Julien Dubus

Nathalie Leonhardt

Christelle Latrille
email: christelle.latrille@cea.fr

Multi-cation exchanges involved in cesium and potassium sorption mechanisms on vermiculite and micaceous structures

Keywords: Cesium, cation exchange, interlayer collapse, vermiculite, potassium

Vermiculite and micaceous minerals are relevant Cs sorbent in soils and sediments. To understand Cs bioavailability in soils resulting from multi-cation exchanges, Cs sorption onto clay minerals have been carried out in batch experiments with solutions containing Ca 2+ , Mg 2+ and K + . A sequence between a vermiculite and various micaceous structures were achieved by conditioning a vermiculite at various amounts of K. Competing cation exchanges were investigated according to the concentration of Cs. The contribution of K on trace Cs desorption is probed by applying different concentrations of K on Cs-doped vermiculite and micaceous structures. Cs sorption isotherms at chemical equilibrium were combined with elemental mass balances in solution and structural analyses. Cs replace easily Mg 2+ > Ca 2+ and competes scarcely with K. Cs is strongly adsorbed on the various matrix and a K/Cs ratio about a thousand is required to remobilize Cs. Cs is exchangeable as long as the clay interlayer space remains open to Ca 2+ . However, excess of K, as well as Cs, in solution leads to the collapse of the interlayer spaces that locks the Cs into the structure. Once K and/or Cs collapse the interlayer space, the external sorption sites are then particularly involved in Cs sorption. Subsequently, Cs + exchanges preferentially with Ca 2+ rather than Mg 2+ . Mg 2+ is extruded from the interlayer space by Cs + and K + adsorption, excluded from short interlayer space and replaced by Ca 2+ as Cs + desorbs.

Introduction

Subsequently to the nuclear contamination in the Fukushima prefecture, numerous studies have been dedicated to the understanding of radiocesium mobility to predict their impact in the environment and so to anticipate potential risks on health [START_REF] Klika | Cesium uptake from aqueous solutions by bentonite: a comparison of multicomponent sorption with ion-exchange models[END_REF]; [START_REF] Nakao | Radiocesium sorption in relation to clay mineralogy of paddy soils in Fukushima, Japan[END_REF][START_REF] Liu | Cation exchange model to describe Cs + sorption at high ionic strength in subsurface sediments at Hanford site, USA[END_REF]; [START_REF] Kasar | Sorption and desorption studies of Cs and Sr in contaminated soil samples around Fukushima Daiichi Nuclear Power Plant[END_REF]; [START_REF] Siroux | On the use of a multi-site ion-exchange model to predictively simulate the adsorption behaviour of strontium and caesium onto French agricultural soils[END_REF]). To counteract the bioavailability of cesium in soils, K fertilization was recommended in Japan [START_REF] Kato | Potassium Fertilizer and Other Materials as Countermeasures to Reduce Radiocesium Levels in Rice: Results of Urgent Experiments in 2011 Responding to the Fukushima Daiichi Nuclear Power Plant Accident[END_REF] to deplete Cs incorporation by plants by acting on competing rule between Cs and K in plants as well as in soils [START_REF] Kato | Potassium Fertilizer and Other Materials as Countermeasures to Reduce Radiocesium Levels in Rice: Results of Urgent Experiments in 2011 Responding to the Fukushima Daiichi Nuclear Power Plant Accident[END_REF]; [START_REF] Kubo | Analyses and countermeasures for decreasing radioactive cesium in buckwheat in areas affected by the nuclear accident in 2011[END_REF][START_REF] Kubo | Effect of exchangeable potassium content on cesium absorption and partitioning in buckwheat grown in a radioactive cesiumcontaminated eld[END_REF]. Nevertheless, Cs transfer to plant is highly dependent on the clay mineralogy, especially as soils are enriched in micaceous minerals and vermiculite [START_REF] Kubo | Potassium behavior and clay mineral composition in the soil with low effectiveness of potassium application[END_REF]. Weathering micaceous minerals are able to release K + to reduce Cs + uptake by plants. On the other hand, biotite, vermiculite, and aluminous smectite are known to adsorb strongly Cs + compared to other cations [START_REF] Sakalidis | Caesium selectivity and xation by vermiculite in the presence of various competing cations[END_REF][START_REF] Cornell | Adsorption of cesium on minerals: a review[END_REF] Indeed, these clay minerals provide selective sorption sites that enhanced Cs sorption [START_REF] Brouwer | Cesium and rubidium ion equilibriums in illite clay[END_REF]; [START_REF] Park | Selective adsorption and irreversible xation behavior of Cesium onto 2:1 layered clay mineral: a mini review[END_REF], which appear in some instances as Cs xation sites (Kikushi et al. 2015). Cs + sorption is mainly controlled by an ion exchange process on clay mineral surfaces [START_REF] Mishra | Distribution and retention of Cs radioisotopes in soil affected by Fukushima nuclear plant accident[END_REF].

Due to isomorphic substitutions in tetrahedral and octahedral layers and hydroxyl groups with amphoteric character at the particle edges, these minerals hold different types of sorption sites. Generally, sorption sites are structurally located on the basal planes of the phyllosilicate layer, on the crystal border and in the interlayer space. Weathered micaceous minerals and especially illite exhibit frayed edges which refer to the transition zones between collapsed and open interlayer space. Since [START_REF] Sawhney | Selective sorption and xation of cations by clay minerals -review[END_REF], particular reactive properties have generally been attributed to this speci c space. Due to its con guration, it can accept only low hydration energy cations or small size cations including K + and Cs + compared to Ca 2+ and Mg 2+ . Moreover, Cs + can deeply penetrate inside the closed interlayer space by ionexchange [START_REF] Kogure | XRD and HRTEM evidence for xation of cesium ions in vermiculite clay[END_REF][START_REF] Okumura | Radiocesium interaction with clay minerals: theory and simulation advances Post-Fukushima[END_REF].

