation, expression, or formula.
Object name is mcq098eqn2.jpg

Values of the MRE close to zero indicate an absence of bias in the model predictions.

RESULTS

Plant growth and P and Ca in biomass

Shoot and root dry biomasses of durum wheat increased significantly after 21 d of growth in contact with the soil material (Table 1). Plant biomass increased 14-fold from the pre-culture to the culture stages. The root : shoot ratio of durum wheat was larger in soil-grown plants than in plants at transplanting. Conversely, after 21 d of growth in contact with our P-deficient soil, P concentrations in both roots and shoots had decreased by 93 % and 91 %, respectively. Calcium concentration in plant shoots decreased as well between the pre-culture and the culture stages. Only in roots did Ca concentration increase after 21 d of contact with soil. Lastly, plant P and Ca contents increased significantly during the 21 d of contact with the soil material (Table 1).

Table 1.

Dry biomass, P and Ca concentrations in shoots and roots of durum wheat and plant P and Ca content (n = 60) for two growing stages: at transplanting (pre-culture) and after 21 d of contact with soil (culture)

Phosphorus and Ca availability in untreated soil samples

The measured and simulated values of P and Ca availability in the untreated bulk soil and rhizosphere (i.e. without addition of alkali or acid) for both CaCl₂ and water extractions are shown in Fig. 1.

Fig. 1.

Phosphorus (A) and Ca (B) concentrations resulting from extraction either by CaCl₂ or water (i.e. P and Ca availability) in the untreated bulk soil and rhizosphere. Open columns and closed columns stand for the measured values in the bulk soil (B) and (more ...)

Phosphorus and Ca concentrations measured in CaCl₂ extracts were significantly lower in the rhizosphere than in bulk soil (Fig. 1). Contact with roots led to a decrease in P and Ca availability by 23 % and 18 %, respectively. In contrast, P availability as measured in water extracts was significantly higher in the rhizosphere than bulk soil while Ca availability decreased by up to 66 % between the bulk soil and rhizosphere. Regardless of the extraction method, soil pH significantly increased by about 0·6 pH units in the rhizosphere compared with bulk soil.

Phosphorus and Ca concentrations in the bulk soil and rhizosphere were successfully simulated for both extractions (Fig. 1). In the bulk soil, simulated and measured P and Ca availability were well matched in both CaCl₂ (RMSE = 1·1 µg kg⁻¹, MRE = 2·5 µg kg⁻¹ and RMSE = 13 mg kg⁻¹, MRE = −13 mg kg⁻¹ for P and Ca, respectively) and water extracts (RMSE = 17·2 µg kg⁻¹, MRE = −2·3 µg kg⁻¹ and RMSE = 18·2 mg kg⁻¹, MRE = 16·9 mg kg⁻¹ for P and Ca, respectively). In the rhizosphere, P availability was more accurately predicted with the third scenario (P uptake, alkalization and Ca uptake). An RMSE of 2·1 µg kg⁻¹ and 18 µg kg⁻¹, and a MRE of 0·3 µg kg⁻¹ and −2·1 µg kg⁻¹ were obtained with CaCl₂ and water extracts, respectively. The third scenario also made it possible to simulate Ca availability in the rhizosphere for the two extractions (RMSE = 28 mg kg⁻¹, MRE = 16·5 mg kg⁻¹ and RMSE = 32 mg kg⁻¹, MRE = 0·1 mg kg⁻¹ with CaCl₂ and water extracts, respectively). Conversely, the modelling performed according to first scenario (only P uptake) did not properly reproduce P availability (see Fig. 1). As a matter of fact, the sole decrease in total P concentration did not permit the simultaneous modelling of the increase in P availability as measured by water extraction and the decrease in P availability as measured by CaCl₂ extraction (RMSE = 13·1 µg kg⁻¹, MRE = 5·0 µg kg⁻¹ and RMSE = 43·6 µg kg⁻¹, MRE = −46·7 µg kg⁻¹ for CaCl₂ and water extracts, respectively). Results obtained with the second scenario (P uptake and alkalization) were better with respect to P availability as measured by CaCl₂ (RMSE = 6·1 µg kg⁻¹, MRE = 0·8 µg kg⁻¹) and water extractions (RMSE = 28·3 µg kg⁻¹, MRE = −34·1 µg kg⁻¹).

Phosphorus and Ca availability versus soil pH

Figures 2 and and33 show the values of P availability as a function of soil pH in the bulk soil and rhizosphere as evaluated by means of CaCl₂ and water extractions. Regarding Ca availability, the results are shown in Figs 4 and and55.

Fig. 2.

Phosphorus concentrations resulting from extraction by CaCl₂ (i.e. P availability) in the bulk soil and rhizosphere as a function of soil pH (n = 20). Open symbols stand for P extracted in the bulk soil, closed symbols for P extracted in the rhizosphere. (more ...)

