J. Phys. Chem. C 2009, 113, 8635–8644
8635
Dynamics of Water in Voids between Well-Defined and Densely Packed Spherical Nanocages Acting as Polyprotic Inorganic Acids Antonio Faraone,*,†,‡ Emiliano Fratini,§ Ana Maria Todea,| Bernt Krebs,⊥ Achim Mu¨ller,| and Piero Baglioni*,§ National Institute of Standards and Technology (NIST) Center for Neutron Research, 100 Bureau DriVe, Gaithersburg, Maryland 20899, Department of Materials Science and Engineering, UniVersity of Maryland, College Park, Maryland 20742, CSGI and Department of Chemistry, UniVersity of Florence, 50019 Florence, Italy, Fakulta¨t fu¨r Chemie, UniVersita¨t Bielefeld, 33615 Bielefeld, Germany, and Institut fu¨r Anorganische und Analytische Chemie, UniVersita¨t Mu¨nster, 48149 Mu¨nster, Germany ReceiVed: October 29, 2008; ReVised Manuscript ReceiVed: March 30, 2009
Using quasielastic neutron scattering, we have investigated the water dynamics of powders of the compound with the stoichiometry of [Mo72Fe30O252(CH3COO)12[Mo2O7(H2O)]2[H2 Mo2O8(H2O)](H2O)91] · ≈ 150H2O. It contains about 150 crystal water molecules in the voids between the spherical {Mo72Fe30} nanocapsules, which are considered unique polytropic inorganic acids with well-defined hydrophilic surfaces due to the presence of H2O and O atoms. It has been proposed that {Mo72Fe30} can be used as a structurally wellconstrained experimental model of oxide mineral surfaces for earth scientists.1 In this respect, it is of fundamental importance to understand the dynamics of the water molecules at the surface of the nanoclusters. Our measurements show that the dynamics of these water molecules is as expected profoundly different from that of bulk water at the same temperature, especially because of the strong hydrogen bonding between the crystal and cluster surface water molecules. In fact, our data show a non-Debye relaxation behavior. The momentum transfer dependence of the dynamics is close to that expected for a purely diffusive motion. This suggests that the nonexponentiality of the dynamics originates from a distribution of relaxation times, probably related to the different local environments experienced by the water molecules. The dynamics of the crystal water in the voids between the well-defined and arrayed nanocages is significantly slower than that of bulk water at the same temperature that has often been reported for interfacial water. In the investigated range, the temperature dependence of the relaxation time can be described in terms of an Arrhenius law, indicating that the dynamics is triggered by the breaking of the bonds connecting the crystal water molecules with the hydrophilic nanocage surfaces. Introduction Understanding the dynamics of interfacial water is a problem that has not been fully solved, even though many studies have been devoted to clarify how water molecules behave when confined in nanoporous cavities or when they are at the interface of hydrophobic and hydrophilic surfaces.2-9 Interest in the topic arises not only from a purely scientific curiosity, but also because it has many applications in earth sciences, catalysis, and biology. Quasielastic neutron scattering10 (QENS) is one of the most valuable techniques for understanding the dynamics of water because of the extremely high neutron scattering cross-section of hydrogen atoms (compared to others) and to the space-time sensitivity of the technique. For example, by using QENS, some of the authors have investigated the dynamics of water confined in silica matrices with cylindrical nanopores of less than 20 Å in diameter.11 In this extreme confinement, water does not freeze, even below the homogeneous nucleation temperature. Thus, some of the authors found a transition of the translational * To whom correspondence should be addressed. E-mails: afaraone@ nist.gov (A.F.) and
[email protected] (P.B.). † National Institute of Standards and Technology (NIST) Center for Neutron Research. ‡ University of Maryland. § University of Florence. | Universita¨t Bielefeld. ⊥ Universita¨t Mu¨nster.
