J. Phys. Chem. 1996, 100, 8079-8084
Water Dynamics in Na3PW12O40‚nH2O: A 2H-NMR and
31P-NMR
8079
Investigation
Salvatore Di Benedetto, Giuseppe Chidichimo, Attilio Golemme,* and Daniela Imbardelli Chemistry Department, UniVersity of Calabria, 87036 ArcaVacata di Rende (CS), Italy ReceiVed: August 2, 1995; In Final Form: January 26, 1996X
The dynamics of water molecules adsorbed in the secondary lattice structure of sodium dodecatungstophosphate (Na3PW12O40‚nH2O) has been investigated by 31P-NMR and 2H-NMR at different temperatures and hydration levels (n). 2H-NMR spectra show that for T e 173 K only one type of adsorbed water is present. In the temperature interval between 173 and 293 K three differently adsorbed and mutually exchanging water components are observed. The chemical exchange range and population ratios of the differently chemisorbed water molecules were determined by computer simulation of 2H-NMR spectral profiles. The activation energy of the exchange process and the shape of 2H-NMR spectra indicate that the different water components correspond to twice hydrogen bound, mono hydrogen bound, and not bound D2O molecules. A further investigation of samples at different hydration levels has been performed, at room temperature (293 K), by 31 P-NMR spectroscopy. The line width (∆(H)) and the longitudinal relaxation time (T1) of the 31P lines have been measured using both H2O and D2O for hydration. The experimental data have been used to estimate the contribution to ∆(H) and T1 due to the protons-phosphorus dipolar interactions: ∆(H) and T1(H) respectively. These parameters, combined with the values of population ratios of the differently adsorbed water molecules, allow knowledge of the correlation times of the water molecules’ motions.
I. Introduction The dodecatungstophosphoric acid and its salts are compounds well-known for their catalytic activities.1 Such properties are mainly due to their particular structure, which consists of Keggin units2 inserted in a secondary lattice where the counterions, the water molecules, and other possible guest molecules are chemisorbed. X-rays and neutron diffraction studies3 have confirmed that the Keggin cages are formed by 12 edge-sharing octaedra of oxygen atoms (each having at the center a metal atom) sharing four oxygens, with the PO4 tetrahedron sitting at the center of one cage. 1H-NMR relaxation studies and electrical conductivity measurement4 of Na3PW12O40‚nH2O have shown that, for n ) 11, the temperature dependence of the spin-spin relaxation time T2 consists of two linear sections with different slopes, indicating that two groups of protons are present in the salt: for the first one (lowtemperature section) the activation energy is 0.45 eV (10.4 kcal/ mol), which practically coincides with the conduction activation energy; for the second type of proton (high-temperature section) the activation energy is 0.6 eV (13.8 kcal/mol). As n decreases, relaxation curves show that the proton mobility gradually decreases, and with n e 6 it disappears entirely (conductivity becomes 2.5 × 10-6 Ω-1 cm-1 for Na3PW12O40‚2.4H2O). For these reasons, it is believed that in the salt Na3PW12O40‚6H2O each Na+ ion coordinates two water molecules, whose protons lose their translational mobility and do not participate in conduction; the activation energy, 0.6 eV, should correspond to “annulation diffusion” of protons belonging to this type of water molecule. In the case of n > 6 the excess water molecules form a network of hydrogen bonds, interact with the terminal oxygen atoms of the heteropolyanions, and participate in conduction through the formation of fluctuating protons. The catalytic activity for reactions proceeding in the bulk catalyst (“bulk-type” reactions) of Na3PW12O40‚nH2O is little dependent on the pretreatment temperature of the sample:5 it is likely that although the secondary structure changes during X
Abstract published in AdVance ACS Abstracts, March 15, 1996.
