Radiocesium interaction with clay minerals: Theory and simulation advances Post–Fukushima

Insights at the microscopic level of the process of radiocesium adsorption and interaction with clay mineral particles have improved substantially over the past several years, triggered by pressing social issues such as management of huge amounts of waste soil accumulated after the Fukushima Dai–ichi nuclear power plant accident. In particular, computer– based molecular modeling supported by advanced hardware and algorithms has proven to be a powerful approach. Its application can now generally encompass the full complexity of clay particle adsorption sites from basal surfaces to interlayers with inserted water molecules, to edges including fresh and weathered frayed ones. On the other hand, its methodological schemes are now varied from traditional force–field molecular dynamics on large–scale realizations composed of many thousands of atoms including water molecules to first–principles methods on smaller models in rather exacting fashion. In this article, we overview new understanding enabled by simulations across methodological variations, focusing on recent insights that connect with experimental observations, namely: 1) the energy scale for cesium adsorption on the basal surface, and the of nuclear of radiocesium. Key experimental observations that motivate these simulation advances are also summarized.


Introduction
The 2011 Great East Japan Earthquake (Japan Meteorological Agency, 2011) and subsequent tsunami caused a severe accident at the Fukushima Dai-ichi Nuclear Power Plant (FDNPP) (International Atomic Energy Agency, 2015), which released huge amounts of radioactive nuclides into the environment (Yoshida and Takahashi, 2012;Mikami et al., 2015;Ministry of Education, Culture, Sports, Science and Technology, 2011). Among the released radionuclides, the foremost contributor to radioactive exposure in the region surrounding the power plant is 137 Cs, which has a half-life of 30.1 years and a strong tendency to bind to soil fine particles. Over the last seven years, the Japanese Government has led an extensive decontamination campaign aimed particularly at decreasing exposure to 137 Cs (Ministry of Environment, 2011). The standard procedure -the removal of top soil-has proven arduous yet effective at reducing air dose rates and the area of the evacuation zone (Japan Atomic Energy Agency, 2014a, 2014b; Miyahara et al., 2015).
A new issue, however, has arisen as a by-product of this success: namely, a tremendous amount of waste soil (about 15,600,000 m 3 ) has accumulated in temporary storage facilities (Ministry of Environment, 2011). In response to this issue, the Japanese Government created an interim storage facility surrounding the FDNPP while announcing plans to commission a permanent disposal site outside the Fukushima Prefecture (Ministry of Environment, 2011). Implementation of the final disposal plan, however, requires that the waste volume be significantly reduced to minimize the costs and safety challenges associated with site construction, waste transportation, and longterm site management. These challenges have motivated renewed efforts to develop volume reduction schemes for Cs-contaminated soils. To date, however, no scheme has yet been demonstrated to perform suitably at scale in real field conditions. A major reason is the absence of scientific consensus regarding the binding mechanisms, thermodynamics, and kinetics of Cs in complex soils and sediments.
This lack of consensus derives partly from the inherent complexity of soils and partly from the fact that Cs adsorption in natural environments involves multiple binding sites, the most important of which have very low density, very high affinity, and complex kinetics of cesium uptake and release. The very low density of these sites makes them challenging to observe and characterize even using the most cutting-edge microscopic techniques. To overcome these constraints, computational microscopic simulations have proven useful (Kubicki, 2016) with particularly rapid advancement of computing resources since the earliest investigations (e.g., Smith, 1998;Young and Smith, 2000;Rosso et al., 2001). For example, classical molecular dynamics (MD) techniques can reveal the collective behaviors of thousands of atoms at the clay-water interface and can now account for the effects of particle morphology . Moreover, first-principles MD (FPMD) techniques, though restricted to smaller system sizes, have been widely employed due to their strong transferability to various situations without the need for deriving force field models.
Here we review recent developments in microscopic understanding of Cs adsorption on clay minerals given by state-of-the-art computational molecular simulations. In particular, the last five years after the FDNPP accident have seen significant advances. In the remainder of this article, we introduce key techniques, summarize the insights gained, and discuss their implications for waste volume reduction.
2. An overview of Cs adsorption on illite The adsorption and fixation of radiocesium to fine particles has been a recurrent question since the dawn of the nuclear age (Sawhney, 1972;Cornell, 1993;Delvaux et al., 2000). One of the most important findings is that illite, a micaceous clay mineral that is common in soils and sediments, is a particularly strong adsorbent of Cs. In this section, we give a brief review of Cs adsorption on illite as characterized using experimental studies at various scales.