Fig. 3.

Logarithm of P concentrations resulting from extraction by water (i.e. P availability) in the bulk soil and rhizosphere as a function of soil pH (n = 20). Open symbols stand for P extracted in the bulk soil, closed symbols for P extracted in the rhizosphere. (more ...)

Fig. 4.

Calcium concentrations resulting from extraction by CaCl₂ (i.e. Ca availability) in the bulk soil and rhizosphere as a function of soil pH (n = 20). Open symbols stand for Ca extracted in the bulk soil, closed symbols for Ca extracted in the rhizosphere. (more ...)

Fig. 5.

Logarithm of Ca concentrations resulting from extraction by water (i.e. Ca availability) in the bulk soil and rhizosphere as a function of soil pH (n = 20). Open symbols stand for Ca extracted in the bulk soil, closed symbols for Ca extracted in the rhizosphere. (more ...)

Over the investigated range of soil pH (4–8·5), P availability measured in CaCl₂ extracts was on average 23 % lower in the rhizosphere than bulk soil. Similar results were obtained in untreated samples. In contrast, in water extracts such a decrease in P availability in the rhizosphere was only observed at pH < 6, whereas it increased above pH 7, as observed in untreated samples. Calcium availability was significantly lower in the rhizosphere than in the bulk soil over the entire range of soil pH with the two extraction methods. Calcium availability decreased on average by 17 % and 32 % in the rhizosphere with CaCl₂ and water extracts, respectively.

In CaCl₂ extracts, a significant increase in P availability in the bulk soil and rhizosphere was also observed relative to the values measured in untreated soil samples at pH > 4, between pH 5·6 and 6, and above pH 7·5, respectively. In water extracts, a significant increase in P availability in both bulk soil and rhizosphere was only obtained above pH 7·5.

From the most acid to the most alkaline values, Ca availability decreased in both bulk soil and rhizosphere. Calcium availability as determined by CaCl₂ extractions decreased by 44 % and 49 % in the bulk soil and rhizosphere respectively. In water extracts, a decrease in Ca availability of 88 % and 95 % was obtained in the bulk soil and rhizosphere, respectively.

The use of mechanistic adsorption models also made it possible to simulate Ca and P availability in both rhizosphere and bulk soil at different soil pH values. Phosphorus availability in the bulk soil (see Figs 2 and and3)3) was appropriately simulated in both CaCl₂ (RMSE = 1·2 µg kg⁻¹, MRE = −0·1 µg kg⁻¹) and water extracts (RMSE = 15·4 µg kg⁻¹, MRE = 2·9 µg kg⁻¹). Concerning the modelling of Ca availability (see Figs 4 and and5),5), a good fit was obtained according to the RMSE, which was 15·0 mg kg⁻¹ and 17·2 mg kg⁻¹ for CaCl₂ and water extracts, respectively. However, modelling significantly underestimated Ca availability in the bulk soil (MRE = −53·8 mg kg⁻¹ and MRE = −69·0 mg kg⁻¹ for CaCl₂ and water, respectively). In the rhizosphere, P availability, as measured by the means of the two extraction methods (see Figs 2 and and3),3), was satisfactorily predicted over the whole range of soil pH with the third scenario (P uptake, alkalization and Ca uptake). An RMSE of 1·6 µg kg⁻¹ and 22 µg kg⁻¹ and an MRE of 5 µg kg⁻¹ and 21·2 µg kg⁻¹ were calculated, with CaCl₂ and water extracts, respectively. MRE values show that modelling in the rhizosphere led to a slight overestimation of P availability over the range of soil pH investigated in this study. This trend was particularly significant in water extractions as MRE of up to 21·2 µg kg⁻¹ was calculated. The model also made it possible to simulate Ca availability in the rhizosphere for the two extractions (RMSE = 31 mg kg⁻¹, MRE = 35 mg kg⁻¹ and RMSE = 45 mg kg⁻¹, MRE = 15 mg kg⁻¹ for CaCl₂ and water extracts, respectively). In contrast with the results obtained in bulk soil, modelling in the rhizosphere thus slightly overestimated Ca availability (see Figs 4 and and55).

Distribution of adsorbed P

The mechanistic modelling of P availability carried out according to the third scenario (P uptake, alkalization and Ca uptake) further made it possible to determine the contribution of the different soil minerals to the adsorption of P in the bulk soil and rhizosphere over the range of soil pH values considered here.

Overall, Fe oxides adsorbed more P, and clay minerals adsorbed less P in water extracts than in CaCl₂ extracts over the range of soil pH values (Fig. 6). In addition, Fe oxides and, to a lesser extent, kaolinite contains the majority of the adsorbed P under acidic conditions (pH < 6) whereas the second clay mineral of the soil, illite, became the major P-adsorbing phase under alkaline conditions (pH > 7·5).

Fig. 6.