S0022-3654(95)02267-2 CCC: $12.00
pretreatments by the removal of the water of crystallization, subsequent rearrangements occur, under reaction conditions that make the secondary structure independent of the pretreatment. Probably, water formed by the reaction makes this rearrangement easier.6 On the other hand, we have shown7,8 that 2H-NMR and 31PNMR spectroscopies give valuable informations on the structure and dynamics of water molecules chemisorbed in the acid H3PW12O40‚nH2O. In fact, 2H-NMR spectral profiles recorded from deuterated crystallization water can be used to establish the type of motion and the related characteristic times,7 while the line width and relaxation time of the single spectral line generated by the 31P nucleus are both sensitive to water dynamics and structure.8 We give here a contribution to the investigation of water dynamics in sodium dodecatungstophosphate (Na3PW12O40‚nH2O) as a function of temperature and content of crystallization water, carried out using 2H-NMR and 31P-NMR. The layout of the paper is as follows: in section II the details of sample preparation and NMR spectra acquisition are given; in sections III and IV the data obtained by 2H-NMR and 31PNMR are illustrated and discussed in terms of suitable theoretical models; in section V conclusions are summarized. II. Experimental Section Na3PW12O40‚nH2O has been purchased from Merck and used without further purification. The content of crystallization water has been determined by thermal gravimetric analysis (TGA). Samples with variable contents of H2O have been prepared by heating the commercial salt for 25-180 min at 150 °C and always using TGA to check the number of residual H2O molecules. Samples rehydrated with D2O have been obtained by exposing the anhydrous salt to D2O vapors. Anhydrous Na3PW12O40 has been prepared9 by heating the commercial salt at 200 °C for almost 2 h. The number of moles of D2O for the polyanion has been easily regulated by the appropriate choice of exposure time (5-180 min) of the anhydrous salt to the D2O vapors. Even © 1996 American Chemical Society
8080 J. Phys. Chem., Vol. 100, No. 20, 1996
a
Di Benedetto et al. the number of crystallization water molecules (n) and of temperature. Expanded versions of some spectra at T ) 293 K are shown in Figure 1b. At first glance it can be seen that the spectra are almost independent of the amount of crystallization water, while they are strongly affected by temperature. For the sake of clarity before starting the discussion of the spectral data of Figure 1a,b, let us consider that, for an ensemble of D2O molecules, randomly oriented in space and not undergoing any kind of rotational motion, as it should be in the case of the crystallization water of Na3PW12O40‚nD2O at low temperature, the 2H-NMR spectra should consist of a powder pattern having (a) two external shoulders with spectral separation equal to (3/ 2)νQ, νQ being the quadrupole coupling constant,10 which is proportional to the electric field gradient along the O-D bond, and is equal to 213 kHz;11 (b) two inner peaks separated by (3/4)νQ. Now, even in the case of the spectra recorded at the lower temperature of 173 K, the profile is quite different from that expected for frozen molecules. In fact, the maximum spectral width is only 200 kHz and the inner singularities are separated by 20 kHz. This indicates that the field gradient tensor (V) acting on the deuterium nuclei must be averaged in such a way that in its principal axis system the following conditions hold:12
b
νjQ )
eQ V h ZZ
(1a)
p
with νjQ < 213 kHz, and
0eη)
Figure 1. (a) 2H-NMR spectral profiles, at different temperatures, recorded from Na3PW12O40‚nD2O. (b) 2H-NMR spectral profiles, at two different vertical scales, recorded from Na3PW12O40‚nD2O at T ) 293 K. From the integral, which is also shown, we can obtain the relative intensity of the different spectral components. The integral NMR line is proportional to the number of nuclei contributing to the specific line.