The adsorption process depends on Cs concentration, solution ionic-strength, competing cation and pH [START_REF] Fuller | Ionic strength and pH dependent multi-site sorption of Cs onto a micaceous aquifer sediment[END_REF][START_REF] Missana | Modeling cesium retention onto Na-, Kand Ca-smectite: effects of ionic strength, exchange and competing cations on the determination of selectivity coe cients[END_REF]). This involves the compensating cation placed on the negative surface charges of phyllosilicates and cations in solution. At trace concentration, Cs + is easily replaced by Mg 2+ [START_REF] Morimoto | Desorption of Cs + ions intercalated in vermiculite clay through cation exchange with Mg 2+ ions[END_REF][START_REF] Tamura | Desorption of Cs + ions from a vermiculite by exchanging with Mg 2+ ions: effects of Cs + -capturing ligand[END_REF]) on vermiculite, whereas Cs is stronger adsorbed on illite [START_REF] Wissocq | Application of the multi-site ion exchanger model to the sorption of Sr and Cs on natural clayey sandstone[END_REF]) but remains exchangeable [START_REF] Latrille | Cs selectivity and adsorption reversibility on Ca-illite and Ca-vermiculite[END_REF]. At high Cs concentration, it has been assumed that weakly hydrated Cs + sorbed to the frayed-edges of micaceous minerals is dehydrated which results in a partial collapse of the interlayer [START_REF] Mukai | Cesium adsorption/desorption behavior of clay minerals considering actual contamination conditions in Fukushima[END_REF][START_REF] Sawhney | Selective sorption and xation of cations by clay minerals -review[END_REF]; [START_REF] Kikuchi | Cs-sorption in weathered biotite from Fukushima granitic soil[END_REF][START_REF] Park | Selective adsorption and irreversible xation behavior of Cesium onto 2:1 layered clay mineral: a mini review[END_REF]). Likewise, Cs incorporated in the vermiculite interlayer by ion exchange with Mg 2+ , Ca 2+ and Na + , induces subsequent interlayer collapse in vermiculite [START_REF] Sawhney | Selective sorption and xation of cations by clay minerals -review[END_REF]; [START_REF] Lee | Studies on the sorption and xation of cesium by vermiculite[END_REF][START_REF] Lee | Studies on the sorption and xation of cesium by vermiculite II[END_REF] Mg and varying by their K concentrations at 0, 0.125, 1.25, 6.25 and 12.5 10 - 2 mol/L K. Batches of 1.5 g of vermiculite were dispersed in 120 mL of solutions with a 12.5 g/L solid/solution ratio, end to end shaken for three days and centrifuged at 10596 g during 40 min to replace the supernatant by the same conditioning solution. These operations were repeated three times. Three similar operations were successively realized with the same solution composition diluted 12.5 times, named K(x) solution (x = 0, 0.1, 1, 5 or 10) with cation composition detailed in Table 1, in order to equilibrate the solids with operating solutions. The solids were nally rinsed with ethanol to eliminate residual salt. After centrifugation, the ve conditioned materials were left to air-dry for two days. The effects of K + concentrations on Cs + desorption were investigated by batch experiments on conditioned vermiculites with K(0) and K(5) solutions doped in 137 Cs at 7.6 10 8 mol/L (6.62 10 - 6 mol/kg of adsorbed Cs). For that, 70 mg of dried conditioned and doped vermiculite was dispersed in 6 mL of K(0) solution added of KCl solutions. For vermiculite exempt of K (in K(0)), the introduced KCl concentrations were ranged between 3 10 - 6 mol/L and 5.9 10 - 2 mol/L whereas KCl concentrations were ranged between 1.5 10 - 4 and 4.9 10 - 2 mol/L for conditioned vermiculite with K(5). The suspensions were orbital shaken during 14 days and centrifuged as above described. The supernatants were collected for electrolyte concentration analysis, 137 Cs counting and to check the pH at equilibrium.

Aqueous cation concentrations were measured by ion chromatography (standards Chem-Lab). The measurement uncertainties were 5 10 - 6 mol/L 2σ (i.e 10 - 6 eq). The radioactivity of 1 ml supernatant was measured by gamma counting (Perkin Elmer Wizard 3). pH values were determined using a combined glass pH electrode (Mettler Toledo) equipped with an Ag/AgCl reference electrode. The electrode was calibrated with buffer solutions at pH 4.0, 7.0 and 12.0. Uncertainties were calculated by error propagation and established at ± 0.2 pH unit.

Cations adsorption and desorption by exchange with cations in solution at chemical equilibrium are expressed by:

m X - i -N n + + nM m + = n X - i m -M m + + mN n + {( ) } { ( ) }
with X - i -N n + and X - i -M m + the adsorbed cations on the X - i sorption sites, and M m+ and N n+ , the cations in solution. These reactions are described by the apparent exchange constants according to the mass action law, such as:

K * N n + / M m + = [ X - i m -M m + ] n N n + m γ m N n + [ X - i n -N n + ] m M m + n γ n M m + = 1 /K * M m + / N n +
where K * is the apparent exchange constants, i is the type of sorption site, [ ] is the concentration of species in solution (mol/L) or sorbed species (mol/kg of dry solid) and γ is the activity coe cient of species in solution.

Both Cs adsorption and desorption isotherm results were expressed in terms of distribution coe cient K d , which is de ned by the ratio of the adsorbed Cs concentration ([Cs] ads , eq in mol.kg - 1 ) over the Cs concentration in solution ([Cs + ] sol,eq in mol.L - 1 ). Thanks to 137 Cs radioisotope, K d can be also estimated by the Cs activity initially introduced (A ini in Bq) and measured in solution at equilibrium (A sol,eq in Bq).

K d = [Cs] ads , eq [Cs + ] sol , eq = [Cs] ini Cs + sol , eq -1 = A ini A sol , eq -1 V m
Mass balance expressed the variation of the chemical composition that occurred in solution during the cation exchange process. Each cation concentration in solution was converted to equivalent of cation (mole of positive charge) in the system. Mass balance in each batch (Δeq) was therefore calculated by the equivalent of cation at equilibrium in solution subtracted from the equivalent of cation initially introduced by the K(x) solutions. For adsorption experiments, the introduced solutions K(x) were added with Cs whereas for desorption experiments, the K(x) solutions are free of Cs. Negative values express an uptake onto the solid. Conversely, positive values represent a release into the solution.

Experimental errors were hence calculated for each batch following the propagation errors theory. The variance of a G function of different x i variable can be calculated from the variances of the variables x i using this expression:

σ 2 G = n ∑ i = 1 ∂G ∂x i 2 σ 2 i + 2 ∑ i ∑ j ∂G ∂x i ∂G ∂x j σ ij
where (∂G/∂x i ) is the partial derivative of G with respect to x i , σ 2 is the variance of x i and σ ij the covariance of the x i and x j variables. If these variables are independent, the covariance term is then equal to zero.

( ) ( ) ( ) [ ] ( ) [ ] ( [ ] ) ( ) ( )
2.3. Crystal-structure analysis X-ray diffraction (XRD) analyses were performed using a XRD 5000 INEL powder X-ray diffractometer using Cu Kα radiation, equipped with a CPS120 curve detector Si/Li. The XRD patterns were scanned between 3° and 110° 2θ angle at 30 kV and 30 mA with a Cu-target tube at room temperature of 22°C. Patterns were cumulated every few seconds during 10 minutes. Analyses were performed on oriented clay deposits to characterize the cation exchanges that occur in the interlayer space. The peak for (001) re ection was scanned to detect shifts due to occupancy change (Yin et

Results And Discussion

Exchange capacity of conditioned vermiculites

The conditioning of vermiculites with various K(x) solutions leads to impose the composition of compensating cations on vermiculite negative charges. Moreover, it permits to select various intercalated K structures in a sequence between vermiculite and depleted K micaceous structures. The analyses of the cations extracted with NH 4 Cl at pH 7 were performed on each conditioned vermiculite. The sum of these exchangeable cations leads to the CEC (Table 2). The vermiculite conditioned with the K-free solution (K(0)V) indicates the highest CEC at 127 cmol(+)/kg. The K is largely extracted from the original vermiculite by the conditioning process. This is controlled by XRD analysis that shows a (001) re ection with a d-value at 14.6 Å indicating a major di-hydrated Ca, Mg occupancy in the interlayer space (Fig. 1).