Concentrations of P adsorbed onto soil minerals as a function of soil pH in the bulk soil (A, B) and in the rhizosphere (C, D) as calculated by BS (modelling in the bulk soil) and third scenario (P uptake, alkalization and Ca uptake), respectively. Results (more ...)

In the untreated rhizosphere relative to the corresponding bulk soil (Table 2), the modelling investigation showed us that the plant roots decreased by 9·5 % and 6·5 % the P adsorbed onto goethite with CaCl₂ and water extraction, respectively. In contrast, the concentration of adsorbed P onto illite increased by 11·7 % and 8·3 %.

Table 2.

Effects of root-induced chemical changes on the distribution of total adsorbed P (μg kg⁻¹) on soil minerals

DISCUSSION

Influence of Ca uptake

The results of the modelling investigation first revealed an important promoting effect of Ca uptake on P availability, which is in addition to the effects of P uptake and root-induced alkalization. The inclusion of this root-induced mechanism in the third modelling scenario made it possible to obtain an accurate fit between measured and simulated values of P (see Figs 1 1–3) and Ca availability (see Figs 1, ,44 and and5)5) in untreated samples and over a broad range of soil pH values for the two extractions. Therefore, the present study made it possible to relate P and Ca availability to their bioavailability for durum wheat under experimental conditions.

The influence of Ca is an important finding as the uptake of nutrients other than P is not usually considered in the literature for its potential influence on rhizosphere P availability (Hinsinger, 2001; Vance et al., 2003; Raghothama and Karthikeyan, 2005; Rengel and Marschner, 2005), except for the role of the form of nitrogen on P availability through its effect on rhizosphere pH changes (e.g. Gahoonia et al., 1992; Hinsinger and Gilkes; 1995; Hinsinger, 2001; Zhang et al., 2004). A few studies have also considered the direct influence of anion uptake on adsorbed P, e.g. Geelhoed et al. (1997b) who found that sulfate uptake by maize directly affected P availability by decreasing the competition between P and sulfate ions for the adsorption onto goethite. A competitive effect between P and arsenate ions for the adsorption onto goethite was also reported in the rhizosphere of maize (Vetterlein et al., 2007). The observed increase of P availability as measured by water extraction (see Fig. 1) has been commonly explained by the effect of the exudation of organic anions (e.g. Hinsinger, 2001; Jones et al., 2003). This is illustrated well by the work of Kirk et al. (1999) who used a model to show that citrate exudation increased P availability in the rhizosphere of rice (Oryza sativa). However, such a promotion of P availability driven by organic anion exudation can be neglected in the present study because wheat releases relatively few organic anions (Pearse et al., 2006).

One of the interests of using mechanistic models is to unravel the nature of the mechanisms accounting for experimental data. The influence of Ca uptake on P availability was caused by the promoting effect of Ca adsorption on P adsorption, which occurred through the addition of positive charges at mineral surfaces counterbalancing the repulsion effect between P ions and mineral surfaces (Devau et al., 2009). This adsorption mechanism particularly occurred onto clay minerals (mainly illite) because of their higher anion-repulsive surface area relative to Fe oxides (goethite and ferrihydrite). The high intensity of this promoting mechanism for illite has also been observed by Smith et al. (2002) for the case of arsenate (which exhibits similar properties as phosphate) in the presence of Ca.

Here it was observed that Ca uptake decreased the promoting influence of Ca adsorption on P adsorption and thus increased P availability in the rhizosphere as measured by water extraction (see Figs 1 and and3).3). The additional Ca provided by CaCl₂ masked the effect of Ca uptake, leading to lower concentrations of extracted P (see Figs 1 and and2).2). The effect of this root-induced chemical mechanism was more marked under alkaline conditions, when the repulsion between soil minerals and P is larger because all mineral surfaces are deprotonated to a greater extent (e.g. Barrow et al., 1980; Hiemstra and Van Riemsdijk, 1999). Therefore, in the rhizosphere of durum wheat where root-induced alkalization occurred, the effect of Ca uptake on P availability was amplified. Root-induced alkalization is attributed to high anion/cation uptake ratio caused by the use of nitrates to feed durum wheat (Riley and Barber, 1971; Haynes, 1990; Hinsinger et al., 2003). McDowell and Sharpley (2001) found for a large number of soils that alkalization increased P availability to a greater extent when Ca concentrations were low. This effect was reinforced in the present investigation as the majority of the Ca taken up by durum wheat was desorbed from illite, which is also the dominant P-controlling phase under alkaline conditions in the rhizosphere (see Fig. 6 and Table 2).