Macroscopic scale
Batch experiments have revealed that Cs adsorption on illite shows a Freundlich-type isotherm (Brouwer et al., 1983;Staunton and Roubaud, 1997;Poinssot et al., 1999;Bradbury and Baeyens, 2000;Zachara et al., 2002;Liu et al., 2003;Steefel et al., 2003;Goto et al., 2008), which implies the existence of multi-component adsorption sites. Actually, the isotherm can be interpreted as a superposition of several isotherms (Brouwer et al., 1983;Poinssot et al., 1999;Bradbury and Baeyens, 2000;Zachara et al., 2002;Liu et al., 2003;Steefel et al., 2003). The adsorption sites corresponding to these isotherms are often referred as type-I, -II, …, sites, whereby lower numbers correspond to sites with stronger affinity and lower capacity, i.e., sites that dominate adsorption at progressively lower Cs loadings. For example, the type-I site has the lowest capacity (only ∼ 0.25% of the total cation exchange capacity (CEC) of illite) but contributes predominantly to Cs adsorption at concentrations below 10 −8 M Cs (Bradbury and Baeyens, 2000). These sites are referred to hereafter as "macroscopic model sites". It has been shown that Cs adsorb selectively at these sites against competitive cations (Na + , K + , Rb + , NH 4 + , Ca 2+ , etc.), i.e., all sites adsorb Cs selectively with the order of strength as type-I > -II > … (Sawhney, 1972;Comans et al., 1991;Brouwer et al., 1983;Poinssot et al., 1999;Bradbury and Baeyens, 2000;Zachara et al., 2002). Based on this Cs selectivity, a useful quantity, referred to as radiocaesium interception potential (RIP), was introduced to estimate the amount of highly selective sites (Cremers and Pleysier, 1973;Wauters et al., 1996). The kinetics of Cs adsorption and desorption have also been studied at the macroscopic scale (Comans et al., 1991;Comans and Hockley, 1992;Poinssot et al., 1999;Zachara et al., 2002;Liu et al., 2003;de Koning and Comans, 2004). A notable outcome of these studies is that a longer initial contact time with the Cs-bearing solution (aging time) decreases the amount of extractable Cs from all sites (Evans et al., 1983;Wauters et al., 1994;de Koning and Comans, 2004).

Mesoscopic scale (∼nm)
A well known limitation of geochemical speciation models is that regardless of their agreement with macroscopic adsorption data they cannot, on their own, unambiguously constrain the physical and chemical details of individual adsorption sites. Nevertheless, macroscopic scale data have guided the development of mesoscopic conceptual models that attempt to explain key features of the macroscopic scale data (Jackson, 1963). The conceptual model of an illite particle shown in Fig. 1 illustrates the five types of adsorption sites that are thought to exist on this mineral. These sites, referred to hereafter as "structural adsorption sites", are the basal surface (planar) site, edge site, hydrated interlayer site, frayed edge site (FES), and anhydrous interlayer site. The conceptual model shown in Fig. 1 is consistent with images of individual illite particles observed using transmission electron microscopy (TEM) (Fuller et al., 2015).
Comparison between the area of the structural adsorption sites and the adsorption capacity of the different macroscopic model sites suggests that the frayed edge and basal sites hypothesized to occur at the mesoscopic scale correspond to the type-I and -III sites used in three-site macroscopic scale adsorption models (i.e., the sites with the smallest and largest Cs adsorption capacity) (Brouwer et al., 1983). This inference is further supported by observations indicating that Cs adsorbs primarily near illite edge surfaces at low loadings (Rajec et al., 1999;McKinley et al., 2004) and on the basal surface at high loadings (Kim et al., 1996).
A particularly interesting feature of the conceptual model described in Fig. 1 is that it has the potential to explain the complex kinetics of Cs adsorption on illite. For example, reports of irreversible Cs adsorption may reflect the collapse of hydrated interlayers or the migration of Cs into core region of illite particles (Jacobs and Tamura, 1960;Sawhney, 1972;de Koning and Comans, 2004), two mechanisms that are supported by TEM observations (Okumura et al., 2014b;Fuller et al., 2015).

Microscopic scale (∼Å)
Although the mesoscopic model outlined above is consistent with various features of Cs adsorption on illite, additional microscopic physical/chemical insight is needed to develop a truly predictive understanding as required, e.g., to develop efficient Cs extraction methodologies. Until about 15 years ago, such nanoscale insight was limited to a few experimental results revealing the atomistic level coordination of adsorbed Cs in a small range of conditions. In particular, NMR experiments showed the existence of two distinct Cs adsorption sites on illite particles (Kim and Kirkpatrick, 1997), while extended X-ray adsorption fine structure spectroscopy (EXAFS) data yielded estimates of the average distribution of Cs-O distances in the first coordination shell of adsorbed Cs (Bostick et al., 2002).