As K + increases in the conditioning solutions, decreases of the CEC of the conditioned vermiculites is observed. Indeed, K + appears very di cult to extract with NH 4 + : the exchangeable K + represents less than 1% of extractable cations for K(0)V to K(5)V with a maxima at 1.4% for K(10)V. Moreover, with the increasing of the amount of K + in the conditioning media, the intensity of the (001) re ection at 14.6 Å decreases and peaks open towards the large angles, while a second broad re ection appears and grows in intensity (Fig. 1). Therefore, some K + are incorporated in the interlayer space of vermiculite during the conditioning process to form vermiculite/ mica mixed layers.

Based on the maximal value of CEC obtained from K(0)V (Table 2), K + accounts for 11, 18, 27 and 33% of CEC for K(0.1)V to K(10)V respectively. While Mg/Ca ratios were maintained to 1.5 in each solution K(x), it decreased from 2.96 to 1.53 for the extractable cations of the structures K(0)V to K(10)V. This indicates the higher Mg 2+ a nity of vermiculite than Ca 2+ in the absence of K + . As K + amount increases in the structure, Mg 2+ amount decreases whereas the incorporated Ca 2+ varies slightly. Then, K + replaces Mg 2+ more easily than Ca 2+ during its incorporation into the structure [START_REF] Robin | Ion exchange reactions of major inorganic cations (H + , Na + , Ca 2+ , Mg 2+ and K + ) on beidellite: Experimental results and new thermodynamic database. Toward a better prediction of contaminant mobility in natural environments[END_REF]. ). This means that the desorption reaction must have released the right Cs amount in the liquid phase to reach equilibrium. This does not imply that the total amount of adsorbed Cs should be desorbed at equilibrium. At Cs concentration below 10 - 7 mol/L, Cs adsorption is reversible until 5 mmol/L of K in solution (Fig. 2). Only 4.3 to 5.6% of the adsorbed Cs is released at the desorption step. This suggests that Cs could be desorbed over an extended time period [START_REF] Murota | Desorption kinetics of cesium from Fukushima soils[END_REF]). For K concentration higher than 5 mmol/L, adsorption becomes partially reversible as shown by the desorption Kd slightly higher than adsorption Kd for K concentration at 10 mmol/L (K( 10)). Between 10 - 7 and 5 10 - 5 mol/L of Cs in solution at equilibrium, the reversible adsorption is the lowest, with very close values whatever the K concentration in the medium. At higher Cs concentration (> 5 10 - 5 mol/L), partial reversible adsorption is observed with the highest Kd of adsorption / desorption ratio for K(0)V. This ratio decreases with the K contents increase in solids and solutions. So, the Cs adsorption capacity ensured by sorption sites located in the interlayer space is reduced due to their occupancy by K, in accordance with the CEC (Table 2) and the (001) re ection distances decrease with K incorporation in the structure (Fig. 1).

These non-linear isotherms are comparable to those of illite and smectite [START_REF] Wissocq | Application of the multi-site ion exchanger model to the sorption of Sr and Cs on natural clayey sandstone[END_REF]), except

the Kd increase at Cs concentration above 10 - 5 mol/L. They emphasize the involvement of several sorption sites distinguishable by their selectivity towards Cs, as seen on Ca-vermiculite (Latrille and Bildstein 2022). Referred to this latter study, at trace concentration, a low capacity and high selectivity site contributes mainly to Cs adsorption. This sorption site type records also a strong K selectivity given the decreasing Kd of Cs when K increases both in solid and solution. It is noticeable that the K concentration must be at least a thousand times higher than Cs for this competition to occur. While the capacity of this site to load Cs is saturated, the Kd of Cs decreases drastically. Thereafter, one or several low Cs a nity sites continue to take Cs up, which explains the decrease of the Kd value. At concentration above 10 - 5 mol/L, the high Cs upload may result from the presence of one or several high capacity sites. [START_REF] Lee | Studies on the sorption and xation of cesium by vermiculite[END_REF][START_REF] Lee | Studies on the sorption and xation of cesium by vermiculite II[END_REF] and Latrille and Bildstein (2022) observed a similar trend onto Ca, Mg or Na saturated vermiculite and explained it by the penetration of Cs into the interlayer space depending on the compensating cation. In the case of several cations involved in the Cs uptake by conditioned vermiculites, the cation mass balance of the solution compositions gives the variation of element amounts in the solution compared with the initial solution K(x). As a result, this was used to evaluate the ongoing reactional processes. Focus was made on the cation mass balances obtained on adsorption and desorption solutions resulting from equilibrium between vermiculites K(0)V and K(5)V in solution K(0) and K( 5) respectively (Figs. 3 and4). Effectively, these two sorption conditions are selected to highlight two Cs adsorption behaviors depending on the rate of K intercalated in the vermiculite structure. In the initial state, compensating cations on K(0)V and K(5)V are mainly Ca 2+ and Mg 2+ , and K + appears as poorly exchangeable in both vermiculites structures (Table 2). Note that the chemical compositions of solutions K(0) and K(5) ( At the adsorption step (Fig. 3), cations content in solution at equilibrium are compared with those of K(x)

solutions doped with Cs. The Cs adsorptions on K(0)V and K(5)V at concentration below 10 - 4 mol/L Cs (Fig. 3) indicate that the solutions composition remain mainly similar to the initial solutions. The Δeq of Ca and Mg in solution are not signi cant (ca. 1 10 - 6 eq) for K-free media whereas the signi cant release of Mg and Ca are of few extents (ca. 2 10 - 6 eq) in media containing K. Cs adsorption in trace level does not vary signi cantly the cation composition of solution. Whatever the Cs amounts uptake until 2 10 - 5 mol/L Cs concentration in solution, Ca and Mg tend to equally exchange with Cs. Moreover, Cs adsorbed on K(0)V is of the same amount as on K(5)V (Fig. 3). K + and H + amounts remain constant in solution whatever the Cs concentration introduced; therefore, they do not contribute in the exchange with Cs (SI2). Hence, this corroborates the fact that the K incorporated in the vermiculite structure such as K(5)V remains non exchangeable with Cs. Beyond 10 - 4 mol/L of Cs, Cs depletes largely from the solution and is compensated by Mg 2+ > Ca 2+ desorption. Larger Cs adsorption occurs on vermiculite K-free in accordance with its larger CEC than on the K incorporated vermiculite. At the highest Cs concentration, Cs + compensates 74% of the K-free vermiculite CEC compared to 81% of the K incorporated vermiculite. Mass balance of cations remain equilibrated in all tested conditions. This further advocates for a cation exchange process to describe Cs adsorption. The cation exchanges observed on the intermediate Kvermiculite, K(0.1)V and K(1)V in SI2, indicate the same trends : below 10 - 4 mol/L Cs, release of Mg and Ca are of few extent and become progressively signi cant with increasing K in the media. This suggests easier desorption of Mg 2+ and Ca 2+ in presence of K + even though the K + concentration remains constant in solution. This should be related to a slight structural change which will be discussed below.

