Ion exchange selectivity in clay is controlled bynanoscale chemical–mechanical couplingMichael L. Whittakera,b, Laura N. Lammersa,c, Sergio Carreroa,b, Benjamin Gilbertb, and Jillian F. Banfielda,b,c,1

aEnergy Geosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720; bDepartment of Earth and Planetary Science, University ofCalifornia, Berkeley, CA 94720; and cDepartment of Environmental Science, Policy, and Management, University of California, Berkeley, CA 94720

Edited by Patricia M. Dove, Virginia Tech, Blacksburg, VA, and approved September 22, 2019 (received for review May 10, 2019)

Ion exchange in nanoporous clay-rich media plays an integral rolein water, nutrient, and contaminant storage and transport. Inmontmorillonite (MMT), a common clay mineral in soils, sediments,and muds, the swelling and collapse of clay particles through theaddition or removal of discrete molecular layers of water alters cationexchange selectivities in a poorly understood way. Here, we showthat ion exchange is coupled to the dynamic delamination andrestacking of clay layers, which creates a feedback between thehydration state of the exchanging cation and the composition of theclay interlayer. Particles with different hydration states are distinctphases with unique binding selectivities. Surprisingly, equilibriumachieved through thermal fluctuations in cation concentration andhydration state leads to the exchange of both ions and individualMMT layers between particles, a process we image directly with high-resolution transmission electron microscopy at cryogenic conditions(cryo-TEM). We introduce an exchange model that accounts for thebinding selectivities of different phases, which is likely applicable tomany charged colloidal or macromolecular systems in which thestructural conformation is correlated with the activities of water andcounterions within spatially confined compartments.

montmorillonite | ion exchange | dynamic equilibrium | cryo-TEM

Clay minerals are by far the most abundant inorganic nano-material in the lithosphere (1). As nanomaterials, their

properties are very sensitive to the microscopic details of particlearrangements. Changes to the structure of clay minerals mayhave environmental-scale impacts because swelling clays (smec-tites) like montmorillonite (MMT) can control the rheologicaland mechanical properties of soils, sediments, and muds (2), andthe transport of solutes through them (3).The structures of smectites arise from molecular-scale inter-

actions between 2:1 aluminosilicate layers, the counterions thatbalance charge arising from isomorphic substitutions within thelayers, and associated waters of hydration (Fig. 1). Variation inthe types and proportions of interlayer species causes face-to-face stacks of 2:1 layers of MMT to expand or collapse reversibly(4, 5). Despite the importance of ion exchange in many envi-ronmental and geological systems containing smectites, currentmodels poorly describe the feedbacks between solution compo-sition, ion exchange, and interlayer swelling state that determinepore structure and macroscopic transport.A challenge for developing an improved understanding of ion

exchange in confinement is that, to date, neither computationalnor experimental approaches have been able to directly access thetimescales over which both exchange and swelling/collapse occur.Molecular dynamics simulations have produced free-energy rela-tionships for a narrow range of solution conditions (2), but sim-ulations are restricted to small system sizes and timescales.Experiments often probe equilibrium swelling states under a va-riety of conditions (4) but have not directly captured the rapidprocess of exchange. Neither simulations nor experiments havebeen able to explore the impact of rotation, translation, or bendingof layers on ion exchange during swelling and collapse.We use in situ time-resolved simultaneous small-, medium-,

and wide-angle X-ray scattering (SAXS/MAXS/WAXS) to probe

the dynamics of ion exchange upon rapid mixing of homoionicsodium- or potassium-MMT suspensions with solutions containingthe opposite cation. Transmission electron microscopy at cryogenicconditions (cryo-TEM) of hydrated samples in aqua provides acomplementary snapshot of particle arrangements with near-atomicresolution. Combined, both techniques establish a consistentframework for determining the thermodynamics of ion exchangeand offer insights into the molecular mechanisms underlying clayparticle structures and dynamics.

