Selective Filtration of Fluids in Materials with Slit-Shaped Nanopores

Problems associated with a qualitative increase in the selectivity of fluid filtration remain the major challenge in a variety of areas such as fluid transport through porous materials and media, ion separation, water desalination and purification, and many others. A promising way to solve these problems is to design and develop membranes with slit-shaped nanopores. In the paper, we studied the selectivity and permeability of slitshaped nanosized pores in the natural mineral (hydroxyapatite) with the use of the nonequilibrium molecular dynamics approach with all-atom models. We showed that the subnanometer-wide slit-shaped pores in hydroxyapatite are able to demonstrate both good salt rejection and relatively high water permeability. In particular, the numerically predicted water permeability of hydroxyapatite with 0.4 nm thick slit-shaped nanopores reaches about 200 L/(m2 h bar) that is higher than that of commercial membranes and has the same order of magnitude as the theoretically predicted water permeability through single-layer MoS2 nanoporous membranes. An increase in the nanopore thickness is accompanied by a multiple growth in permeability, which is comparable with advanced 2D-CAP (2D-conjugated aromatic polymer) membranes, but in so doing the filtration selectivity is lost. The results show that nanoporous materials with the connected network of slit-shaped nanopores is a promising filter material for water treatment including seawater desalination and other important technical and environmental applications.


INTRODUCTION
.ast climate change, rapid growth of the human population, and the permanently increasing mancaused impact on the ecological system of the Earth pose new challenges for mankind. One of the key modern problems is the need for high-quality selective filtration of fluids of various molecular composition on an industrial scale. Topical areas that require high filtration selectivity are, for example, transport of liquids through porous media [1], water desalination and purification [2], hydrogen purification [3,4], gas separation [5], ion separation [6], DNA sequencing [7], transplantation of islets for noninvasive cure of pa-tients with type 1 diabetes [8] and many other. The most important requirements for selective filtration are excellent rejection of impurity ions or organic molecules, minimal resistance to flow of the main fluid, high energy efficiency and the ability to scale the filtering nanosystem up to the scale of practical application. Progress in advanced filtration technologies is determined by the development of new selective/semipermeable membranes with the given geometric and electrostatic characteristics of the pore surfaces. Specific requirements for the characteristics of the pore space and pore surface of membranes are determined by the features of the field of application. In this pa-per, we consider some of the fundamental questions related to the effect of the pore size and shape on the quality and efficiency of ion-selective filtration of salt water.
The modern widely used membranes for purification and desalination of water are typically characterized by either very high salt rejection and comparatively low water permeability or insufficient salt rejection and very high water permeability [9]. The recent development of the nanotechnology-based filtration membranes with nanosized pores, including nanostructured ceramic membranes [10], nanoporous graphene nanosheets [11], nanotube-based membranes [12,13], nanoporous boron nitride nanosheets [14], peptide-based membranes [15], and even biologically inspired aquaporin-based membranes [16], promises to provide the breakthrough in this area. Different aspects of the use of nanomaterials and nanostructured materials for water treatment are reviewed elsewhere [1719].
The origin of the ion rejection in narrow nanopores is the ion size exclusion and/or solvation shell loss mechanisms. The first one takes place in the case of ions that have the atom diameter larger than dimensions of both the water molecule and nanopore entrance. The second mechanism is associated with the energy penalty for the hydrated ion entry to the nanopore, when the ion (partially or fully) loses neighboring water molecules from its solvation shell [20]. To achieve high salt rejection, pores should be of the subnanometer dimension. However, a decrease of the nanopore size leads to a decrease in its water permeability because the water molecule can also face the energy barrier, thus rearranging the network of hydrogen bonds with its neighbors when entering the nanopore from the bulk solution. A promising way to solve this problem is to design the nanoporous material with preferentially oriented rectangular (slit-shaped) nanopores, which are characterized by high aspect ratios. These nanopores should have a subnanometer size in one direction (thickness of slit) and a much larger size in perpendicular directions. The slit-like geometry of the nanopore provides a straight path that presents a shorter distance for molecules to travel as compared to the traditional pore geometry.
The recent study on ultrafiltration showed that membranes with slit-shaped pores are able to provide a higher efficiency and selectivity at the given value of permeability than membranes with cylindrical pores [21]. A striking example is the recently synthesized crystalline 2D-conjugated aromatic polymer (2D-CAP) with nanopores with a rectangular cross section [22]. 2D-CAP is a very prospective base for the production of effective water desalination and ion separation membranes. An almost 100% ion rejection and high water permeability 1172 L/(m 2 h bar) were numerically predicted for the 2D-CAP membrane [23], which is more efficient than any commercial membrane. The limiting case of rectangular geometry of the nanopore cross section is a slit with the subnanometer width. In addition, the nanoporous material with slit-shaped pores has typically a large specific area of the internal surface, which can be potentially used as adsorbent for different species (e.g. ions, heavy metals, halides/oxyhalides, organics, etc.) depending on the material surface structure and composition.
The results of the above-mentioned studies suggest that slit-shaped nanopores would demonstrate a higher liquid permeability than that of cylindrical (nanotubelike and hole-like) nanopores of the same diameter as the slit width as well as a fairly good ion rejection due to the subnanometer size of the pore entrance (slit width). Therefore, it is important to obtain estimates of the ion rejection and water permeability of a material sample with slit-shaped nanosized pores. The present study is focused on slit-shaped nanopores in the natural biomineral, namely, in hydroxyapatite (HAP) since it is an environmentally safe, nontoxic and biocompatible material. HAP has a pH-dependent structure and charge distribution on the surface, which further can be important for the pore selectivity control, including selective permeability and competitive adsorption properties.
The study was carried out by means of the nonequilibrium molecular dynamics (NEMD) computer simulation. Note that at present time, molecular level computer simulations have become a powerful and widely used tool for the study of nanoscale systems and processes, including the molecular structure and property prediction [24], nanoparticlecell interaction [25], the study of hybrid [26,27] or heterogeneous nanosystems [28] and nanoconfined matter [29], ion and molecule adsorption [30,31], and molecular transport through nanopores [1,32]. NEMD is the wellknown direct numerical way to study salt water filtration through nanopores, including the estimation of fluid fluxes, ion rejection, and ion selectivity [10,23]. In the present paper, we employed NEMD for numerical simulation of the salt water (~800 mM) filtration through slit-shaped nanopores with the subnanometer width. PHYSICAL  (ii) model 2 with the slit-shaped wide nanopore of the ~0.78 nm width.
.igure 1 shows equilibrium structures of the systems at 0.1 MPa and T = 300 K. The periodic boundary conditions (PBC) are applied along the y and z directions (z is the vertical axis, and axis y is directed away from the observer, see the coordinate system in .ig. 1). The {y, z} dimensions of the simulation boxes of models 1 and 2 are {3.2621, 3.2545} nm and {3.2621, 3.6161} nm, respectively. The size of the models along axis x is about 20 nm. Due to the use of PBC along the y axis, the nanopore geometry is infinite along axis y.
The length of the nanopore along axis x is 3.7668 nm in both the models. The nanopore walls are {001} surfaces of hydroxyapatite (HAP). They are formed by protonated phosphate groups H 2 PO 4 . This corresponds to pH = 5. The hydroxyapatite model is developed based on the data derived by Lin and Heinz [33,34]. The INTER.ACE .. force field developed by Heinz et al. [35] is utilized to parameterize the models.

