Nanofluidic Transport in Branching Nanochannels: A Molecular Sieve

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Nanofluidic Transport in Branching Nanochannels: A Molecular Sieve Based on Y-Junction Nanotubes Ling Liu and Xi Chen* Columbia Nanomechanics Research Center, School of Engineering and Applied Sciences, Mail Code 4709, Columbia UniVersity, New York, New York 10027-6699 ReceiVed: January 23, 2009; ReVised Manuscript ReceiVed: March 26, 2009

Using molecular dynamics (MD) simulations, we study the fundamental partitioning and screening behaviors of nanofluids confined in Y-junction nanochannels, and demonstrate their feasibility as efficient molecular sieves. A flow of gas or liquid molecules is partitioned at the junction and separated into the two side branches with different volume fractions. The opening gaps of the side branches are manipulated, and the sieve characteristics are explored as the gas phase, mixture composition/ratio, and opening dimensions are varied. The studies provide design principles for a molecular sieve with maximum probability passing one type of molecule into a screening branch, and meanwhile maximizing the rejection rate of other types of molecules. Introduction 1–4

Nanofluidics has attracted considerable attention in the past decade owing to its scientific implications for biological transport5 and the potentials in drug delivery, sensing, energy dissipation, conversion and storage, and environmental science and engineering, etc.6–9 These applications are made possible by the unique atomistic interaction between nanochannels and liquids, which results in fundamental transitions of molecular,10 energetic,11 and fluidic12,13 characteristics to the liquid from a bulk state to a confined state.14 Importantly, such transition may be fine-tuned by modifying solid and liquid properties, such as adding surface charge to the nanopores,11,15 or adding cation and anion to the liquids.16–18 The manipulation and control of nanofluidic behavior enables various promising applications for practical engineering. Most previous nanofluidic studies dealt with straight channels, e.g., carbon nanotubes and other straight nanopores, yet the investigation of fluid transport in branching nanochannels is still scarce.19 Nevertheless, since the tree-like branching channel networks have been widely employed in micro- and larger-scale fluidic systems,20–22 the understanding of fundamental fluidic behaviors in branching nanochannels, especially the transport and partition of monophase or mixed fluids at the junction,23 is of significant value to future nanodevices. As the size of a nanochannel is reduced to a few nanometers or smaller, molecular selection as a unique feature for nanofluids may be involved, which provides a new solution for molecular separation. Conventionally, there are two categories of air separation devices: (1) porous membrane which distinguishes molecules by their diffusion/transport rates24–26 and (2) absorber which separates molecules according to their absorptive capabilities/rates.27–29 Carbon nanotube (CNT) as a fast transporter30,31 has drawn increasing attention in its applications as molecular separators;32–36 some of these applications are based on the diffusion/transport rate mechanism,32–34 while some others perform the screening directly based on the molecular size.35,36 The latter designs introduce constriction35 or kink36 to a CNT such that only smaller molecules can pass the artificially formed * Corresponding author. Phone: +1-212-854-3787. Fax: +1-212-8546267. E-mail: [email protected].

valve and larger ones are effectively screened. While promising, a problem that potentially exists is the accumulation of larger molecules at the inlet side of the valve, which may “clog” the channel and adversely affect the diffusion of smaller molecules through the valve. To overcome such a disadvantage of a straight channel separator and to enable a clog-free system, the present paper adopts a Y-junction CNT37–39 as a model branching nanochannel with sustained high screening performance. It is expected that one branch screens molecules and the other evacuates the screened molecules to avoid molecular accumulation at the junction region. To achieve such a goal, the two outlet branches must have different sizes, smaller for the screening branch and larger for the evacuation side. Such a difference can be controlled quite precisely by mechanical loads or various designs of nanovalves.40,41 The manipulation and optimization of the branch sizes may realize different screening/sieve functions, making the overall system more flexible and promising. For nanofluidics in branching nanochannels, one of the most fundamental issues that needs to be elucidated is the balance between the rejection of large molecules and passing of small molecules through the screening valve. As the screening channel becomes smaller than the evacuation valve, the probabilities of all types of particles passing through the screening valve should be lower than those at the other side. However, for high system performance, it is desired to have both the passing rate of small molecules and the rejection rate of large molecules to be as high as possible at the screening valve. Thus, an optimized combination of valve sizes should be sought, which is related to the mixture composition, liquid/gas phase, and tube characteristics, elaborated below. Model and Method The Y-junction CNT (Figure 1; only the junction section is shown) considered in this study has three braches, all of which are made of (10,10) single walled CNTs with the same radius of 13.56 Å. Gas is pumped into the main branch (inlet), partitioned and screened at the junction, and then transported to the two side branches (outlets, for screen and evacuation, respectively). The branch opening is controlled precisely in our study by applying mechanical loads. For each outlet branch,