ResultsStatic X-ray Scattering. Hydrated MMT particle structures wereinvestigated with static X-ray scattering, which was used as astandard for comparison to cryo-TEM images and as a basis setfor the fitting of time-resolved X-ray scattering. HomoionicWyoming MMT (SWy-2) was resuspended in NaCl (1 M) or KCl(1 M) to a concentration of 20 mg/mL (herein called Na-MMTor K-MMT). SAXS/MAXS/WAXS were acquired simultaneouslyon 3 separate detectors (6). K-MMT exhibited a larger basalspacing scattering vector (q001 = 0.40 Å−1, 15.9 Å), compared toNa-MMT (q001 = 0.33 Å−1, 19.0 Å), consistent with 2 and 3 mo-lecular layers of interlayer water, respectively. Peak intensity atq001 of K-MMT was much lower than the intensity of Na-MMTðI001K-MMT=I

001Na-MMT = 0.28Þ and was much broader (0.05 and 0.13 Å−1

for Na-MMT and K-MMT, respectively; Fig. 1 and SI Appendix),indicating a larger deviation from the average interlayer spacingand a higher fraction of poorly stacked layers in K-MMT.Higher-order diffraction at ℓ · q001, where ℓ is the integer dif-

fraction order (ℓ= 1, 2, 3, 4, and 6 for Na-MMT and ℓ= 1, 3, 5 forK-MMT), is an indication that the particles are homogeneouswith no interstratification. Potassium resides in close proximity to,

Significance

We directly visualize hydrated clay with near-atomic resolutionand find that potassium and sodium bind in different config-urations that result in distinct free energies. The way in whichthese ions bind affects the structure of the clay, which in turnchanges the binding selectivity, creating a feedback that is notaccounted for in current exchange models. We find that clayminerals can be far more dynamic than previously envisionedand that rapid fluctuations may have long-term consequencesfor the fate of ions in clay-rich environments.

Author contributions: M.L.W., B.G., and J.F.B. designed research; M.L.W. and S.C. per-formed research; L.N.L. contributed new reagents/analytic tools; M.L.W. and L.N.L. ana-lyzed data; and M.L.W., B.G., and J.F.B. wrote the paper.

The authors declare no competing interest.

This article is a PNAS Direct Submission.

Published under the PNAS license.

Data deposition: All data discussed in the paper have been deposited in Zenodo (DOI:10.5281/zenodo.3478540).1To whom correspondence may be addressed. Email: jbanfield@berkeley.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1908086116/-/DCSupplemental.

First published October 16, 2019.

22052–22057 | PNAS | October 29, 2019 | vol. 116 | no. 44 www.pnas.org/cgi/doi/10.1073/pnas.1908086116

Dow

nloa

ded

by g

uest

on

Mar

ch 9

, 202

1

or partially within, the silicate sheets, while sodium ions reside bothnear the silicate sheet and ∼2.5 Å to either side of the interlayermidplane, on average (7). Electron density, ρ, profiles along thestacking direction are derived by inverse Fourier transformation ofthe 00ℓ structure factors. X-ray–derived ρ profiles are largely con-sistent with contrast profiles measured directly from low-dose cryo-TEM images (discussed below) and qualitatively agree with mo-lecular models, which suggest that potassium makes inner-spherecomplexes with ditrigonal cavities in the silicate sheet (8), while themore tightly bound hydration shell of sodium increases its proba-bility of residence near the interlayer midplane (Fig. 1 C and F)(9). However, ρ profiles obtained from direct imaging indicate thatsodium resides in close proximity to the basal surface with a higherfrequency than expected from simulations or X-ray scattering. This

is likely because transformation of reciprocal-space data does notaccount for peak width and asymmetry. Similarly, interlayer po-tassium may exhibit greater deviations from its average positionthan expected from X-ray scattering.

Time-Resolved X-ray Scattering. Ion exchange was performed bymixing a KCl solution (1 M) with Na-MMT in a stopped-flowmixer at 4 volume ratios, r, where r = [K+]/[Na+]: 2, 1, 0.5, and0.33. After mixing with KCl, the Na-MMT basal spacing peak at0.33 Å−1, decreased in intensity and a separate peak at 0.40 Å−1

emerged (Fig. 2A). Two distinct peaks were clearly resolved in allcases, and fitting confirmed that the peak positions did notchange appreciably during exchange. This is a strong indicationthat the collapse front within an interlayer region is sharp and/ormoves rapidly on the timescale of the measurements (∼50-ms ac-quisition time). A single broadened peak with a maximum betweenthe homoionic end members was not observed under any in situconditions in this study, excluding the possibility of extensive in-terstratification of collapsed and uncollapsed interlayers (10), inagreement with cryo-TEM observations (below).Ion exchange proceeded much more rapidly than collapse and

swelling. While the ℓ= 2 peak intensity for Na-MMT was ∼4% ofthe ℓ = 1 intensity at equilibrium (SI Appendix), the intensitydropped significantly after the first acquisition following mixing.The total noise level in the ℓ = 2 region (0.56 < q < 0.76 Å−1)after mixing was far less (by a factor of 2.7 to 9.6) than the in-tensity expected in this region by taking 4% of the 19-Å peakintensity, such that this peak would be resolved if present. Weakintensity in this region that fades after the first acquisition wasoften observed in such cases, even when collapse did not go tocompletion, an indication of interlayer cation mixing.The collapse rate was quantified using the integrated intensity

from the basal spacing peaks (Fig. 2B), expressed as the in-stantaneous fraction of the 19-Å hydrate, f(t), from the following:

f ðtÞ =I001Na-MMT

I001Na-MMT + I001K-MMT= ð1− f Þe−at + f , [1]

where f = f(t → ∞) is assumed to represent equilibrium, and a isa chemical–mechanical rate constant. The total intensity from