Progress in experiments since the Fukushima accident
In this section, we give a brief review of relatively recent experimental insights into Cs binding in clay particles motivated by the FDNPP accident. In particular, we highlight experiments that provide a more robust basis for the molecular modeling studies discussed in the rest of this paper.
One of the most important observations regarding radiocesium adsorption in Fukushima soils is that weathered biotite is a primary adsorbent Mukai et al., 2014Mukai et al., , 2016aMukai et al., , 2016bKikuchi et al., 2015). For example, recent experiments showed that illite and weathered biotite are the primary radiocesium-bearing phases in silt-and sand-size fractions of Fukushima soil (Tanaka et al., 2018). Note that biotite in this article is defined as a Fe-rich phlogopite and/or a Mg-rich annite with the chemical formula K(Mg,Fe) 3 AlSi 3 O 10 (F,OH) as identified by X-ray diffraction (XRD), energy dispersive X-ray spectrometry (EDS) and TEM (Kikuchi et al., 2015;Mukai et al., 2016a). Although some observations prior to the Fukushima accident had identified the potential importance of weathered biotite as a Cs adsorbent (Sawhney, 1966;McKinley et al., 2001McKinley et al., , 2004Zachara et al., 2002), this observation is particularly critical in the Fukushima case because weathered granite, which contains weathered biotite, is a dominant source rock in the Fukushima area (Kikuchi et al., 2015;Mukai et al., 2016b;Takahashi et al., 2017). Despite the structural similarity between biotite and illite, macroscopic experiments showed that biotite has stronger affinity of Cs than illite (Mukai et al., 2016b).
Important insight into Cs adsorption in Fukushima soils is provided by XRD and TEM observations of Cs uptake on weathered biotite and vermiculite (a related phyllosilicate with high structural charge density). In particular, Cs readily incorporates in anhydrous vermiculite interlayers and tends to segregate itself by almost full monoionic replacement in some interlayer spaces (Kogure et al., 2012). Furthermore, exposure to artificially high Cs concentrations was shown to cause a collapse (dehydration) of the interlayers of weathered biotite collected from the Fukushima Prefecture (Kikuchi et al., 2015). Finally, small-angle X-ray scattering (SAXS) studies revealed differences between the mesoscopic structural changes of vermiculite and weathered biotite caused by Cs adsorption (Motokawa et al., 2014a); in particular, experimental results indicate that weathered biotite contains wedge--shape interlayer structures, i.e., FES structures similar to those of illite ( Fig. 1). Motokawa et al. (2014b) also showed details of collective structural changes of vermiculite caused by Cs adsorption.
Local atomic environments around adsorbed Cs in clay minerals have been measured primarily using X-ray absorption spectroscopy methods. EXAFS studies of additional Cs adsorbed to natural samples of actual Fukushima soil revealed that the local structure surrounding Cs is very close to ones in mica and that Cs in Fukushima soils forms both of inner-and outer-sphere surface complexes (Qin et al., 2012). The observed interlayer collapse due to migration of Cs in vermiculite extracted from actual Fukushima soils (Tsuji et al., 2014) is thought to originate from the low hydration energy of Cs, which is reflected as a poor organization of water molecules around the hydrated Cs ion (Ikeda and Boero, 2012;Machida et al., 2015). EXAFS studies of the impact of pH on the atomic environment around Cs in vermiculite indicate that inner-sphere complexes become increasingly more predominant as pH increases from 3.0 to 7.0 (Fan et al., 2014a). Fan et al. (2014b) found a correlation between the availability of strong adsorption sites and the ratio of inner-sphere complexes with respect to both (inner-and outer-sphere) complexes in illite, vermiculite, and montmorillonite by a study on relation between EXAFS analysis and RIP evaluation. Real-time-resolved EXAFS revealed rapid adsorption of Cs on vermiculite . Using near-edge XAFS, the influence of water molecule coordination on the chemical state of unoccupied molecular orbitals in Cs was examined (Honda et al., 2016).