At the desorption step (Fig. 4), cation composition in solution at equilibrium is compared with those of fresh K(x) solutions. No signi cant adsorption of K + , Ca 2+ and Mg 2+ (< 1 10 - 6 eq) is recorded in compensation of trace Cs release. This expresses that media remains mainly at equilibrium during Cs exchange. The released Cs concentrations are too low to disturb the Ca 2+ , Mg 2+ and K + in major concentration in solution, in these experimental conditions. Moreover, trace Cs desorbed from K(0)V is of same amount than from K(5)V. As Cs concentration becomes competitive with major cations, beyond 3 10 - 5 mol/L Cs, Cs release is accompanied by Mg 2+ release which are compensated by Ca 2+ adsorption for K-free vermiculite (Fig. 4a). For K intercalated structures (Fig. 4b), Cs release is mainly compensated by Ca 2+ and to a lesser extent by K + (> 1 10 - 6 eq). This suggests a higher selectivity of site loading Cs + for Ca 2+ than Mg 2+ or a lack of site accessibility for Mg 2+ . At high Cs concentration, the more K is initially intercalated in the structure the higher the amount of Cs desorbed. Indeed, the amount of Cs released from K(5)V (5.4% of the CEC) is greater than that from K(0)V (1.2% of the CEC) although its CEC is lower (Fig. 4 andSI2). It therefore appears that Cs desorption is easier in K intercalated than in vermiculite Kfree structures. This suggests a competition between Ca and K with Cs or a structure collapse inhibiting the Cs desorption as previously observed in many studies (Kogure et 2). The low ratios of Cs amounts desorbed in solution with those adsorbed re ect the high Cs selectivity towards the structures. When the Cs concentration exceeds 10 - 5 mol/L, the cation competition between Ca 2+ , Cs + and Mg 2+ takes place: Cs replaces mainly Mg 2+ for adsorption whereas Ca 2+ replaces mainly Cs for desorption. Cs sorption sites seem more available for cation exchange in a K incorporated structure than in a K-free structure.

K competition with Cs on desorption process

In order to better understand the K + competition towards Cs, Cs + desorption was studied by imposing various amounts of K on Cs doped K-free vermiculite (K(0)V) and K intercalated vermiculite (K(5)V). For this purpose, vermiculites were doped with Cs in trace level (6.6 10 - 6 mol/kg) and dispersed in solutions (K(0) and K(5) respectively) with added various concentrations of K.

For the K-free vermiculite doped with Cs in trace, Fig. 5 shows the mass balance of cations Ca 2+ , Mg 2+ , K + and Cs + (Fig. 5a andb) and the interlayer space evolution (Fig. 5c) as a function of the K + in solution at equilibrium. When the K(0) solution is used, the Cs desorption result is the same as the desorption isotherm (Fig. 4a). The Cs desorption amount (Fig. 5b) remains equal until 0.4 mmol/L K introduced without any signi cant exchange with Ca 2+ and Mg 2+ , and the interlayer space remains fully open (i.e. d (001) re ection at 14.6 Å in Fig. 5c). The Cs desorption increases with increasing K introduced between 0.7 to 5 mmol/L (Fig. 5b). The K + uptake is rstly balanced by Mg 2+ then Ca 2+ released in solution. The interlayer spaces are maintained at 14.6 Å without any signi cant mixed layer at 12.5 Å although K + introduced in solution represents at most 35% of the CEC but the adsorbed K represents only 5.3% of the CEC. A large amount of K + is then necessary to extract no more than 4% of the adsorbed Cs from the vermiculite (i.e., 2.65 10 - 7 mol/kg of Cs). This represents 3.7 to 27.9 times more than the K fertilizer amended (250 mg/kg soil K 2 O) on Japanese soils [START_REF] Kubo | Analyses and countermeasures for decreasing radioactive cesium in buckwheat in areas affected by the nuclear accident in 2011[END_REF][START_REF] Kato | Potassium Fertilizer and Other Materials as Countermeasures to Reduce Radiocesium Levels in Rice: Results of Urgent Experiments in 2011 Responding to the Fukushima Daiichi Nuclear Power Plant Accident[END_REF]. Above 10 mmol/L K introduced (Fig. 5a), K + is largely loaded onto mineral and Mg 2+ > Ca 2+ are released in solution while no Cs desorption occurs. From 10 mmol/L K introduced (i.e. 12.5 times less than conditioning solution for K(10)V), the structural analysis records the decrease in intensity and the spreading of the peak at 14.6 Å in favor of a peak at 12.5 Å, characteristic of a vermiculite /mica mixed layer [START_REF] Kogure | XRD and HRTEM evidence for xation of cesium ions in vermiculite clay[END_REF]). The latter shifts towards 12 Å and spreads towards the large angles until reaching 10.8 Å for the highest K concentration. The interlayer space collapse is therefore evidenced with this structure change as reported by [START_REF] Kogure | XRD and HRTEM evidence for xation of cesium ions in vermiculite clay[END_REF]. This collapse is then related to the K adsorption corresponding to 11.4% of the sites available.

For the vermiculite initially loaded with K (K(5)V), the mass balances of cations Ca 2+ , Mg 2+ , K + and Cs + as a function of the K + in solution at equilibrium is given in Fig. 6a to 6c. This indicates a K + release balanced by a Ca 2+ and Mg 2+ uptake from solution when the contact solution has initially lower K concentration than the K( 5) solution (Fig. 6b). In this case, the higher the K concentration, the lower the exchange with Ca and Mg. So, the Mg > Ca exchange, mainly with K, as Cs desorption remains unchanged with the decrease of K concentration in solution. This results in the opening of the interlayer space of vermiculite (Fig. 6c), as expressed by the increase of diffraction peak intensity at 14.6 Å and a slight depletion of the mixed layer peak intensity at 12.5 Å (d (001) at 0 mmol/L K compared with that at 5 mmol/L K). Consequently, among the interlayer spaces, those containing exchangeable K seem particularly affected by this exchange. When the K(5) solution is used, the Cs desorption result is the same as the desorption isotherm (Fig. 4b). As K concentration becomes higher than the K(5) solution (> 5 mmol/L K), the solid uptakes K and releases rst Mg 2+ and Ca 2+ . Then Cs desorption declines until stops between 10 and 25 mmol/L K concentration. As long as the Cs desorption occurs, no change of the interlayer space dimensions is recorded (see d (001) at 10 mmol/L K in Fig. 6c). When Cs desorption no longer occurs, characteristic peaks of mixed layer at 12.5 Å, 12 Å (7.5° 2θ) and the broad re ection at 10 Å (8.6° 2θ) indicate an increasing and mixing proportion of micaceous layer. This again evidences the collapse of the interlayers. Meanwhile, K adsorbed represents only 2.33% of the K(5)V CEC for 25 mmol/L K concentration. Hence, K intercalates and locks at least the vermiculite interlayer space which inhibits the release in solution of Cs mainly located at this structural site.

