Cosolvent impurities in SWCNT nanochannel confinement: length

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Cosolvent impurities in SWCNT nanochannel confinement: length dependence of water dynamics investigated with atomistic simulations Priti Roy, Brataraj Ghosh, Prathit Chatterjee, and Neelanjana Sengupta J. Chem. Inf. Model., Just Accepted Manuscript • Publication Date (Web): 25 Mar 2019 Downloaded from http://pubs.acs.org on March 25, 2019

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Cosolvent Impurities in SWCNT Nanochannel Confinement: Length Dependence of Water Dynamics Investigated with Atomistic Simulations

Priti Roy,1# Brataraj Ghosh,1# Prathit Chatterjee2 and Neelanjana Sengupta1* 1Department

of Biological Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur 741 246, India

2Advanced

Polymer Lab in association with Polymer Research Centre, IISER Kolkata

ADDO ADDITIVES MFG. PVT. LTD., 201/A, Nadibhag 2nd lane, Madhyamgram, Kolkata 741 246, India

* Correspondence: [email protected] #

These authors contributed equally

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ABSTRACT The advent of nanotechnology has seen a growing interest in the nature of fluid flow and transport under nanoconfinement. The present study leverages fully atomistic molecular dynamics (MD) simulations to study the effect of nanochannel length and intrusion of molecules of the organic solvent, hexafluoro-2-propanol (HFIP), on the dynamical characteristics of water within it. Favorable interactions of HFIP with the nanochannels comprised of single-walled carbon nanotubes traps them over timescales greater than 100 ns, and confinement confers small but distinguishable spatial redistribution between neighboring HFIP pairs. Water molecules within the nanochannels show clear signatures of dynamical slowdown relative to bulk water even for pure systems. Interestingly, the presence of HFIP causes further rotational and translational slowdown in waters only when the nanochannel dimension falls below a critical length of 30 Å. The enhanced slowdown in presence of HFIP is quantified from characteristic relaxation parameters and diffusion coefficients in the absence and presence of HFIP. It is finally seen that the net flow of water between the ends of the nanochannel shows a decreasing dependence with nanochannel length only when the number of HFIP molecules is small. These results lend insights into devising ways of modulating solvent properties within nanochannels with cosolvent impurities.

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Introduction Concurrent with advances in nanotechnology, the last two decades have observed a growing interest in fluid transport within molecular confinement1–4. Such studies are valuable in the design of controlled transporters within micro- and nano-fluidic devices. In general, phase, structural and dynamical and characteristics of fluids under confined geometries are different from those in bulk5– 7. It has been established that the spontaneous entry of a fluid such as water within the confines of carbon nanotubes (CNTs) is favorable thermodynamically8. Experimental studies demonstrate that CNTs confer a fluid flow rate enhancement of a few orders of magnitude over those predicted within the hydrodynamic framework9,10. In the case of water, these observations are well supported by theoretical considerations, and can be explained by the strong propensity of hydrogen bonding between water molecules, a depletion layer at the water-CNT interface, and an effective sharp reduction in the frictional coefficient due to the curvature of the CNT surface11–13. In addition to manifold ramifications in nano-technological applications, understanding water flow under confinement is of crucial importance in biology, in large part due to the vast landscape of its functions in maintaining charge balance and homeostatis across the cellular membrane14–16. The ability of molecular dynamics (MD) simulations to connect atomic-level information with measurable quantities has been leveraged extensively to probe solvent behavior within axial nano-channels. MD simulations enable examination of the influence of intrinsic CNT characteristics as well as the application of non-equilibrium effects on flow properties8,17,18. It is observed that confined water shows bulk-like properties beyond CNT diameters of 1.4 nm8. It has been suggested that solvent characteristics within CNT is associated with thermal fluctuations of the connected bath19. Flow control has primarily been achieved by applying pressure or an electric field along the axial direction20,21. It is noticed that the flow is markedly enhanced over those yielded by the no-slip Hagen Poisseuille relationship9,10,19. Interestingly, it has been reported that surface roughness and introduction of defects affects water flow associated with CNTs22,23. Furthermore, the presence of ions and organic co-solvents have differential effects on water flow. While presence of salts can drive osmotic flow through CNTs separating compartments with differential concentration24, interactions of CNT aromatic rings with cations can hinder the effective flow of water25. In contrast, hydrophobic methane and the polar methanol molecules fully displace water in a step-wise fashion to enter CNTs of narrow diameter and form single chains or biwires within26,27. Simulations with urea indicate the molecule’s preferential interaction with CNT, resulting in structured flow and markedly longer lifetimes over water28,29. These results suggest that tuning molecular interactions within the CNT cavity could be leveraged to control water transport through nanochannels. Characteristics of confined water are distinct from those in the bulk phase3,30–32. Studies of these differences have several important bearings, including the role of biological water under confinement and in the design of micro- and nanofluidic devices. Water within nanoscalar confinement can be slower than bulk water depending on interfacial geometry and physico-