Progress in microscopic modeling
Atomistic simulations using Monte Carlo (MC), classical MD, and density functional theory (DFT) techniques have played an important role in elucidating the structure and reactivity of clay minerals on a microscopic scale (Kubicki, 2016), in concert with experimental and theoretical studies (Liebau, 1985;Mottana et al., 2002). The importance and utility of these methods is illustrated, for example, by the existence of multiple sets of interatomic potential parameters developed for classical MD simulations of clay minerals (Skipper et al., 1989;Cygan et al., 2004;Heinz et al., 2005;Sakuma and Kawamura, 2011;Pitman and van Duin, 2012;Tesson et al., 2016). To date, however, much of the atomistic simulation effort has focused on the basal surfaces of smectite and kaolinite clay minerals rather than on the edges, frayed edges, and interlayers of illite and weathered biotite.
From a molecular modeling perspective, illite and weathered biotite are likely to have common site-specific properties. Both minerals are thought to have a common mesoscopic structure characterized by the five sites shown in Fig.  1. In addition, both minerals have similar chemical formulae: K 1-x Al 2 (Si 3- in the case of illite and biotite, respectively. The major crystallographic difference is that the octahedral sheets of illite and biotite are di-and tri-octahedral, respectively. Though this difference in octahedral sheet occupancy may cause some difference in the adsorption properties of the two minerals, illite is often used as a representative model for both minerals. In some cases, phlogopite has been used a convenient trioctahedral proxy for weathered biotite. Advances in the atomistic level modeling of the adsorption sites of illite, phlogopite and related minerals is reviewed below.

Basal surface site
As discussed in section 2, NMR experiments have revealed that Cs can adsorb on the basal surface in significant proportions (Kim et al., 1996). Subsequently, advances in experimental and theoretical techniques have led to the determination of the energetics of Cs adsorption as well as the atomic-scale structure of adsorbed Cs ions and interfacial water molecules at the basal surface.
The basal surface has a simple flat structure that facilitates measurements with techniques such as X-ray reflectivity (XRR) and atomic force microscopy (AFM). Consequently, ion adsorption phenomena on the basal surfaces of phyllosilicates have been extensively studied (Lee et al., 2012(Lee et al., , 2013Pintea et al., 2016;Araki et al., 2017). In particular, detailed experimental data have been reported on the distribution of Cs ions above the basal surface (Lee et al., 2012(Lee et al., , 2013Pintea et al., 2016;Araki et al., 2017).
Molecular simulations are well-suited to study in isolation the individual factors that control Cs adsorption (Vasconcelos et al., 2007;Sakuma and Kawamura, 2011;Bourg and Sposito, 2011;Kerisit et al., 2016;Loganathan and Kalinichev, 2017;Bourg et al., 2017). For example, Kerisit et al. (2016) used classical MD simulations to systematically study the effect of the magnitude and location of the permanent charge on the free energy of Cs adsorption on phyllosilicate basal surfaces (Fig. 2) for a range of model phyllosilicates (pyrophyllite, illite, muscovite, phlogopite, celadonite, and margarite). In addition to a shallow minimum associated with outer-sphere adsorption, all phyllosilicates, except pyrophyllite, showed a strong preference for adsorption as an inner-sphere complex, whereby Cs + adsorbed directly above a six-membered ring cavity and was coordinated to six surface oxygen atoms and five to six water molecules (Kerisit et al., 2016). The simulations further revealed a linear correlation between the magnitude of the layer charge and the free energy of formation of the innersphere complex (Kerisit et al., 2016). The structure of the octahedral layer and the distance to neighboring surface K + ions were also found to have a significant influence on the adsorption free energy; for example, Cs adsorption was found to be more favorable on muscovite than on phlogopite, because the tri-octahedral sheet structure of the latter leads to a shorter hydroxide H-Cs distance than the di-octahedral sheet of the former (Kerisit et al., 2016). More recently, Loganathan and Kalinichev (2017) showed that the location of aluminum substitutions within the surface tetrahedral layer affects the adsorption free energy of Cs. Finally, MD simulations by  were found to accurately reproduce experimental X-ray reflectivity data on the structure of water on a Cs-bearing basal surface of muscovite mica as well as experimental data on the free energy of exchange between Na, K, Rb, and Cs. Overall, these recent numerical simulations reveal that the atomic-scale structure of the basal surface significantly modulates Cs adsorption affinity.

Edge sites
The edge surfaces of clay minerals on a microscopic scale have been extensively studied because of their important roles in protonation/ deprotonation, dissolution/growth, and adsorption of transition metals and oxyanions. In the specific case of Cs adsorption by (and extraction from) micaceous minerals, they are of interest particularly because of their role in the formation of hydrated interlayer sites with/without FES (Fuller et al., 2015), in the dissolution of the clay framework (Kuwahara, 2006), and potentially as a distinct adsorption site . Despite the importance of clay edge surfaces, however, their exact structure remains incompletely understood (Meunier, 2006), in part because the preferred crystallographic orientation of clay edges is sometimes challenging to observe (Bourg et al., 2007;Tournassat et al., 2016).