The decrease in Ca availability in the rhizosphere (see Figs 4 and and5)5) does not fully agree with the literature. An increase in Ca availability in the rhizosphere, although seldom measured, is regarded as normal, given that mass flow of Ca from soil towards roots is expected to be greater than the plant's requirement (e.g. Marschner, 1995). The quite large uptake of Ca measured here in untreated soil samples may have been induced to maintain the electrical neutrality of root cells as modified by the uptake of nitrate, which was the sole form of nitrogen supplied in the present device. This hypothesis has also been suggested by Shahbaz et al. (2006) and Takeda et al. (2008) for oilseed rape (Brassica napus). The large uptake of Ca that was observed in this study is within the range reported for ryegrass and maize under similar conditions of Ca availability (Loneragan, 1968; Loneragan and Snowball, 1969; Bertrand et al., 1999).

Effect of pH on P availability

The satisfactory fit obtained over a broad range of soil pH values between simulations and measurements of P availability in both bulk soil and rhizosphere (see Figs 2 and and3)3) suggests that overall mineral adsorption properties were essentially unaltered by root activity during the course of the present experiment (21 d). Morel and Hinsinger (1999) made the same finding by studying the rhizosphere of oilseed rape, pea (Pisum sativum) and maize. The slight overestimation of P availability in the rhizosphere by modelling and the corresponding underestimation of adsorption properties could be due to several mechanisms. For example, Bertrand et al. (1999) and Violante et al. (2003) reported the remobilization of Fe oxides in the rhizosphere of maize, corresponding to the dissolution of goethite and the precipitation of more amorphous Fe oxides. Such a transformation would increase the adsorption capacity in the rhizosphere, as the binding site concentration of amorphous Fe oxides is much larger than for goethite (see the Appendix).

The marked increase in P availability measured with the two extractions at alkaline pH values (see Figs 2 and and3)3) was caused by the extensive deprotonation of all the mineral surfaces under these conditions, which apparently cannot be compensated for by the adsorption of sufficient amounts of Ca. The more moderate increase in P availability measured in CaCl₂ extracts can be explained by the extra Ca added through the use of CaCl₂, which decreased the repulsion effect between P ions and mineral surfaces. The increase in P adsorption caused by increasing protonation of mineral surfaces under acidic conditions was observed in water extracts only. Opposite results were obtained with CaCl₂. The increase in P–CaCl₂ observed at pH < 4 can be explained by the competition between P and Cl ions for adsorption onto clay minerals and the low strength of P surface complexes (Devau et al., 2009). Note that the significant increase in P availability measured with CaCl₂ extraction between pH 5·5 and pH 6 can be related to an important desorption of P from kaolinite (see Fig. 6). Desorbed P was re-adsorbed onto illite under more alkaline conditions.

Origin of P taken up by durum wheat

This modelling investigation also made it possible to determine the origin of the P pool used by durum wheat to grow in such low-P conditions. It was found that durum wheat depleted only the inorganic P pool, adsorbed onto minerals. This result is consistent with other studies (Zhang et al., 2004; Vu et al., 2008; Wang et al., 2008). However, Li et al. (2008) found for the same soil and durum wheat genotype that the organic P pool was depleted in the rhizosphere. This discrepancy may stem from the growth stage of plants, which differs between the present study and that of Li et al. (2008), who also did not measure any significant pH change in the rhizosphere. Indeed, microbial phosphatase activities and thus their effects on the organic P pool vary with the growth stages of wheat and pH conditions (e.g. Marschner et al., 2006).

The effect of plant roots on the distribution of P adsorbed onto the soil minerals (see Table 2) indicated that plant roots recovered part of the P transferred from kaolinite and from Fe oxides (mainly goethite) to illite. Calculated changes in the distribution of adsorbed P between the bulk soil and rhizosphere resulted from complex interactions between P uptake, root-induced alkalization, Ca uptake and the adsorption of these ions by soil constituents. In brief, root alkalization led to the increase in P adsorbed onto illite (see Fig. 6), and this increase was not compensated for by Ca uptake and the accompanying desorption of P caused by plant-induced Ca desorption.

The low bioavailability of P measured in the present experiment can be related to the high root : soil ratio induced by the cropping device and to the very low P availability of the soil. The same problems were encountered in other root mat/rhizobox experiments, such as those of Bertrand et al. (1999) for maize and more recently by Li et al. (2008) who used the same soil and durum wheat genotype as here. In addition, it was found that the increase in P content between plants at transplanting and after contact with the soil was mostly recovered in the roots (see Table 1). Under the high P-deficiency conditions of the present study, this result can be attributed to (a) the lower inhibition of root growth relative to shoot growth because roots act as a dominant sink for photosynthates under P-deficient conditions (Lambers et al., 1998) and/or (b) the transfer of P from mature leaves to roots under such conditions (Jeschke et al., 1997). This response of the plant to P deficiency resulting in preferential allocation of carbon to roots is a well-known strategy to increase root growth and exploitation of soil resources for the acquisition of P (Marschner, 1995; Vance et al., 2003). The results showing an increase in the root : shoot ratio for plants in contact with the soil were in agreement with this strategy.