chemical nature of the confining surface33–36. MD simulations show that slowdown in both translational and orientational dynamics sets in at nanochannels below a critically low diameter37. Yet, combined MD simulations and density functional theory (DFT) studies show that water retains its bulk-like hydrogen bonding network even under extreme confinement38. Water localization and ordering is found to depend on the nature of the chemical environment within the confinement38,39. Anomalous effects and liquid-liquid phase transitions of water confined in CNTs are reported to shift to lower temperatures40. In the present work, we leverage fully atomistic MD simulations to investigate how the presence of an organic molecule, namely the fluorinated alcohol hexafluoro-2-propanol (HFIP) affects the equilibrium characteristics of water within nanochannels connecting single-walled carbon nanotubes (SWCNTs) of variable length that connect aqueous reservoirs. HFIP is a versatile organic solvent41, and moreover, is frequently used to tune solvent effects on biomolecular structure and dynamics42–45. The trifluoromethyl (CF3) groups present in HFIP have a propensity for favorable interactions with aromatic carbons46,47. Our simulations show that HFIP enters the SWCNT axial cavity spontaneously by replacement of water molecules, exhibits a retarded orientation inside, and unlike water, does not exit the channel on nanosecond timescales. These characteristics prevent its lateral association and molecular wire formation within the SWCNT nanochannel. In this context, therefore, we are able to treat HFIP as a molecular contaminant within the SWCNT and evaluate its influence on water dynamics as a function of nanochannel length. Our investigations show that in the absence of the molecular contaminant, the slowdown in translational and rotational dynamics of confined water over bulk water is largely independent of nanochannel length, and the diffusion coefficients calculated within the GreenKubo framework show only small variation with length. Intrusion and confinement of HFIP molecules brings about a further, distinct slowdown only for water molecules within nanochannels of lengths shorter than 30 Å; the diffusion coefficients do not change significantly within longer nanochannels. We find that for low HFIP number, the equilibrium water flow decreases with channel length in a manner similar to that obtained with external effects.

Methods System setup Nine armchair SWCNTs of (10, 10) chirality and diameter of 13.6 Å, with varying length (L) were generated with using Visual Molecular Dynamics (VMD)48. We point out that the SWCNT diameter chosen is nearly amenable to bulk-like characteristics of confined water8 . The SWCNT lengths (L) chosen were 10 Å, 15 Å, 20 Å, 25 Å, 30 Å, 35 Å, 40 Å, 45 Å, and 50 Å. The axis of each SWCNT was made parallel to the z-axis of the coordinate systems, with its mid-point coinciding with the origin. Each SWCNT end was combined with a square graphene sheet measuring 10 Å on each side, with the graphene plane perpendicular to the SWCNT axis. The


