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Quantum Coherence and Temperature Dependence of the Anomalous State of Nano-Confined Water in Carbon Nanotubes George F. Reiter, Aniruddha Deb, Yoshiharu Sakurai, Masayoshi Itou, and Alexander I. Kolesnikov J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b02057 • Publication Date (Web): 17 Oct 2016 Downloaded from http://pubs.acs.org on October 20, 2016

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The Journal of Physical Chemistry Letters

Quantum Coherence and Temperature Dependence of the Anomalous State of Nano-Confined Water in Carbon Nanotubes George F. Reiter, 1 Aniruddha Deb,*,2 Y. Sakurai,3M. Itou,3 and A. I. Kolesnikov4 1

Physics Department, University of Houston, Houston, TX 77204, USA, 2Department of

Chemistry, University of Michigan, Ann Arbor MI, 48109, USA, 3Japan Synchrotron Radiation Research Institute (JASRI)/SPring-8, Sayo-cho, Hyogo 679-5198, Japan, 4Chemical and Engineering Materials Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA.

AUTHOR INFORMATION Corresponding Author Aniruddha Deb, [email protected]

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ABSTRACT: X-ray Compton scattering measurements of the electron momentum distribution in water confined in both single walled and double walled carbon nanotubes (SWNT and DWNT), as a function of temperature and confinement size, presented here, together with earlier measurements of the proton momentum distribution in the same systems, using neutron Compton scattering, provide a coherent picture of an anomalous state of water that exists because of nanoconfinement. This state cannot be described by the weakly interacting molecule picture. It has unique transport properties for both protons and water molecules. We suggest that knowledge of the excitation spectrum of this state is needed to understand the enhanced flow of water in cylinders with diameters of the order of 20 Å.

TOC GRAPHICS

KEYWORDS Nano-confined water, Water in Carbon nanotubes, Temperature dependence of nano-confined water, electron momentum distribution, Compton scattering

There has been considerable interest in water confined in carbon nanotubes, as a model for the flow of water in biological channels, and in its own right, as a filtration system due to the super-


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rapid (compared to Poiseuille) flow observed in tubes of the same diameter. Water is usually assumed to be a molecular liquid, the water molecules interacting weakly through hydrogen bonds. Simulations of water in the nanotubes have assumed the molecular liquid picture, and used classical empirical force field models to calculate the flow rates and other properties of the system. It has been shown recently that water confined in Nafion, is in a new state, not describable by the usual picture, with the protons delocalized over distances of the order of 0.20.3 Å, and the electron momentum distribution strongly perturbed from its value in bulk water.1-2 It was conjectured that this state was not specific to Nafion, but is a direct result of confinement, and would occur when water was confined on a scale of 20 Å. We show, for the first time, that this state exists in water confined in carbon nanotubes, and that it is sensitive to both temperature and the size of confinement. This anomalous state exists in water confined in single wall carbon nanotubes (SWNT) of nominal diameter 14 Å and double walled carbon nanotubes (DWNT) of nominal diameter 16 Å. Previous measurements of the proton momentum distribution have shown that there is a strong difference between the SWNT and DWNT systems, with the momentum distribution narrowing in the former case,3 and broadening in the latter1. The temperature dependence of the proton momentum width is also very different, with the width being essentially constant in the SWNTs until the temperature exceeds 230 K, and then broadening, while in the DWNTs the width and shape of the proton momentum distribution changes continually with temperature up to room temperature, in a non-monotonic way. It was conjectured that the strong size dependence of the width of the proton momentum distribution and its size dependent temperature dependence was due to the existence of a quantum coherence length for the motion of the protons. Using x-ray Compton scattering, we show here that the electron momentum distribution shows a temperature dependence and shape of the electron