Model applicability

According to the additive approach, the parameter values used in this study (see the Appendix) can legitimately be used in an attempt to model P availability in other soils containing the same minerals. It is only necessary to estimate the relative abundance of the mineral and organic constituents, as well as the ratio of fulvic and humic acids in soil organic matter, in each new soil studied. The present modelling approach of plant–soil interactions could be applied to study other plant species as well, as long as the relevant plant parameters such as P and Ca bioavailability are measured.

We believe that a major limitation of the modelling approach presented here resides in the values used to describe the surface properties of the mineral phases, particularly their specific surface areas, since a range of values can be found in the literature. Values for goethite, gibbsite and illite were used (see the Appendix) that corresponded to the lower end of the range of values reported in the literature: i.e. from 80 to 200 m² g⁻¹ for goethite, from 50 to 120 m² g⁻¹ for gibbsite and from 20 to 66 m² g⁻¹ for illite (Schwertmann and Taylor, 1989; Sahai and Sverjensky, 1997; Liu et al., 1999; Violante and Pigna, 2002). A narrower range of specific surface areas is found for kaolinite (from 19 to 25 m² g⁻¹) because isomorphous substitutions barely occur in this mineral (Dixon, 1989). It is well known that the value of the specific surface area for a given mineral is inversely related to its crystallinity (e.g. McBride, 1989). Therefore, the low values of specific surface area used here indicate that minerals were well-crystallized in the soil used in the present experiment. Our consideration of the occurrence of well-crystallized minerals in the Mediterranean soil studied seems correct for Fe and Al oxides (Carreira and Lajtha, 1997; Martin-Garcia et al., 1999). Semi-quantitative XRD analyses made by Durn et al. (1999) also suggested that clay minerals can also be considered as well-crystallized in weathered Mediterranean soils. However, a number of soil processes can lead to the occurrence of poorly crystalline forms in other soils, e.g. the interactions with bacteria that can lead to the deposition of extremely fine-grained precipitates with high surface area and formation of mixed-layer clay minerals (Hiebert and Bennett, 1992). By the same token, mineral surfaces in natural systems can also be coated by secondary minerals or/and organic matter. Coatings have been shown to affect the site density and the electrostatic double-layer properties of minerals (Coston et al., 1995, Goldberg et al., 2007; Weng et al., 2008). An effect of organic coatings can be expected in the present case, based on the relatively large amount of organic matter in the soil (31 g kg⁻¹ of organic C). It is thus conceivable that the values of specific surface area used for modelling were underestimated compared with their actual values (i.e. without coatings). As a consequence, the actual crystallinity of goethite and/or gibbsite and/or clay minerals would be less than can be inferred from the values used in the present study. This clearly demonstrates that adjustments of surface properties of the mineral phases may be taken into consideration in applying the model to other soils, in order to ensure an adequate simulation of the adsorption process. The same consideration can be made with respect to the effect of organo-mineral assemblages (i.e. aggregation), wherein contact areas of the different constituents should not be reacting with solutions and thus should not be included in the model. Even the concentrations of some constituents such as clay minerals and the abundance of fulvic and humic acids cannot be well estimated in some cases because of the lack of fully developed experimental protocols (Davis et al., 1998; Gustafsson, 2001; Lumsdon, 2004; Goldberg et al., 2007).

Another limitation of the present modelling approach could reside in the presence of a gradient in P availability as a function of the distance to the root mat, as has been widely reported in the literature (e.g. Kirk, 2002; Hinsinger et al., 2005). However, the occurrence of such a gradient under the present experimental conditions seemed unlikely. Indeed, the average linear distance of diffusive movement of ions with time (e.g. Barber, 1995), applied to the diffusion of P over 21 d of contact time, ranges from 0·6 mm to 1·9 mm depending on the value taken for the diffusion coefficient, which ranges from 1·10⁻⁰⁹ cm² s⁻¹ to 1·10⁻⁰⁸ cm² s⁻¹ (Barber, 1995). Other ions such as Ca and H⁺/OH⁻ ions diffuse faster than P ions in soils (e.g. Barber, 1995), thus leading to larger linear distances. Moreover, Gahoonia et al. (2001) measured an average length of root hairs for wheat of approx. 0·8 mm and showed that P availability was homogeneously depleted up to 1 mm from the root surface. The mean root hair diameter is much lower than the size of the polyamide mesh that was used to separate the root mat from the soil layer.

Lastly, even in the unlikely event of the establishment of a gradient in P availability (or in any chemical variable involved in this study) through the 1-mm-thick soil layers, neither the foundations nor the findings of the present study would be altered. Indeed, P availability was measured and modelled on the same scale, i.e. that of the soil layer, wherein properties (e.g. mineral concentrations) and variables (e.g. pH and P availability) correspond to the value of the integral of any gradient in such properties through the soil layer. The same approach was used by several authors, such as Geelhoed et al. (1997b) to simulate changes in P availability in the rhizosphere of maize. Nevertheless, we are aware that adsorption models used in this study should be incorporated into plant nutrition and reactive transport models for a comprehensive account of the spatial and temporal dimensions of the rhizosphere (e.g. Geelhoed et al., 1999; Nowack et al., 2006; Szegedi et al., 2008).