relaxation time, from a Vogel-Fulcher-Tammann (VFT) behavior to an Arrhenius behavior at a crossover temperature Tc ≈ 225 K.12 Early transition metal oxide-based clusters in the form of polyoxometalates (POMs) belong to a large and rapidly growing class of compounds.13 These have a wide range of possible applications in fundamental and applied science, including catalysis.14 In fact, their molecular properties such as composition, size, shape, charge density, acidity, and solubility can be extensively modified to match different requirements. As a matter of fact, POMs can be rendered soluble in nearly all media from H2O to hydrocarbons, and most of the elements in the periodic table can be incorporated into the structural framework of these compounds. The recently synthesized nanosized polyoxomolybdate clusters15 (e.g., Mo132, Mo154, and Mo368) are the largest members of the POM family, while their properties were investigated worldwide by several groups.15 In particular, the icosahedral cluster {Mo72Fe30} molecule16 is interesting because it has a hydrophilic surface and is a novel polyprotic acid.17 In Figure 1, we show the structure of the spherical cluster present in [Mo72Fe30O252(CH3COO)12[Mo2O7(H2O)]2[H2Mo2O8 (H2O)] (H2O)91] · ≈ 150H2O (1). The cluster exhibits a nanometer-sized cavity and 20 pores equivalent to 20 Mo3Fe3O6 rings. The diameter of the nanocapsule is ≈25 Å. {Mo72Fe30} can be considered a polyprotic
10.1021/jp809555s CCC: $40.75 2009 American Chemical Society Published on Web 04/24/2009
8636
J. Phys. Chem. C, Vol. 113, No. 20, 2009
Faraone et al.
Figure 1. Structure (simplified) of the spherical {Mo72Fe30} type cluster (diameter ≈25 Å) built by 12 pentagonal (Mo)Mo5 type units (blue in polyhedral representation) spanning an icosahedron and 30 Fe(H2O) linking groups at the surface, which are characteristic for the polyprotic acid (Fe atoms are yellow; O are atoms red). The 72 Mo atoms have on the surface terminal O atoms (about 62) and about 10 H2O ligands. Note: there is an 80% to 20% disorder related to the corresponding ligands inside and outside the cavity.
nanoacid because of the presence of 30 FeIII(H2O) groups on the surface, which allow pH-dependent deprotonations.17 The {Mo72Fe30} clusters have unique structural, electronic, and magnetic properties and show self-assembly in solution into blackberry type structures because of their polyprotic nature (H2O ligands are acidic).17,18 The icosahedral cluster contains 91 water ligands coordinated to the Fe and Mo atoms (40 outside and 51 inside). Moreover, about 150 discrete H2O molecules are present, 25 inside the cavity and the rest in the voids between the clusters, while interacting with their surfaces via hydrogen bonds. Using QENS, we have studied the single particle dynamics of the latter type of water molecules incorporated into the structure and attached to the surface of the {Mo72Fe30} clusters. This investigation is relevant not only for possible technological applications of {Mo72Fe30}, but also for a better understanding of the chemical and physical properties of interfacial water under special conditions. Quasielastic neutron scattering measurements have been performed using two state of the art spectrometers working in the energy domain and allowing the investigation of a time window from ≈4 ps to ≈2 ns. In the Experimental Section, we will describe the details of the performed measurements and include information about the instruments used. Then, we will explain the data analysis procedure, with references to the physical models employed. These models were verified using data taken on a third instrument, a neutron spin echo spectrometer (NSE), with a time window spanning from ≈5 ps to 15 ns. Finally, we will report our results on the dynamics of hydration water, concluding with a critical comparison with bulk water.
Experimental Section The investigated sample was prepared according to a published preparation method.16 QENS measurements of compound 1 have been performed at the National Institute of Standards and Technology (NIST) Center for Neutron Research (NCNR), using a disk chopper spectrometer (DCS)19 and a high-flux backscattering spectrometer (HFBS).20 The sample was put in an annular aluminum sample holder. The thickness of the annulus was ≈1 mm in order to ensure ≈90% neutron beam transmission through the sample. The sample holder was mounted onto a closed-cycle refrigerator, which ensured temperature control within 0.5 K. For the measurements on DCS, the incoming neutron wavelength was set to λ ) 9 Å, and the instrument was operated in the “low resolution” configuration.19 The obtained energy resolution function, measured using a standard vanadium sample, was with good approximation a Gaussian function of ≈20 µeV full width at half-maximum (fwhm). The 913 DCS detectors cover the scattering angle range from θ ) 5° to 140°. Using the package Mslice in the data reduction software DAVE,21 the data were grouped into 16 spectra of constant momentum transfer
Q)
2mn [2Ei - E - 2 cos θ√Ei(Ei - E)] p
where mn is the neutron mass, Ei is the incoming neutron energy, E is the exchanged energy, and θ is the scattering angle. Data were collected in the temperature range from 300 to 250 K. An additional measurement at 20 K was performed to determine
Dynamics of Water in Voids between Nanocages
J. Phys. Chem. C, Vol. 113, No. 20, 2009 8637
Figure 3. Quasielastic neutron scattering data at Q ) 1.00 Å- 1 for a hydrated sample of 1 at 20 and 300 K and for the dried sample, in a logarithmic scale. The inset shows the same data on a linear scale to better appreciate the different relative weights of the quasielastic and elastic components of the three spectra. The details of the dried sample and the sample at 20 K are superimposed, indicating that both have no quasielastic broadening.