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momentum distributions that is consistent with the systematic changes in the proton momentum distributions. The scale of these changes is so large that they cannot to be due to independent changes within single molecules, but must require the coherent motion of multiple protons to be of the magnitude observed. The temperature dependence of both the x-ray and neutron Compton profiles are only marginally a result of thermal excitation from the ground state of local vibrations. They arise from structural differences in the low lying states of the system. The temperature dependence, varied as it is, can be a strong clue to understanding the mechanism for the existence of these anomalous low energy states. The transport properties of these states in SWNT and DWNT are also anomalous, and broadly consistent with the anomalous transport in Nafion and reverse micelles.4 The high-quality samples of single walled carbon nanotubes (SWNT) and double-walled carbon nanotubes (DWNT) were prepared by MER Corporation using methods described elsewhere.5-6 The high purity and the narrow variation of the nanotube diameter were quantified by transmission electron microscopy, Raman measurements, and small angle neutron diffraction. The 2-D hexagonal lattices of the carbon nanotube bundles were evident in the neutron diffraction data. The estimated mean tube inner (outer) diameters of SWNT and DWNT were 14±1 Å and 16±3 Å (23±3 Å), respectively. The nanotube ends were opened by exposing the purified material to air at 420°C for about 30 min. The water absorption was controlled by the following procedure7-8: SWNT and DWNT were equilibrated for 2 hours in an enclosed volume at 110°C with deionized H2O; the excess water adsorbed in the exterior of the nanotubes was then evaporated at 35°C until reaching the targeted water mass fraction. In the present work SWNT and DWNT samples were loaded with approximately 11 wt.% of water.


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Our previous proton momentum distribution measurements were done at ISIS on the VESUVIO instrument.1, 3 Three carbon nanotube samples were used, two SWNT and one DWNT, prepared as above. The proton momentum distribution in the SWNT samples, showed no observable change with temperature between 4K and 230K.3 The kinetic energy below 230K was approximately 30% less than that of ice or bulk water at room temperature. There was a large change in the momentum width (kinetic energy) in going from 230K to 300K. The lack of variation of the momentum distribution between 4K and 230K is what one would ordinarily expect if the proton was confined in a local Born-Oppenheimer potential which didn't change significantly due to the motion of the surrounding ions. Indeed, one would expect the lack of variation to persist up to room temperature. Vibrational excitations of the potential in bulk water seen by the proton are on the order of at least 100 mev, and would not be strongly excited. The change in going from 230K to 300K would be rather small, and not the qualitative change observed. We conclude that the change in going from 230K to 300K is a change in the confining potential itself. The proton momentum distribution in the DWNT sample, by contrast, varies continuously and non-monotonically from 4K to 300K, and has kinetic energies that are nearly 30% larger than that of bulk water or ice. In this system, the confining potential, as inferred from the proton momentum distributions, varies continuously. Changes in the confining potential must be due to redistribution of the valence electrons. Such a redistribution can be observed by x-ray Compton scattering, which provides information on the structure of a molecular system via the electron momentum density. We show here that the changes with temperature and nanotube diameter in the electron distribution track the systematic changes in the effective confining potentials, and hence the proton momentum distributions these effective confining potentials were inferred from.


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For an isotropic system as in this case, x-ray Compton scattering provides information on the ground state electron momentum density n(p) through the Compton profile J(pq)9 where the two are related by: 1 = Ω 1 2

where pq is the momentum transfer along q, with pq= (ω – ћq2/2me)/|q|, and ћω and ћq are the transferred energy and momentum respectively. The experiments were performed at the high energy inelastic scattering beam line BL08W, at SPring-8, Japan. The samples were confined in a 3 mm thick Al sample holder, with Kapton windows (10 µm thick) used as the x-ray window and the sample was placed in a vacuum chamber. The measurements were performed with a beam size of 3 mm (H) x 1 mm (V) at the sample, at incident energy of 180 keV, at a scattering angle of 178.3°. Compton-scattered x-rays were detected by a 10-element Ge-solid state detector and the total momentum resolution was q ≈ 0.5 atomic units (a.u.). For this investigation experiments were performed at 10K, 170K and 300K. Temperature-induced changes in the Compton profile are small (a few percent) and hence the data were constantly monitored by checking for consistency, i.e., for variation larger than the statistical accuracy, after every 12 minutes. The samples were also carefully monitored, weighed before and after the measurements, and showed no significant weight change (the weight change was less than 0.5%). To obtain good statistics, the total counts in each raw spectrum under the Compton peak was more than ~5 x 109 counts. The measured spectra were then corrected for the necessary energy dependent corrections, absorption, detector efficiency, and multiple scattering, before converting to the momentum scale utilizing the relativistic cross-section correction.


