Controlling water transport in carbon nanotubes

Nanofluidics is the study of fluid behaviors in confined geometries of nanometer scales. A good understanding of such nanofluidic phenomena is important as new fluidic functionalities can be developed into solutions for many global challenges such as energy harvesting, CO₂ utilization, health risks and clean water [1]. Carbon nanotubes (CNTs), which are nano-sized cylindrical carbon molecules, have emerged as ideal conduits in nanofluidics owing to their hollow structures,tunable diameters and lengths, mechanical and chemical stabilities as well as the inherently hydrophobic and molecularly smooth graphitic inner surfaces [2]. More importantly, single CNT can be isolated to create single-channel platforms even though this remains technically challenging to date [3,4]. As such, nanofluidic studies using individual CNTs offer compelling opportunities for precise flow measurements to elucidate the underlying mechanisms of nanoscale fluid transport.

Overview of nanofluidics inside CNTs

The fundamentals of nanofluidics inside CNTs stem from two origins: the bulk hydrodynamics and the dynamics of fluid (e.g. water) at the carbon interface. Bulk hydrodynamics are commonly described by a classical continuum framework using the Navier-Stokes equations (see original paper). The Navier-Stokes equations stay valid even when the diameter of the CNTs gets down to the limit of ∼1 nm [7]. As the diameter of the CNTs reduces below 1 nm, molecules are subjected to extreme confinement and, in the case of water molecules, initiate a single- file configuration inside the CNTs (Fig. 1a). This gives rise to an ultrafast stochastic transport [8]. The classical continuum hydrodynamic framework breaks down at this point and a conceptual length scale known as slip length is introduced to rationalize this non-continuum phenomenon. Applying a Navier’s boundary condition to water at the CNT surface, the slip length is found to be inversely proportionate to a friction coefficient, which defines the liquid-solid interface friction (see Refs. [1,7,9] for a comprehensive review of the principles). The slip length and friction coefficient are metrics used in many simulation and experimental studies to explain for the fast water transport inside CNTs. In principle, the longer the slip length, the lower is the liquid-solid friction and the greater is the enhanced water flow rates. However, reported slip lengths and water flow enhancements span across 4–5 orders of magnitude between various simulation and experimental studies [10–12]. The controversy is also further intensified because of the uncertainties in the experimental results due to technical challenges in fabricating well-controlled nanoscale structures. For example, membranes made of vertically aligned CNT forests consist of non-uniform nanochannels together with inconsistently low porosity due to blockage of the CNT pores [13,14]. This lack of reliable experimental data fails to provide essential feedback for simulation studies, leading to a severe impediment to the nanofluidic research of fluid transport inside CNTs [9].

Nanoconfinement is the key

Recently, Secchi and coworkers gave an answer to this problem by measuring the water flow rate through individual CNT with well-defined radii and lengths [15]. They sealed a CNT that was bridging two reservoirs of water, applied a pressure drop across and monitored the water jets that emerged out of the CNT into the permeating reservoir. Existing techniques are unable to probe tiny mass flow through a single CNT, which was as low as 1 fL (10−15 L) per second [16]. As such, polystyrene nanoparticles were introduced as tracers into the permeating reservoir. By tracking the displacement of the tracers as water jets emerged from the CNT, the velocity profiles were mapped and this allowed the water flow rates to be accurately determined. Unlike previous studies, their approach brings about a methodological breakthrough in nanofluidics by offering an unprecedented sensitivity in addition to the direct and unambiguous measurements of flow rates through individual CNTs of well-established dimensions.

Their results also showed certain reconciliation of the previous differences in flow rate measurements by concluding a strong dependence of slip length on the CNT radius. According to them,the slip length increased to 300 nm as the radius of the CNT decreased to 15 nm. Successively, the water flow rate through the smallest CNT was also ∼24 times higher than that predicted using a no-slip boundary condition [15]. The observations not only suggest that slippage of water in CNT is radius-dependent but more implicitly demonstrate the impact of nanoconfinement on the curvature-dependent friction at the water-carbon interface. This is in agreement with a previous study by the same group which computed that the graphitic interface exhibited a curvature-induced shift and projected a smoother interaction energy landscape for water molecules to be transported within a relatively roughnessfree nanochannel as the CNT radius became narrower (Fig. 1b) [18]. Thomas and McGaughey also suggested a weakening of the interfacial binding between water molecules and the carbon surface as CNT radius decreases [21]. Essentially, this accounts for the near frictionless transport and thus the high slip length as the CNT narrows. However, Walther et al. believed that the high flow enhancements cannot be attributed solely to the interfacial interactions of water with CNT [22]. Alternative mechanisms such as effects of polarization, external driving forces (e.g. electric field) and gated entry at the end of the CNT can also provide valuable insights [23]. Nevertheless, from a practical perspective, the unexpectedly high slip length measured by individual CNT with 15 nm radius can be potentially improved further by employing CNTs of smaller radii. This opens up new opportunities to capitalize on narrower CNTs to control ultrafast water transport by exploiting the diminishing interfacial friction as a result of nanoconfinement. The question therefore remains on the technical feasibility in fabricating well-controlled nanostructures, such as membranes made up of well aligned CNTs with uniform radii, in an economical and scalable manner to unlock this capacity for potential applications [24].