The role of K on trace Cs desorption is evidenced by mechanically scavenging Cs in the mineral structure of vermiculite and K incorporated vermiculites. Moreover, chemical competition between K and Cs is highlighted when the vermiculite interlayer space remains fully open and K is introduced in the medium.

Then Cs selectivity at trace level of vermiculite and micaceous structures are higher than the one of K.

Mechanism of Cs sorption on vermiculite and micaceous structures

In order to establish the Cs sorption mechanism on vermiculite and micaceous structures in multi-cation media, cation exchange analyses were complemented with structural analyses on these structures.

Indeed, Cs sorption isotherms and their corresponding cation mass balances showed that cation exchange takes place differently according to the K occupancy in the interlayer space of conditioned vermiculites. Structural site types, interlayer and external sites, involved in the Cs sorption are then inferred based on structural analyses by XRD (Fig. 7). These latter were performed on batch slurries from Cs desorption experiments at varying Cs concentrations for the K-free vermiculite and the K loaded vermiculites (Fig. 2, 4 and SI2).

Two distinct behaviors are evidenced depending on Cs concentration in contact with the various clay structures, synthetized in Fig. 8. At trace Cs level (until 10 - 6 mol/L of Cs), regardless the conditioned vermiculite, during Cs adsorption and desorption the original structure remains (Fig. 7) with only slight changes. Indeed, the (001) re ection of the K-free vermiculite expresses only one peak around 14.6 Å.

Likewise, the XRD re ections of the K incorporated vermiculites show two peaks (Fig. 1). For reversible adsorption, the (001) re ections intensity at 14.6 Å decreases without signi cant enhancement of the mixed layer peak at 12.5 Å (except for K(10)V) and both re ections slightly shifts to larger angles. This can be related to a slight dehydration taking place in the interlayer space [START_REF] Dzene | Nature of the sites involved in the process of cesium desorption from vermiculite[END_REF]. The (001) re ection intensities are higher at 10 - 6 mol/L Cs than at 10 - 9 mol/L Cs. This re ects the reincorporation of hydrated cations in the interlayer space subsequently to trace Cs desorption. This latter appears in larger amount at 10 - 6 mol/L Cs than at 10 - 9 mol/L Cs, con rmed by cation mass balances, and is made possible by the su ciently opened interlayer space until a distance of 12.5 Å. However, the intensity and peak positions do not recover the original values, hence cations mixture have a whole lower hydration state in the interlayer space. Hence, the ratio between Ca to Mg in the interlayer space occupancy have changed. As Cs concentration increases above 10 - 5 mol/L in solution, the intensity of the vermiculite peak at 14.6 Å decreases, shifts towards large angles 2θ, and nally disappears to the bene t of mixed layer peak at 12.5 Å (Fig. 7) or less regardless of the initial mineral structure. This observation supports the hypothesis of an interlayer collapse subsequent to Cs incorporation and explains the partial reversibility of Cs sorption. The more vermiculite is initially charged with K, the smaller the d (001) value subsequent to Cs adsorption/desorption. Also, the more vermiculite are initially charged with K, the higher the amount of released Cs (i.e. 48.8 to 11.9% for K(10)V compared to 15.8 to 1.7% for K(0)V between 10 - 5 et 10 - 3 mol/L Cs). Moreover, Cs adsorption Kd (Fig. 1) decreases with increasing K loaded in the structure, and the Cs adsorption reversibility increases. Then, Cs desorption implies the role of external sites and the interlayer space when su ciently opened. In K free media, the more Cs is absorbed, the more the collapse interlayer spaces and the fewer proportion of Cs released. K occupying the Cs selective sorption sites and being strongly incorporated in the structure, is not replaced by Cs.

When K disturbs the chemical equilibrium, the interlayer distance reduces to 10 Å (Figs. a, b), interlayer collapse subsequent to K incorporation may provide fresh planar adsorption sites for Cs. This is in accordance with the higher Cs desorption ability of K incorporated vermiculites. Due to its high exchange capacity, the interlayer space permits to load a large amount of Cs which remains free as long as the interlayer is su ciently opened. Reactional scheme of the K + impact on Cs + exchange with Ca 2+ , Mg 2+ and K + on vermiculite and K intercalated vermiculites is displayed in Fig. 9.

The involvement of the speci c structural site, usually named frayed edge site (FES) [START_REF] Sawhney | Selective sorption and xation of cations by clay minerals -review[END_REF] was investigated by arti cially reducing the interlayer distance by incorporating K during the conditioning process. By reducing the vermiculite CEC with K xation, it mimics a sequence between true vermiculite and vermiculitized-mica. Consequently, it was expected to increase the FES occurrence by letting available cations stay into the space close to the layer edge [START_REF] Akemoto | Interpretation of the interaction between cesium ion and some clay minerals based on their structural features[END_REF]). High selectivity and low capacity sites are usually assimilated to the FES. So, this site type should be evidenced with Cs behavior at trace level. Partial Cs sorption reversibility in trace level (Fig. 1) is just evidenced on the highest K loaded vermiculite (K(10)V). In accordance with the structural analysis (Fig. 7c), the interlayer space reduction leads to constrain the diffusion of trace Cs adsorbed in the dehydrated interlayer space lower than 12.5 Å. So, Cs is adsorbed on basal, edge and interlayer space larger than 12.5 Å for this intercalated K vermiculite. Furthermore, Kd desorption is similar to Kd adsorption for other experimental conditions. Moreover, trace Cs adsorption decreases with K structural incorporation, while selectivity for Cs should increase. These results indicate that mixed layers at 12.5 Å, created by K incorporation, are not related to a structural FES site enhancement, responsible of the high a nity and sorption irreversibility.

There is also no evidence that FES are really created under these operating conditions and that FES holds the chemical reactivity of the high selectivity and low capacity site.

Cs exchange sequences accounting for structural site involvement can be proposed by combining the results. As seen above, K + in solution does not mainly interact in the ion exchange with Cs, given that the matrices are equilibrated with major cations in solution and intercalated K is mainly not exchangeable. ).This is evidenced by scanning the cation exchanges occurring at desorption step, especially for K loaded vermiculites. As Cs adsorption leads to close the interlayer space, only few percent of adsorbed Cs may desorb. This Cs appears adsorbed on less a ne sites. Ca 2+ easily replaces the desorbed Cs + but Mg 2+ is highly limited (Fig. 4 and SI2). So Mg 2+ a nity is lower than Ca 2+ for all sorption sites. In addition to K incorporated in the structure, the interlayer spaces show shorter distances. Consequently, desorbed Cs appears to come mainly from external sites (basal and edge site) when interlayer space is closed due to Cs adsorption. This interpretation is supported by the Robin et al. ( 2015) study on beidellite.

These authors highlighted a preferred Ca 2+ sorption on the external sites rather than Mg 2+ . Cs adsorption reversibility is also dependent on the crystal structure. K/Cs competition occurs for K concentration thousand times higher than that of Cs. Indeed, high K amount is required to easily desorb Cs at trace concentration (above 7 10 - 4 mol/L K in excess). Moreover, Cs is locked in the interlayer space with K incorporation. Consequently, K has a high selectivity for vermiculite and micaceous structures but remains lower than that of Cs.