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Finally the positive and negative momentum sides of the intrinsically symmetric CPs were averaged. The spectra were then subtracted from each other to produce the difference curves shown in the figures. The contribution of multiple scattering in the sample was evaluated by a Monte Carlo simulation and subtracted from the corrected profiles. The subtraction of the signals at different temperatures effectively removes the core contributions, which are not expected to be temperature sensitive over the range of the measurements, so that the difference signals are due to changes in the spatial configuration of the valence electrons, as reflected in the momentum distribution of those electrons.

Figure 1. (Color online) Difference of x-ray Compton profiles for SWNT and temperatures shown in the inset. Amplitude given by axis on left. Solid curves are comparisons with calculations for D replacing H in bulk water, Nygard et. al.,10 and varying O-H distance in alcohol water mixtures, Jurrinen et. al.11 The amplitudes are represented by the axes on right.


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We show in Figure1 the difference x-ray Compton profiles for the SWNT sample between 10K and 170K, 170K and 300K, and 10K and 300K. This is what one would expect from the neutron Compton scattering (NCS) measurements, where there was no observable change in the proton momentum distribution between 5K and 230K. If the proton momentum distribution isn't changing, the effective confining potential isn't either, and hence we would expect to see very little change in the electron distribution. Conversely, if the momentum distribution changes greatly over a relatively small temperature range, it must be due to changes in the effective confining potential, which requires a rearrangement of the valence electrons, and hence significant changes in the difference Compton profile for 170K-300K, as observed. The solid curve labeled Nygard et. al.10 is the same form that was used to fit the Compton profile difference data on Nafion. The shape is that of the difference between bulk D2O and H2O. The solid curve labeled Juurinen et. al.11 is a more recent calculation used to fit the data for the difference between a solution of 5% alcohol and bulk water. It corresponds to all of the O-H bonds in the sample being larger by 0.003 Å. The scales on the right are those in the original publications. Both are purely empirical fits here. The one that seems most appropriate to fit the large difference between 170K and 300K, from the shape, is that of Juurinen et al.11 Comparison of the scales on the left and right shows that the variation at p=0 in our measurements is ~30 times that in theirs. For small changes in the bond length, it has been shown that this variation is linear in the bond length. If that linearity extends to our measurement, the O-H bonds have all stretched (as shown by the sign of the difference profile at zero momentum transfer) by 0.09 Å. We note that because we are doing momentum measurements, the positions of the protons cannot be determined. While, from the shape of the momentum distribution, the protons appear to be in double wells, we cannot tell from our measurements where those wells are with respect


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to the oxygen ions. Neutron diffraction measurements of O-O and O-H correlation functions that could reveal the relative location of the oxygen and hydrogen are not practical for H2O in the nanotubes, because of the small coherent cross-section and the large Debye-Waller factor for the protons. In contrast with Figure 1, we see in Figure 2, that the electron Compton profile changes significantly between 10K and 170 K, as well as between 170K and 300K. This is consistent with the neutron Compton measurements that show the proton momentum distribution of the water in the DWNTs varying continuously with temperature.1 Comparing scales for the calculated curve of Juurinen et. al.,11 again assuming linearity, we would have to conclude that the O-H bonds have stretched a distance of 0.22 Å from 10K to 300K. While this is comparable to the delocalization distance of the protons seen in the NCS experiments, it too large to be encompassed by a model in which the individual molecules retain their integrity and interact only weakly. It is also too large to be calculated by the methods used so far for electron Compton profiles, which assume small deviations from a hydrogen bonded water dimer for the electronic calculation, and small deviations from classical configurations of a collection of water molecules to obtain a distribution of dimer configurations.12 The difference between the proton momentum distributions of the nano-confined state of the SWNT and the DWNT, where the inner diameter goes from an average of 14 Å to 16 Å is remarkable. The differences in the electron momentum distribution are equally remarkable. The maximum amplitude of the 10K-300K difference curve in the DWNT is more than twice that of the same difference curve for the SWNT sample, and the minimum of the curve is shifted from 1.5 a.u. to 1.8 a.u. The changes in the two measurements are broadly consistent. The reduction in the average momentum width of the protons in the SWNT from that of bulk water, and the


