Evidence for an anomalous quantum state of ... - APS Link Manager

PHYSICAL REVIEW B 85, 045403 (2012)

Evidence for an anomalous quantum state of protons in nanoconfined water G. F. Reiter,1 A. I. Kolesnikov,2 S. J. Paddison,3 P. M. Platzman,4 A. P. Moravsky,5 M. A. Adams,6 and J. Mayers6 1

Physics Department, University of Houston, Houston, Texas 77204, USA Neutron Scattering Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 3 Department of Biomolecular Engineering, University of Tennessee, Knoxville, Tennessee, USA 4 80 Addison Road, Short Hills, New Jersey, 07078, USA 5 MER Corporation, 7960, South Kolb Road, Tucson, Arizona 85706, USA 6 ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0QX United Kingdom (Received 25 October 2011; published 3 January 2012)

2

Deep inelastic neutron scattering provides a means of directly and accurately measuring the momentum distribution of protons in water, which is determined primarily by the proton ground-state wave function. We find ˚ this wave function responds to the details of the confinement, corresponds that in water confined on scales of 20 A, to a strongly anharmonic local potential, shows evidence in some cases of coherent delocalization in double wells, and involves changes in zero-point kinetic energy of the protons from −40 to +120 meV difference from that of bulk water at room temperature. This behavior appears to be a generic feature of nanoscale confinement. It ˚ inner diameter carbon nanotubes, two different hydrated proton exchange membranes is exhibited here in 16 A ˚ diameter carbon nanotubes. (PEMs), Nafion 1120 and Dow 858, and has been seen earlier in xerogel and 14 A The proton conductivity in the PEM samples correlates with the degree of coherent delocalization of the proton. DOI: 10.1103/PhysRevB.85.045403

PACS number(s): 61.46.−w, 61.25.Em, 82.47.Gh

I. INTRODUCTION

The properties of water that make it particularly suited to its role in sustaining life are the properties of the hydrogen bond network. This network is usually treated as a collection of molecules, interacting weakly electrostatically. The hydrogen bonds that form are also regarded as primarily electrostatic. This picture is sufficiently accurate to give an excellent description of the structure of water, as measured by the pair correlations of the ions, and has been successfully incorporated into water models using empirical interaction potentials.1 The quantum delocalization of the protons can be incorporated in these models as well and gives only small quantitative changes in the pair correlations. Deep inelastic neutron scattering (DINS) or neutron compton scattering measures the proton momentum distribution, determined primarily by the ground state of the proton in the combined intra and intermolecular potential. The momentum distribution is far more sensitive to the details of the local potential felt by the proton than measurements of structure, and, for suitable crystals, the momentum distribution can be inverted to obtain an effective Born-Oppenheimer potential for the protons.2 In liquids, the rotational averaging prevents a direct reconstruction, but the width of the distribution is a direct measure of the spatial localization of the proton. Measurements of the width of the momentum distribution in bulk water from room temperature to the supercritical state have shown that the momentum distribution cannot be readily calculated from the electrostatic model, except in the supercritical phase, where the density is significantly lower than in bulk water, and the model might be expected to work best.1 Recent simulations using high-order multipole expansions to represent the interactions of the water molecules and an essentially exact single molecule potential surface to represent the intramolecular potential have demonstrated that this is not simply an inadequacy in the ability of the empirical potentials to capture correctly the electrostatic interactions.3 It is an inadequacy, revealed in 1098-0121/2012/85(4)/045403(5)