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nanotube and sheets were held fixed with harmonic forces of 20 kcal mol-1 Å-2. A well-equilibrated water reservoir containing 2322 TIP3P49 water molecules was added to each side of the graphene sheet to generated systems that were purely aqueous (designated ‘pure’ systems). In addition, a separate equilibration was carried out of a solvent box of same dimensions but with an appropriate number of waters replaced with 27 hexafluoro-2-propanol (or HFIP). Prior to incorporation in the systems, each solvent reservoir was first independently equilibrated for several nanoseconds in the isothermal-isobaric ensemble at a temperature of 300 K and a pressure of 1 bar. Accordingly, nine systems with a water-HFIP equilibrated solvent reservoir on one side and a pure water reservoir on the other side were generated (designated ‘mixed’ systems). Representative snapshots of a ‘pure’ and a ‘mixed’ system for L = 25 Å is depicted in Figure 1. Simulation details Graphene and SWNT carbon atoms were modeled as the sp2 hybridized carbon atoms of the CHARMM22 force field50,51 and the HFIP force field reported by Fioroni et al were used52. We point out that these parameters have been used in conjunction with standardized force fields and water mixtures in previous simulation studies42,43,53,54. The NAMD 2.9 simulation package was used55. Energy minimizations of 15000 steps were first performed for each system using the conjugate gradient method, followed by MD simulations of 120 ns in the isothermal-isobaric (NPT) ensemble at a constant temperature of 300 K and a constant pressure of 1 bar. Orthorhombic periodic boundary conditions were applied. The nanotube axis was aligned along the system’s zaxis, and the origin coincided with the system’s center of mass. Periodic boundary conditions (PBC) were used. The PBC size in the z-direction was set to be several times the system size in the z-direction, ensuring that the water-HFIP reservoir does not interact with the pure water reservoir in the mixed systems. This approach is similar to those applied in earlier simulations of nanochannel and membrane bilayer systems with separated solvent reservoirs56,57. A cut-off of 12 Å was used for non-bonded interactions with the smoothing starting at 11 Å. Particle mesh Ewald (PME) was used for the long-range electrostatics calculation58. Constant temperature was maintained using Langevin Dynamics with a collision frequency of 1 ps-1, and constant pressure using by Nosé-Hoover Langevin piston method59. Lengths of the bonds involving hydrogen atoms were constrained using the SHAKE algorithm60. Single trajectories were generated for each of the system using a timestep of 2 fs, with coordinates and velocities saved every 1 ps. In case of 10 Å mixed system, another trajectory of 250 ns was generated with 2 fs of timestep and snapshot saved every 1 ps. For the autocorrelation analysis, four short trajectories were saved every 100 fs, over four 400 ps windows, starting at 86 ns, 100 ns, 110 ns and 120 ns of the parent trajectory. In addition, one pre-equilibrated trajectory over 400 ps windows, saved every 100 fs, were generated beginning 8 ns of the parent trajectory for 20 Å mixed system. The number of HFIP molecules and water molecules were constant over these short trajectories. Trajectory analyses



VMD was used for all visualizations48. Normalized autocorrelation functions were calculated by averaging over multiple time origins, and over multiple molecules, using high frequency trajectories saved over specified time windows mentioned in simulation details. This approach is routinely adopted in MD simulation studies of solvent dynamics61–64. See SI for details of solvent rotational relaxation (𝑃2(𝑡)); mean squared displacement (〈(𝑧(𝑡) ― 𝑧(0))2〉); velocity autocorrelation functions (𝐶𝑣𝑂(𝑡)).

Results I. Characteristics of nanochannel filling Consistent with previous reports, we find spontaneous entry of water molecules within a few picoseconds of the start of the simulations in all pure and mixed systems of this study. On the average, each nanochannel of the mixed systems is filled by 1.5 waters per Å of SWCNT within a few picoseconds of the start of the simulations. However, early entry of water is not accompanied by co-entry of HFIP in the mixed systems. In Figure 2, we present the water occupancy number (Nw) and the HFIP occupancy number (NHFIP) as a function of simulation time for the simulation of each CNT system. HFIP is found to enter the CNT nanochannels one molecule at a time and display an overwhelmingly high probability to stay within. The corresponding Nw plots demonstrate that each HFIP intrusion leads to a step-wise expulsion of water molecules from the nanochannel that appears more pronounced in the shorter nanochannels. We point out here that for the pure systems, the number of water molecules after equilibration in the pure system is consistent with theoretical estimates using the Lennard-Jones parameter σCO involving the CNT-water oxygen interaction65 (see Table 1). On the average, 6 water molecules are expelled from the nanochannel at the entry of one HFIP molecule. We note that any transient exit of an HFIP molecule occurring at the end of the nanochannel is found to be followed immediately by a reentry event. Overall, the displacement of water molecules by HFIP from the nanochannel interior is irreversible within timescales of tens of nanoseconds. Interestingly, no HFIP molecule is expelled into the pure water reservoir at the other end. This phenomenon is corroborated by one longer trajectories of the mixed systems (250 ns for 10 Å systems), presented in Figure S1. In Figure 3, we present the z-coordinate of the center of mass of each HFIP molecule for the nanochannel of three representative lengths. We observe a large fluctuation in the z-coordinate, indicating the tendency of each molecule to rapidly traverse the confines of the nanochannel in the axial direction. It is noteworthy that the z-coordinate of no two molecules is identical at the same instance, indicating that unlike the water molecules, the HFIP molecules do not occupy positions that are lateral to each other. Furthermore, the apparent randomness in the z-coordinate indicates that unlike other co-solvents reported earlier, HFIP does not obey a single-file flow, but rather has a high tendency to positionally fluctuate within the longitudinal confines of the nanochannel.