Water Permeability through Slit-Shaped Nanopores
Series of eight NEMD simulations of the salt water filtration through two slit-shaped nanopores of different widths (~0.42 and ~0.78 nm) at the pressure differences 50, 100, 150, and 200 MPa are performed. The total time of each simulation with the narrow nanopore is 100120 ns, but the filtration process is steady-state only during first 50100 ns because of the closed system and the limited number of water mol-ecules. This steady-state stage can be observed by the near-linear shape of the curves in .igs. 2a and 2b. Note that the duration of water flow through the wide nanopore in the steady-state regime (1020 ns) is 5 times shorter than that through the narrow nanopore because of the about five-fold higher flow rate.
We estimate molecular water fluxes in the steadystate filtration regime for all eight cases (.ig. 2c). One can see that the water flux for each system is a linear function of the applied hydrostatic pressure. This implies constant water permeability at least within the range of the atmospheric pressure drop up to 200 MPa. Here pure water permeability is conventionally defined as the volume of water that passes through the membrane (or the layer of permeable material) per unit time per unit area and per unit of transmembrane/translayer pressure. The estimation of water permeability through the narrow slit-shaped nanopore is 4.7 L/(cm 2 day MPa) or 196 L/(m 2 h bar). The obtained value is higher than that of commercial membranes and has the same order of magnitude as the numerically predicted water permeability rate through the single-layer MoS 2 nanopo-  rous membrane [42] and the water permeability of nanoporous graphene [43].
The wide slit-shaped nanopore of model 2 demonstrates a water permeability about 5 times higher than that of the nanopore of model 1: 27 L/(cm 2 day MPa) or 1119 L/(m 2 h bar). This value is comparable with that of the 2D-CAP membrane, which is 1172 L/(m 2 h bar) [23]. However, as it will be seen in the next section, 2D-CAP membranes possess a much better salt rejection property than the 0.78 nm wide slit-shaped nanopore in HAP.
.or a quantitative comparison, it is important to keep in mind that water permeability depends on the density (concentration) of pores. The direct comparison of pore densities is not exactly correct on account of completely different geometries of hole-like and slitshaped nanopores. In the examined nanoporous HAP fragments the densities of slit-shaped nanopores are about 0.3 nm/nm 2 . This means that each 1 nm 2 of the working cross section has 0.3 nm of the total length of slits (the value is independent of the pore width). By increasing the nanopore density, it is possible to increase permeability of the membrane (the ion rejection would remain the same). However, this possibil-ity is limited above by features of the synthesis and production processes.