the momentum distribution, of the electrostatic model itself. There must be significant overlap of the electronic wavefunctions of the donor and acceptor molecules in the hydrogen bond. Such an overlap already has been seen in x-ray Compton scattering.4,5 The electronic structure of bulk water is then a connected network, and the possibility exists that the network can respond in a manner that substantially differs from what the interacting molecule model would suggest. We present evidence here that this is occurring in nano-confined water, ˚ The departures of the water confined on the scale of 20 A. momentum distribution of the protons from that of bulk water are so large, and so sensitive to the details of the confinement, that we believe that the nano-confined water can be properly described as being in a quantum ground state that qualitatively differs from that of bulk water. We begin with the proton momentum distributions for the protons in ˚ inner-diameter double-wall carbon nanotubes water in 16 A (DWNT), comparing the results with water confined in ˚ single-wall carbon nanotubes (SWNT) and the mo14 A mentum distribution in bulk water. We find that the proton delocalizes in the nanotubes, relative to its wave function in water, and is confined by a strongly anharmonic effective potential. We then compare the momentum distributions for the protons in water confined in Nafion and Dow858, two proton exchange membranes (PEMs), one used in commercial fuel cells and the other a modified structure with higher conductivity, with previous measurements of water confined in xerogel. In these cases, all of which are at room temperature, the proton is again delocalized relative to bulk water, and in a strongly anharmonic, indeed, a double well, potential. There is a correlation between the conductivity of the PEMs and the degree of quantum delocalization of the protons. II. EXPERIMENTAL DETAILS

The measurement of the momentum distribution of protons and other light ions is made possible by having sufficient

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©2012 American Physical Society

G. F. REITER et al.


S( q ,ω) =

h ¯ q2 p M ˆ n(p)δ ω− − q · d p = J (y,q), 2M M q (1)

where n(p) is the momentum distribution of the protons, h ¯ω and h ¯ q are the transferred energy and momentum, respectively, and M is the mass of the proton. The scattering function, which is directly proportional to the double differential scattering cross section, is a function only of the rescaled q2 variable y = Mq (ω − h¯2M ), the longitudinal momentum, and the direction of the vector q. In our case, where all the samples are isotropic, it depends only on y and we have S( q ,ω) = Mq J (y). No information is lost in J (y), which may be inverted to obtain n(p).6,8 The instrument used was Vesuvio, at ISIS, the pulsed neutron source at the Rutherford-Appleton Laboratory in England. In the current experiment, we use 48 detectors, arranged with scattering angles from 35◦ to 75◦ on both sides of the beam. The data are corrected for multiple scattering9 and a γ -ray background.10 The parameters of the fit are obtained by simultaneously fitting the data from all the detectors. The DWNT material was synthesized by chemical vapor deposition technique. The raw nanotube SWNT sample was produced by direct current arc vaporization of graphite-metal composite anodes. The metal component consisted of Co/Ni catalyst in a 3:1 mixture. The subsequent purification with hydrochloric acid was followed by the oxidation of nontube carbon components in air at 300–600◦ C. These preparation and purification steps produced micrometer-long nanotubes of a high purity, that is, with low metal catalyst content and low nontube carbon content. The nanotube ends were opened by exposing the purified material to air at 420◦ C for about 30 min. The samples were characterized by transmission electron microscopy (TEM) and small-angle neutron diffraction. For both the SWNT and DWNT, the (0,1) reflection of the two-dimensional hexagonal lattice of the bundle was evident in the diffraction data. The mean diameter of the SWNT ˚ and the mean inner and outer diameters of was 14 ± 1 A, ˚ and 23 ± 3 A, ˚ respectively. The the DWNT were 16 ± 3 A water absorption in SWNT and DWNT samples was controlled as follows: A mixture of deionized water and the nanotube material was equilibrated for 2 h in an enclosed volume at 110◦ C; excess water was then evaporated at 45◦ C until reaching the targeted water mass fraction. In this work, 3.0 g of SWNT and 2.8 g of DWNT samples were loaded with 11 and 13 wt.% of water, respectively. We recently became aware of the work of Kayakuno et al..11 We disagree with their conclusions with regard to the location of the water in the nanotubes at low temperatures.