Fig. 1. Static X-ray scattering from Na-MMT and K-MMT. (A and D) Whole-pattern SAXS/MAXS/WAXS fitting. (B and E) Electron density profiles calcu-lated from MAXS diffraction peaks (red) or integrated TEM image contrast(black; 1 SD in gray). (C and F) Atomic models depicting the structures inferredfrom the electron density profiles (interlayer water not explicitly shown). Notethat cation occupancy is fixed by the structural charge of the layers.

Fig. 2. Collapse dynamics during ion exchange between KCl (1 M) and Na-MMT. (A) Time dependence of the extent of collapse, f(t). (B) Stacked SAXS in-tensity curves showing the emergence of a 2-layer hydrate peak at q = 0.395 Å−1 (15.9 Å) as a function of time after mixing. All samples reach a regime ofchemical (ion exchange) and mechanical (layer collapse) equilibrium within 1 to 2 s. (C) Composition phase diagram. The red circles represent experimentalconditions reported in this study.

Whittaker et al. PNAS | October 29, 2019 | vol. 116 | no. 44 | 22053

EART

H,A

TMOSP

HER

IC,

ANDPL

ANET

ARY

SCIENCE

S

Dow

nloa

ded

by g

uest

on

Mar

ch 9

, 202

1

both peaks decreases during exchange, even when accounting forparticle dilution, while the total clay scattering signal remainsconstant. This requires that the total coherent scattering volumedecreases as collapse progresses and therefore that particlesmust rearrange into configurations that scatter less stronglyduring collapse.Both f and a were strong functions of the potassium concen-

tration, but neither exhibited a strong temperature dependence(SI Appendix). This behavior contrasts with ion diffusion-limitedexchange in anhydrous phyllosilicates (11), which increases ap-preciably with temperature through the Arrhenius behavior ofthe diffusion coefficient (12). Interlayer water diffusion has astrong temperature dependence (13), while species exchange,including water, between bulk solution and the interlayer is es-sentially barrierless (14, 15), indicating that neither processlimits collapse.These data are consistent with a dynamic equilibrium between

2 populations of particles (16–19) in a ratio that is determined bythe solution composition. Current models of ion exchangeequilibria in smectites (20–23) do not account for the discreteequilibria between distinct hydration states and do not in-corporate the change in water activity at each hydration state.However, it is known that the hydration state significantly altersion binding selectivity. Therefore, we introduce a model to ac-count for these observations.

Thermodynamic Exchange Model. Ion exchange equilibrium be-

tween 3-water layer MMT ðMMTÞ, 2-water layer MMT ðMMTÞ,and bulk aqueous solution can be expressed as follows:

NaxK1−xMMT ·mH2O + nK+aq ⇔ Nax−nK1−x+nMMT

+ mH2O+ nNa+aq, [2]

with x establishing the fraction of cation sites occupied by so-dium, m water molecules released upon collapse, and n cationsexchanged, per unit of structural charge. The law of mass actiondefines the equilibrium constant, Keq, for this reaction as follows:

Keq =�ðNa+ ÞðK + Þ

�n

amw

Naðx−nÞKð1−x+nÞMMT

!0@NaxKð1−xÞMMT ·mH2O

1A, [3]

where quantities in parentheses refer to activities and aw is theactivity of water. Commonly reported values of interlayer waterdensity (24, 25) give m ≅ 10. Thus, the composition of the solidphases, which must obey n ≤ x, can be constrained to the range0.69 < x < 1 (SI Appendix). This establishes the unique chemicalcomposition of each collapse/swelling state. The standard Gibbsfree energy, ΔG°, can be determined from Keq such that ΔG° <4.2 kT/unit of structural charge. This confirms that 2- and 3-water layer hydrates are separate coexisting phases in equilib-rium and separated by a difference in free energy that allowsspontaneous interconversion via the thermal energy (SI Appen-dix). This model was extended over a range of sodium and po-tassium concentrations, allowing for the determination of acomplete composition-phase diagram (Fig. 2C and SI Appendixfor detail).