in this case the D2O content has always been determined by TGA. To keep constant the water content, samples have been flame sealed in glass NMR tubes. NMR spectra have been recorded on a multinuclear Bruker MSL300 spectrometer, equipped for variable temperature analysis, where the deuterium and phosphorus resonance frequencies are 46.073 and 121.490 MHz, respectively. The quadrupolar echo technique, with a 30 µs spacing between two 90° pulses (pulse width = 3.5 µs), has been used to record 2HNMR spectra. One thousand scans were needed to reach a sufficiently good signal/noise ratio. The T1 values of the 31P magnetization have been measured using the progressive saturation technique. Each T1 measurement was based on 15 different spectra taken at different relaxation intervals. In this case eight scans were enough for a convenient signal/noise ratio. For experiments at variable temperature, the accuracy of temperature control was (1 °C. III. Deuterium NMR 2H-NMR
spectra from D2O adsorbed in the secondary lattice of Na3PW12O40‚nD2O are shown in Figure 1a as a function of
h YY V h XX - V V h ZZ
e1
(1b)
with |VYY| e |VXX| e |VZZ|, where η, e, Q, and p are the asymmetry parameter, the electron charge, the quadrupole moment of the deuterium nucleus, and the Planck constant, respectively. If the averaged field gradient tensor is not axially symmetry, the spectra show two inner shoulders split by (3/ 4)νjQ (1 + η) and two inner peaks split by (3/4)νjQ (1 - η), in addition to the external shoulders split by (3/2)νjQ, on the frequency scale. If η is almost equal to 1, the two inner shoulders will overlap with the external shoulders and the inner peaks will appear very close, as in the spectrum shown in Figure 1. A fitting of the spectrum recorded at the lowest temperature is obtained with (3/2)νjQ ) 200 kHz and η ) 0.8, and it is shown in Figure 2. It remains to explain which kind of molecular motion is responsible for the shape of the spectral pattern observed at 173 K. One possibility which accounts for the very high value of η is consistent with a π-flipping motion of the water molecules around their C2 symmetry axis. In this case the final averaged splitting is simply related to the reorientational angle, 2R, of the principal quadrupole axis (in this case coinciding with the DOD angle) and the static quadrupole coupling constant, νQ, with the following principal component:13
( (
) )
νj1 )
3 cos2 R - 1 3 νQ 2 2
νj2 )
3 sin2 R - 1 3 νQ 2 2 νj3 ) -
(2)
3 ν 4 Q
where νj1 is along the C2 symmetry axis of the molecule, νj2 is
Water Dynamics in Na3PW12O40‚nH2O
J. Phys. Chem., Vol. 100, No. 20, 1996 8081 during the acquisition time is given by the equation
G(t) ) W h exp{(iω c +π c )t}‚1h
(3)
where W h is a vector whose components are the probabilities of finding the molecule at different sites, ω c is the diagonal matrix of the NMR frequencies at the different sites, π c is the matrix of transition probabilities among different sites, and 1h is the unitary vector. Since the quadrupolar echo pulse sequence has been used to get the NMR spectrum, the following modified version of eq 3, due to Woessner,116 was used:
G(t) ) G*(τ) exp{(iω c +π c )t}‚1h
(4)
where G*(τ) is the initial condition of the FID after the second pulse,
G*(τ) ) W h exp{(-iω c +π c )τ}
(5)
and τ the interval between the rf pulses in the quadrupolar echo pulse sequence (π/2)x-τ-(π/2)y-τ acquisition. A further modification of eq 4 is needed in order to take into account the additional broadening due to quadrupolar and dipolar relaxation processes as well as to the field inhomogeneity. These effects can be introduced by multiplying eq 4 by a Gaussian relaxation function,17 in such a way that the final FID result is Figure 2. Simulated (left) and experimental (right) spectra recorded from Na3PW12O40‚7.2D2O at different temperatures.
in the plane of the molecule and perpendicular to νj1, and νj3 is perpendicular to both νj1 and νj2. As it is not possible to obtain from 2H-NMR spectra the sign of the averaged quadrupole splitting components but only their absolute values, two equally possible situations are present: for the first one, νj1 ) -20 kHz, νj2 ) +200 kHz, and νj3 ) -180 kHz; in the second case νj1 ) 20 kHz, νj2 ) 180 kHz, and νj3 ) -200 kHz. In both cases, however, the asymmetry parameter is 0.8. Using eq 2 we obtain νQ ) 240 kHz and 2R ) 114.04° or νQ ) 266 kHz and 2R ) 105.46° for the first or second case, respectively. Of the two possibilities, the first one is in agreement with literature: since it is obviously expected that in the Na3PW12O40‚nD2O water molecules are coordinated to the Na+ ions, then a good reference value for the νQ of the O-D bond is the one measured in the case of solid dehydrated NaOD. It has been found by Amm et al.14 