Todos los jueces pueden evaluar una exposición, pero no deben entregar un formulario de evaluación como integrantes del panel evaluador. Los Consejos de

Todorokite MnO2 is a unique structure among the transition metal oxides owing to

its exceptionally high porosity, and more specifically, large channel size. While todor- okite is typically defined as a 3 by 3 tunneled manganese oxide mineral, its true

atomistic structure has not been previously resolved. As most functional applications of todorokite, from molecular sieving to charge storage, depend on the precise geome- try of its large conductive tunnel, this ambiguity presents a fundamental challenge to the development of structure-property relationships for this phase. Using high angle annular dark field (HAADF) imaging, my collaborators revealed the inhomogeneous structure of todorokite-MnO2, resolving the diversity of tunnel sizes coexisting even

in well-crystallized particles[197]. Here, I rationalize the formation and persistence of this distribution of tunnel sizes using first-principles thermochemical calculations, demonstrating the stabilization of a range of todorokite-like environments by the in- tercalation of partially solvated Mg2+ cations. Our results not only help resolve the

structural character of the todorokite MnO2 phase, but also suggest generalizeable

principles determining the selectivity of off–stoichiometric structure-selection.

In this section, we refer to the todorokite family of structures as 𝜏-MnO2, where

a structure with a N by 3 tunnel framework is denoted as belonging to the 𝜏(Nx3) phase. As the 𝜏(2x3) and 𝜏(4x3) structures are crystallographically constrained to appear as doubled cells, we model their behavior as an ordered integrowth of a 2 by 3 and 4 by 3 tunnel, which we refer to the as the 𝜏(2x3 + 4x3) phase.

Experimentally, the 𝜏-MnO2family of structures form from aqueous, Mg2+–containing

solutions[190, 194, 197]. As alkali ions and hydration have been recently discussed as thermodynamic structure–directing agents in MnO2 frameworks[90], we have investi-

gated the role of Mg2+ in driving the formation of the 𝜏-MnO

2large tunnel structures.

Configurational enumeration of the 𝜏(3x3), 𝜏(1x3), 𝜏(2x3 + 4x3), and 𝜏(5x3) phases across Mg𝑥MnO2 and Mg𝑥MnO2 · yH2O compositions reveals that in all cases Mg2+

occupies sites at the corner of the MnO2 tunnel. As can be seen in Figure 4-5a for

the example of the traditional 𝜏(3x3) todorokite structure, these sites provide the maximal coordination of Mg2+ _{by lattice oxygens. When H}

2O is present, the oxygen

from the water molecule orients towards the Mg2+, further increasing its coordination,

0.0 0.2 0.4 0.6 0.8 1.0 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 ∆G f (eV/Mn) x in Mg_xMn₂O₄ β α λ τ(1x3) τ(3x3) τ(5x3) τ(2x3+4x3) α τ(1x3) τ(3x3) τ(5x3) τ(2x3+4x3) Mg_xMn₂O₄ Mg_xMn₂O₄ • yH₂O c. H₂O Mn O Mg τ(3x3) - Mg_0.33Mn₂O₄ • 1.0H₂O τ(5x3) - Mg_0.5Mn₂O₄ • 1.5H₂O a. b. τ(3x3) τ(5x3) τ(2x3+4x3) β-MnO2 λ-MgMn2O4

Figure 4-5: Stabilization of the 𝜏-MnO2 phase by the co-intercalation of Mg2+ and

H2O. The partially desolvated Mg2+-H2O complex occupies tunnel corner sites, sta-

bilizing not only the (a.) traditional 3 by 3 tunnel todorokite structure, but also a range of other 𝜏-MnO2 structures such as the (b.) 5 by 3 tunnel structure. (c.)

Relative Gibbs free energies of formation of the 𝜏-MnO2 phases at 200 𝑜C across the

Mg𝑥MnO2 · yH2O composition space with respect to the low–energy 𝛽, 𝛼, and 𝜆

Mg𝑥MnO2 phases. For each value of 𝑥, the solid lines denote the formation energy

of the non–hydrated Mg𝑥MnO2 structure, while the dashed lines denote the expected

formation energy for the most stable Mg𝑥MnO2 · yH2O structure. The free energy

of the N by 3 tunnel structures with either Mg2+ _{or H}

2O intercalation is consistently

higher than that of the other low-energy phases in the Mg-MnO2-H2O space. How-

ever, the co-intercalated 𝜏-Mg𝑥MnO2 · H2O structures are much lower energy and

stable with respect to the 𝛽-MnO2 and 𝜆-MgMn2O4 endpoint phases.

complexes. This result is at odds with the picture of todorokite presented earlier[198], which placed Mg2+ _{in the tunnel center site. However, but this earlier refinement was}

highly uncertain in its chemical identification due to the similar X-ray scattering po- tential of Mg and O. Our analysis suggests that instead, the tunnel center is much

more likely to be occupied by a water molecule.