Figure 2. Elastic neutron scattering intensity as a function of the exchanged wave vector for the original sample 1, containing crystal water under different conditions. Panel a) reports the data from an X-ray measurement22 and from the DCS data in the energy window of (0.2 meV at 20 and 300 K and for a dried sample. The agreement between the different measurements is excellent, confirming the quality of the sample. Notice the effect of sample drying on the size of the cage. Panel b) shows the results from a measurement using the NSE spectrometer, which uses polarized neutrons to allow for the separation of the coherent and incoherent contributions. Throughout this paper, error bars represent one standard deviation.
the sample dependent resolution function of the instrument. Then the indium seal of the aluminum can was removed, and the sample was evacuated (without removal from the can) for ≈5 h at ≈10- 3 Torr using a rotary pump. A weight loss of 15.5% was recorded. This amount is in agreement with a weight loss of 163 water molecules per formula unit, under the assumption that only the hydration water was lost. This finding confirms that the hydration level expected from 1 is correct. Finally, a measurement of the dry sample was performed. Figure 2a shows the neutron scattering intensity measured on DCS in the energy window (0.2 meV as a function of the exchanged wave vector for a sample of {Mo72Fe30} at 20 and 300 K and for the dried sample. The data are compared with the results of an X-ray diffraction measurement.16 The X-ray and neutron scattering data on sample 1 confirm the existence of the icosahedral structure with three intramolecular peaks. Interestingly, the structure of the dried sample appears to be different, with a shift of the position of the peaks toward higher Q values indicating that the characteristic cell dimensions are smaller than expected due to the drying effect. The dried nanocapsules containing much less water at the surface appear to be shrunk, with respect to the hydrated one. Figure 3 reports a comparison between the spectra collected on the normal samples with crystal water at 20 and 300 K with those collected for the dried sample. As expected, there is no clear signature of quasielastic broadening in the sample at 20 K, and later we
will use this measurement as the experimental resolution function. From Figure 3, it can be seen that the dried sample has little or no quasielastic broadening. This would imply that the hydrogen atoms of the water ligands forming the cage are immobile on the experimental time scale. This is a reasonable hypothesis for these water molecules. However, we should consider the presence of the 12 methyl groups of the internal acetate ligands, which have incoherent scattering amounts equal to about 15% of the incoherent scattering of the dried sample and could also have dynamics in the time window of DCS.10 From the measured spectra, we can conclude, with good approximation, that the dried sample has no observable dynamics in the investigated time scale at all temperatures. Therefore, we subtracted the spectra measured for the dried sample from the DCS spectra of the original sample at different temperatures, after proper normalization for the transmission factors. The effect of the coupling of water to the methyl groups was neglected. In this way, our study is focused on the dynamics of the crystal water only. Incidentally, we realized that the area of the spectra of the dried sample amounts to 40% of the area of the spectra of the original sample at 20 K, which is within the accuracy of our measurements. This result is in agreement with the cross section of the calculated incoherent scattering of the dried sample and crystal water. Because of the presence of the Bragg peaks in the original and dried sample, the spectra collected at Q ≈ 0.5 and 0.8 Å-1 have been eliminated. Moreover, the spectra at the two lowest Q values have been neglected because of the very poor signalto-noise ratio. The resulting Q range investigated was from 0.25 to 1.28 Å-1. The HFBS spectrometer is operated with an incident neutron wavelength that is varied by Doppler shifting about a nominal value of 6.271 Å. The final energy of the detected neutrons is fixed by Bragg reflection from the analyzer crystals. In this way, with a Doppler frequency of 50 Hz, it was possible to investigate an energy window of (36 µeV, with an instrumental energy resolution of ≈1 µeV, as measured for the sample at 20 K. The HFBS spectrometer has 16 detectors, which collect the neutrons scattered at 16 Q values in the range from 0.25 to 1.75 Å-1.
