H_aq⁺ Structures in Proton Wires inside Nanotubes

Nanoscale science focuses attention on how bulk properties are altered when substances are confined to small spaces and reduced dimensionality. For example, theory suggests that water takes on novel “ice” structures when confined inside carbon nanotubes.¹ Calculations also support the idea that confinement of H_aq⁺ to narrow channels creates a proton wire² having up to 40 times faster proton transport than in bulk.³ These findings are relevant to proton mobility in nanoscale channels of fuel cell membranes and also to biological proton transport where chains of water molecules are found in channels of trans-membrane proteins involved in proton pumping and cellular pH control.⁴ Counterintuitively, these protein channels are often lined with non-polar residues suggesting that nature may be exploiting special properties of hydrophobically-confined chains of water molecules.⁵

Structurally well-defined channels containing H_aq⁺ are rare so experimental opportunities to investigate these hypotheses are few.⁶ Herein, we report several novel structural features of H_aq⁺ when it is confined to a hydrophobic nanotube.

Saturated aqueous solutions of the carborane acid H(CHB₁₁I₁₁)⁷ deposit crystals of the nominally octahydrated acid H(CHB₁₁I₁₁)·8H₂O whose X-ray structure reveals 1.1 × 0.5 nm diameter elliptical channels of H_aq⁺ encased by walls of carborane anions (Fig. 1). This structural motif contrasts with the discrete ionic lattice structures of all other [H(H₂O)_n⁺][carborane⁻] salts having smaller, less polarizable anions e.g., [H₉O₄]−[CHB₁₁H₅Br₆],⁸ [H₅O₂][CHB₁₁Cl₁₁]⁹ and [H₃O][CHB₁₁Cl₁₁].¹⁰ Multiple inter-anion I⋯·I distances (3.68-3.96 Å) are less than the sum of the van der Waals separation suggesting that I⋯·I dispersion forces are important in creating the tubular structure.

Figure 1.

Four unit cells of the tubular structure of H(H₂O)_n⁺ cations (red, white) enclosed by CHB₁₁I₁₁⁻ anions (black, yellow, magenta) in tube A of H(CHB₁₁I₁₁)·8H₂O.

The unit cell contains six H⁺, six CHB₁₁I₁₁⁻ anions and 48 water molecules. There are two crystallographically distinct water-filled tubes containing H_aq⁺ cations, labeled A and B. The water structure in tube A is crystallographically ordered (a so-called “ice”) while that in tube B is partially disordered, indicating weaker organizational forces and suggesting unequal H⁺ distribution between the two tubes.

Direct X-ray determination of the locations of H⁺ and the H atoms of water is not possible because of their low electron density. In addition, the standard procedures built into crystallographic software for modeling their locations fail because the dimensional constraints of normal H-bonding do not apply to H_aq⁺ clusters. Nevertheless, the locations of the excess protons are revealed by the shortening of O⋯·O separations. When shorter than those in hexagonal ice (2.76 Å)¹¹ or liquid water (2.85 Å)¹² they are candidates for bridging H⁺. The presently known range of O⋯·O distances for O–H⋯O bonds considered to carry positive charge in H(H₂O)_n⁺ cations is 2.39-2.59 Å.^7,13 Short O⋯·O separations (≤2.42 Å) are associated with symmetrical H-bonding in Zundel-type H₅O₂⁺ ions^9,14 while longer separations (2.52-2.55 Å) are typical of standard unsymmetrical H-bonds such as those in the H₃O⁺·3H₂O Eigen-type ion.⁸

A survey of short O⋯·O separations in the unit cell of tube A (Fig. 2) indicates three structurally different types of H_aq⁺ clusters: cluster I with a single short O10–O10″ distance of 2.567(12) Å, two sites of cluster II with a pair of adjacent short O⋯O distances of 2.623(8) and 2.618(7) Å indicating an H₇O₃⁺ core formulation, and an unprecedented cluster III with a nearly square O5–O12–O5″–O12″ arrangement having 2.636(8) and 2.668(8) Å rectangular sides. This stoichiometry leaves only 2 H_aq⁺ sites for tube B and two symmetry-related H₇O₃⁺ ions of type II with O⋯O separations of 2.582(13) and 2.573(9) Å are found amongst the ordered water molecules. There are no other short O⋯·O separations. The 4:2 partitioning of H⁺ between channels A and B corresponds to an average composition of 6 H₂O per H⁺ in A and 12 H₂O per H⁺ in B and is consistent with the disorder (and partial occupancy) of water molecules observed in channel B.