CONCLUSIONS

A set of mechanistic adsorption models (1-pK TPM, ion exchange and Nica–Donnan) was used successfully to simulate the variations in P availability as determined by CaCl₂ and water extraction in both rhizosphere and bulk soil. These results thus confirm a control of P availability by adsorption reactions and extend it to the rhizosphere of durum wheat.

The major finding of this work is the effect of the uptake of Ca (i.e. Ca bioavailability) on P availability, which is in addition to the effects of P uptake (i.e. P bioavailability) and rhizosphere alkalization. Calcium taken up by durum wheat directly increased P availability by decreasing the promoting effect of Ca adsorption on P adsorption, as opposed to the effect of N uptake on P availability that indirectly acts upon P availability via pH changes in the rhizosphere. This influence of Ca uptake on P availability was more marked with increasing pH, as under these pH conditions the promoting effect of Ca adsorption onto P adsorption was larger due to the high repulsive effect between mineral surfaces and P ions under these conditions. Therefore the root-induced alkalization amplified the effect of this mechanism. Results of this study further revealed that the prime source of P for durum wheat growth in the studied soil was inorganic P and more precisely P desorbed from goethite and kaolinite, which is partly adsorbed by illite because of root alkalization.

Another finding from this study was the relative stability of the adsorption properties in the rhizosphere compared with the bulk soil. Only a little overestimation of P availability was found by keeping the adsorption properties of the rhizosphere soil identical to the bulk soil. The corresponding moderate increase in the adsorption capacity of the rhizosphere may be related to the remobilization of Fe oxides.

By making it possible to find out that Ca uptake can be an important root-induced chemical mechanism for the control of P availability, the present study demonstrates that (a) geochemical models are a promising tool for a better understanding of the effect and nature of root-induced chemical changes; (b) cation uptake (or release) can be an important driver for P acquisition by plants.

ACKNOWLEDGEMENTS

The authors are indebted to the technical assistance provided by Jean-Louis Aznar, Michaël Clairotte, Didier Arnal, Gérard Souche and Nicole Paoletti in the laboratory. The comments and suggestions of two anonymous reviewers and Prof. W. Van Riemsdijk are greatly appreciated. The English text was revised by Alan Scaife. This work was supported by the Languedoc Roussillon Regional Authorities.

APPENDIX

Adsorption models for minerals

The 1-pK triple plane model (TPM) included a multi-site complexation model (Hiemstra et al., 1989) and a charge distribution model based on three electrostatic planes (Hiemstra and Van Riemsdijk, 1996). The adsorption of ions such as phosphates and the protonation/deprotonation of the hydroxyl sites bound to Al or Fe atoms (denoted SOH^0·5−) of the mineral structure are represented as equilibrium-controlled reactions. The concentration of surface hydroxyl sites on a mineral is calculated by the following reaction:

A mathematical equation, expression, or formula.
Object name is mcq098eqnU1.jpg

where ρ represents the concentration of the given mineral (g L⁻¹), A its specific surface area (m² g⁻¹), N_s its the site density (sites nm⁻²) and N_A is Avogadro's number.

The electrical charge of an adsorbed ion is distributed between three electrostatic planes representing the structure of the double diffuse layer surrounding a surface (Hiemstra and Van Riemsdijk, 1996). The first plane (0-plane) is the mineral surface, the 1-plane separates the inner and outer Stern layer and the third electrostatic plane (2-plane) separates the Stern layer from the diffuse layer (Fig. A1). This formalism allows innersphere surface complexes to be distinguished from outersphere surface complexes. Innersphere and outersphere surface complexes are formed by means of specific and non-specific interactions with mineral surface sites, respectively. Ligands are shared with the surface sites when innersphere complexes are formed while outersphere complex formation involves electrostatic interactions between the adsorbed ion and the surface sites. Electrostatic interactions are simulated by considering three electrostatic components, P₀, P₁ and P₂ (Hiemstra and Van Riemsdijk, 1996):

A mathematical equation, expression, or formula.
Object name is mcq098eqnU2.jpg

Fig. A1.

Representation of the diffuse double layer at a mineral surface according to the triple plane model (TPM). Three electrostatic planes separate innersphere complexes and outersphere complexes, which share ligands with the surface sites and are electrostatically (more ...)

where the subscripts 0, 1 and 2 stand for the 0-, 1- and 2-plane of the diffuse layer, respectively. F is the Faraday constant (96485·34 C), R is the gas constant (8·3144 J mol⁻¹ K⁻¹), T is the absolute temperature (K) and ψ is the electrostatic potential (V) of a plane.