While Mg2+ _{appears to strongly prefer the tunnel corner site, this site occupancy}

does not uniquely constrain the remaining Mn–O framework. In general, the hy- drated Mg2+ _{ions occupying tunnel corner sites must be sufficiently separated from}

each other to avoid steric repulsion, but they do not directly interact with the Mn–O framework outside of the tunnel corner, leaving the overall tunnel size unconstrained. Consequently, a range of tunnel sizes exhibit the same behavior with partially hy- drated Mg2+ _{occupying tunnel corner sites, such as in the 𝜏(5x3) structure shown in}

Figure 4-5b. Similar behavior can even be observed in the smaller 2 by 2 tunnel found in the 𝛼-MnO2 phase, although the strong electrostatic repulsion between adjacent

Mg2+ _{ultimately destabilizes this smaller–tunnel phase[90].}

The favorable Mg2+_{–O coordination afforded by the tunnel corner site and hy-}

dration significantly stabilizes the Mg–intercalated 𝜏-MnO2 structure. The formation

energies of these phases with respect to the 𝛽–MnO2 and 𝜆–MgMn2O4 endpoint

phases shown in Figure 4-5c reveal that while the 𝜏-Mg𝑥MnO2 phases have high for-

mation energies for all tunnel sizes, 𝜏–Mg𝑥MnO2 · yH2O have much lower formation

energies, and in the case of 𝜏(3x3), are thermodynamically stable with respect to 𝛽–MnO2, 𝜆–MgMn2O4 and water at 200 𝑜C. This result suggests that the formation

of the 𝜏-MnO2 phase by hydrothermal growth from a Mg2+–containing solution is

thermodynamically controlled and indeed driven by the compatibility of this phase and the Mg2+_-H

2O complex.

The impact of the partially–solvated Mg2+-H

2O complex in stabilizing the 𝜏-MnO2

family of structures suggests a plausible explanation for the diversity of tunnel sizes observed experimentally. The intercalated cation stabilizes the local Mn–O envi- ronment corresponding to a tunnel corner, and strongly repels other cations owing to its divalent charge, driving the formation of relatively large tunnel sizes. These structure–selection criteria are satisfied to varying degrees by the 𝜏(3x3), 𝜏(1x3),

𝜏(2x3+4x3), and 𝜏(5x3) structures. Accordingly, all these phases have relatively low formation free energies as shown in Figure 4-5c. While we find the 𝜏(3x3) phase to be lowest in free energy, the nucleation of this phase does not exclude the coher- ent formation of domains corresponding to the other low–energy 𝜏-MnO2 structure.

While the total energy of such a non–equilibrium domain in a macroscopic particle is high, at the nucleation stage these diverse domains may be expected entropically. Of course, an alternative explanation for the experimental results is that we simply have not been able to resolve the configuration of the more complex, low–symmetry 𝜏(2x3+4x3) and 𝜏(5x3) structures as well as that of the 𝜏(3x3), as the relaxation of the hydrated configurations in particular are fairly uncertain and prone to errors due to numerous local–minima. In this case, we may still conclude that the various 𝜏-MnO2 phases are stabilized by the partially–solvated Mg2+-H2O complex without

forming any bonding environments that would strongly prefer a particular tunnel size. Thus, the todorokite–like structure formed experimentally is unequivocally thermo- dynamically favored by the co-intercalation of Mg2+_{and H}

2O, with disorder in tunnel

sizes arising as a consequence of the diversity of Mn–O frameworks which accommo- date the stable Mg2+_-H

2O bonding environment.

A stark contrast to the lack of structure-selecting constraints and resulting poly- typism in the todorokite family of structures is the unique 2 by 2 tunnel size observed in hollandite MnO2 structures. The origin of this difference lies in the geometry of

stabilizing alkali intercalants in the tunnel structure, and their effectiveness at con- straining degrees of freedom in the structure. Polytypism of the 𝜏(Nx3) family arises from the fact that the partially solvated Mg2+ _{cation that stabilizes this tunnel oc-}

cupies the tunnel corner site and only interacts strongly with the Mn-O framework immediately adjacent to this single tunnel corner. The lack of strong bonds spanning the width of the tunnel leaves the total tunnel size unconstrained, and results in a range of large tunnel sizes close in energy to each other. In contrast, the 2 by 2 tunnel seen in the hollandite structure is generally not stabilized by cations occupying corner sites, and instead is found with larger cations such as K+ _{in the tunnel center site.}

These cations interact strongly with all sides of the Mn-O tunnel and thus constrain its size. The unique stable cation site in hollandite thus suppresses polytypism and promotes the formation of a single type of local environment. Generalizing from this observation, we speculate that among intercalation-stabilized phases, the structural selectivity provided by a stabilizing cation is directly proportional to the fraction of structural degrees of freedom constrained by the cations’ local bonding environment.