Porous Ti3C2Tx MXene Membranes for Highly Efficient Salinity Gradient Energy Harvesting

Extracting osmotic energy through nanoporous membranes is an efficient way to harvest renewable and sustainable energy using the salinity gradient between seawater and river water. Despite recent advances of nanopore-based membranes, which have revitalized the prospect of blue energy, their energy conversion is hampered by nanomembrane issues such as high internal resistance or low selectivity. Herein, we report a lamellar-structured membrane made of nanoporous Ti3C2Tx MXene sheets, exhibiting simultaneous enhancement in permeability and ion selectivity beyond their inherent trade-off. The perforated nanopores formed by facile H2SO4 oxidation of the sheets act as a network of cation channels that interconnects interplanar nanocapillaries throughout the lamellar membrane. The constructed internal nanopores lower the energy barrier for cation passage, thereby boosting the preferential ion diffusion across the membrane. A maximum output power density of the nanoporous Ti3C2Tx MXene membranes reaches up to 17.5 W·m–2 under a 100-fold KCl gradient at neutral pH and room temperature, which is as high as by 38% compared to that of the pristine membrane. The membrane design strategy employing the nanoporous two-dimensional sheets provides a promising approach for ion exchange, osmotic energy extraction, and other nanofluidic applications.

The grey outline in the inset is traced from the TEM image, and the diameter of the black dashed circle is estimated from the area of the irregular-shaped hole. Figure S2 (a-b) TEM images of individual Ti3C2Tx MXene sheets on lacey carbon and along with the corresponding selected area electron diffraction (SAED) pattern. (c) Size distribution of Ti3C2Tx MXene sheets, investigated using SEM over 244 sheets. The width and length of all the sheets deposited on Si/SiO2 substrates and porous AAO membranes, respectively, are analyzed for the size analysis. (d) Topological mapping of a single layer Ti3C2Tx nanosheet deposited on a Si/SiO2 substrate, investigated by AFM (Scale bar: 2 μm). A sheet-to-sheet procedure from the overlapped region was used to determine the thickness of the single nanosheets to exclude instrumental artifacts or the influence of possible contaminants on substrates.  Figure S4 (a) Effective ion transport area across the nanoporous Ti3C2Tx lamellar membrane (b) Salt concentration-dependent conductances across the pristine and nanoporous Ti3C2Tx-stacked membranes, respectively.

Effective fluidic channels across lamellar MXene membranes
We assumed that the single Ti3C2Tx sheet possesses the same width and length, which are approximated from experimentally averaged lateral sizes of the MXene sheets. The total number of parallel 2D channels per unit area can be estimated as by ~ 2N(N+1), and the resulting number of channels is ~ 10 7 across the employed lamellar membranes with a full area of 78.54 mm 2 . The effective fluidic area is approximately 2.5×10 -2 mm 2 , and the corresponding fraction of the nanochannels on the total membrane area is estimated to be less than 0.1 % (Figure S4a). The perforated holes are responsible for geometric alterations in penetrating fluidic channels, changing the intrinsic property of membranes. As displayed in Figure S4b, the improvement from the nanoporous membrane, normalized to the thickness, is attributable to its increased ion conductivity of the membrane in the presence of pores. Notably, at high salt concentration of 1 mol·L -1 , governed by the bulk transport, i.e., directly determined by the given channel geometries rather than surface charges, the change of channel geometries is evidently verified by the observed higher conductance of the nanoporous membrane. The higher conductivity can be explained mostly by a combination of shorter channels and augmented ion transport routes provided by the etched pores. The fraction of the effective transport area is likely to be comparable to that of the pristine membrane. The resultant higher porosity also leads to increased cation selectivity of membranes.
The perforated holes might act as cation channels, linking 2D interplanar channels produced between adjacent sheets in lamellar membranes. The internal pores lower the energy barrier for cation passage, thereby boosting the preferential ion diffusion across the membrane.

Figure S5
Comparative study on the osmotic power conversion as a function of a salt concentration gradient (a) energy conversion efficiency and (b) relative ionic mobility ratio across the nanoporous and the pristine Ti3C2Tx MXene membranes, respectively. Figure S6 3D Bode maps of maximum osmotic power density-membrane thickness-salt concentration gradient for the pristine Ti3C2Tx MXene membrane. Figure S7 (a) analytical model for ionic penetration through the interconnected channels of 2D interplanar slit and perforated pore. (b) Ionic conductances obtained at variable length of nanocapillary and diameter of pore, respectively. Here, the surface charge density is presumed to be 0.1 C·m -1 in accordance with previous study. 1 The ionic concentration at 10 -2 mol·L -1 is employed for approximate evaluation.

Analytical approximation of fluidic resistance across nanoporous channels
To understand the impact of geometric factors on total conductances, we define a single conduit by serially combining a two-dimensional interplanar slit and etched pores with varying diameters. The ionic resistance ( 2 ) through the interplanar spacing in between neighboring sheets can be approximately described by 2 where is the elementary charge; is the density of cation or anion; + and − are mobility of cation (7.62 × 10 -8 m 2 ·V -1 s -1 for K + ) and anion (7.91 × 10 -8 m 2 ·V -1 s -1 for Cl -), respectively; 2 is the surface charge density of 2D sheets; , ℎ, and are, respectively, width, effective height (0.61 nm) and length of the 2D slit channel. The width of 2D slit is assumed to be identical of diameter of etched pores. Note that the left term indicates a bulk conductance, linearly dependent on the salinity, and the right term is a contribution from the electro-osmotic flow of excess counterions, typically described as surfacecharge-governed transport.
The pore resistance ( ) through the etched pore on the basal plane can also be demonstrated with analogous contribution from bulk behavior and confined electrical double layers as 3 where and are the diameter and length of the etched pore, respectively, and is the surface charge density of pore. Recent studies on the ion selectivity of transmembrane nanopores suggest that the charge selectivity across the pores is mainly governed by the charge separation within the Debye layer formed on the outer charged surfaces rather than the inner walls of the pores. Even after the chemical etching process, the sheets surrounding the holes remain their crystallinity and presumably surface functional groups attracting counterions. Furthermore, contrary to the nanopores open to electrolytic bulk environment, the nanopores surrounded by the confined Debye screening layers in between adjacent sheets can work as the interconnected counterion channels in the lamellar Ti3C2Tx membrane, and possibly boosting preferential diffusion of cations. Consequentially, the surface charge density inside the pores is assumed to be same as that (0.1 C·m -1 ) of the 2D Ti3C2Tx sheets in accordance with previous study.

S6
Aside from the resistances through the open structures, the access resistance ( ) through the atomically thin nanopore is another factor that strongly influences the ionic resistance, as shown by 4 Ionic conductance of single conduit can be approximately estimated by serially connecting respective resistance as We have employed equation (S4) to calculate the ionic conductances through the interconnected channels of 2D interplanar slit and perforated pore. In general, we found that the access resistance governs total conductance through the etched pore, which suggests that pore diameter is the only geometric factor that influences the conductance through the pore. Taking this into account, the total ionic conductance of single fluidic channel across membrane is shown by equation S5: where is the thickness of lamellar membrane; is the interlayer spacing between neighboring sheets. Overall conductance across the lamellar membrane can be derived from equivalent conductance for a parallel combination of the individual channels.