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increase of that width for DWNT would imply a more delocalized proton in the SWNT than in the DWNT. One would expect the valence electrons of the system would also be more delocalized in the SWNT system than the DWNT. To the extent that scale of variation with temperature in Figures 1 and 2 reflects the overall scale of the Compton profiles, one would expect to see a narrower variation of the difference profile in the SWNT than the DWNT, as observed. The differences between the SWNT and DWNT results are not unexpected. Classical simulations show that the low temperature structures are very sensitive to the radius, with a single sheet of square ice surrounding a chain of single water molecules for the SWNTs (14 Å),7 but two hydrogen bonded sheets in the case of the DWNTs (16 Å).8 While the classical simulations may not capture the correct configurations, given our results, they do indicate that the local structure in the two systems is likely to be different.


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Figure 2. (Color online) Difference of x-ray Compton profiles for DWNT and temperatures shown in the inset. Amplitude given by axis on left. Comparison with calculations for D replacing H in bulk water, Nygard et. al.,10 and varying O-H distance in alcohol water mixtures, Juurinen et. al.11 The amplitudes are represented by the axes on right.

To explain the sensitivity of the proton momentum distribution to the size of the nanotubes, and the blue shift of the water O-H stretch mode in the SWNTs7 despite the softening of the one particle effective potential in the nano-confined ground state, it was conjectured that correlated motion of the protons exists over distances comparable to the diameter of the nanotubes.3 If the protons do not move independently but are in synchronization over distances of this order, variations in the valence electron density on a particular site can be significantly larger than would be obtained from individual uncorrelated motion, and conversely, a BornOppenheimer surface that supports such correlated motion in the ground state would be expected to have large deviations in the valence distributions from the nearly independent molecule ground state, as observed in both SWNTs and DWNTs. There have been observations by others that we attribute to the distinct properties of nanoconfined water. The abrupt change in the behavior of the nanotube confinement system with nanotube diameter has been observed also in transport measurements.13 Transport of ions through a single nanotube is observed to go in bursts, as a large ion blocks the channel for a time until it leaves the nanotube. While we might expect the magnitude of the blocking current, and the time the ion spends in the channel, to be monotonic functions of the diameter of the channel, they are not. A dramatic increase (approximately six-fold) in the current and a highly irregular dwell time are seen on going from 14 Å to 16 Å diameter nanotubes.13


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NMR measurements of the mean square displacement (MSD) of water molecules in 14 Å nanotubes, just below the freezing point of bulk water show that the displacement scales as t1/2, not t. 14 This was interpreted as single file diffusion, but the structure of the water in the nanotube at this temperature does not support this interpretation. The square ice sheets lining the nanotube channel, with a chain of molecules down the center, which exists, according to classical simulations at low temperatures,7 have melted in favor of a liquid configuration filling the channel by about 200K.15 We assign this result to the properties of nano-confined water when the confinement is on this scale. NMR measurements of water molecules in larger nanotubes, 22 Å and 65 Å average diameters16 show normal MSD, proportional to t for short times, but a slowing down at longer times, consistent with a smaller exponent. The data is not sufficient to obtain an asymptotic exponent for long times. A crossover from bulk to anomalous behavior, with an asymptotic exponent for return times of half the bulk value, occurring at shorter times with smaller confinement scales, is seen also for the proton diffusion in Nafion and reverse micelles.4 The momentum distribution, of either the protons or the electrons, is an equilibrium property of the system. Both are local probes, in the sense that they are determined by one proton or one electron density matrices, and respond to the environment of that particle. The strong and varied temperature dependence seen in the SWNT and DWNT systems indicates that there is low-lying energy states in nano-confined water whose energies are less than that which the tetrahedrally coordinated molecular state preferred in bulk water and ice would have if confined to the same volume. From our measurements, these states are separated by only tens of meV. The direct observation of the local structural changes through the momentum distributions makes it clear that the local structure of these states differs markedly from what one thinks of as a hydrogen bond. The spread of the proton wave function is 2-3 times what it is in bulk water, where the rms