The electrical potential (ψ) and the charge (σ) of the electrostatic planes are linked as follows:

A mathematical equation, expression, or formula.
Object name is mcq098eqnU3.jpg

where the subscripts 0, 1 and 2 stand for the 0-, 1- and 2-plane of the diffuse layer, respectively. The parameters C₁ and C₂ (F m⁻²) denote the molecular capacitances of inner and outer Stern layers, respectively.

Mineral concentrations and surface properties used in this study are shown in Table A1. The stoichiometry of the surface reactions and their intrinsic equilibrium constants are given in Table A2. The equilibrium constant for protonation/deprotonation reactions corresponds to the point of zero charge of the mineral. The values of the equilibrium constants used in a given application for bidentate and protonated bidentate P–surface complexes should be calculated from Hiemstra and Van Riemsdijk (1996):

A mathematical equation, expression, or formula.
Object name is mcq098eqnU4.jpg

with K and K_int being the equilibrium constant to be used in the model application and the intrinsic equilibrium constant, respectively.respectively.

Table A1.

Mineral concentrations and surface properties

	Goethite	Ferrihydrite	Gibbsite	Kaolinite	Illite
ρ (concentration in g l⁻¹)	6·174	0·324	1	35·12	39·94
A (specific surface area in m² g⁻¹)	105^a,*	750^c	54^d	23·6^e	25·19^h
N_s (site density in site nm⁻²)	6·15^a	4^c	4^c	0·82^e	2·5^h
X- (basal site density in mmol kg⁻¹)	−	−	−	4·5^f	5·15^g
C₁ (innersphere capacitance in F m⁻²)	0·9^b	0·9^†	1·1^c	1·5^g	1·5^g
C₂ (outersphere capacitance in F m⁻²)	0·74^b	0·74^†	0·74^‡	5^g	5^g

* Values taken from: ^a Hiemstra and Van Riemsdijk (1996), ^b Hiemstra and Van Riemsdijk (2006), ^c Gustafsson (2001), ^e Manning and Goldberg (1996), ^g He et al. (1997), ^h Gu and Evans (2008).

^† Assumed to be equal to those of goethite; ^‡ assumed to be equal to those of Fe-oxides.

Table A2.

Surface species, surface reactions and related parameters used in this study

Surface reactions	Goethite	Ferrihydrite	Gibbsite	Kaolinite	Illite
1 SOH^0·5− + 1H⁺ SOH₂^0·5	9·2 (1, 0, 0)^a,*	8·5 (1, 0, 0)^b	10 (1, 0, 0)^b	4·36 (1, 0, 0)^h	3·46 (1, 0, 0)^d
1 S₃O^0·5− + 1H⁺ S₃OH^0·5	9·2 (1, 0, 0)^a	−	−	−	−
1 SOH^0·5− + 1H⁺ + 1PO₄³⁻ SOPO₃^2·5− + H₂O	20·8 (0·25, −2·25, 0)^a	19·7 (0·25, −2·25, 0)^b		25·1 (0·25, −2·25, 0)^f	18·5 (0·25, −2·25, 0)^f
2 SOH^0·5− + 2H⁺ + 1PO₄³⁻ SO₂PO₂²⁻ + 2H₂O	29·2 (0·5, −1·5, 0)^a	29 (0·5, −1·5, 0)^b	28·5 (0·5, −1·5, 0)^b	28·3 (0·5, −1·5, 0)^f	26·4 (0·5, −1·5, 0)^f
2 SOH^0·5− + 3H⁺ + 1PO₄³⁻ SO₂POOH⁻ + 2H₂O	35·4 (1, −1, 0)^a	35·6 (1, −1, 0)^b	36·1 (1, −1, 0)^b	35·4 (0·5, −0·5, 0)^f	29·4 (0·5, −0·5, 0)^f
1 SOH^0·5− + 3H⁺ + 1PO₄³⁻ SOPO₃H₂^0·5− + H₂O	−	−	32·5 (0·8, −0·8, 0)^b	−	−
1 SOH^0·5− + 1Ca²⁺ SOCaOH^0·5 + H₂O + 1H⁺	−8·63 (0·25, 0·75, 0)^e	−8·63 (0·25, 0·75, 0)^†	−15 (0·25, 0·75, 0)^f	−	−8 (0·25, 0·75, 0)^f
1 S₃O^0·5− + 1Ca²⁺ S₃OCaOH^0·5 + H₂O + 1H⁺	−8·63 (0·25, 0·75, 0)^e	−	−	−	−
2 SOH^0·5− + 1 Ca²⁺ SO₂CaOH + 2H₂O + 1H⁺	−	−	−15 (0·62, 0·38, 0)^f	−	−
2 SOH^0·5− + 1 Ca²⁺ SO₂CaOH⁻ + 2H₂O + 2H⁺	−	−	−	−5 (0, 0·62, −0·58)^f	−
1 SOH^0·5− + 1Ca²⁺ SOCa^1·5 + H₂O	−	−	−	−	3·4 (0, 0·33, 1·67)^f
2 SOH^0·5− + 1Ca²⁺ SO₂Ca⁺ + 2H₂O	−	−	4 (0·62, 1·38, 0)^f	3·1 (0·62, 1·38, 0)^f	1·5 (0, 0·62, 1·38)^f
2 X⁻.H⁺ + 1Ca²⁺ 2 X⁻.Ca²⁺ + 2H⁺	−	−	−	0·32^f	0·62^f
1 SOH + 1H⁺ + 1Cl⁻ SOH₂Cl^0·5−	7·1 (1, 0, −1)^a	7·1 (1, 0, −1)^b	7·8 (1, 0, −1)^g	7·5 (1, 0, −1)^c	7·5 (1, 0, −1)ⁱ