10.1021/jp900721h CCC: $40.75  2009 American Chemical Society Published on Web 04/14/2009

Nanofluidic Transport in Branching Nanochannels

Figure 1. Y-junction carbon nanotube as an illustrative model of branching nanochannels. Valves are formed via mechanical loads (right inset) to control nanofluidic flows into the two side branches. When the characteristic dimensions of the two valves are properly chosen, fluidic partition at the junction may be accompanied by optimized molecular screening functions. Some types of molecules may be rejected by the screening valve (left inset) and evacuated through the evacuation valve. Purified gas is achieved at the overdeformed (screening) outlet.

two parallel rigid lines act like a scissor to “squeeze” the channel; as the two rigid edges are approaching each other, due to the van der Waals (vdW) interaction, the outlet branches are deformed accordingly (right inset of Figure 1). The deformed cross section can be characterized by a characteristic gap size length, L, defined as the smallest opening. Note that there are various ways to control the size of the nanovalve, yet the present study serves as an illustrative model with an adjustable valve opening parameter, L. With the properly controlled branch size, LS (characteristic opening of the screening channel) and LE (characteristic gap of the evacuation valve), molecular selection may be achieved in the screening side, as illustrated in the left inset of Figure 1. In this example, larger molecules (blue) are screened by the valve and some smaller molecules (red) have passed the valve and flew into the side branch. In order to quantify such flow partition through the outlet valve, the mass fraction of each phase at the outlet is evaluated. For any given phase in a mixture, suppose NS molecules pass the screening valve and NE molecules are evacuated to the other branch; then, the mass fraction flowing to the screening side is defined as VS ) NS/(NE + NS), and the mass fraction flowing to the evacuation side is VE ) 1 - VS. For sieve purposes, VS is desired to be as high as possible for small molecules and as low as possible for large molecules. For general nanofluidic studies, the mass fraction is also an important parameter to describe the fluidic partition for various combinations of phases. Molecular dynamics (MD) simulation is performed using the LAMMPS (large-scale atomic/molecular massively parallel simulator) package.42 Four representative gas components (H2, O2, N2, and CO2) and their mixtures are considered. H2 is modeled as a single particle,43 while O2,44 N2,44 and CO245 are modeled by full molecular models with harmonic bond descriptions, U(r) ) K(r - r0)2/2, where K and r0 are the energy parameter and equilibrium bond distance, respectively. Carbon atoms constructing the nanochannel, denoted as C*, are modeled by the Amber96 forcefield.46 All nonbond interactions are described by the 12-6 Lennard-Jones (LJ) empirical forcefield, U(r) ) 4ε[(σ/r)12 - (σ/r)6], where r denotes the distance between particles and ε and σ are energy and length parameters, respectively. Solid-gas interaction is critical to accurately

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Figure 2. Partitioning and screening characteristics of pure gases (H2, O2, N2, or CO2) in the Y-junction nanochannel. The characterizing gap sizes of the screening and evacuation valves are varied in a wide range, while LE - LS ) 0.225 Å is fixed. A critical valve size is obtained for each case below which VS retains a low level.