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width is determined primarily by the covalent bond with the donor oxygen. The deviations in the electron momentum distribution are an order of magnitude larger than can be accounted for by plausible changes in the intra and intermolecular configurations of something whose structure resembles bulk water. The response to perturbations of these low-lying states for water flowing through the nanotubes by irregularities in an otherwise smooth cylinder is unlikely to be similar to that of bulk water. It is the momentum carrying excitations from the ground state of nano-confined water that determine the flow rate through the nanotubes. These flow rates in nanotubes of comparable size to those used here have been observed to be 60 times larger than to be expected by imagining the water inside to be bulk fluid with the viscosity of water.17 Efforts to simulate the flow rates with classical empirical molecular models have not been successful in reproducing the experimental phenomenology, and typically get values that are far too large for the flow enhancement factor.18 We see from the work here that as a consequence of the coherent motion of the protons, a fully quantum mechanical treatment of transfer of momentum from the confining surfaces of nano-confined water to the interior is likely to be necessary to understand the properties of water confined on the scale of 20 Å. The flow of ions through biological channels of this size, the transport of protons within cells, where the separation between elements of the cell is of this order, and the flow of water through nano-tubes of comparable dimension, are all determined by the properties of this anomalous state. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]


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Notes The authors declare no competing financial interest. Funding Sources G. Reiter's work was supported by the DOE, Office of Basic Energy Sciences under Contract No.DE-FG02-08ER46486. ACKNOWLEDGMENTS G. Reiter's work was supported by the DOE, Office of Basic Energy Sciences under Contract No.DE-FG02-08ER46486. He thanks Dirar Homouz and Jamal Hassan of Khalifa University for useful conversations and sharing their work prior to publication, we would also like to thank Christian J. Burnham for proving us with the SWNT simulation, shown as a part of the TOC. These experiments were performed with approval of the Japan Synchrotron Radiation Research Institute (JASRI)/SPring-8, Proposal Nos. 2011A1074 and 2015B1098. Work at ORNL was supported by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. We thank Alexander P Moravsky of MER Corporation for supplying the high-purity carbon nanotube samples. REFERENCES 1. Reiter, G. F.; Kolesnikov, A. I.; Paddison, S. J.; Platzman, P. M.; Moravsky, A. P.; Adams, M. A.; Mayers, J. Evidence for an anomalous quantum state of protons in nanoconfined water. Phys. Rev. B 2012, 85, 045403. 2. Reiter, G. F.; Deb, A.; Sakurai, Y.; Itou, M.; Krishnan, V. G.; Paddison, S. J. Anomalous ground state of the electrons in nanoconfined water. Phys. Rev. Lett. 2013, 111, 036803. 3. Reiter, G.; Burnham, C.; Homouz, D.; Platzman, P. M.; Mayers, J.; Abdul-Redah, T.; Moravsky, A. P.; Li, J. C.; Loong, C. K.; Kolesnikov, A. I. Anomalous behavior of proton zero point motion in water confined in carbon nanotubes. Phys. Rev. Lett. 2006, 97, 247801. 4. Spry, D. B.; Goun, A.; Glusac, K.; Moilanen, D. E.; Fayer, M. D. Proton transport and the water environment in nafion fuel cell membranes and AOT reverse micelles. J. Am. Chem. Soc. 2007, 129, 8122-8130.