Values stand for the log of the intrinsic equilibrium constants of the different surface reactions. Values given in parenthesis correspond to the charge distribution in the electrostatic terms (P₀, P₁ and P₂). [equivalent]

SOH^0·5− stands for a reactive surface hydroxyl bound to a metal (Fe or Al) at the surface of a metal oxide mineral or an aluminol group outcropping at the clay mineral edges, [equivalent]

X⁻ represents the permanent negatively charged sites on basal plane of clay minerals. [equivalent]

S₃O^0·5− stands for the second reactive surface hydroxyl at the surface of goethite.

* Values taken from: ^a Hiemstra and Van Riemsdijk (1996), ^b Gustafsson (2001), ^c He et al. (1997), ^d Liu et al. (1999), ^e Rahnemaie et al. (2005), ^f Devau et al. (2009), ^g Sahai and Sverjensky (1997), ^h Duc et al. (2005), ⁱ Gu and Evans (2007).

^† Assumed to be equal to those of goethite.

Table A3.

Model parameters used to simulate Ca ions and proton adsorption onto natural organic matter (from Milne et al., 2001, 2003)

	Fulvic acid		Humic acid
	Carboxylic sites	Phenolic sites	Carboxylic sites	Phenolic sites
Q_max (mol.kg⁻¹)	5·88	1·86	3·35	2·55
n_H	0·66	0·76	0·81	0·63
n_Ca	0·85	0·8	0·78	0·75
p	0·59	0·7	0·62	0·41
logK_H	2·34	8·6	2·93	8
logK_Ca	−2·13	−3	−1·37	-0·43

Kaolinite and illite exhibit two types of adsorption sites (Lackovic et al., 2003; Gu and Evans, 2007, 2008): (a) the edge sites (noted [equivalent]

SOH^0·5−), where the adsorption of ions is modelled with the 1-pK TPM (see above); and (b) permanent negatively charged sites associated with basal siloxane surfaces (noted [equivalent]

X⁻). The adsorption of calcium on permanently negatively charged sites can be described as a surface reaction without electrostatic effects. In the calculations, the concentration of the permanent negatively charged sites was set as a fraction of the edge site concentration (for further details, see Devau et al., 2009).

Adsorption model for natural organic matter

To take into account the adsorption of Ca by natural organic matter, whether in soluble or insoluble form, the NICA–Donnan model (e.g. Kinniburgh et al., 1996, 1999) was used. Thus the common assumption was made that the binding properties of the natural organic matter can be approximated by those of humic substances; i.e. humic and fulvic acids (Dudal and Gérard, 2004). The binding sites for cations and protons are carboxylic and phenolic groups and the binding affinity of each group exhibits variations that follow a bimodal distribution. The total amount of the ith component (protons or cations) adsorbed by a fulvic or humic acids, Q_i_,tot (mol kg⁻¹), is expressed (Kinniburgh et al., 1999) as:

A mathematical equation, expression, or formula.
Object name is mcq098eqnU5.jpg

where the subscript i corresponds to a cation or a proton, the subscript j corresponds to the type of binding sites (carboxylic or phenolic), n_i_{, j} and n_H,j represent ‘non-ideal’ behaviour of the adsorption reaction between a binding of the type j and a cation or a proton, respectively, Q_j_,max stands for the maximum number of sites of type j (mol kg⁻¹), C_i refers to the dissolved concentration of the ith cation (mol L⁻¹), K_i_{, j} is the median equilibrium constant for the adsorption of a cation i to the binding site j, p (0 < p ≤ 1) stands for the width of the distribution of each group of sites, K^el_i is the electrostatic contribution of the ith adsorbed cation.

Electrostatic effects are taken into account through a Donnan model, in which the electrostatic potential surrounding humic substances is assumed constant and uniform within the domain of the gel phase and drops to zero in the free solution.

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