4.

Cs transfer to plant is highly dependent on the clay mineralogy of soil, especially as soils are enriched in micaceous minerals and vermiculite. To understand Cs bioavailability of radionuclides in soils, Cs sorption-desorption behavior on micaceous minerals and vermiculite was studied in chemical environment close to a natural soil. For this purpose, a sequence between vermiculite and weathered mica was produced by saturating a vermiculite with K at various content. Experiments involve simultaneous Cs + exchange with Ca 2+ , Mg 2+ and K + at thermodynamic equilibrium. By coupling sorption isotherms, cation mass balances and structural analysis by XRD, reactional scheme and involvement of structural sites on Cs adsorption and desorption on clay minerals in multi-cations solutions are inferred.

Then K + competition on Cs + desorption is characterized by imposing various amounts of K on trace Cs doped vermiculite and K intercalated vermiculite. K concentrations were selected to mimic a K amendment in the elds, a K depletion in the solution due to plant uptake or weathering event, and to provide insight into the Cs location on the mineral structure.

Two Cs sorption behaviors were evidenced. At trace level, Cs exchange with Mg 2+ and Ca 2+ in a reversible adsorption process. External sites and interlayer sites remain available during exchange process whatever the amount of K incorporated in the structure. As Cs becomes to compete with major cations, Cs + replace rstly Mg 2+ then Ca 2+ . Cs + excess, as well as K + , leads to a reduction and to a collapse of the interlayer space. In this case, Mg 2+ is excluded from the interlayer space and Cs located in this structural site is blocked and becomes non exchangeable. The residual exchangeable Cs is then assigned to the external sites. Lower Cs amount is loaded on micaceous structure than vermiculite. This is due to their lower cation exchange capacity resulting from K incorporation. In contrast, Cs adsorption on micaceous structure is more reversible, suggesting the dominant involvement of external sorption sites. Trace Cs + is seldom removed by K + . Cs is strongly adsorbed on the various matrix and a K/Cs ratio in solution of about thousand is needed to remobilize Cs. The present study provides strong evidence for the fact that interlayer sorption is responsible for the incomplete reversibility of Cs + sorption on clay minerals. In the Figures

Mass balances of Cs + , K + , Ca 2+ , Mg 2+ and H + in solution at equilibrium from adsorption step performed with (a) the K-free vermiculite (K(0)V) and (b) the vermiculite at 27% occupancy by K (K(5)V).

Mass balances of Cs + , K + , Ca 2+ , Mg 2+ and H + in at equilibrium from desorption step performed with (a) the vermiculite exempt of K (K(0)V) and (b) the vermiculite at 27% occupancy by K (K(5)V).

  ; Maes et al. 1999; Mukai et al. 2016; Durrant et al. 2018; Wissocq et al. 2018; Ogasawara et al. 2019; Kitayama et al. 2020). Moreover, illite and partially-vermiculitized biotite sorb Cs + more strongly than vermiculite (Sawhney 1972; Brouwer et al. 1983; Maes et al. 1999; Kitayama et al. 2020; Latrille and Bildstein 2022).

Fig. 2 )

 2 were performed on the ve conditioned vermiculites in function of Cs concentration in the multi-cation K(x) solutions at chemical equilibrium. Cs repartition between solid and liquid is expressed by the Kd value. Similarly, to illite and smectite, Cs adsorption on vermiculite is non-linear with the Cs concentration in solution (Durrant et al. 2018; Wissocq et al. 2018; Latrille and Bildstein 2022).Regardless of the matrix and the solution composition, when the Cs concentration increases in solution, the Cs adsorption K d decreases to reach a local minimum between 2 and 4 10 - 6 mol.L - 1 , then increases to a local maximum between 0.38 and 2.4 10 - 4 mol/L Cs depending on the solution, before decreasing again at the highest Cs concentrations. The highest Cs adsorption occurs on vermiculite in K-free solution (K(0)) at Cs concentration below 2 10 - 6 and up to 10 - 5 mol/L. At Cs trace concentrations (< 10 - 7 mol/L), the more the K amount in the conditioned vermiculites and their respective conditioning solution, the lower the Kd value (for K less than 1 mmol/L). Above 5 mmol/L K in the media, the Kd of Cs in trace becomes slightly larger. All matrices give a similar lowest Kd value at about 10 - 6 mol/L Cs in solution.Conversely, the highest K loaded vermiculite (K(10)V) records the lowest Cs adsorption Kd above 10 - 5 mol/L Cs.Adsorption reversibility is veri ed when the apparent exchange constant for adsorption reaction is the inverse of the apparent exchange constant for desorption reaction at chemical equilibrium (K to the mass action law. As major cation concentration remains constant for both reactions, especially at low Cs concentration, Cs adsorption Kd is similar to the Cs desorption Kd[START_REF] Durrant | Cesium sorption reversibility and kinetics on illite, montmorillonite, and kaolinite[END_REF][START_REF] Wissocq | Application of the multi-site ion exchanger model to the sorption of Sr and Cs on natural clayey sandstone[END_REF]

  ; Kogure et al. 2012; Dzene et al. 2015; Yin et al. 2017; Kitayama et al. 2020). Cesium trapped in the interlayer space is consequently excluded from desorption (Kogure et al. 2012; Motokawa et al. 2014a, b; Yamamoto et al. 2019) or is poorly displaced by hydrated divalent cations (Sawhney 1964; Yin et al. 2017). Only adsorbed Cs on planar and edge sites remain exchangeable (Dzene et al. 2015; Yin et al. 2017). Kitayama et al. 2020; Murota et al. 2020), which quali es a different reactional pathway than the adsorption process. The partitioning between solid and solution, usually named Kd, is nally recommended to verify the adsorption reversibility (Wissocq et al. 2018; Kasar et al. 2020). The Kd valueof adsorption and desorption have to be aligned on the concentration isotherm. This implies control of the chemical exchange at equilibrium by respecting the mass action law and thus the cation mass balance in the system. Cs sorption on clay mineral is often studied in single cation pair exchange or far from a natural context. Although cation adsorption/desorption depends on competitions with surrounding cations in solution, especially major cations, few studies have been focused on Cs sorption competing simultaneously with several cations in soil solution[START_REF] Kasar | Sorption and desorption studies of Cs and Sr in contaminated soil samples around Fukushima Daiichi Nuclear Power Plant[END_REF].The aim of this study is to further understand the Cs adsorption and desorption behavior on micaceous minerals and vermiculite in chemical environment close to a natural soil. In order to mimic the transition between weathered mica and vermiculite, a vermiculite was K saturated at various degree of interlayer closing. Their exchange properties were then controlled. Finally, Cs adsorption/desorption behavior is investigated in multi-cation solutions. This involves simultaneous Cs + competition with Ca 2+ , Mg 2+ and K