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II. HFIP interaction with the nanochannel The tendency of spontaneous entry of organic co-solvents into CNT nanochannels with water displacement has been rationalized in earlier studies with their strong interactions with the CNT and via lowering of the thermodynamic cost for their solvation. In Figure S2, we report the interactions with the entrant HFIP molecules with 1 Å length segments of the CNT over the last 40 ns of the simulation for 3 representative systems; the interaction with the waters within the nanochannels are shown as well. The data is presented as averages for each water and HFIP molecule within. Additionally, we report distributions of the total interaction strength of all individual HFIP molecules with the nanochannel; see Figure S3. We note that on average, an HFIP molecule interacts more strongly with the CNT compared to a water molecule in the inner segments by about 3.5 kcal mol-1. As mentioned earlier, trifluoromethyl groups are shown to have highly favorable interactions with aromatic groups in previous studies. This emerges from the breakup of the interactions of the CNT with chemical groups of the HFIP molecule presented in Table 2, wherein the trifluoromethyl groups are noted to be responsible for the bulk of the favorable interactions. Spatial pair correlation functions indicate that Cc pair distances in pure HFIP have a first and second maximum at about 4.3 Å and at a distance between 5 to 9 Å, respectively52. In HFIPwater mixture in the isotropic bulk phase, the second maximum gains growing prominence over the first with increasing dilution. In this light, we estimated the probability distributions of the distance between the central carbon atoms (Cc) between HFIP molecules that form a nearest neighbor pair within the confines of the nanochannel; corresponding distributions were also estimated for distance between Cc and water oxygens within the nanochannel. We find that the CcCc distance shows bimodality when the number of water molecules within the channel is high, commensurate with lower number of HFIP molecules under confinement. On the other hand, the Cc-O has a single peak. An interesting pattern of results, depicted in Figure 4, emerge from comparing normalized probability distributions over different CNT lengths. For the shortest CNT of 10 Å length, the Cc-Cc distance probability is maximum at about 5 Å, the Cc-O distance distribution is the broadest with a long tail extending to about half the length of the nanochannel. For the CNT of 20 Å length, first peaks in the Cc-Cc distribution at about 4.5 Å though the second peak has a marginal shift to higher distances; the Cc-O peaks at the same distance of ~3.5 Å as the shortest CNT system For CNTs of longer lengths, the second peak in the Cc-Cc distribution gains prominence but is broader and generally shifts to the right. For the 40 Å system, the second peak occurs at about 6 Å, while there is a noticeable shoulder at this distance for the 50 Å system. Importantly, for the systems with longer CNTs, the Cc-O peak are sharp at ~3.5 Å with no tail at higher distances. This analysis shows that the increased solvation tendency of HFIP with nanochannel length disrupts the spatial correlation between the molecules (see Figure 5). For insights into the effect of HFIP confinement on its flipping tendency, we calculated the normalized orientational time correlation function (P2(t), as described in SI for HFIP) within the channel and over multiple time origins as described in Methods. This result is reported in Figure 7 Environment ACS Paragon Plus


6, averaged over four data sets (See Figure S4), and compared with equivalent functions calculated for HFIP in the reservoir. While a marked slowdown in the rotational tendency is noted for HFIP within confinement, we observe, in general, a greater slowdown with increase in the number of entrant molecules per unit length. This value (NHFIPʹ) is reported in Table S1 along with the average times (τe) required for the correlation functions to reach (1/e) of their values at t = 0. We note at least a six-fold increase in τe for all the nanochannel systems over the reservoir value 2.6. However, the length of the channel appears to have a slight influence, with lower increases in the longer channels, possibly due to greater solvation and a lesser degree of confinement. Collectively, these results demonstrate that HFIP molecules have negligible tendency to exit the confines of the nanochannel, and show low inter-molecular spatial correlation, and preference for solvation over clustering. Furthermore, they do not traverse as a single file of molecules along the nanochannel axis while demonstrating a slowed re-orientational tendency.