Figure 2.

Structures of the three H(H₂O)_n⁺ clusters I, II and III. Thermal ellipsoids are at 50% probability level.

Cluster I is topologically a tetrahydrated H₅O₂⁺ Zundel ion, but the O⋯·O distances are quite anomalous. Sitting on a crystallographic center of symmetry, its central O⋯·O distance of 2.57 Å is very long compared to those in other H₅O₂⁺ cations (2.39-2.42 Å).^9,13,14 It is even longer than the O⋯·O distances in the H₃O⁺·3H₂O Eigen ion (2.52-2.55 Å).⁸ The four O⋯·O distances to the second sphere water molecules in I (2.70 Å) are also large compared to those in the H₅O₂⁺·4H₂O ion (2.52 Å)¹⁴ and only slightly below those in hexagonal ice (2.76 Å). This means that the positive charge of H⁺ is significantly more delocalized in I than in classical Zundel-type H₅O₂⁺ ions.

Cluster II is formulated as a hydrated H₇O₃⁺ ion with the two central O⋯·O distances that are equal within experimental error. It typically occurs when H(H₂O)_n⁺ cations are ion paired⁷ and is consistent with location of these clusters near the anion walls, removed from sites of crystallographic symmetry. One water molecule (O2) solvates the central O atom of the H₇O₃⁺ core with a somewhat short O⋯·O distance of 2.69 Å. This reflects delocalization of the positive charge onto this water molecule and illustrates the close relationship between monohydrated C_2v H₇O₃⁺ ions and C_3v H₉O₄⁺ Eigen-type ions. Four other water molecules (O4, O7, O8″ and O12″) solvate cluster II at O⋯·O distances 2.77-3.03 Å.

Cluster III is unprecedented for a proton hydrate. Four O-atoms share H⁺ in a nearly square arrangement whose center has crystallographic inversion symmetry. Four solvating water molecules are close enough to qualify for inclusion in the cluster (O7, O7″, O3, O3″ with O⋯·O distances all close to 2.72 Å) leading to an H₁₇O₈⁺ formulation. The next closest are O11 and O11″ at 3.03 Å but since these distances are even greater than that of liquid water (2.85 Å) they are not considered to carry positive charge from H⁺. The novel structure of this ion must be the result of the electrostatic field peculiar to this inversion symmetry site within the tube. A related square core structure of eight water molecules, but having much longer O⋯·O distances (2.91-3.02 Å) because an excess proton is absent, has been observed in the crystal structure of a hydrated lanthanide chelate.¹⁵ The diversity of static H_aq⁺ cluster structures trapped in the tubes is a reflection the highly dynamic nature of the excess proton in water.¹⁶

Clusters I, II and III all have much longer O⋯·O separations than would be expected from the existing knowledge base of X-ray structures of crystalline acid hydrates^7-10,13,14 or the computed structures of gas phase ions, even those having greater than 20 water molecules.¹⁷ This is compelling evidence for greater delocalization of positive charge in these clusters. It suggests that H_aq⁺ in the present extended tubular environment (and presumably in liquid water) is uniquely different from the discrete H(H₂O)_n⁺ ions in crystalline salts or the gas phase.

The delocalization of positive charge has another interesting consequence. Clusters I and III in tube A form an infinite chain of short O⋯·O separations i.e., a true proton wire (Fig. 3). These clusters lie along the central axis of the tube and contain individual centers of symmetry. They are linked by common atoms (O3 and O3″) whose O⋯·O distances of 2.70 Å and 2.72 Å to the core O atoms of the clusters are shorter than those of liquid water or hexagonal ice. This indicates an infinite 1D delocalization of positive charge. It is tempting to speculate that H⁺ mobility would be especially fast along this chain.

Figure 3.

Portion of a proton wire comprised of type I (blue) and III (green) H(H₂O)_n⁺ clusters in tube A with O⋯·O separations < 2.72 Å. Dotted bonds represent O⋯·O separations > 2.72 Å. Cluster II, depicted in orange, is not part of the proton wire. Thermal ellipsoids at 50%.

In summary, three structural types of H_aq⁺ have been identified in nanotubular crystals of H(CHB₁₁I₁₁)·8H₂O. One is without precedent and all have unexpectedly long O⋯·O separations compared to those in discrete H(H₂O)_n⁺ moieties, reflecting more extensive positive charge delocalization. The confined centrosymmetric H(H₂O)_n⁺ cations aggregate into infinite proton wires whose short inter-cation distances suggest a mechanism for enhanced one-dimensional H⁺ mobility.