modeling nanofluidics. In this paper, the forcefield parameters of C*-H2 are obtained via scattering experiments47 and those of C*-N and C*-O (O2) are determined by quantum mechanical calculations.48 All other intermolecular parameters are evaluated by the Lorentz combining rule. For each simulation, the two side branches of the Y-channel are independently deformed to reach the desired gap sizes, LS and LE. The deformed nanochannel is taken to be rigid during the subsequent dynamic simulation, so that we can focus on the fluidic characteristics. The main branch is initially filled with a pure gas or a gas mixture, which is then forced to flow toward the junction by a rigid piston moving at a constant velocity of 5 m/s. The time increment is set to be 1 fs. For each considered combination of gas phases and gap openings, VS is evaluated for all gas phases/components, based on which the general nanofluidic characteristics and screening performances are investigated. Each case of simulation is repeated several times; the average and deviation of VS are calculated, respectively, to characterize nanofluidic behaviors under the specified channel and fluidic conditions. Results and Discussion Pure gas flow is first examined for studying the basic fluidic characteristics in branching nanochannels. In order to functionalize the two branches, one side is relatively overdeformed to serve as the screening end, while the other is less deformed to evacuate the screened molecules. The difference between the two characteristic openings is set to be a small yet effective value, i.e., LE - LS ) 0.225 Å, while both LS and LE are varied in wide ranges. The four pure gases are simulated independently to obtain the value of VS at the screen outlet. In Figure 2, it is readily seen that, for any given gas phase, VS is close to 50% if the gap is sufficiently large; with increasingly constrained valves (i.e., decreasing LS), VS first sharply reduces and then gradually converges to 0%. In other words, with more “tight” valves, gas molecules are more likely to avoid the overdeformed branch and to enter the evacuation side. Energetically, in order to pass through the valve, a molecule may adjust its spatial position and bond orientation with respect to the surrounding atoms (especially the solid atoms at the tight valve) so as to

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TABLE 1: Length Parameters of Harmonic Bonds and van der Waals Interactions with Carbon Atoms (C*) Constructing the Nanochannel gas LS/2 (Å) r0 (Å) σ (Å) re (Å)

H2 2.52 C*-H2 2.97 3.33

O2 2.83 1.21 C*-O2 3.27 3.67

N2 3.06 1.10 C*-N 3.54 3.97

CO2 2.79 1.16 C*-C C*-O2 3.09 3.23 3.47 3.63

relieve as much interaction energy as possible. In other words, to minimize the system energy, the gas molecules may choose a more “comfortable” and “energetically efficient” way to exit the main branch, and the option of flowing into the more loosely constrained evacuation branch outlet is certainly attractive to the molecules. An interesting observation from Figure 2 is that, at a certain opening level, VS goes down to a very low level such that the gas is largely rejected by the overdeformed side. That is, the screening valve is effectively closed for the specific gas. The critical LS that blocks a certain type of gas, LS,Cr, is an important index for the applications of Y-junction branching nanochannels as molecular sieves or molecular valves. Table 1 lists LS,Cr for the four gases studied in this paper; these values are estimated from Figure 2 (with VS ) 5% adopted as a threshold). (Note that the value of LS,Cr depends on LE - LS, as well as gas composition in the case of a mixture, as discussed below.) While H2, O2, and N2 are effectively distinguished by their LS,Cr, CO2 and O2 appear to have almost the same LS,Cr although their molecular structures are distinct. In essence, the critical valve size is related to the characteristic size of the gas molecule. A qualitative comparison between LS,Cr/2 and rE and r0 is shown in Table 1. Here, for each gas phase, rE ) 21/6σ is the equilibrium distance between two particles interacting with each other via vdW force, and r0 is the equilibrium bond length. Note that large force/potential energy may be invoked when the neighboring particles are too close compared to the equilibrium length/distance. As shown in Table 1, LS,Cr/2 is about 0.8-0.9 Å smaller than rE for all gas phases studied, which implies a very high energy barrier for molecules to pass the valve, thus effectively rejecting them. If LS/2 is sufficiently small, a decent amount of molecules may still pass through the screening branch. Moreover, despite their distinct bond structures, the fact that O2 and CO2 have similar rE and r0 suggests that molecules may adjust their bond orientations to pass through the valve (and because these two molecules have similar lateral sizes determined by the O atom, that leads to similar LS,Cr for these two phases). (Note that, since the effectiveness of the system largely relies on the molecular size, it may encounter difficulty for separating gases that are indistinguishable in LS,Cr, e.g., O2 and CO2 illustrated in the present study.) The different values of LS,Cr for different gas phases in Table 1 suggests that a combination of screening/evacuation valves may exist such that one type of gas is rejected whereas the other one flows through, and that provides an inspiration of the design of the molecular sieve via Y-junction branching nanochannels. According to Figure 2, a combination with LS ) 6.115 Å and LE ) 6.34 Å may offer a VS value lower than 5% for N2 but 37% for O2. It is envisioned that with a branching nanochannel thus designed, highly purified O2 may be extracted from a mixture of O2 and N2. To validate such a concept, MD simulation is carried out for a mixture of originally 50% O2 and 50% N2, and the separation efficiency of the gas phases through the Y-junction branching nanochannel is calculated. The results of VS for all gas phases