that the quadrupole coupling along the O-D bond of the solid NaOD is equal to 245 ( 2 kHz. Also the value of 2R ) 114.04° for the DOD angle appears to be quite reasonable, since the water bond angle measured in solid heteropolyacids is larger than the tetrahedral angle.15 We can then conclude that below the temperature of 173 K the only motional degree of freedom available to water molecules is a π flip around the C2 axis. This implies that every water molecule is at least involved in one hydrogen bond with the oxygens of the Keggin cages, besides being coordinated by a Na+ ion. The hydrogen bonds could also be two, as observed from X-ray measurements3 in the case of H3PW12O40‚6H2O. At higher temperature the situation becomes more complex. The shape of the spectra changes in such a way that it is no longer possible to assume a single spectral component. Moreover, spectra do not show anymore well-defined shoulders or singularities, a situation which often occurs when dynamically different molecular species in mutual chemical exchange are present. Despite the complex situation, basic information concerning the molecular dynamics and populations of the different species can be obtained by a computer simulation of the spectral profiles. For this purpose, we have used the theory of chemical exchange,12 according to which the NMR free induction decay (FID) signal given by a nucleus jumping among different sites
G(t) ) {G*(τ) exp[(iω c +π c )t]‚1h}R(Θ0,t+2τ)
(6)
where
[
R(Θ0,t) ) exp
]
-t2σ2(Θ0) 2
(7)
the width being18
σ(Θ0) ) a + b[|P2(cos Θ0)| - 1]
(8)
where a and b are parameters to be adjusted for the best line shape fitting and P2 is the V(2,0) Legendre polynomial (Θ0 will be defined in the following equation). Given the hypothesis that the spectral profiles shown in Figure 1a,b are dominated by the chemical exchange of water molecules among different adsorption sites, where as a site we can also consider an area of isotropic or nearly isotropic reorientation, it was necessary to start with a reliable assumption on the number of different sites. We have simulated the spectra obtained from the sample with n ) 7.2, in the temperature interval between 193 and 293 K, under the following assumptions: (1) two spectral components, due to as many types of water molecules having different mobility, contribute to spectra; (2) the above different kinds of water molecules are under mutual exchange and this affects their NMR signal. If the two water species are defined as A and B, the related frequencies are12
{
} (9)
{
}
ωA 1 3 ) ( νQA P2(cos Θ2) + ηA sin2 Θ0 cos 2Φ0 2π 4 2 ωB 1 3 ) ( νQB P2(cos Θ0) + ηB sin2 Θ0 cos 2Φ0 2π 4 2
where the νQ and η parameters are defined as in eqs 1a and 1b, and Θ0 and Φ0 are the polar angles giving the direction of the magnetic field H0 with respect to the averaged principal axis of the quadrupolar interaction. Θ0 and Φ0 in our powder samples are, of course, randomly distributed, and the FID is obtained by averaging the function G(t) over the values of Θ0
8082 J. Phys. Chem., Vol. 100, No. 20, 1996
Di Benedetto et al.
TABLE 1: Fitting Parameters Obtained by Simulation of 2H-NMR Spectral Profiles Recorded from Na3PW12O40‚7.2D2O at Different Temperatures T (K)
WR ) WA/WB
(3/2) νQA (kHz)
(3/2) νQB (kHz)
ηA
ηB
πAfB × 10-4 (rad/s)
173 ( 1 193 213 233 293
0.15 ( 0.01 0.25 0.70 3.50
100 ( 1 5 1 1
200 ( 1 200 194 172 100
0.85 ( 0.01 0.00 0.00 0.00
0.80 ( 0.01 0.82 0.75 0.95 0.95
6.7 ( 0.1 8.3 1.0 2.0
and Φ0 assuming that all possible orientations have equal probability. Spectra profiles are finally calculated by Fourier transforming the FID. A modified version of the exchange program19 has been used. This program is based on the theory of chemical exchange previously described (eqs 3-9) and simulates 2H-NMR spectra in the case of two mutually exchanging nuclear species. The input parameters are (1) the population ratio of the two different water components, WR ) WA/WB; (2) the maximum averaged quadrupole splittings and asymmetry parameters of the two species, (3/2) νQA, ηA, (3/2) νQB, ηB; (3) the exchange rate πAfB (jumping frequency) from site A to site B; (5) the broadening parameters a and b (which have been kept constant for all the simulated spectra). The results of the spectra simulation are shown in Figure 2, where the line fitting of the spectrum recorded at 173 K (which is not influenced by the exchange mechanism) is also illustrated, and in Table 1, where the values of the fitting parameters are reported. It is possible to conclude the following. (1) At 193 K D2O molecules with higher mobility, perhaps mono hydrogen bound to the polyanion oxygens, in chemical exchange with the twice hydrogen bond molecules and with a population ratio of 0.15, are present in the secondary lattice of