Low-Dose Cryogenic Transmission Electron Microscopy.High-resolutionimages of the interlayer structure of single Na-MMT and K-MMTlayers and basal spacing of particles (Fig. 3) confirm that they aredistinct phases. Contrast profiles measured parallel to the stacking

direction were in agreement with the electron density profiles cal-culated from X-ray scattering basal spacing peak intensities (Fig. 1B and E). Although layers were oriented edge-on with respect to thebeam direction, Na-MMT layers were rarely also aligned along ahigh-symmetry zone axis and thus have no appreciable contrastvariation within the layer (Fig. 3A). By chance, some Na-MMTlayers were oriented along a high-symmetry axis, but these layershad no special orientational relationship with their neighbors (SIAppendix). This is consistent with turbostratic stacking commonlyobserved for MMT.However, many K-MMT particles exhibited intraparticle lat-

tice fringes that maintained correlated orientations across mul-tiple neighboring layers (Fig. 3 B–H). Enlargement of a regioncontaining only 4 unit cells of MMT in each layer (Fig. 3 C, E,and G) revealed contrast that is entirely consistent with atomicmodels of MMT viewed along 3 high-symmetry crystallographicaxes (Fig. 3 D, F, and H). Based on the expected angle at whichthe atomic potentials make and the cation–cation separationwhen viewed edge-on, the orientation of each layer wasuniquely attributed to a <100>, <110>, or <�110> zone axis.Most Na-MMT particles had an average of 4.4 layers and were

mostly coplanar, even preserving their spacing across gently de-formed regions, while K-MMT particles had only 2.5 layers onaverage and were often twisted and bent (SI Appendix). This is

Fig. 3. Low-dose high-resolution cryo-TEM of MMT. (A) Na-MMT particle,viewed edge-on. (B) K-MMT particle aligned along high-symmetry zoneaxes. (C–H) Enlarged portions of B corresponding to the top, middle, andbottom layers, respectively, and atomic models that are consistent withimage contrast (arrows are the same length; K, orange; Si, blue; Al, teal;other atoms not shown for clarity).

22054 | www.pnas.org/cgi/doi/10.1073/pnas.1908086116 Whittaker et al.

Dow

nloa

ded

by g

uest

on

Mar

ch 9

, 202

1

consistent with lower X-ray scattering basal spacing peak intensity(Fig. 1D) and, along with the observation of decreasing total basalspacing intensity in X-ray scattering during collapse in the presenceof potassium, indicates that the MMT particles undergo de-lamination as a consequence of the ion exchange process.Particles in r = 0.5 mixtures exhibited partially delaminated

domains consisting of more than one layer not in contact withadjacent layers along their entire length due to local bending(SI Appendix). Because these images are taken from a timepoint (>10 s) well after the initial collapse (1 to 2 s), this isstrong circumstantial evidence confirming that particles de-laminate. Moreover, it also suggests that individual layers dy-namically restack at equilibrium, since layers were not found tobe completely delaminated.Two distinct populations of particles exhibited either ∼16- or

∼19-Å interlayer spacings in cryo-TEM images (SI Appendix),also in agreement with SAXS data. Average interlayer spacingswere determined from integrated Fourier transforms from 8different particles comprising a total of 81 layers (over 104-nmtotal layer length with 0.074-nm pixel width, for a total of over106 observations). Two particles (30 layers) retained ∼19-Åspacing, while 6 particles (51 layers) were collapsed and hadan average of ∼16-Å interlayer spacing. The fraction of collapsedlayers (30/81 = 37%) is comparable to f at this compositionmeasured from X-ray scattering (48 ± 8%; Fig. 2B) given theunderrepresentation of K-MMT from X-ray scattering on a per-layer basis.

DiscussionSummary of Geochemical Model. Ion exchange of potassium forsodium in MMT causes phase separation, resulting in 2 pop-ulations of particles that are noninterstratified and chemicallyhomogeneous. Each has a distinct cation selectivity that is de-termined by its hydration state with a free energy difference of