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5. Costa, P. M. F. J.; Friedrichs, S.; Sloan, J.; Green, M. L. H. Structural studies of purified double walled carbon nanotubes (DWNTs) using phase restored high-resolution imaging. Carbon 2004, 42, 2527-2533. 6. Chiang, I. W.; Brinson, B. E.; Huang, A. Y.; Willis, P. A.; Bronikowski, M. J.; Margrave, J. L.; Smalley, R. E.; Hauge, R. H. Purification and characterization of single-wall carbon nanotubes (SWNTs) obtained from the gas-phase decomposition of CO (HiPco process). J. Phys. Chem. B 2001, 105, 8297-8301. 7. Kolesnikov, A. I.; Zanotti, J. M.; Loong, C. K.; Thiyagarajan, P.; Moravsky, A. P.; Loutfy, R. O.; Burnham, C. J. Anomalously soft dynamics of water in a nanotube: a revelation of nanoscale confinement. Phys. Rev. Lett. 2004, 93, 035503. 8. Mamontov, E.; Burnham, C. J.; Chen, S. H.; Moravsky, A. P.; Loong, C. K.; de Souza, N. R.; Kolesnikov, A. I. Dynamics of water confined in single- and double-wall carbon nanotubes. J. Chem. Phys. 2006, 124, 194703. 9. Cooper, M. J., Mijnarends, P.E., Sakai, N., Bansil, A. X-ray compton scattering, oxford science publications, 2004. 10. Nygard, K.; Hakala, M.; Pylkkanen, T.; Manninen, S.; Buslaps, T.; Itou, M.; Andrejczuk, A.; Sakurai, Y.; Odelius, M.; Hamalainen, K. Isotope quantum effects in the electron momentum density of water. J. Chem. Phys. 2007, 126, 154508. 11. Juurinen, I.; Nakahara, K.; Ando, N.; Nishiumi, T.; Seta, H.; Yoshida, N.; Morinaga, T.; Itou, M.; Ninomiya, T.; Sakurai, Y.; et. al. Measurement of two solvation regimes in waterethanol mixtures using X-ray compton scattering. Phys. Rev. Lett. 2011, 107, 197401. 12. Hakala, M.; Nygard, K.; Manninen, S.; Huotari, S.; Buslaps, T.; Nilsson, A.; Pettersson, L. G. M.; Hamalainen, K. Correlation of hydrogen bond lengths and angles in liquid water based on compton scattering. J. Chem. Phys. 2006, 125, 084504. 13. Choi, W.; Ulissi, Z. W.; Shimizu, S. F. E.; Bellisario, D. O.; Ellison, M. D.; Strano, M. S. Diameter-dependent ion transport through the interior of isolated single-walled carbon nanotubes. Nat. Commun. 2013, 4, 2397. 14. Das, A.; Jayanthi, S.; Deepak, H. S. M. V.; Ramanathan, K. V.; Kumar, A.; Dasgupta, C.; Sood, A. K. Single-file diffusion of confined water inside SWNTs: an NMR study. Acs Nano 2010, 4, 1687-1695. 15. Takaiwa, D.; Hatano, I.; Koga, K.; Tanaka, H. Phase diagram of water in carbon nanotubes. Proc. Natl. Acad. Sci. USA 2008, 105, 39-43. 16. Liu, X.; Pan, X. L.; Zhang, S. M.; Han, X. W.; Bao, X. H. Diffusion of water inside carbon nanotubes studied by pulsed field gradient NMR spectroscopy. Langmuir 2014, 30, 80368045. 17. Qin, X. C.; Yuan, Q. Z.; Zhao, Y. P.; Xie, S. B.; Liu, Z. F. Measurement of the rate of water translocation through carbon nanotubes. Nano Lett. 2011, 11, 2173-2177. 18. Ma, M.; Grey, F.; Shen, L. M.; Urbakh, M.; Wu, S.; Liu, J. Z.; Liu, Y. L.; Zheng, Q. S. Water transport inside carbon nanotubes mediated by phonon-induced oscillating friction. Nat. Nanotechnol. 2015, 10, 692-695.


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Quantum Coherence and Temperature Dependence of the

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