the Na3PW12O40‚7.2D2O sample. (2) At 213 and 233 K spectra are again fitted in terms of two components: one due to almost free D2O molecules (3/2 νQA very small) and the other to hydrogen-bound water molecules, undergoing π-flipping and librational motions. Since the splitting of the bound water appears in this case to be lower than that attributed to double hydrogen bound water, it is possible that the wider spectral component results from a dynamical equilibrium between twice hydrogen bound water and mono hydrogen bound water. In other words, at 213 and 233 K, even if the spectra have been simulated by a dynamical overlapping of two spectral components, they are consistent with the averaged signal of three mutually exchanging species: free, mono hydrogen bound, and double hydrogen bound water molecules. (3) At 293 K two spectral components are present. We have not taken into account the wider component, only observable in highly expanded spectra (see Figure 1b), which from the magnitude of the splitting should be due to twice hydrogen bound D2O in exchange with more mobile molecules. The fitting of the very intense central part (the only visible part at normal magnification) suggests that at 293 K almost 80% of the D2O molecules are not bound since (3/2) νQA is very small and WA/WB ) 3.50, but they chemically exchange with a water species that could be chemisorbed through a single hydrogen bond. The existence of mono hydrogen bound water molecules is supported by the following consideration: from the previous discussion it is evident that the jumping rates reported in Table 1 regard a process during which D2O molecules that at low temperature undergo only π flips become more and more mobile. If we assume that at 173 K they are twice hydrogen bound to the Keggin cage oxygens, the whole process can be
Figure 3. Arrhenius plot of the exchange rate from site A to site B, πAfB (rad‚s-1), of D2O molecules in Na3PW12O40‚7.2D2O.
regarded as a gradual breaking of such bonds with increasing temperature, during which mono hydrogen bound species are formed before free or almost free water is obtained at higher temperatures. The Arrhenius plot of the jumping rates should then give a straight line, even if the exchanging species are not always the same in the full range of temperature. This can, in fact, be observed in Figure 3. It is interesting to notice that the activation energy from more or less bound states is about 4.5 kcal/mol, which corresponds quite well with the energy required to break a hydrogen bond.20 The activation energy for the inverse process is about 1 kcal/mol, and it is probably related to a rotational diffusion process of the water or of Na+-water complexes. We discussed the fitted spectra in the case of n ) 7.2. As is evident from Figure 1a,b, the temperature dependence for larger and smaller n is similar, and similar conclusions can be drawn about water mobility at different levels of hydrations. IV.
31P-NMR
We have shown in a previous paper8 that the 31P-NMR T1 relaxation time and line width can be used to study the dynamics of the water molecules contained in the secondary lattice of heteropolyanions. The method consists in estimating the contribution of T1 and the line width of the 31P-NMR signal due to the 31P-1H dipolar interactions. This objective can be fulfilled by measuring the T1 and the line width of the phosphorus signal once in the presence of D2O and again in the presence of H2O. We followed the procedure outlined in ref 8 and considered that in the samples rehydrated by D2O and 1H magnetization is completely absent. We supposed that line widths of samples hydrated with deuterated and protonic water are affected by the same relaxation mechanisms. They arise from the following interactions: (a) dipolar interaction 31P-183W; (b) chemical shift anisotropy; (c) dipolar interaction with paramagnetic centers; (d) dipolar interaction 31P-1H. The contribution due to the dipolar interaction 31P-1H is present only in the samples hydrated with protonic water, while 31P2H dipolar contribution is assumed to be negligible in samples hydrated with D2O. If we call ∆(H2O) and ∆(D2O) the line widths measured in the presence of H2O and D2O, respectively, the contribution to
Water Dynamics in Na3PW12O40‚nH2O
J. Phys. Chem., Vol. 100, No. 20, 1996 8083
TABLE 2: Experimental 31P-NMR Longitudinal Relaxation Times, T1 (s), and Linewidths, ∆ (Hz), Measured for Na3PW12O40‚nD2O and Na3PW12O40‚nH2Oa n
T1(D2O)
T1(H2O)
T1(H)
∆(D2O)
∆(H2O)
∆(H)
1.4 1.9 2.7 3.3 5.4 7.2 9.1
660 809 845 810 625 575 530
380 452 500 520 345 150 143
896 1020 1220 1450 770 203 196
638 546 395 382 370 358 348
800 755 675 615 440 412 390
162 209 280 233 70 54 42
a T1(H) and ∆(H) are estimated according to eqs 10 and 12 (see text).