III. Water dynamical characteristics The dynamical characteristics of water at interfaces of nanoscopic dimensions and under nanoscopic dimensions deviates markedly from those observed in bulk water. Signatures of the extent of deviation from bulk behavior, estimated frequently by leveraging atomistic MD simulations, provide valuable information about the system’s properties. Herein, we report the results of our investigations of the dynamical characteristics of water within the nanochannels with varying CNT length and varying number of HFIP intrusions. In Figure 7a-c, we depict the normalized orientational time correlation function (P2(t), as described in SI for water) calculated for water within the nanochannel confinement for systems that do not contain HFIP, along with the corresponding function for bulk water at the same temperature. A noticeable slowdown in rotational dynamics is observed for the confined water. Interestingly, in the absence of any cosolvent impurities, the slowdown shows only marginal variation with the nanochannel’s length. This is confirmed by examining the values of the time, τepure, taken for P2(t) of these ‘pure’ systems to reach a value of (1/e), reported in Table 3. In the absence of HFIP, the average value of τepure is 0.65±0.02. Figs 7d-f depicts the P2(t) of water molecules in the systems containing HFIP which is averaged over four different data sets (see Figure S5). Unlike the pure systems, we observe that the presence of confined HFIP molecules confers a broad divergence between the systems in the pattern of P2(t); the corresponding τemix, the time taken to reach a value of (1/e), are reported in Table 4. For the nanochannels with CNT length between 10 and 25 Å, τemix is greater than τepure by a factor of 1.58 and 3.81; for channels of longer length, this factor varies between 0.11 and 0.65. Thus, the intrusion of the co-solvent impurities confers a noticeable length dependence on the rotational dynamics of the water molecules within the nanochannel’s confinement, wherein channels 30 Å and longer show the least slowdown.


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We next examined the mean squared displacement , in the direction parallel to the channel axis. The results, compared with corresponding for isotropic bulk water, are presented in Figure 8 (a-c for pure system; d-f for mix system that is averaged over four data set). The data at four different time of each mixed system is shown in Figure S6 of SI. Similar to the observation in rotational dynamics, the translational dynamics parallel to the nanotube axis is slower than the dynamics in bulk water. Furthermore, the longitudinal translational dynamics within the channel shows low sensitivity to the length of CNT in the absence of HFIP; the intrusion and confinement of HFIP, however, brings about divergent behavior in the longitudinal translational dynamics within the systems. For comparison, we report the slopes of the between 9 and 10 ps by fits of the corresponding data to a straight line; these values for the pure (mpure) and the mixed (mmix) systems are reported in Table 3 and Table 4 respectively. We find that mpure varies between 0.53 and 0.76, showing little variation and no distinct dependence on the CNT length. On the other hand, mmix varies between 0.09 and 0.11 for CNT lengths between 15 and 25 Å, and increases markedly to higher values between 0.29 and 0.54 from 30 Å onwards. We do note, however, that the shortest nanochannel of length 10 Å describes an anomalous behavior with an enhancement in the longitudinal translational dynamics of water with the intrusion of HFIP; the mmix for this system is 0.50. We further investigate the velocity autocorrelation function (VACF) of the confined water molecules as a function of channel length and the number of confined HFIPs. As discussed earlier, the VACF describes the collective translational dynamics of a solvent and yields the diffusion coefficient within the Green-Kubo formalism. In Fig 9, we depict the VACF calculated for the water molecules within the simulated channel for the pure and the mixed systems; for the latter, averages calculated from four time windows are presented (see Figure S7 for individual results). The data have been compared with the VACF for bulk water. The diffusion coefficient values obtained for the pure systems (Dpure), and the averages for the mixed (Dmix) systems are reported in Table 3 and Table 4 respectively. As evident in Figure 9a-c, the variation in the VACF is minor and shows no clear trend with nanochannel length in the absence of HFIP; under these conditions, the average value of Dpure is (3.29±0.52) x10-5 cm2s-1 compared to a value of about 5.9 x10-5 cm2s-1 for bulk water. With the intrusion of HFIP, however, the diffusion coefficients of water show a variation with channel length, with Dmix changing by a factor varying from 0.04 to 0.21 over the average Dpure. This analysis shows that changes in the diffusive properties of water within the nanochannel with the inclusion of trapped co-solvent impurities is dependent on the longitudinal dimensions. For insights into the apparently anomalous translational behavior observed at the shortest nanochannel system, we calculated the number of HFIP molecules per Å of nanochannel axial dimensions corresponding to the trajectory segments used for the autocorrelation functions. This value, NHFIPʹ, is included in Table S1. We notice that NHFIPʹ is markedly larger for the shorter channels with values between 0.3 and 0.4 for CNT lengths 25 Å and below; this value is largest for the shortest CNT length of 10 Å. As discussed, the values of Dmix for these systems deviate the