∼4 kT/unit of structural charge. We show direct evidence thatlayers delaminate after potassium is introduced and suggest thatthis provides a mechanism for the spatial segregation of regionsof different ion selectivities (i.e., different collapse states) andenables Brownian motion that promotes reattachment at (near)crystallographic orientations.Both phase-separated 2- and 3-water layer interlayers are in

dynamic equilibrium at an abundance (i.e., f) that is determinedby the cation ratio in solution and the water activity. The ob-served end-member structures (Fig. 1) correspond to localminima in free energy in homoionic solutions (8, 26), which aredetermined largely by cation hydration energies (27, 28). Thus,we introduce an equilibrium model in which ion exchange driveschanges in interlayer hydration state.Beyond determining selectivity coefficients of multicomponent

electrolytes that depend on the swelling state, this thermodynamicmodel can be used in the prediction of swelling pressures or volu-metric strain associated with chemical perturbations in smectite-richmaterials (29). For example, it predicts higher swelling pressures inlower bulk K/Na clays due to increased swelling free energies.Swelling state distributions in high dry bulk density compacted claysare expected to favor more collapsed states due to the decreasedactivity of water. However, the model only accounts for uniaxialpressure normal to the stacking direction and it does not capturethe effects counterion composition on average particle size.

Chemical/Mechanical Exchange Mechanism. Water determines bothion selectivities (8, 27, 30, 31) and exchange rates, which areorders of magnitude slower in anhydrous phlogopites (11) andillites (32) than in hydrated smectites (33). A striking findingof this work is that layer collapse is significantly slower thanthe replacement of potassium for sodium by diffusion within theinterlayer. A simulation of potassium diffusion at r = 1 using themeasured layer size distribution shows that complete intercalation is

Fig. 4. Model of ion exchange and collapse. (A) Edge-on view of initial turbostratic stacking of 3 layers in Na-MMT. (B) Hypothetical distribution of sodium inproximity to the top of the middle layer, viewed face-on. (C and D) Exchange of potassium for sodium that proceeds prior to collapse. (E and F) Partial collapseinduced by critical local potassium concentration. (G and H) Collapse propagates throughout the interlayer, expelling sodium and a single layer of water.Layers dynamically delaminate and restack.

Whittaker et al. PNAS | October 29, 2019 | vol. 116 | no. 44 | 22055

EART

H,A

TMOSP

HER

IC,

ANDPL

ANET

ARY

SCIENCE

S

Dow

nloa

ded

by g

uest

on

Mar

ch 9

, 202

1

expected to occur in less than a millisecond (SI Appendix) whilecollapse occurs on the timescale of seconds. It is important to notethat anions are excluded from the interlayer in the crystallineswelling regime (34) and are not explicitly considered.The initial, transient regime of collapse from a uniform pop-

ulation of 3-water layer Na-MMT immediately following mixingprovides crucial insight into the dynamic equilibration process.Both the rate and extent of collapse are largely invariant withtemperature (SI Appendix), which is consistent with the non-Arrhenian cation diffusion previously observed for MMT (13,35), but inconsistent with other processes that could be proposedto limit collapse. We propose that diffusional demixing within theinterlayer is the first step in the process of collapse, both in theinitial transient regime and during the subsequent period of dy-namic equilibrium, and is promoted through positive feedback(36) between the local chemical composition and the interlayerspacing (Fig. 4).Dynamic fluctuations of MMT interlayers, in which the com-

position, hydration state, and basal spacing are all tightly coupled,must be common and an important aspect of ion-driven swellingand collapse. Differences in hydration energy between 2- and 3-water layer hydrates are 0 to 4 kT/unit cell of clay, with barriers ofcomparable size in between (8, 26, 27), suggesting that both statesare regularly explored in fluctuations from the average basalspacing (37). These fluctuations may present the continuallychanging migration barriers responsible for non-Arrhenian diffusion(38). Direct measurements of interlayer spacings in cryo-TEM (Fig.3 C, F, and H) exhibit SDs of ∼15%, or ∼2 to 3 Å, consistent withregular exploration of both hydration states with a barrier of ∼2 to3 kT/unit cell between them. Because these fluctuations are on thesame energy scale as the binding selectivity (8, 27, 30, 31), theseprocesses must be tightly coupled.Based on the foregoing evidence, we propose a mechanism of

collapse outlined in Fig. 4. Ion intercalation into initially homo-ionic Na-MMT (Fig. 4 A and B) is rapid, but collapse is not im-mediate (Fig. 4 C and D). As the composition in the interlayerequilibrates with the surrounding solution, potassium diffusesthroughout the basal surface of the MMT layer, and collapse isinitiated by demixing within an interlayer. Demixing promotespotassium colocalization across both sides of an interlayer (Fig. 4 Eand F), eventually reaching a sufficient size to overcome fluctuationsand initiate collapse. Once an interlayer collapses, neighboringlayers can be expanded or collapsed (36), promoting a cascade ofindividual exchange and hydration/dehydration reactions that leadto demixing of the entire particle. In some cases, layers can beliberated through delamination and may then rotate into preferredrotational configurations via Brownian motion (Fig. 4 G and H).