half line, width at half-intensity coming from 31P-1H dipolar interactions, ∆(H), can be obtained by the formula
∆(H) ) ∆(H2O) - ∆(D2O)
(10)
Following our previous work8 and references reported therein, ∆(H) is then connected to the second moment due to phospho2 ) and to the correlation time of the rus-proton interaction (ωPH proton motion (τc) as follows:
∆(H) )
ωPH2 τc γH2 γP2pτcn ) 4π 20πr 6
(11)
PH
where γi is the gyromagnetic ratio of nucleus i (i ) 31P, 1H); n is the number of protons around the 31P nucleus; rPH is the mean P-H approach distance; and p is the Plank constant. The above equation is valid in the fast motion regime of the protons, that is to say when the correlation time is much smaller than the inverse of the second moment due to the 31P-1H dipolar interaction. This condition has been proved correct in a previous study.8 Similarly, the contribution to T1 given by the fluctuations of 31P-1H dipolar interactions can be derived by using the equation
1 1 1 ) T1(H) T1(H2O) T1(D2O)
(12)
where T1(H2O) and T1(D2O) are the longitudinal relaxation times measured in the samples containing H2O and D2O, respectively. Using the random field model,21,21 T1(H) can be calculated from molecular parameters according to the equation
τc 1 An ) 6 T1(H) rPH 1 + (ωτc)2
(13)
where ω is the resonance frequency and A is a constant equal to 0.78979 × 1010 Å6 s-1. The results of 31P-NMR T1 and line-width investigations of Na3PW12O40‚nD2O and Na3PW12O40‚nH2O samples, at the temperature of 293 K, are reported in Table 2 and illustrated in Figure 4a,b. Values of ∆(H) and T1(H), estimated according to eqs 10 and 12, are also shown. It is not possible to reproduce these values of ∆(H) and T1(H) inserting in both eqs 11 and 13 the same value of n (the number of hydration water molecules) and for a single value of the correlation time τc. On the other hand, the analysis of 2H-NMR spectral profiles, as stated before, leads to the conclusion that water molecules exist both in bound states and in the free state. Consequently, it has been taken into account the hypothesis that the line width is dominated by the interactions of the bound molecules undergoing slow motion, while the longitudinal relaxation time is influenced by the free water undergoing fast diffusional motions. Under these hy-
Figure 4. (a) Longitudinal relaxation times of the 31P-NMR signal in Na3PW12O40‚nD2O, T1(D2O), and Na3PW12O40‚nH2O, T1(H2O), as a function of the number of hydration water molecules (n). T1(H) is the contribution to T1 given by the 31P-1H dipolar interaction (see text). (b) Line width of the 31P-NMR signal in Na3PW12O40‚nD2O, ∆(D2O), and Na3PW12O40‚nH2O, ∆(H2O), as a function of the number of hydration water molecules (n). ∆(H) is the contribution to line width due to the 31P-1H dipolar interaction see text).