most from the corresponding values of Dpure. For the nanochannels of lengths between 30 and 50 Å, NHFIPʹ varies between 0.09 and 0.23, commensurate with Dmix values that largely remain invariant over the corresponding Dpure values. In Figure 10, we have plotted the ratios (τepure/τemix), (mpure/ mmix) and (Dpure/Dmix) as a function of the SWCNT axial length. For each quantity, a clear deviation in the trend occurs at an axial length of 25 Å, indicating a critical changeover at such a nanochannel length for systems with the chosen co-solvent. For additional insights, we estimated the P2(t) and the VACF for the mixed system of 20 Å length, over a short time segment starting at 8 ns of the simulation, before equilibration is reached (see Supporting Information). In this short time window, the value of NHFIPʹ is only 0.1, compared to the value of 0.3 after equilibration. As seen in Fig S8 and Table S2, P2(t) shift towards more bulk-like values with an increase in τemix to 1.60, and an increased (τepure/τemix) of 0.41. Correspondingly, the Dmix obtained from the VACF increases to 3.68 cm2 s-1, and (Dpure/Dmix) lowers to 0.89.

Discussion and Conclusion In this exposition, we report the entry of an organic co-solvent, hexafluoro-2-propanol (HFIP) from a reservoir into SWCNT nanochannels of fixed diameter and varying lengths by displacement of water molecules, and the associated dynamics of the confined waters upon attainment of equilibrium. While HFIP entry is spontaneous and results in equal water expulsion per entry in each nanochannel, their spatial distributions depend on the length of channel, with HFIP spaced closer together in shorter nanochannels of length up to 25 Å. Despite highly favorable interactions with the SWCNT walls, HFIP describes random axial movement without evidence of lateral configurations involving more than one molecule. Interestingly, the HFIP molecules do not exit from the channel within the simulated timescales, even into the bottom water reservoir. Such confinement of HFIP confers dynamical consequences on the water molecules that co-exist within the nanochannel. The re-orientational dynamics of water, while distinctly slower than bulk, are found to vary negligibly with nanochannel length in the absence of co-solvent. Entry of HFIP triggers a general slowdown on the re-orientational dynamics, especially on the shorter channels of lengths up to 25 Å. The mean square displacement along the axis is also slower, except at the shortest length. The diffusion coefficient for each system is estimated from the velocity autocorrelation function using the Green-Kubo formalism. As with the reorientation dynamics, the diffusion is slowed down significantly up to a channel length of 25 Å, above which differences with systems without HFIP are not distinguishable. Moreover, larger fluctuations in diffusion coefficients for water in the presence of HFIP within shorter nanochannels are observed. The plausible reasons for these observations could be the smaller number of water molecules within the shorter nanochannels in the presence of HFIP (see NHFIPʹ values in Table S1). Our results may lend useful insights into design of manipulating flow control within nanochannels and design of nanofluidic devices. Herein, we note exiting reports that show that an exponential decrease in flow rate with length of a nanochannel under the effect of external forces19,21. For a preliminary understanding, we have estimated the average flow rate across the


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mixed systems as a function of length with varying number of HFIP. This calculation, described in Supporting Information., considers metastable time-windows corresponding to a constant number of HFIP molecules within the channel. As seen in Figure S9, the average flow rate decreases with increasing nanochannel length is noticeably sharp when HFIP intrusion is restricted to 3 molecules or lower. For number of confined HFIPs exceeding this number, the flow shows little variation, if any, with length. In the light of emerging insights on the mechanistic aspects of solvent permeability across channels66,67, our continuing work will focus on the correlation between effective chemical potential difference owing to HFIP concentrations across the nanochannel as a function of nanochannel length. Detailed studies are further necessary to correlate how factors such as temperature may play a role in these observations, and how combining molecular impurities with external effects such as pressure and electric field may offer better modulation of the flow rate.