Impact on Clay Structures. MMT layers can stack with mica-likecrystallographic order at relative orientations of only 0 or 180°.However, at relative particle rotations of ∼60°, neighboring particlescan come into near-crystallographic alignment along the <110>,<�110> , and <100> directions. It has long been known that, in theinitial steps of illitization, mica-like stacking order develops afterrepeated wetting and drying cycles in the presence of potassium(39), resulting in this type of near-crystallographic ordering (40). Weshow that this order first arises in suspension as a result of phaseseparation following potassium exchange and is maintained across

up to 6 Å (2 molecular layers) of water. Bending moduli of indi-vidual clay layers vary with crystallographic orientation (41), andthus, (nearly) oriented layers are expected to be more rigid and lesssusceptible to perturbations through fluctuations, preserving theirrelative orientations.The cooperative process of ion exchange and collapse is a

clear demonstration that nanoscale chemical–mechanical cou-pling controls both the rate and products of ion exchange and thestructures that result from collapse in hydrated MMT. Employ-ing exchange equilibria in which multiple swelling states arepresent will improve the predictive capacity of exchange modelsof ion binding in swelling clays. We show, for example, that acomposition-phase diagram can be used to predict the co-existence of distinct swelling states, and thus the exchange se-lectivity, of the crystalline hydrates. We demonstrate that thereaction rate is largely unaffected by temperature, but thatswelling and collapse hysteresis, a widely observed phenomenonin natural systems, can be attributed, in part, to a decreasingcollapse rate.

Materials and MethodsMaterials. SWy-2, obtained from the Source Clays Repository of The ClayMinerals Society (http://www.clays.org/sourceclays_data.html), was usedthroughout this study. Aqueous solutions of NaCl and KCl were preparedfrom reagent-grade salts.

Static X-ray Scattering. X-ray scattering was performed at beamline 5ID-D ofthe Advanced Photon Source at Argonne National Laboratory in order toobtain high photon fluxes necessary for time-resolved experiments. SAXS/MAXS/WAXS was collected simultaneously on 3 Rayonix charge-coupleddevice detectors with sample−detector distances of 8,505.0, 1,012.1, and199.5 mm, respectively. The wavelength of radiation was set to 1.2398 A(10 keV), resulting in a continuous range of scattering vector, q = 0.017−4.2Å−1. Additional details are given in SI Appendix.

Cryo-Transmission Electron Microscopy. Suspensions of Na-MMT or K-MMTwith particle concentrations of 5 mg/mL were deposited as 2- to 3-μL ali-quots onto 300-mesh lacy carbon Cu grids (Electron Microscopy Sciences),which had been glow-discharged in air plasma for 15 s. Excess solution wasremoved by automatic blotting (1 blot for 10 s, blot force 10 at 100% rel-ative humidity) before plunge-freezing in liquid ethane using an automatedvitrification system (FEI Vitrobot). Imaging was performed with a Titan KriosTEM operated at 300 kV, equipped with a BIOQuantum energy filter. Imageswere recorded on a Gatan K2 IS direct electron detecting camera with a pixelsize of 0.74 A/pixel. Imaging was performed under cryogenic conditionsusing a low electron dose rate (<10 e−·A·s−1) to minimize sample damage.Acquisition was automated with SerialEM software.

ACKNOWLEDGMENTS. This research was supported by the US Departmentof Energy (DOE), Office of Science, Office of Basic Energy Sciences, ChemicalSciences, Geosciences, and Biosciences Division, through its GeoscienceProgram at Lawrence Berkeley National Laboratory under Contract DE-AC02-05CH11231. Portions of this work were performed at the DuPont–Northwestern–Dow Collaborative Access Team (DND-CAT) located at sector5 of the Advanced Photon Source. DND-CAT is supported by NorthwesternUniversity, E.I. DuPont de Nemours and Co., and The Dow Chemical Com-pany. This research used resources of the Advanced Photon Source, a US DOEOffice of Science User Facility operated for the DOE Office of Science byArgonne National Laboratory under Contract DE-AC02-06CH11357. Datawere collected using an instrument funded by the National Science Founda-tion under Award 0960140. Access to the FEI Titan Krios was providedthrough the Bay Area Cryo-EM facility at the University of California, Berkeley,and we thank Dan Toso and Elizabeth A. Montabana for technical assistance.