In the absence of experimentally established edge crystallographic structures, computational and theoretical studies have played an important role in generating plausible models. Almost all of these studies have relied on the initial assumption that the ratio of octahedrally-to tetrahedrallycoordinated cations at the edge surface is identical to that in the bulk crystal despite experimental evidence that the edge surfaces of clay minerals exposed to low-or high-pH solutions may become enriched in Si or Al, respectively (Carroll and Walther, 1990). Within the framework of this assumption, the picture that emerges from DFT calculations of dry and hydrated clay edge surfaces is consistent with the predictions of earlier periodic bond chain theory calculations (White and Zelazny, 1988): the most stable edge surfaces correspond to the (110) and (010) crystallographic planes (Churakov, 2006;Kwon and Newton, 2016); the edge surfaces carry significantly under-or over-coordinated edge O atoms that are stabilized by bond-length relaxation such that the edges are essentially uncharged at near-neutral conditions (Bickmore et al., 2003;Liu et al., 2014;Tournassat et al., 2016); finally, octahedral Al atoms exposed at clay edge surfaces can readily become five-coordinated through the detachment of an -OH2 functional group (Liu et al., 2015;Lammers et al., 2017;Okumura et al., 2017).
Few molecular simulation studies have investigated the sorption of Cs + to edges of layered silicate minerals. MD simulations of Cs sorption to the neutral (110)-edge of K-illite show that Cs ions form predominantly innersphere complexes located in the same plane and relative position as interlayer K ions, such that the edge sorption site resembles a continuation of the interlayer . Excess Cs sorption is greatest adjacent to edge sites with comparatively lower charge density. Ion exchange selectivity between Cs and Na at edge sites increases with decreasing Cs content, with a maximum value of log K Na/Cs of ∼1.4. Thus, edge sites have intermediate Na/Cs ion exchange selectivity coefficients compared to the basal surface sites and frayed edge or interlayer sites, which are discussed in section 4.4 and 4.5.
To gain a deeper insight into the adsorption states of hydrated interlayer cations in clay minerals, model systems have been used for FPMD simulations. Ikeda et al. (2015) performed a series of constant pressure FPMD simulations at P = 1 atm and T = 300 K for the three kinds of 2:1 type clay minerals corresponding to saponite (Sap), beidellite (Bei), and montmorillonite (Mnt) containing alkali cations in the interlayer. Fig. 3 shows the resultant structural modes of Cs-Sap, Cs-Bei, and Cs-Mnt clays, each of which has formally the same amount of layer charge of -e/3 per O 10 (OH) 2 introduced by the isomorphic substitution, typical of the smectite group.
Then, Ikeda et al. (2015) investigated systematically the adsorption states of alkali cations in their swelling clay minerals via FP-metadynamics (MTD) simulations (Laio and Parrinello, 2002;Iannuzzi et al., 2003). Fig. 4 shows the reconstructed free energy profile ΔF representing the adsorption states of Na + and Cs + in the interlayer of Sap clays obtained from their FP-MTD simulations along with the adsorption structure corresponding to its minimum. The computed ΔF shows that an inner-sphere complex is preferentially formed for Cs + in the interlayer of Sap, whereas an outersphere complex tends to be formed for Na + instead. Such strong preference for an inner-sphere complex of Cs + observed in Sap is not shown in Bei and Mnt, indicating that the reactivity of O b atoms in tetrahedral sheets varies significantly depending on the detailed composition of 2:1 type clay minerals even if they have the same amount of layer charge. Indeed, the local density of states (LDOS) lying just below Fermi level (E F ) at O b sites differ significantly among the three model clays as shown in Fig. 5, where the corresponding LDOSs at the neighboring apical O (O a ) sites are also shown for comparison. The observed variation of LDOS just below E F suggests that the Lewis basicity of O b atoms decreases in the order of Sap > Bei > Mnt in good accordance with that of the affinity of Cs + with O b atoms suggested from FP-MTD simulations. Furthermore, the Cs-O b interactions in the innersphere complex preferentially formed in Sap-like clays include nonnegligible covalency resulting mainly from the electron donation from O b 2p to Cs + 5d empty orbitals. In addition, Cs + aggregation is suggested to occur in hydrated regions between Fe 3+ -rich clay layers in weathered biotites from FPMD simulations (Ikeda, 2016) performed by employing model systems containing Fe 3+ ions rather than Fe 2+ and a certain quantity of vacancies in octahedral sheets, which are known to result from the chemical weathering of biotite.