8638
J. Phys. Chem. C, Vol. 113, No. 20, 2009
Faraone et al.
The first five detectors are not in full backscattering geometry and were not considered in the analysis. The detectors corresponding to the Bragg peaks, as measured on DCS and to Q values greater than 1.35 Å-1, were also discarded. Data were collected at 250, 240, 230, and 20 K. This latter measurement was used as the instrument resolution function. Although a measurement with a dried sample, which resulted in elastic spectra, was performed, the data were reduced, subtracting the empty can only, and the contribution from the cage was approximated by an elastic component with area of 0.4. The data reduction, including detector efficiency normalization, using the results of a scan on vanadium, was performed using the software DAVE.21 Neutron spin echo measurements were performed at the NCNR, using the NSE spectrometer installed on the NG5 neutron guide.23 NSE is the neutron scattering technique with the highest energy resolution. This is achieved by using a polarized beam and encoding the velocity of each neutron in its spin, which is precessing, before and after the interaction with the sample, in a constant magnetic field. By measuring the memory loss in the scattered beam of the initial polarization state, which is related to the exchanged energy with the sample, we can determine, using NSE spectroscopy, the intermediate scattering function (ISF) of the sample. Because the scattering with a hydrogen atom has a probability of 2/3 of flipping the neutron spin, with an effective reduction of the polarization signal to 1/3, NSE measurements of incoherent dynamics are particularly challenging and time consuming. Moreover, on the NG5-NSE at this Q range, as in most other NSE spectrometers, each Q value has to be measured one at a time. For the NSE experiment, the incoming neutron wavelength was λ ) 6 Å, with a wavelength spread of ≈20%, which allows for an investigated time window from 0.005 to 15 ns, spanning almost 4 orders of magnitude in time. The sample was put in a rectangular niobium sample cell with 2 mm of thickness. Figure 2b reports the diffraction pattern of the sample as measured by NSE. The Q resolution is poor compared to DCS; however, using polarized neutrons, the coherent and incoherent signals can be separated. NSE data were taken at Q ) 0.65 and 0.95 Å-1, where there is no contamination from Bragg peaks. Three temperatures were investigated: 280, 230, and 10 K. The latter set of data was used as the resolution. Here, we will only report NSE data already normalized for the instrumental resolution. No dry sample was investigated; therefore, in the rest of the paper, the spin echo data refers to the hydrated sample. Data Analysis Because of the highly incoherent scattering cross section of H, our QENS measurements are sensitive to the self-particle dynamics of the hydrogen atoms in the sample. In the case of the time-of-flight measurements, the collected data are proportional to the dynamic structure factor S(Q,ω), where E ) Ei - Ef ) pω is the energy exchanged by the neutron with the sample, with Ef being the final energy of the neutron. NSE is instead a technique that works in the time domain, determining the normalized ISF, I(Q,t)/I(Q,0), with I(Q,0) being the diffraction pattern. The two quantities are related by a Fourier transform in the time domain
S(Q, ω) ) FTt[I(Q, t)] )
1 π
∫0∞ dt cos(ωt)I(Q, t)
(1)
The ISF is the time correlation function of the spatial Fourier transform of the hydrogen atoms positions. Under the assump-
tion that the incoherent scattering is dominant only the selfterm needs to be considered
b [b Is(Q, t) ) 〈exp{-iQ r i(t) - b r i(0)]}〉
(2)
where the s superscript indicates the self-part of the intermediate scattering function. Is is often described as the spatial Fourier transform of the van Hove self-correlation function, Gs(r,t), which describes the probability of finding an atom at time t displaced from its original position at time 0 by a distance r. The single particle dynamics of water is the result of three kinds of motions: translation of the center of mass (coinciding with good approximation to the oxygen atom position), rotation of the molecule around the center of mass, and vibration of the hydrogen atoms around their equilibrium position. It is wellaccepted that the vibrational motion effect is a global reduction of the total area of the spectra, which is usually identified with the Debye-Waller factor. In the time domain, this corresponds to a reduction of Is(Q,t f 0) from its theoretical value 1, where with t f 0, we indicate the extrapolation of the data collected in the experimental time window to zero