Acknowledgements P.R acknowledges CSIR for her Junior Research Fellowship. B.G acknowledges UGC for his Junior Research Fellowship. N.S acknowledges Science and Engineering Research Board (SERB) for the funds used to procure computational resources (EMR/2016/001108). The authors thank Brij Kishore Agrawal for his initial contributions; Dr. Saikat Dutta Choudhury and Sneha Menon are thanked for help during manuscript preparation.

Supporting Information Calculation details of the confined water number density (Nwpure) within the nanochannel, evolution of HFIP and water number in nanochannel over 250 ns simulations for 10 Å mixed system; interaction energy of 1 Å segments of SWCNT with confined HFIP and water; probability distribution plots of HFIP and SWCNT; NHFIP, NHFIPʹ and τe values corresponding HFIP rotational relaxation for each mixed systems; comparison of water P2(t) and VACF for 20 Å mixed nanochannel system with varying NHFIP′; τe and Dmix values for 20 Å mixed nanochannel system with varying NHFIPʹ; flow rate with varying nanochannel length for different NHFIP numbers.

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Figure 1. Snapshots of a representative a) pure system with only water in both top and bottom reservoirs, and b) mixed system with water-HFIP mixture in top reservoir and only water in bottom reservoir. Planar graphene sheets and the armchair single-walled carbon nanotube are depicted in light blue; water molecules are depicted in red (oxygen) and white (hydrogen); HFIP molecules are depicted in green (fluorine), purple (carbon), red (oxygen) and white (Hydrogen). Systems with channel length of 25 Å are depicted a few picoseconds after start of simulations.


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Figure 2. Number of HFIP (NHFIP) and water (NW) molecules as a function of simulation time for each of the mixed systems. NW are presented as running averages over 1 ns window; corresponding data for each snapshot is shown in light gray.



Figure 3. The z-coordinate of confined HFIP molecules from their time of entry into the nanochannels of the mixed systems of length a) 20 Å (cyan), b) 30 Å (purple) and c) 50 Å (red). The coordinates are presented as running averages over 1 ns window; corresponding data at each snapshot is shown in light gray. Positive and negative z-coordinates indicate positions above and below the mid-point of the SWCNT axis, aligned parallel to the z-axis and whose center coincides with the origin of the coordinate system.


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Figure 4. Top row. Normalized probability distributions of the distance between central carbon atoms of nearest pairs of HFIP molecules within the nanochannels. Bottom row. Normalized probability distributions of the distance between central carbon atom of HFIP and the nearest water oxygen within the nanochannels. Data correspond to the final 40 ns of simulation.



Figure 5. Representative transverse view of the solvent molecules inside the nanochannel of a representative a) pure and b) mixed system at the end of 80 ns simulation. Systems with SWCNT length of 20 Å is shown. For visualization, one half of the channel parallel to the axis is not shown.


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Figure 6. Rotational autocorrelation function of the HFIP molecules within the confinement of the nanochannels averaged over four trajectories at+ different time windows saved at high frequency. Broken lines describe the rotational autocorrelation functions for HFIP molecules in the top reservoir. See text for details of calculation.

Figure 7. Rotational autocorrelation function of the water molecules within the confinement of the nanochannels. Top row (a-c) shows data for the pure systems. Bottom row (d-f) shows data averaged over four trajectories over different time windows saved at high frequency for the mixed systems. Broken lines describe the rotational autocorrelation functions for bulk water. See SI. for



details of calculation.

Figure 8. Mean squared displacement along the channel axis of the water molecules within the confinement of the nanochannels. Top row (a-c) shows data for the pure systems. Bottom row (d-f) shows data averaged over four trajectories over different time windows saved at high frequency for the mixed systems. Broken lines describe the mean squared displacement along one spatial direction for bulk water. See SI. for details of calculation.


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Figure 9. Velocity autocorrelation functions of water oxygens within the confinement of the nanochannels. Top row (a-c) shows data for the pure systems. Bottom row (d-f) shows data averaged over four trajectories over different time windows saved at high frequency for the mixed systems. Broken lines describe the velocity autocorrelation functions of bulk water. See text for details of calculation.