	and their dilution with ultrapure water (milli-Q, 18.2 MΩ.cm - 2 , Millipore ® ). Salts of KCl (VWR Chemical),
	Ca(NO 3 ) 2 4H 2 O (VWR Chemical), Mg(SO 4 ) 7H 2 O (VWR Chemical), Mg(NO 3 ) 2 6H 2 O (VWR Chemical) were
	used. Acidi cation was done with ultrapure nitric acid (Chem-Lab) and phosphoric acid (Sigma Aldrich)
	diluted at appropriate concentrations when needed. The 20-25 µm vermiculite fraction was partitioned in
	ve batches, each conditioned with ve solutions remaining to 2.5 10 - 2 mol/L Ca and 3.75 10 - 2 mol/L
	The Cs + sorbed to micaceous minerals are generally weakly exchanged by competitive cations such as
	K + and NH 4
	2. Materials And Methods
	2.1. Materials and conditioning process
	A commercial vermiculite (Sigma Aldrich) was selected for this study. The chemical analysis of the raw
	vermiculite gives the following structural formula
	(	Si 2.905 Al 1.021 Fe 0.075 Fe 0.311 Mg 2.624 Ti 0.06 O 10 (OH) 2 K 0.204 Ca 0.034 Mg 0.201 . XRD analysis ) ( )
	revealed a pristine vermiculite associated with a vermiculite/mica mixed layer. CEC determined by NH 4
	exchange at pH 7 is 109.6 ± 1.2 meq/100g compared to the theoretical CEC estimated to 166 meq/100g.
	The non-exchangeable K by NH 4 is consistent with a mixed layer vermiculite/mica. Raw vermiculite was
	initially nely crushed and suspended in ultrapure water for one night, sonicated in a tank and sieved to
	isolate the 25 - 20 µm particles. Conditioning and experiment solutions were prepared by dissolving salt

+

[START_REF] Liu | Cation exchange model to describe Cs + sorption at high ionic strength in subsurface sediments at Hanford site, USA[END_REF][START_REF] Ohnuki | Adsorption behavior of radioactive cesium by non-mica minerals[END_REF]

despite their similar chemical properties. This indicates that the minerals are more selective for Cs + than K + and NH 4 + . NH 4 + extracts smaller amounts of Cs than hydrated Mg 2+ and Ca 2+ ; K + is the most e cient compared to the other cations

[START_REF] Yin | Effects of NH 4 + , K + , Mg 2+ , and Ca 2+ on the cesium adsorption/desorption in binding sites of vermiculitized biotite[END_REF]

). Furthermore, dehydrated K + originally in the interlayer space of micaceous minerals remains non exchangeable in contrast to those of expanding phyllosilicate. Only the weathering process partially releases interlayer cations from micas

[START_REF] Benedicto | Interlayer collapse affects on cesium adsorption onto illite[END_REF][START_REF] Sawhney | Selective sorption and xation of cations by clay minerals -review[END_REF]

. Then, superimposed to chemical ion-exchange, a physical mechanism leads to the capture of cations at low hydration potential into the mineral. Competition between K + and Cs + is associated with their location in the mineral structure and Cs sorption properties of micaceous minerals differ according to their degree of weathering (Kitayama et al. 2020; Murota et al. 2020). Consequently, sorption properties of pristine minerals deviate from those which are weathered in soils. To understand bioavailability of radionuclides in soils, knowledge of sorption-desorption behavior in soilwater systems remains crucial (Kasar et al. 2020). At chemical equilibrium, the reversibility of the adsorption process can be validated by desorption respecting the same physico-chemical condition. However, Cs desorption properties of clay minerals are frequently deduced from forced ion-exchange accounting chemical extractants (Brouwer et al. 1983; Dzene et al. 2015; Yin et al. 2017; Mukai et al. 2018; + . Cesium concentration isotherms are acquired in batch experiments performed in controlled physicochemical conditions at thermodynamic equilibrium. Desorption experiments performed with the same cation species allow to test the Cs adsorption reversibility. Cation mass balances are checked for each chemical condition to highlight cation competitions and selectivities occurring during Cs sorption. Then K + competition on Cs + desorption is studied by imposing various amounts of K on trace Cs doped vermiculite and K intercalated vermiculite. K + concentrations were selected to mimic a K amendment in the elds, a K depletion in the solution due to plant uptake or weathering event, and to provide insight into the Cs location in the mineral structure. Subsequent chemical disturbance in solution were recorded through cation mass balances. Finally, chemical results coupled with structural analyses by XRD lead to propose a reactional scheme for Cs adsorption and desorption in multi-cations solutions. Structural localization of sorption sites is addressed and discussed.

Table 1

 1 Desorption experiments were carried out on the slurry resulting from the adsorption step. K(x) solutions were used to exchange Cs + with cations in solutions respecting pH, solid/solution ratio and contact time used in the adsorption step. Activity from the residual adsorption solution not recoverable from the slurry, was taken into account to de ne the initial adsorbed 137 Cs activity of the vermiculites for desorption step.137 Cs and cations (Ca 2+ , Mg 2+ , K + ) in solution were analyzed by gamma counting and ion chromatography respectively, on supernatants collected after a new centrifugation cycle. Total Cs concentration is deduced from 137 Cs activity by assuming no isotopic fractionation between 137 Cs and

		Cation composition of K(x) solutions
	solution	Ca 2+	Mg 2+	K +
		(10 - 3 mol/L)	(10 - 3 mol/L)	(10 - 3 mol/L)
	K(0)	2	3	0
	K(0.1)	2	3	0.1
	K(1)	2	3	1
	K(5)	2	3	5
	K(10)	2	3	10
	Cation exchange capacities (CEC) of conditioned vermiculites are deduced from compensating cations
	exchanged by NH 4 at pH 7. Firstly, 50 mg of dried conditioned vermiculite was dispersed in 4 mL of 0.1
	mol/L NH 4 Cl, end to end shaken for one week and centrifuged at 33000 g during 40 min. Cation
	concentrations of supernatants were analyzed by ionic chromatography and low K concentrations were
	re ned by ICP-AES (Activa, Horiba Jobin Yvon) measurements.
	2.2. Cs adsorption/desorption at equilibrium
	The effects of Cs concentration were investigated by sorption isotherms for each conditioned vermiculite
	following the approach described in Wissocq et al. (2017) and Siroux et al. (2021). For all these batch
	experiments, 70 mg of dried conditioned vermiculite was dispersed in 6.1 mL of K(x) solution, leading to a
	solid/solution of 11.4 g/L. Each batch suspension was spiked with 137 Cs by adding 30 µL of a source
	( 137 CsCl in HCl 0.1 mol/L) containing an activity of 7000 Bq, corresponding to 4.6 10 - 8 mol/L of Cs
	introduced. For higher concentrations required, stable isotope (CsCl solution, Fluka Ultra) were added to

133

Cs, as previously veri ed by

[START_REF] Wissocq | Application of the multi-site ion exchanger model to the sorption of Sr and Cs on natural clayey sandstone[END_REF]

. Moreover, no natural Cs amount was measured on raw vermiculite. pH was also checked at equilibrium.

  al. 2017). This re ection gives the interlayer distance of vermiculite structures. Basal spacings (d (001) ) are ranged between 14.3 Å to 14.9 Å for mixed interlayer occupancy by Ca and Mg, whereas d (001) spacing is reduced to 10.4 Å for K occupancy or 10.8 Å to 11.4 Å for Cs occupancy in vermiculite (Brindley and Brown 1980; Dzene et al. 2015; Kogure et al. 2012). For this purpose, the XRD patterns were recorded on samples resulting from Cs desorption experiments. Vermiculite slurries were dispersed in pure water, dropped on glass slides and air dried to obtain oriented preparations.