Electronic structures of CNT show promise

The other intriguing discovery by Secchi and coworkers is the dependency of slip length on the electronic properties of the nanochannels. This was illuminated when boron nitride nanotubes (BNNTs) were used in the flow measurements and showed no substantial slippage of water like in CNTs. BNNTs and CNTs are both crystallographically similar but fundamentally different in electronic properties with BNNTs being insulating while CNTs semi-conductive or metallic. As a result, BNNTs demonstrated at least ∼100-folds lower slip length in contrast to CNTs of comparable radius and almost no enhancement in flow rates relative to that as predicted using a no-slip boundary condition [15]. Interestingly, this result echoes a similar conclusion by Tocci and colleagues but to a way larger extent. The previous ab initio simulation study highlighted only a ∼3-folds larger friction coefficient on boron nitride (BN) flat surface than on a graphene flat surface [25]. The lower estimation may originate from the fact that the simulation was carried out on flat surfaces, which did not incorporate curvature dependent friction as aforementioned [18]. More work is definitely needed to reason out this huge difference. Nevertheless, Secchi and coworkers have successfully demonstrated the importance of empirical parameters to initiate more accurate simulations of the interfacial dynamics and predictions of flow behaviors.

Another implication of their work is that it inspires new avenues to explore the fine-tuning of electronic properties of CNTs for controlling ultrafast water transport. Generally,tuning of the electronic properties of CNTs can be achieved through changing the geometrical structures such as the chirality of the CNTs [26], applying of external forces such as strain [27], chemical functionalizing of CNT side-walls [28] and heteroatom or charge-transfer doping of CNTs (Fig. 1c) [29]. These strategies are typically focused on adjusting the bandgap between the valence and conduction bands either through mechanical deformation of the CNTs or disruption of the - electron networks [28–30]. By doing so,the electronic structure can be exploited to manipulate the energy landscape felt by the water molecules in contact, such that the potential well of the landscape can be smoothened or corrugated to control the friction of water on the carbon interface (Fig. 1b) [25]. As an attestation of this concept, Falk and coworkers performed a theoretical study using CNTs of different chiralities. Their findings demonstrated that armchair CNT (metallic)indeed showed a lower friction coefficient than its zigzag counterpart (semi-conductive) when the CNT radius was below 3 nm [18]. Over and above, fine-tuning of the electronic properties via chemical methods also create defects on the graphitic surface, which inevitably changes the chemical properties of the CNTs. This defect-induced interfacial chemistry might have a strong coupling to nanofluidic transport motivated by the chemical nature of the defects and their ability to partake in hydrogen bonding with water molecules [31]. Looking forward, these insights indicate that controlling friction at the solid-liquid interface by tuning the electronic properties of CNTs maybe a promising direction for creating novel applications of nanofluidics.

Ongoing challenges

Better understanding of water transport at the nanoscale level has significant implications for addressing global issues. Translating nanofluidic phenomena into high-performance practical applications remains a challenge. In particular, the lack of technology for efficient mass production and isolation of CNTs with well-defined structural and electronic properties as well as controllable integration of CNTs into functional devices has hitherto undermined the progress. Continuous efforts on CNT synthesis, sorting and assembly should therefore grow in tandem with nanofludic studies so that the fundamental knowledge in controlling water transport inside CNTs can be leveraged for next generation CNT based membranes, energy harvesting devices and biosensors.

Acknowledgements

Author affiliations: Singapore Membrane Technology Center, Nanyang Environment and Water Research Institute, Nanyang Technological University, Singapore 637141, Singapore; Nanyang Technological University, School of Chemical and Biomedical Engineering, Singapore 637459, Singapore; The University of Sydney, School of Chemical and Biomolecular Engineering, NSW 2006, Australia.

The authors would like to thank funding support from Australian Research Council under the Future Fellowships scheme (FT160100107) and the Faculty of Engineering & Information Technologies, The University of Sydney, under the Faculty Research Cluster Program. We would also like to give appreciation to the Singapore Economic Development Board for funding supportto the Singapore Membrane Technology Center.

This article was originally published in Nano Today 14 (2017) 13–15.

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