Frayed edge sites
As noted above, FES are often invoked as the possible origin of the very strong affinity of Cs for illite and weathered biotite at very low loadings. These sites are characterized by the existence of a "wedge--shaped" nanopore structure in regions where the phyllosilicate layers transition from anhydrous to hydrated interlayers (Jackson, 1963). Strong Cs adsorption at these sites is generally though to result from the low hydration free energy of Cs, though some studies have pointed out that the low hydration energy of Cs does not fully explain its highly selective adsorption (Brouwer et al., 1983).
In order to gain insight into the K-Cs exchange selectivity of FES, Okumura et al. (2013) constructed a toy model as shown in Fig. 6, in which free energy of K-Cs exchange between FES and liquid water was predicted as a function of a distance d characterizing the degree of opening of the FES. The definition can be represented as follows, where E FES (A + ; d) is the energy of the FES model system with A + ion and interlayer distance d, which is evaluated by DFT calculation without any thermal effects for simplicity, and G hyd (B + ) is the experimental hydration energy of ion B + (Okumura et al., 2013). The result (Fig. 7) showed that Cs is preferentially adsorbed by FES, relative to K + , only when d becomes larger than 1.1 nm. The energy difference reaches −23 kJ/mol at d = 1.3 nm, which is consistent with the experimentally-derived value of −27 kJ/mol (Brouwer et al., 1983). This quantitative agreement suggests that this model succeeded in capturing an aspect of FES.
The origin of the result shown in Fig. 7 can be interpreted as a combination of size matching between the ionic radius of the adsorbing ion and the interlayer distance and the difference in hydration energies of Cs and K (Okumura et al., 2013). This interpretation is explained by the following decomposition of Eq. (1), where ΔE site and ΔE hyd represent the energy difference between FES with Cs and potassium and the hydration energy difference, respectively. This equation clearly illustrates that the difference in hydration energies (ΔE hyd ) does not fully explain the strong adsorption of Cs to FES; the difference in the free energy of interaction between each cation and the adsorption site (ΔE site ) is also critical.
More recently, MD simulations of FES were performed with a large model of Al-hydroxy interlayered vermiculite, which also has the wedge structure (Zaunbrecher et al., 2015). This model has hydrated interlayer sites, in contrast, the DFT model represents only the wedge structure without hydrated interlayer sites. This analysis gives consistent results with the DFT calculations, i.e., adsorption of larger cations such as Cs and Rb can be energetically highly favored at FES.

Interlayer sites
Anhydrous interlayer sites of the 2:1 layered silicates are the final and most elusive adsorption sites in radiocesium-contaminated soils. The study of ion exchange involving interlayer sites has a long history (Barshad, 1954;Scott and Smith, 1966;Reichenbach and Rich, 1969;Sawhney, 1972;Sánchez-Pastor et al., 2010). Many studies have shown that exchange of K+ for ions with relatively large hydration enthalpies, including Na + , Ba 2+ , Sr 2+ , Ca 2+ and the hydronium ion (Rausell-Colom et al., 1965;Quirk and Chute, 1968;Rich, 1968, 1969;Sánchez-Pastor et al., 2010), lead to layer expansion or "decollapse". However, the presence of even trace amounts of aqueous K + or NH 4 + in solution can strongly inhibit exchange by solvated counterions (Scott et al., 1960;Scott and Smith, 1966) due to the strong thermodynamic penalty for replacement of K + by hydrated ions in the interlayer (Rausell-Colom et al., 1965). On the other hand, Cs + migration into deep anhydrous interlayer sites without "decollapse" has been observed (Okumura et al., 2014b;Fuller et al., 2015). In addition, the exchangeability of Cs adsorbed to natural weathered vermiculite is highly limited even in strong acid, and it decreases over time (Mukai et al., 2016b).
Based on these observations, there are two candidate pathways by which Cs can enter and become "fixed" in the interlayer region (1) decollapse-driven exchange, and (2) direct exchange (Fig. 8). Simulations of Namontmorillonite showed low energy barriers for Cs and Na migration from the micropore into hydrated interlayer nanopores (Rotenberg et al., 2009) and relatively rapid diffusion of Cs in hydrated interlayers (Marry and Turq, 2003;Kosakowski et al., 2008;Bourg and Sposito, 2010). These results illustrate that Cs can exchange rapidly with interlayer Na in 2-layer Namontmorillonite, and likely cannot explain the decreasing exchangeability of interlayer Cs with time (Evans et al., 1983;Wauters et al., 1994;de Koning and Comans, 2004).