Table 2

 2 CEC and cations exchangeable compositions of vermiculites conditioned with ve K(x) solutions.

	Matrix	CEC	Exchangeable cations
			Ca 2+	Mg 2+	K +
		cmol+/kg	cmol+/kg	cmol+/kg	cmol+/kg
	K(0)V	127.1	32.0	94.8	0.3
	K(0.1)V 113.2	29.5	83.3	0.4
	K(1)V	104.3	28.2	75.6	0.5
	K(5)V	93.6	27.9	64.9	0.8
	K(10)V	86.5	33.7	51.6	1.2
	3.2. Cs sorption behavior on vermiculite and micaceous
	structure in multi-cation media

Cs adsorption and desorption isotherms (

Table 1

 1 Theyexpress the Cs mobility taking into account the cations selectivity and chemical competitions. Mass balances of cations involved in cation exchanges with Cs on K(0.1)V, K(1)V and K[START_REF] Kato | Potassium Fertilizer and Other Materials as Countermeasures to Reduce Radiocesium Levels in Rice: Results of Urgent Experiments in 2011 Responding to the Fukushima Daiichi Nuclear Power Plant Accident[END_REF]V are displayed in SI2. Signi cant Δeq is delimited by the quanti cation limit by ion chromatography and the cumulated mass balance uncertainties, xed to 10 - 6 equivalent (+) charge for Ca, Mg and K and the experimental uncertainty to4 10 - 13 Eq. (2σ) calculated for Cs + .As cation exchange with H + may occur for Cs sorption onto clay minerals[START_REF] Wissocq | Application of the multi-site ion exchanger model to the sorption of Sr and Cs on natural clayey sandstone[END_REF][START_REF] Durrant | Cesium sorption reversibility and kinetics on illite, montmorillonite, and kaolinite[END_REF]), the pH of the adsorption and desorption solutions were monitored along the isotherms at equilibrium. The pH value did not vary signi cantly around 5.6 (initial solutions pH) except for the adsorption experiment performed with the highest Cs concentration (SI3) in which pH falls to 5.1. However, this pH value variation, although signi cant, associates a negligible amount of protons that could be involved in the exchanges (i.e. 3.7 10 - 8 mol of H + ) with Ca 2+ , Mg 2+ and K + . Moreover, H + acts slightly on Cs adsorption/desorption behavior (Latrille and Bildstein 2022) in this pH range.

) contain Cs at various concentrations for adsorption step whereas these solutions are initially free of Cs for desorption step. The cations mass balances evidence the Ca 2+ , Mg 2+ , K + and H + exchanges involved with Cs adsorption and desorption, depending on Cs concentration.

  al. 2012; Dzene et al. 2015; Latrille and Bildstein 2022). As intercalated K is higher in the structure, Mg 2+ and Ca 2+ replace Cs + (see K(10)V in SI2). This argues for Cs desorption from easily accessible sorption sites. So, two Cs sorption behaviors are evidenced by chemical analyses of solutions in equilibrium with vermiculites at various K incorporation rates. As expected, K incorporated in the structure is not signi cantly displaced by Cs during the Cs adsorption/desorption process. Major cation composition of solutions remains stable during Cs adsorption/desorption in trace concentration due to the difference in concentration between major cations and Cs involved in the exchange. The reversible adsorption process is veri ed by Kd of Cs values (Fig.

  5 and 6) upon Cs adsorption. Such a small distance is not reached by Cs introducing. Then, K is incorporated in the interlayer space by exchange with Ca 2+ and Mg 2+ and subsequently locks the Cs in trace speci cally adsorbed on high selective and low capacity sites. This speci c site should also be present on structural basal site, by considering a sheet merging as shown by the disordered stacking on XRD pattern (broad re ection peak between 12 and 10 Å)(Motokawa et al. 2014 a, b). Similarly, to Cs(Motokawa et al. 2014

  Chemical composition of solutions re ects the sequence of cation exchange: at rst, Mg 2+ is exchanged with Cs, as Cs starts competing with Ca 2+ , this latter is released in solution. This explains the dehydration and secondly the reduction of the interlayer distance, in accordance with the cation hydration enthalpy ordered as Mg 2+ > Ca 2+ >K + >Cs + , inversely to their cation radius[START_REF] Noyes | Thermodynamics of ion hydration as a measure of effective dielectric properties of water[END_REF]; Yin et al. 2017). Consequently, K + and Cs + promote the decrease of the interlayer distance and are easily dehydrated resulting in the interlayer collapse (Sawhney 1972, Okumura et al. 2018, Motokawa et al. 2014 a,b). Part of the Cs is mechanically locked in the interlayer space (Kikushi et al. 2015). As the interlayer space opens, Mg 2+ , Ca 2+ occupy both interlayer space and external sites. Because the hydration energy of Mg 2+

is higher than that of Ca 2+

[START_REF] Yin | Effects of NH 4 + , K + , Mg 2+ , and Ca 2+ on the cesium adsorption/desorption in binding sites of vermiculitized biotite[END_REF]

, Ca 2+ reincorporation is favored over Mg 2+ , which is consistent with the observed cation exchanges at high Cs concentration. Once the interlayer space is closed or reduced to 12 Å, hydrated Mg 2+ appears too large to enter in shorter space

[START_REF] Okumura | Radiocesium interaction with clay minerals: theory and simulation advances Post-Fukushima[END_REF]

Acknowledgments

The authors acknowledge the French "Programme Investissement d'Avenir" (ANR 11-RSNR-0005 DEMETERRES, https://anr.fr/ProjetIA-11-RSNR-0005) and the French Alternative Energies and Energy Commission for their nancial supports. The authors thank Hélène Isnard and Nathalie Coreau for their analytical support in ICP/MS and ion chromatography. Olivier Bildstein is acknowledged for his helpful English proofreading.

Funding

The received nancial support from the French "Programme Investissement d'Avenir" (ANR 11-RSNR-0005 DEMETERRES, https://anr.fr/ProjetIA-11-RSNR-0005) and the French Alternative Energies and Atomic Energy Commission.

Availability of data and Not applicable.

Code availability Not applicable.

The authors have no relevant nancial or non-nancial interests to disclose.

The authors declare that they have no competing interests.

case of soil contamination by Cs, K + amendment only leads to a weak enhancement of Cs desorption, more so for vermiculite than for micaceous minerals. Ca and Mg amount in natural systems will therefore affect Cs bioavailability. Figure 8 Reactional conceptual scheme of Cs + exchange with Ca 2+ , Mg 2+ , K + on vermiculite and K intercalated vermiculites.

Declarations

Reactional conceptual scheme of the K + impact on Cs + exchange with Ca 2+ , Mg 2+ and K + on vermiculite and K intercalated vermiculites.

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