III. EXPERIMENTAL RESULTS

We show in Fig. 1 the measured Compton profile J (y) for water in the DWNTs (the present work) and SWNT s (measured earlier),12 both at a temperature of 170 K, and bulk water at 300 K. Compared to bulk water, the width of the Compton profile narrows in the case of water in the SWNT, and broadens for the water in the DWNT. These are essentially smooth cylindrical containers for the water, with diameters differing ˚ and similar average densities on average by only 2 A, of water in the nanotubes, and yet, in the two cases, the water responds completely differently to the confinement. The structure of the water at 170 K in these systems, as determined by classical simulations using empirical potential ˚ models, consists of a cylindrical square ice sheath, about 3 A in from the carbon, with, in the case of the SWNT, a single chain of water molecules down the center13 and, in the case of the DWNT, a smaller inner cylinder of water down the center.14 In both cases, most of the water is in the ice sheath. We conclude that the quantum state of the protons in confined water is very sensitive to the nature of the confinement and responds to the global configuration of the hydrogen bond network. Further differences between the two systems, and further evidence of the sensitivity of the hydrogen bond network to confinement, are evident by comparing the temperature dependence of the proton momentum distributions. As reported in an earlier work12 , the momentum distribution in the SWNT was temperature independent, to within the errors of our measurement, up to 230 K. Figure 1 would not look observably different if we replaced the SWNT data at 170 K with that at 5 K. The DWNT data are, however, strongly temperature dependent. We show in Fig. 2 the momentum distributions as a function of temperature in the DWNT. DINS is sensitive to coherent delocalization, the spreading out of the wave function into a bimodal distribution as in a double-well system. The oscillation seen in the momentum distribution is characteristic of such a system.6,8 Evidently, a significant number of the Fittted Compton Profile J(y) (arb. units)

high-energy neutrons (2–100 eV) available that the scattering takes place in the impulse approximation limit.6 In this limit, the scattering occurs on such a short time scale (10– 100 × 10−18 s) that the forces from the surroundings on the proton do not have time to act and the proton is effectively a free particle for the duration of the interaction.7,8 The scattering function then simplifies to

0.1 0.08 Bulk water-300K SWNT-170K errors DWNT-170K

0.06 0.04 0.02 0

0

10

20

-1

30

Longitudinal momentum y (Å ) FIG. 1. (Color online) The measured Compton profile J (y) for ˚ SWNTs at 170 K, 16 A ˚ DWNTs at 170 K and bulk water in 14 A water at 300 K. The dashed lines are one standard deviation error bars.

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Radial momentum distribution (arb. units)

EVIDENCE FOR AN ANOMALOUS QUANTUM STATE OF . . .


0.1 T=4.2K errors T=170K T=120K T=300K, Bulk water T=290K 0.05

0

0

10

20

30

Momentum (Å-1)

FIG. 2. (Color online) The radial momentum distribution, ˚ DWNT as a function of 4πp 2 n(p), of the water protons in 16 A temperature, compared with that of bulk water at room temperatures. The nanotube 290 K signal and the bulk water signal have been displaced upward by 0.02 units for clarity.

protons in DWNT are in that state, and, further, the separation of the wells, which can be inferred from the position of the minimum (π /pmin ), is changing with temperature, getting smaller from 4.2 K to 120 K, and then getting larger at 170 K. Confinement effects are also observed in hydrophilic environments. Carbon nanotubes are smooth, and the interaction of the water with the surface of the nanotube is primarily Coulomb repulsion and Van de Waals attraction. There is no chemical binding to speak of between the water and the nanotube walls. These conditions are not present in an earlier room-temperature experiment that was done on the confinement of water in the pores of xerogel,15 which can be thought of as a glass sponge. The surface of the pores contains Si-O-H (silanol) groups, to which the water can hydrogen bond, and the proton can be ionized and become mobile in the confined water. It was observed that the momentum ˚ pores could be distribution of the water in nominally 23 A described as though all the molecules in the pore were confined ˚ it appeared in a double-well potential. For larger pores, 83 A that the average momentum distribution was much closer to that of bulk water. The interpretation at the time was that the water in the surface layer was being affected by the interaction with the silanol groups and somehow the surface effects propagated throughout the water in the small pore. That is, the result was due to a particular interaction of the surface with the water. Given the results in the nanotubes, we think now that the effect on the water, rather than being due to local interactions at the surface with the silanol groups, was a direct ˚ is the scale size effect of the confinement itself and that 20 A at which this effect becomes apparent. Two systems that are similar in some respects to the xerogel system are the following perfluorosulfonic acid membranes: Nafion 1120 and Dow 858.16 These are ionomers with hydrophobic poly(tetrafluoroethylene) (PTFE) backbones and randomly pendant perfluoroether side chains terminating with sulfonic acids. The ionomers when hydrated exhibit a nanophase separated morphology where the water and