Figure 3. Partitioning and screening characteristics of the O2/N2 mixture in the proposed Y-junction nanochannel. (a) The O2/N2 mixture is equally fractioned; LE - LS ) 0.225 Å is fixed, while LS and LE are varied. (b) The mixing ratio of O2/N2 is varied, where a proven effective sieve with LE ) 6.25 Å and LS ) 6.025 Å is used. (c) The O2/N2 mixture is equally fractioned; LS ) 6.025 Å is fixed, while LE is varied.

are shown in Figure 3a with varying sizes of valves. The sieve works just as predicted; i.e., most nitrogen molecules are screened from the overdeformed side and the screening branch produces almost pure oxygen. In addition, we note that VS of

Nanofluidic Transport in Branching Nanochannels gases is affected by the mixture composition; compared with the pure phase, for the oxygen in the mixture, its VS is increased, and for the nitrogen in the mixture, its VS is slightly decreased. This is understandable because, in the current case, the traffic in the evacuation branch is mainly intended for the relatively larger nitrogen molecules, forcing a decent amount of oxygen molecules to the screening end although there is a larger energy barrier. With a proven effective sieve with LE ) 6.25 Å and LS ) 6.025 Å, multiple simulations are performed as the volume fraction of O2 in the mixture is varied from 0 to 100%. As shown in Figure 3b, the sieve keeps a high rejection rate of N2 on the screening side, while VS for O2 is moderately reduced with increasing volume fraction of O2 in the mixture. The latter is again attributable to the traffic of N2 in the evacuation side. Very importantly, if the gas mixture collected from the evacuation branch is recycled, the process of purification may be expedited by the fact that less O2 in the mixture causes less O2 flowing to the evacuation branch, and eventually highly purified N2 can be obtained from the evacuation outlet. In this case, the two gas components can be totally separated after four to five cycles of pushing evacuated gas for screening process. In the above discussions, the size difference between the two valves is set at a moderate value, with which LS,Cr is identified for each pure gas phase and a corresponding molecular sieve for the gas mixture is successfully constructed. If LE - LS is variable, the screening performance could be substantially influenced. In Figure 3c, LS is fixed to be 6.025 Å while LE is perturbed around 6.25 Å, to examine the performance of the molecular sieve for an originally 50%-50% N2/O2 mixture. As LE gets smaller, in the screening side, the nanochannel retains a high rejection rate of N2, yet the productivity of O2 is reduced. When LE is larger, relatively more O2 may be produced in the screening branch, but it may be blended with more N2. This represents a trade-off between efficiency and quality of the sieve that requires further design/optimization investigations. On the basis of the above investigations, in particular the distinct LS,Cr for fluids, it is possible to build a tunable molecular sieve for separating multiple gas/fluid components, first the smallest, then the second smallest, one by one to the largest, finally. A gas mixture composed of equally fractioned H2, O2, and N2 is studied as an illustration. The first objective is to reject O2 and N2 from the screening branch, i.e., having their VS as low as possible, while keeping a relatively high VS for H2. Figures 2 and 3c suggest that a gap size of LS,Cr ) 5.66 Å could work well for screening the second largest molecule, O2, from the H2/O2/N2 mixture. The design is validated by results shown in Figure 4. At the first Y-junction where LS is constrained to be 5.755 Å, VS for O2 is already controlled below 5%, while that for H2 is as high as 40%. Purified H2 is successfully produced at the screening outlet. With four to five more cycles, a two-component mixture of O2 and N2 can be generated which may be used in the next round of separation. In the second sieve setup, LE ) 6.25 Å and LS ) 6.025 Å is proven to work well for evacuating N2 from the N2/O2 mixture, and a repeated circulation through such junction will yield purified N2 and O2, respectively. Conclusion MD simulations are employed to study the fundamental partitioning and screening behaviors of nanofluids at the junction of branching nanochannels, and to demonstrate the feasibility of a tunable Y-junction molecular sieve system for separating gas mixtures composed of multiple phases. For one of the four