1. M. F. Hochella, Jr et al., Natural, incidental, and engineered nanomaterials and their

impacts on the Earth system. Science 363, eaau8299 (2019).2. I. C. Bourg, J. B. Ajo-Franklin, Clay, water, and salt: Controls on the permeability of

fine-grained sedimentary rocks. Acc. Chem. Res. 50, 2067–2074 (2017).3. P. Alt-Epping et al., Benchmark reactive transport simulations of a column experiment

in compacted bentonite with multispecies diffusion and explicit treatment of elec-

trostatic effects. Computat. Geosci. 19, 535–550 (2014).4. K. Norrish, The swelling of montmorillonite. Nature 1, 120–134 (1954).5. C. C. Tester, S. Aloni, B. Gilbert, J. F. Banfield, Short- and long-range attractive forces that in-

fluence the structure of montmorillonite osmotic hydrates. Langmuir 32, 12039–12046 (2016).

6. S. J. Weigand, D. T. Keane, DND-CAT’s new triple area detector system for simulta-

neous data collection at multiple length scales. Nucl. Instrum. Methods Phys. Res. A

649, 61–63 (2011).7. D. M. Moore, C. Robert, J. Reynolds, X-ray Diffraction and the Identification and

Analysis of Clay Minerals (Oxford University Press, New York, NY, ed. 2, 1997).8. X. D. Liu, X. C. Lu, A thermodynamic understanding of clay-swelling inhibition by

potassium ions. Angew. Chem. Int. Ed. Engl. 45, 6300–6303 (2006).9. F.-R. C. Chang, N. T. Skipper, G. Sposito, Monte Carlo and molecular dynamics simu-

lations of electrical double-layer structure in potassium-montmorillonite hydrates.

Langmuir 14, 1201–1207 (1998).

22056 | www.pnas.org/cgi/doi/10.1073/pnas.1908086116 Whittaker et al.

Dow

nloa

ded

by g

uest

on

Mar

ch 9

, 202

1

10. E. Ferrage, Investigation of smectite hydration properties by modeling experimentalX-ray diffraction patterns: Part I. Montmorillonite hydration properties. Am. Mineral.90, 1358–1374 (2005).

11. N. Sánchez-Pastor, K. Aldushin, G. Jordan, W. W. Schmahl, K+–Na+ exchange in

phlogopite on the scale of a single layer. Geochim. Cosmochim. Acta 74, 1954–1962(2010).

12. I. C. Bourg, G. Sposito, Connecting the molecular scale to the continuum scale fordiffusion processes in smectite-rich porous media. Environ. Sci. Technol. 44, 2085–2091 (2010).

13. Y. Zheng, A. Zaoui, Temperature effects on the diffusion of water and monovalentcounterions in the hydrated montmorillonite. Physica A 392, 5994–6001 (2013).

14. B. Rotenberg et al., Water and ions in clays: Unraveling the interlayer/microporeexchange using molecular dynamics. Geochim. Cosmochim. Acta 71, 5089–5101(2007).

15. T. A. Ho, L. J. Criscenti, J. A. Greathouse, Revealing transition states during the hy-dration of clay minerals. J. Phys. Chem. Lett. 10, 3704–3709 (2019).

16. D. Eberl, Alkali cation selectivity and fixation by clay minerals. Clays Clay Miner. 28,161–172 (1980).

17. D. A. Laird, C. Shang, Relationship between cation exchange selectivity and crystallineswelling in expanding 2:1 phyllosilicates. Clays Clay Miner. 45, 681–689 (1997).

18. N. Wada, D. R. Hines, S. P. Ahrenkiel, X-ray-diffraction studies of hydration transitionsin Na vermiculite. Phys. Rev. B Condens. Matter 41, 12895–12901 (1990).

19. G. J. da Silva, J. O. Fossum, E. DiMasi, K. J. Måløy, Hydration transitions in a nano-layered synthetic silicate: A synchrotron X-ray scattering study. Phys. Rev. B 67, 094114(2003).

20. J. M. Cases et al., Mechanism of adsorption and desorption of water vapor by ho-moionic montmorillonite. 1. The sodium-exchanged form. Langmuir 8, 2730–2739(1992).

21. B. Laffer, A. Posner, J. Quirk, Hysteresis in the crystalline swelling of montmorillonite.Clay Miner. 6, 311–321 (1966).

22. I. Berend et al., Mechanism of adsorption and desorption of water vapor by homo-ionic montmorillonites: 2. The Li+, Na+, K+, Rb+, and Cs+-exchanged forms. Clays ClayMiner. 43, 324–336 (1995).