Direct exchange is the replacement of anhydrous interlayer (non-exchangeable) K by Cs without a decollapsed (hydrated) intermediate. To investigate the feasibility and pathway of the direct exchange mechanism, Ruiz Pestana et al. (2017) performed MD simulations and DFT calculations that quantified the impact of Cs ions on the mobility of interlayer K in illite. They found that ion diffusion in anhydrous interlayers is likely controlled by ion migration between neighboring counterion sites, and that the magnitude of the energy barrier is controlled by the local basal spacing or Cs content. The K ions located in the vicinity of larger Cs + in the anhydrous interlayer have significantly lower ion migration barriers than K ions in pure K-illite, accelerating K diffusion by orders of magnitude. These simulations suggest that energy barrier lowering by the larger Cs ions promotes subsequent K ion exchange events, allowing the direct exchange of K by Cs to proceed in the absence of interlayer water (Ruiz Pestana et al., 2017). On the other hand, the decollapse mechanism appears to play a crucial role in the case of radiocesium adsorption in divalent cation rich solutions (Benedicto et al., 2014). Therefore, the critical mechanism of radiocesium migration in the anhydrous interlayer ("direct exchange" or "decollapse") may depend on aqueous chemistry conditions. 4.6. Effects of nuclear decay The incorporation of hundreds of thousands of radiocesium atoms (Sassi et al., 2017a) in radioactive soil particles raises questions about the possible effects of radioactive decay on the mineral structure, stability and the longterm fate and transport of Cs, both stable and radioactive. In this section, we focus only on two major processes occurring during 137 Cs beta-decay, namely transmutation and the emission of a high-energy beta-particle. In addition to the obvious safety issues, the lack of experimental investigations is in part due to time--limitation by the half-life of the radioisotope. A useful feature of computational simulations in this case is that they enable the arbitrary acceleration of radioactive decay reactions.
Transmutation involves a chemical and oxidation state change of a compound such as an adsorbed Cs ion. The consequences of these changes have been investigated by ab initio calculations for interlayer radiocesium sorbed in phlogopite (Sassi et al., 2017b). Fig. 9 shows that the sudden appearance of Ba 2+ highly destabilizes phlogopite by 4.3 eV with respect to interlayer radiocesium. The destabilizing energy is primarily due to the presence of a (+2) cation in a (+1) interlayer site. In addition, thermodynamic analysis indicates that Cs vacancies are more favorable than K and H vacancies by 0.1 and 2 eV respectively. These results have two consequences: (i) radiocesium transmutation appears to provide a means to weaken the binding of other Cs by favoring and accelerating its desorption, and (ii) a cation vacancy (K or Cs) is needed to accommodate the charge difference. If radiocesium concentrations in a clay particle are small, K desorption would occur more frequently than Cs desorption. However, the aforementioned recent experimental (Kogure et al., 2012;Okumura et al., 2014b;Tamura et al., 2014) and theoretical studies (Okumura et al., 2014a;Ruiz Pestana et al., 2017), which indicate that Cs ions tend to form Cs dense interlayers in a clay particle, suggest the possibility that Cs + transmutation to Ba 2+ could lead to progressive re-release of residual parent isotope.
The incidence of a high energy beta-particle on defect formation processes in clay minerals has been investigated by determining the threshold displacement energy (TDE) for various atoms in vermiculite from FPMD simulations (Sassi et al., 2016). The results indicate that Mg sites are the most radiation resistant while H sites are the most vulnerable. If the energy transferred by a beta-particle colliding with an atom in vermiculite is higher than the TDE of that site, then Fig. 9 shows the most frequently encountered Frenkel defect structure obtained at the end of the simulation. While displaced Mg atoms generally end at the center of a siloxane ring, displaced tetrahedral Al or Si atoms promote ring opening and the formation of larger rings made of two adjacent rings. For displaced O atoms, siloxane rings can either open or remain closed by creating Si-Si or Al-Si bonds.
These results provide information about structural alterations associated with nuclear decay and their potential impact on the stability of interlayer Cs. Because the density of defects created by nuclear decay reactions obviously will depend on the concentration and distribution of radiocesium in soil, the results should motivate further experimental and theoretical investigations. For example, experiments involving 134 Cs at different concentrations could be used as a proxy to accelerate the consequences of 137 Cs decay and examine the thermodynamics and kinetics of ion-exchange processes in contaminated soil minerals.