FIG. 3. (Color online) The radial momentum distribution, 4πp 2 n(p), of the protons in Nafion1120 (blue) and Dow 858 (magenta) compared with that of bulk water (black), all at room temperature. There are 14 water molecules/sulfonyl group in both materials. The inset is the momentum distribution of water in the ˚ pores of xerogel at room temperature. The dashed red line is a 23 A fit to the data with a single particle in a double-well model.15

ions exist in domains that are only a few nanometers in diameter surrounded by the backbones.17,18 The sulfonic acid group (-SO3 H) donates its proton to the water when there is sufficient water in the pores of the ionomer, making them very good proton conductors. We show in Fig. 3 the momentum distribution at room temperature for the water confined in the pores of the two membranes, at the same water content (14H2 O/SO3 H). The deviation from the bulk water ground state in these two samples is dramatic and corresponds to a kinetic energy difference of 107 meV/proton for Nafion and 124 meV/proton for Dow 858. They are not even qualitatively in the same state as bulk water. The protons in the Dow material are somewhat more delocalized than in the Nafion, judging by the depth and position of the minimum in the momentum distribution. It is intuitive that a proton that delocalizes in two places should have a greater conductivity than one that is localized around a single position, and, indeed, the Dow 858 material has a significantly higher conductivity than does the Nafion at these concentrations of water.16 IV. CONCLUSIONS

In our earlier experiments on SWNT and xerogel12,15 we have analyzed the data in terms of a single particle in a potential model. This model can provide a good phenomenological fit, as can be seen from the inset in Fig. 3. We believe, however, that this model is inadequate. Vibrational densities of states measurements in both sets of nanotubes have shown a slight blue shift of the proton-oxygen stretch mode.13 It is not possible to explain this within a single-particle model. The softening of the potential seen in the momentum distribution, although consistent with the increase in the Debye-Waller factor that was observed earlier,13 is too extreme to accommodate at the same time an increase in the ground state to first excited state stretching transition frequency. Bulk water has a very nearly harmonic potential. It is not possible

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G. F. REITER et al.


˚ −1 . KE is the kinetic associated Laguerre poynomial. p is in units of A

2

− p √ 1 e 2σ 2 ( 2π σ )3 2 energy, 3¯Mh σ 2 .

TABLE I. Parameters for fits to the momentum distributions. n(p) =

· [1 +

∞ n=2

1

2

1

2

p 2 p an (−1)n Ln2 ( 2σ 2 )], where Ln ( 2σ 2 ) is an

Water sample

˚ −1 ) σ (A

KE (meV)