23. P. Vieillard, P. Blanc, C. I. Fialips, H. Gailhanou, S. Gaboreau, Hydration thermody-namics of the SWy-1 montmorillonite saturated with alkali and alkaline-earth cations:A predictive model. Geochim. Cosmochim. Acta 75, 5664–5685 (2011).

24. S. L. Teich-McGoldrick, J. A. Greathouse, C. F. Jove-Colo�n, R. T. Cygan, Swellingproperties of montmorillonite and beidellite clay minerals frommolecular simulation:Comparison of temperature, interlayer cation, and charge location effects. J. Phys.Chem. C 119, 20880–20891 (2015).

25. M. Holmboe, I. C. Bourg, Molecular dynamics simulations of water and sodium dif-fusion in smectite interlayer nanopores as a function of pore size and temperature. J.Phys. Chem. C 118, 1001–1013 (2013).

26. H. D. Whitley, D. E. Smith, Free energy, energy, and entropy of swelling in Cs-, Na-,

and Sr-montmorillonite clays. J. Chem. Phys. 120, 5387–5395 (2004).27. T. J. Tambach, P. G. Bolhuis, E. J. M. Hensen, B. Smit, Hysteresis in clay swelling in-

duced by hydrogen bonding: Accurate prediction of swelling states. Langmuir 22,

1223–1234 (2006).28. H. Heinz, R. A. Vaia, B. L. Farmer, Interaction energy and surface reconstruction be-

tween sheets of layered silicates. J. Chem. Phys. 124, 224713 (2006).29. G. Sposito, Thermodynamics of swelling clay-water systems. Soil Sci. 114, 243–249

(1972).30. B. Rotenberg, J.-P. Morel, V. Marry, P. Turq, N. Morel-Desrosiers, On the driving force

of cation exchange in clays: Insights from combined microcalorimetry experiments

and molecular simulation. Geochim. Cosmochim. Acta 73, 4034–4044 (2009).31. B. J. Teppen, D. M. Miller, Hydration energy determines isovalent cation exchange

selectivity by clay minerals. Soil Sci. Soc. Am. J. 70, 31 (2006).32. L. Ruiz Pestana, K. Kolluri, T. Head-Gordon, L. N. Lammers, Direct exchange mecha-

nism for interlayer ions in non-swelling clays. Environ. Sci. Technol. 51, 393–400

(2017).33. D. Arndt, M. Mattei, C. Heist, A. McGuire, Measurement of swelling of individual

smectite tactoids in situ using atomic force microscopy. Clays Clay Miner. 65, 92–103

(2017).34. C. Tournassat, I. Bourg, M. Holmboe, G. Sposito, C. Steefel, Molecular dynamics sim-

ulations of anion exclusion in clay interlayer nanopores. Clays Clay Miner. 64, 374–388

(2016).35. S. Balme, M. Kharroubi, A. Haouzi, F. Henn, Non-Arrhenian ionic DC conductivity of

homoionic alkali exchanged montmorillonites with low water loadings. J. Phys. Chem.

C 114, 9431–9438 (2010).36. K. Schaettle, L. Ruiz Pestana, T. Head-Gordon, L. N. Lammers, A structural coarse-

grained model for clays using simple iterative Boltzmann inversion. J. Chem. Phys.

148, 222809 (2018).37. J. L. Suter, P. V. Coveney, H. C. Greenwell, M.-A. Thyveetil, Large-scale molecular

dynamics study of montmorillonite clay: Emergence of undulatory fluctuations and

determination of material properties. J. Phys. Chem. C 111, 8248–8295 (2007).38. S. Druger, Ionic transport in polymer electrolytes based on renewing environments.

J. Chem. Phys. 100, 3979–3984 (1993).39. A. Plançon, G. Besson, C. Tchoubar, J. P. Gaultier, J. Mamy, Qualitative and quanti-

tative study of a structural reorganization in montmorillonite after potassium fixa-

tion. Dev. Sedimentol. 27, 45–54 (1979).40. J. Srodon, D. Eberl, Illite. Rev. Mineral. Geochem. 13, 495–539 (1984).41. T. Honorio, L. Brochard, M. Vandamme, A. Lebée, Flexibility of nanolayers and stacks:

Implications in the nanostructuration of clays. Soft Matter 14, 7354–7367 (2018).

Whittaker et al. PNAS | October 29, 2019 | vol. 116 | no. 44 | 22057

EART

H,A

TMOSP

HER

IC,

ANDPL

ANET

ARY

SCIENCE

S

Dow

nloa

ded

by g

uest

on

Mar

ch 9

, 202

1