(
Is(Q,t f 0) ∼ exp -
〈u2 〉 Q2 3
)
(3)
where 〈u2〉 is the mean square vibrational amplitude of the hydrogen atoms. As far as the rototranslational dynamics of water is concerned, this has been the subject of intense research.24-26 From an operational point of view in the analysis of the QENS data, the assumption of the decoupling of the translational and rotational motions (decoupling approximation) is still the hypothesis used most commonly, if the rotational dynamics is of specific interest and data are collected at Q > 1.2 Å-1.27,28 However, it has been shown, using both molecular dynamics (MD) simulations and QENS,29 that the coupling between the two types of motions is very strong, especially at supercooled temperatures. In the case of hydration water, e.g., water adsorbed on inorganic or biological surfaces, it has been found that as a general rule water dynamics is slowed down with respect to that of bulk water and resembles that of water at lower temperatures.30 Although there is a general consensus of this trend, two different models are commonly used. The first model dates to the seminal work by Teixeira et al.,31 and the second model is the relaxing cage model (RCM).32 In their work on supercooled water, Teixeira et al.31 assumed the validity of the decoupling approximation, modeling the ISF as the product of the rotational and translational ISFs: Is ) IRs × ITs. In the rotational ISF, the Q and t dependence can be separated using the Sears expansion for the rotation on a sphere33 ∞
FRs(Q, t) )
∑ (2l + 1)jl2(Qb)Fl(t)
(4)
l)0
where b ) 0.98 Å is the hydrogen atom center of mass distance in water, jl(x) is the lth order spherical Bessel function, and Fl(t) is the lth order rotational correlation function. Usually only the first two terms of the Sears expansion are used for the analysis of the QENS data. As far as the translational dynamics is concerned, Teixeira et al. found that it can be well-described by a Debye relaxation with a Q dependence, following the random jump diffusion model.34 More recently, Chen et al.32 introduced the RCM for describing the single particle dynamics of water at supercooled temperatures. Because of the extensive hydrogen bonding at
Dynamics of Water in Voids between Nanocages
J. Phys. Chem. C, Vol. 113, No. 20, 2009 8639
supercooled temperature, a water molecule is trapped in the cage of its neighbors. Whereas, usually, in supercooled liquids the cage effect arises from an increase in density, for water it originates from the stiffening of the hydrogen bond network. As shown by MD simulations of the center of mass motion, inside this cage water performs harmonic vibrations to ≈0.1 ps.32 This short time dynamics can be modeled, assuming that the water molecule is trapped in a harmonic potential and an analytical expression for the corresponding ISF can be calculated.32 However, such fast harmonic dynamics is not observable in the time window of a QENS experiment and contributes to the spectra with an effective Debye-Waller factor with a root mean square vibrational amplitude of a ≈ 0.4 Å, which is fairly independent of temperature. On the other hand, it originates the inelastic features of water at ≈8 and ≈30 meV as measured by Inelastic Neutron Scattering (INS).35 For times longer than ≈0.1 ps, the water molecule eventually escapes from the cage and diffuses away. Because the diffusive motion requires a cooperative rearrangement of many water molecules, there is strong coupling between the single particle dynamics and density fluctuations. In a way similar to that predicted by the mode coupling theory (MCT) for supercooled liquid, the diffusion process of the water molecule is then described by a stretched exponential function. In the RCM, the ISF is given by the product of an effective Debye-Waller factor, describing the rattling in the cage, and the escape processes
(
Is(Q, t) ≈ exp -
) [ ( )]
t a2Q2 exp 3 τT
β
(5)
In the RCM, a, is the amplitude of the center of mass motion of a water molecule inside the shell of its first neighbors, before the long time diffusive process takes place. The stretching exponent, β, is a measure of the deviation of the relaxation process from a simple exponential decay. If β ) 1, a simple Debye process is retained. The RCM has been further developed to account for the rotational dynamics.36 However, if the investigated Q range is