a2

a3

a4

Bulk-300K DWNT-4,2K DWNT-120K

4.72 ± 0.03 5.40 ± 0.36 5.65 ± 0.06

138 181 198

0.258 ± 0.060 1.20 ± 0.58 2.44 ± 0.31

DWNT-170K DWNT-290K SWNT-170K Nafion 1120-300K Dow858-300K

5.97 ± 0.15 5.26 ± 0.08 4.09 ± 0.07 6.28 ± 0.40

221 172 104 245

1.84 ± 0.19 0.98 ± 0.13 0.0 2.42 ± 0.51

0.0 0.0 2.05± 0.15 0.0 0.0 0.35 ± 0.22 0.0

0.0 0.0 1.07± 0.16 0.0 0.0 0.0 0.0

6.50 ± 0.27

262

2.70 ± 0.36

0.0

0.0

to find a single-particle potential for which the ground-state momentum width decreases, to the extent that it does, relative to a harmonic well, due to the softening of the potential, but the first-excited-state energy increases, relative to that well. We hypothesize that the sensitivity to confinement, and the large departures from the momentum distribution expected for a single water molecule, are due to correlated proton motion in the ground state of the system and expect that there is a quantum coherence length associated with these correlations. There is experimental confirmation of correlated proton motion in the vibrational spectrum of ice19,20 as well as earlier predictions of this effect from simulations.21 Furthermore, ab initio electronic structure calculations in the hydrogen bonded ferromagnets KDP(KH2PO4) and DKDP(KD2PO4)22 have shown that these correlations are necessary to explain the double-well potential observed in KDP.23 Subsequent DINS measurements on DKDP24 were consistent with the existence of a mass-dependent quantum correlation length in these materials. The hydrogen bonded networks in these materials satisfy the same ice rules for the number of protons on the heavy ion unit, PO4 groups in this case and O ions in water, as do the protons in water. We hypothesize that a similar phenomenon is occurring in water, with the correlated motion of the protons producing a response of the electrons that leads to an effective double well for the protons, and that this correlated state, while occurring at higher energies in bulk water than the individual molecule state of bulk water, is sufficiently close in energy that it can become the ground state when the hydrogen bond network of bulk water is disrupted by confinement. The large difference in behavior in the nanotubes at low temperature for a small change in diameter may be a quantum commensurability effect in the electronic state of the ice sheath network or perhaps due to the difference in hydrogen bonding to the central chain or cylinder. There is a transition from a fragile to strong structural fluctuations in the confined water, at 190 K in the DWNT25 and 218 K in the SWNT.26 It is tempting to associate the peculiar behavior of the 170 K DWNT data relative to that at lower temperatures as signaling an approach to this transition, with the absence of any temperature dependence in the SWNT data reflecting a more rigid structure due to the greater

confinement. We have, however, no direct evidence of the relation between the transition at the long time scale of the quasielastic measurements and the changes in the momentum distribution that we see. The dramatic changes in the proton momentum distribution are not a peculiarity of the structure of the water in the nanotubes at low temperature. At room temperature, that structure disappears,13,14 and the water resembles locally the fourfold coordinated hydrogen bond network of the bulk. We see in Fig. 2, however, that significant differences remain at room temperature between the bulk and nano-confined water in the DWNT. The interest in water in carbon nanotubes is partially as a simple model for biological channels. As such, the quantum state of the protons at room temperature is particularly relevant. As is evident from Fig. 2, this state is far from that of bulk water. We see from Table I that the kinetic energy/proton is higher in the confined space of the DWNT by 34 meV than it is in bulk water or, roughly, kT at room temperature. Since there are two protons in each water molecule, the change of the proton zero-point energy with confinement is clearly significant for water entering and leaving the channels. The quantum state of the water in the channels may also be of significance for transport through the channels, which is orders of magnitude greater than continuum fluid flow theories would predict.27 The water confined in the PEM’s is highly acidic, and it might be thought that the acidity is primarily responsible for the dramatic difference between the bulk and confined water. We have observed DINS for bulk HCl solutions at these concentrations and found only small deviations from that of bulk water.28 We think there is no doubt that it is not the free protons that are driving the transition from one quantum state to the other but the confinement itself. The interaction with the surface groups, the sulfonyl and silanol groups, may, however, play a role in the large difference between the nanotube data and that in Nafion and xerogel.29,30 Large shifts in the kinetic energy, associated with an oscillation in the momentum distribution signaling proton coherence, have also been observed in supercooled water,31 where there is no confinement. The disruption of the bulk

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EVIDENCE FOR AN ANOMALOUS QUANTUM STATE OF . . .