Discussion regarding waste-soil volume reduction
Here, we discuss strategies to reduce the volume of waste soils based on microscopic insights reviewed above. One of the most important insights is that radiocesium adsorbs strongly in the anhydrous interlayers of illite or weathered biotite and that the adsorbed form is quite robust against chemical and physical attack. This suggests that effective waste volume reduction likely requires physical fractionation of the waste soils into phyllosilicate minerals (particularly biotite and illite) and other solid fractions. Such a physical separation, if possible, should yield a dramatic reduction of the contaminated soil volume. One possible separation scheme involving superconducting coils acting on the intrinsic magnetic moment of biotite may be promising. However, iron is distributed in a complex manner within the octahedral sheets, because biotite is a part of solution solid series. The details could be clarified by atomic level calculations aided by experiments. The question regarding whether or not there is a useful correlation to be exploited between the magnetic moment and radioactivity remains open and worthy of exploration.
Further volume reduction, if necessary, will likely require radiocesium extraction from the phyllosilicate particles. Extraction schemes proposed for biotite consist of either chemical or physical treatments. In the former, two directions exist, i.e., the extraction without and with destruction of the mineral framework. The most obvious non--destructive chemical method, extraction by cation exchange, is supported by a long history. Unfortunately, the strong adsorption selectivity and very slow reversibility of adsorption on FES and in anhydrous interlayers implies that a significant fraction of radiocesium may be highly recalcitrant to this method on reasonable timescales.
Destructive chemical treatments involve the dissolution of the biotite framework. Surprisingly, strong acids are not enough for complete desorption from weathered biotite, at least under ambient conditions with reasonable short periods. An alternative chemical method involving incineration with alkali salts has been shown to yield up to 100% radiocesium extraction, but at a prohibitively high cost (Shimoyama et al., 2014;Honda et al., 2017), illustrating the need for additional research and optimization.
As for physical extraction methods, one proposed scheme involves use of milling to destroy the phyllosilicate framework. This technique has shown promising results in well-controlled conditions, but it requires specific conditions (such as grain size homogeneity) to perform effectively in reasonable periods. More insights would be beneficial to optimize this approach.
Finally, beyond radiocesium extraction and volume reduction, reuse of the residual decontaminated waste soil is an important relevant consideration, because huge amounts of residual contaminated material below acceptable radioactivity levels is likely to remain in all cases. If this residual waste soil contains sufficiently low radiocesium levels, its safe isolation from the environment may be achievable through its use as fill for embankments coated by concrete, or as aggregate for concrete. In these cases, the longterm fate of trace levels of entrapped radiocesium should be studied, for example through a combination of experiments and atomic-scale calculation techniques such as those reviewed above.

Conclusions
We have reviewed key experimental knowledge and recent developments enabled by computational molecular modeling on clay particles interacting with radiocesium, emphasizing the advances driven by the environmental fate, transport and remediation challenges associated with the FDNPP accident. Overall, state-of-the-art numerical simulations provide detailed insight into the role of microstructural details in controlling Cs adsorption on phyllosilicate minerals, particularly in regards to the atomic-scale and long time-scale processes that are difficult to access by experiment. The scientific understanding in this area continues to progress rapidly owing to the concerted application of advanced experimental and high-performance computational research.
The research reviewed above illustrates three key strengths of computational molecular modeling. The first is the ability to directly access the mechanism of Cs adsorption by easily testing various hypotheses. The second is the ability to evaluate key quantities such as free energies of adsorption on individual surface sites, time constants of radiocesium diffusion, and desorption probabilities of Cs leaching caused by radiation damage. The third is that atomistic simulations provide a safe and economical platform for the study of radioactive or other hazardous substances.
Despite the favorable features summarized above, one should keep in mind that, not unlike experiments, atomistic-level simulations remain inherently sensitive to the approximations made in their implementation. In particular, they require a priori knowledge of the structure of various possible adsorption sites. In the case of classical MD simulations, they also require the use of semi-empirical interatomic potential parameters. As in other scientific areas, advances in computational modeling of radiocesium adsorption go hand-in-hand with microscopic-scale experimental studies: the iteration between modeling and experiments yields lasting insights.
As a final comment, it is worth noting that decisions on waste soil management should, in principle, be based on reliable scientific insights. In this review, we believe we have shown that molecular simulation can contribute effectively to obtaining such insights.