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Figure 4. Partitioning and screening characteristics of a three-phase mixture, O2/N2/H2, through the Y-junction nanochannel. LE is fixed to be 6.25 Å, and LS is varied between 5.665 and 6.025 Å.

representative pure gas phases (H2, O2, CO2, and N2), the volume fraction flowing to the overdeformed (screening) branch, VS, is evaluated when the two valve sizes, LE and LS, are varied in wide ranges. If LE - LS is fixed, with increasingly small valve sizes, the VS value first quickly reduces and then gradually converges to 0%. A critical valve size can be identified for effectively rejecting one type of gas molecule, which is related to the molecular size, mixture composition, and LE - LS. The critical valve size is different for different molecule sizes, which inspires the optimized design of a molecular sieve that could effectively screen larger molecules (which will exist from the evacuation channel) and yield a high passing rate of smaller molecules (via the screening valve). The designed molecular sieve holds a superior performance in the full range of mixing ratios of examined gases. Also, owing to the “traffic jam” caused by larger molecules, higher productivity (VS) is achieved when the smaller molecules take a smaller fraction in the mixture, which could expedite the process of completely separating the components through several iterations. A balance between efficiency and quality needs to be optimized by adjusting the size difference between the two valves. A template of sorting a three-phase mixture is proposed on the basis of the above design principles and validated by simulations. Acknowledgment. The study was supported by the National Science Foundation under Grant No. CMMI-0643726. L.L. acknowledges the support of the Founder’s Prize, through the American Academy of Mechanics, sponsored by the Robert M. and Mary Haythornthwaite Foundation. References and Notes (1) Whitby, M.; Quirke, N. Nat. Nanotechnol. 2007, 2, 87. (2) Holtzel, A.; Tallarek, U. J. Sep. Sci. 2007, 30, 1398. (3) Mattia, D.; Gogotsi, Y. Microfluid. Nanofluid. 2008, 5, 289. (4) Schoch, R. B.; Han, J. Y.; Renaud, P. ReV. Mod. Phys. 2008, 80, 839. (5) Fornasiero, F.; Park, H. G.; Holt, J. K.; Stadermann, M.; Grigoropoulos, C. P.; Noy, A.; Bakajin, O. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 17250. (6) Chen, X.; Surani, F. B.; Kong, X.; Punyamurtula, V. K.; Qiao, Y. Appl. Phys. Lett. 2006, 89, 241918. (7) Guenes, S.; Sariciftci, N. S. Inorg. Chim. Acta 2008, 361, 581. (8) Gyurcsanyi, R. E. TrAC, Trends Anal. Chem. 2008, 27, 627. (9) Healy, K.; Schiedt, B.; Morrison, A. P. Nanomedicine 2007, 2, 875.

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