quantum state in that case may be due to the presence of microcrystallites of ice dynamically forming and disappearing. Coherence, without any shift in the net kinetic energy, has been observed in a partial monolayer of water on a protein.32 As there is no obvious confinement length in the system other than that due to the interaction with the protein surface, and that interaction presumably dominates the water-water interaction in the partial monolayer, we can draw no conclusions about the relevance of that experiment to ours. Whatever the origin of the effects we have observed, it is clear that they can be present in room-temperature confined water, that they respond to the details of the structure of the hydrogen bond network of the water, that they indicate a strongly anharmonic state, and that the zero-point energy shifts can be comparable or greater than kT. The changes in the zero-point motion of the protons in confined water, as in living cells, for instance, can be expected to play a significant

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C. Pantalei, A. Pietropaolo, R. Senesi, C. Andreani, S. Imberti, J. Mayers, C. Burnham, and G. Reiter, Phys. Rev. Lett. 100, 177801 (2008). 2 D. Homouz, G. Reiter, J. Eckert, J. Mayers, and R. Blinc, Phys. Rev. Lett. 98, 115502 (2007). 3 C. J. Burnham, T. Hayashi, R. L. Napoleon, T. Keyes, S. Mukamel, and G. Reiter, J. Chem. Phys. 135, 144502 (2011). 4 E. Isaacs, A. Shukla, P. Platzman, D. Hamann, B. Barbiellini, and C. Tulk, J. Phys. Chem. Solids 61, 403 (2000). 5 A. H. Romero, P. L. Silvestrelli, and M. Parrinello, J. Chem. Phys. 115, 115 (2001). 6 C. Andreani, D. Colognesi, J. Mayers, G. F. Reiter, and R. Senesi, Adv. Phys. 54, 377 (2005). 7 P. Hohenberg and P. Platzman, Phys. Rev. 152, 198 (1966). 8 G. Reiter and R. Silver, Phys. Rev. Lett. 54, 1047 (1985). 9 J. Mayers, A. Fielding, and R. Senesi, Nucl. Instrum. Methods A 481, 454 (2002). 10 J. Mayers, Meas. Sci. Technol. 22, 015903 (2011). 11 H. Kyakuno et al., J. Chem. Phys. 134, 244501 (2011). 12 G. Reiter, C. Burnham, D. Homouz, P. M. Platzman, J. Mayers, T. Abdul-Redah, A. P. Moravsky, J. C. Li, C.-K. Loong, and A. I. Kolesnikov, Phys. Rev. Lett. 97, 247801 (2006). 13 A. I. Kolesnikov, J.-M. Zanotti, C.-K. Loong, P. Thiyagarajan, A. P. Moravsky, R. O. Loutfy, and C. J. Burnham, Phys. Rev. Lett. 93, 035503 (2004). 14 A. Striolo, A. A. Chialvo, K. E. Gubbins, and P. T. Cummings, J. Chem. Phys. 122, 234712 (2005). 15 V. Garbuio, C. Andreani, S. Imberti, A. Pietropaolo, G. F. Reiter, R. Senesi, and M. A. Ricci, J. Chem. Phys. 127, 154501 (2007). 16 K. D. Kreuer, M. Schuster, B. Obliers, O. Diat, U. Traub, A. Fuchs, U. Klock, S. Paddison, and J. Maier, J. Power Sources 178, 499 (2008).


role in the energetics of the cells, where typical distances ˚ Changes in between components are on the order of 20 A. zero-point energy have already been shown to play a major role in the binding of water molecules to DNA.33 The change in the environment for proton transport in the PEM systems such as Nafion can be expected to have a significant effect on the conductivity of these materials and perhaps lead to coherent transport through a series of delocalized states. ACKNOWLEDGMENTS

G. Reiter’s work was supported by the DOE, Office of Basic Energy Sciences under Contract No. DE-FG02-08ER46486. Work at the Oak Ridge National Laboratory was managed by UT-Battelle, LLC, for the DOE under contract DE-AC0500OR22725. The STFC Rutherford Appleton Laboratory is thanked for access to neutron beam facilities.

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