Figure 10. Ratios of the a) τe, b) m, and c) D between pure and mixed systems with varying nanochannel length. See text for details.


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System

Nwpure

Calculated using eqn.1

10 Å

23.63 (1.7)

24.18

15 Å

35.67 (2.04)

36.27

20 Å

47.87 (2.18)

48.36

25 Å

59.52 (2.61)

60.45

30 Å

71.54 (2.62)

72.54

35 Å

83.54 (2.75)

84.63

40 Å

95.49 (3.77)

96.73

45 Å

107.38 (3.12)

108.82

50 Å

119.10 (3.36)

120.89

Table 1. Average water number (Nwpure) and the calculated water number from eqn. 1, confined within the nanochannel for each of the pure system. Standard deviations shown in braces. [See SI info for details]



Page 26 of 29

System

EHFIP

ECF3

EC2OH

EOH

10 Å

-11.72 (1.67)

-8.97 (1.25)

-2.43 (0.56)

-1.15 (0.36)

15 Å

-13.16 (0.81)

-10.28 (0.74)

-2.56 (0.39)

-1.23 (0.27)

20 Å

-13.56 (0.83)

-10.25 (0.63)

-2.98 (0.47)

-1.5 (0.33)

25 Å

-13.68 (0.65)

-10.34 (0.5)

-3.01 (0.41)

-1.53 (0.26)

30 Å

-14.45 (0.6)

-10.8 (0.46)

-3.28 (0.55)

-1.68 (0.36)

35 Å

-14.46 (0.47)

-10.74 (0.37)

-3.35 (0.44)

-1.73 (0.3)

40 Å

-14.27 (0.37)

-10.87 (0.32)

-3.03 (0.35)

-1.54 (0.25)

45 Å

-14.25 (0.7)

-10.78 (0.54)

-3.14 (0.63)

-1.63 (0.41)

50 Å

-14.35 (0.39)

-10.8 (0.31)

-3.2 (0.36)

-1.65 (0.23)

Table 2. Mean and standard deviations in the interaction energy of the SWCNT with a confined HFIP molecule (EHFIP), and its CF3 (ECF3), C2OH (EC2OH) and OH groups (EOH), for all mixed systems over the final 40 ns of simulations. Energies are in units of kcal mol-1.


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System

τepure

mpure

Dpure

10Å

0.62

0.59

3.85

15Å

0.68

0.53

3.51

20Å

0.62

0.54

4.27

25Å

0.66

0.76

3.97

30Å

0.69

0.69

3.84

35Å

0.66

0.60

3.4

40Å

0.65

0.64

3.54

45Å

0.65

0.70

3.23

50Å

0.64

0.67

3.87

Table 3. Data from autocorrelation functions of the pure systems. See text for details. Units for τepure, mpure and Dpure are picoseconds, Å2 ps-1, and 10-5 cm2 s-1, respectively.



System

τemix

mmix

Dmix

10Å

3.13 (2.52)

0.50 (0.15)

2.59 (0.28)

15Å

2.53 (0.4)

0.11 (0.06)

3.11 (0.48)

20Å

1.68 (0.29)

0.13 (0.01)

2.71 (0.4)

25Å

2.65 (0.39)

0.09 (0.03)

2.98 (0.79)

30Å

0.78 (0.03)

0.50 (0.05)

3.58 (0.33)

35Å

0.95 (0.1)

0.36 (0.07)

3.43 (0.32)

40Å

1.07 (0.09)

0.29 (0.03)

3.74 (0.23)

45Å

0.72 (0.02)

0.54 (0.05)

3.86 (0.46)

50Å

0.93 (0.02)

0.36 (0.04)

3.63 (0.29)

Table 4. Mean data with standard deviations from autocorrelation functions of the mixed systems. See text for details. Units for τemix, mmix and Dmix are picoseconds, Å2 ps-1, and 10-5 cm2 s-1, respectively.


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“for Table of Contents use only”

Cosolvent impurities in SWCNT nanochannel confinement: length dependence

of

water

dynamics

investigated

with

atomistic

simulations Priti Roy,1# Brataraj Ghosh,1# Prathit Chatterjee2 and Neelanjana Sengupta1*


Cosolvent impurities in SWCNT nanochannel confinement: length

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