Salt Rejection and Ion Selectivity
During each simulation run, we analyze the numbers of sodium and chlorine ions that are completely translocated from the feed box to the outlet through the nanopore. With the commonly used formula [23,44], we estimate the ion rejection for two nanopore widths at four applied pressures (.ig. 2d).
The narrow (~0.42 nm) slit-shaped nanopore in HAP demonstrates a 100% sodium ion rejection at any considered pressure drop, whereas about 10% of chlorine ions are permeated (88 to 92% of chlorine ions are rejected depending on the pressure drop ∆p). Thus, the narrow nanopore is predicted to possess a high Clto-Na ion selectivity (.igs. 3a and 3b). We also note that in the considered range of pressure drop ∆p the salt ion selectivity of the narrow slit-shaped nanopore is practically independent of the ∆p value.
The wide nanopore (~0.78 nm) has the maximum ion rejection at the minimum considered pressure drop (∆p = 50 MPa): 86% for sodium ions and 81% for chlorine ions (.ig. 2d). An increase in the pressure drop up to 150 MPa leads to a small but systematic decrease in the fraction of rejected ions down to 81% for Na + and 77% for Cl . A further increase in the pressure drop is accompanied by an accelerated deterioration of the selectivity of the nanopore. In particular, at the pressure drop 200 MPa the selectivity to both ion types becomes approximately the same and is only 72%. This value is insufficient for advanced filtering applications.
Therefore, within the pressure drop range 50 150 MPa the wide nanopore demonstrates low Na-to-Cl selectivity, namely, the difference between the numbers of filtered Cl and Na + ions is about 2025%. The selectivity of the water filtration decreases nonlinearly with increasing pressure drop across the nanopore. At >200 MPa the water permeation through the wide nanopore is nonselective at least to sodium and chlorine ions.

CONCLUSIONS
In summary, we show that high requirements for a new generation of filter membranes can be met by using materials with slit-shaped nanopores as the basis of such membranes. The key stage in the development of such materials is the determination of the optimum geometric and electrostatic characteristics of nanopore surfaces. We showed that an effective tool for such a design is molecular level computer simulation.
Advantages of slit-shaped nanopores for highly selective filtration were shown in the paper by the example of nonequilibrium molecular dynamics simulations of salt water filtration through subnanometer slitshaped nanopores (0.42 and 0.78 nm wide) formed by the {001} surfaces of hydroxyapatite, which is an environmentally safe, nontoxic and biocompatible mineral. In particular, it was found that the slit-shaped nanopore of width 0.42 nm demonstrates the 100% Na + rejection and about 90% Cl rejection in the considered range of pressure drops (50200 MPa). At the same time, this nanopore showed the stable Cl versus Na + selectivity and comparatively good water permeability. The predicted water permeability of HAP with 0.42 nm wide nanopores and the 0.3 nm 1 density of pores is 196 L/(m 2 h bar), which is higher than that of commercial membranes and comparable with the predicted water permeability of the MoS 2 -based membrane and nanoporous graphene. The obtained results allow considering the biomineral with ~0.5 nm wide slit-shaped nanopores as a promising filtering material that could be used in the development of en-vironmentally safe plants for seawater desalination and ion separation. Moreover, the results of the study invite further investigation of permeability and rejection properties of rectangular subnanometer nanopores (especially with a high aspect ratio) in nanosheets of graphene, boron nitride, silicon, MoS 2 , WS 2 , and their derivatives.