potheses four unknown parameters enter the problem: the number of bound and free molecules, n(b) and n(f), and the corresponding correlation times, τc(b) and τc(f), at every hydration level. Of course, it would be impossible to determine these parameters by using the 31P-NMR data, but the problem can be overcome if the 2H-NMR spectral profiles are taken into account. A close look at Figure 1b shows that the amounts of bound and free water (n(b) and n(f)) can be estimated from the integral curves, which allow the separation of the contributions of the central sharp line from the wider signal (see magnified spectra) due to bonded water. The line-shape analysis of 2H-NMR spectra for n ) 7.2 indicates that the central sharper spectral component (the only component already visible at normal spectral magnificiation at T ) 293 K) can be attributed to free molecules in chemical exchange with a minor fraction of mono hydrogen bound water molecules. The same interpretation holds for samples with n ) 5.4 and n ) 9.1. On the other hand, the central signal appears to be an almost Lorentzian line for values of n lower than 5.4, indicating that at lower content of water the sharper spectral component can be attributed only to rotating molecules. For the 31P-NMR analysis we adopted the simplifying hypothesis that indpendently from the hydration level, the central peak of 2H-NMR spectra recorded at 293 K represents the equilibrium fraction of unbound water. On the basis of this assumption and using the integral curves illustrated in Figure 1b, the amount of free and bound water has been estimated. Inserting then the value of n(f) and n(b) in eq 13 and eq 11, respectively, the values of the correlation time for the free water and bound water have been calculated at every hydration level. The results are shown in Table 3, which also contains the ratios nf/n, obtained from the integrals of Figure 1b. A simple averaged approach distance between the phosphorus nucleus
8084 J. Phys. Chem., Vol. 100, No. 20, 1996
Di Benedetto et al.
TABLE 3: Values of the Correlation Time, τc (s), and Averaged Distance between the Phosphorus Nucleus and the Protons, ri, for Bound and Free Molecules, at Different Hydration Levels and at T ) 293 Ka n
τc(f)
1.4 1.9 2.7 3.3 5.4 7.2 9.1
8.0 × 10 8.0 × 10-9 8.0 × 10-9 8.0 × 10-9 8.0 × 10-9 1.1 × 10-9 1.1 × 10-9 -9
τc(b)
rf (Å)
rb (Å)
nf/n
5.5 × 5.5 × 10-4 5.5 × 10-4 5.5 × 10-4 2.8 × 10-4 2.8 × 10-4 2.8 × 10-4
4.83 5.25 5.77 6.40 6.50 6.62 6.88
3.9 3.9 3.9 3.9 3.9 3.9 3.9
0.50 0.53 0.55 0.70 0.89 0.93 0.96
10-4
a
The nf/n ratios have been obtained from the integrals of Figure 1b. The values of the correlation time are affected by an error of 1%.
and the protons has always been used. Such averaged distances, which are also reported in Table 3, have been estimated on the basis of literature X-ray data.2,15 In the case of the bound water all the values of ∆(H) have been calculated assuming the rPH distance equal to 3.9 Å. It can be seen that the values of τc(b) remain constant from n ) 1.4 to n ) 3.3 at the value of 5.5 × 10-4 s, while it decreases to the value of 2.8 × 10-4 s from n ) 5.4 to n ) 9.1. In the case of free water the averaged rPH distances have been allowed to increase with the increasing of the hydration content, in accord with the increment of the value of the secondary lattice of the heteropolyanions. The correlation time of the free water remains instead constant and equal to 8 × 10-9 s in the range between n ) 1.4 and n ) 5.4, while it drops to 1.1 × 10-9 s for higher hydrations. Such a short correlation time of the free water agrees with the very high value of the translational diffusion coefficient of water molecules in heteropolyanion systems, which have been previously reported in literature (D ) 6 × 10-6 cm2/s23). The correlation time of the bound water is indeed the correlation time of the motions of water molecules around the polyanion cages. It is not surprising that such a correlation time is much longer with respect to the lifetime of the hydrogen bonding, which can be assumed equal to the reverse of the jumping frequency between the differently chemisorbed water molecules: 1/πBfA ) 0.8 × 10-5 s (with πBfA ) πAfBWA/ WB). It must be instead considered that the wandering of a given water molecule on the surface of a Keggin cage requires the subsequent breaking of two hydrogen bonds and as a consequence the increasing of the correlation time of the rPH vector reorientation, with respect to the lifetime of a hydrogen bond. V. Conclusions In conclusion, our work shows that by combining 2H-NMR and 31P-NMR spectroscopies it is possible (1) to assess the
nature of different chemisorbed water molecules in the secondary lattice of Na3PW12O40‚nD2O, as a function of the content of crystallization water (n); (2) to determine the relative quantities of the differently chemisorbed species; (3) to establish the characteristic exchanging times from different sites; (4) to determine the correlation time of the reorientation of the bound molecule around the polyanion cages. We believe that such a methodology can be also easily applied to other chemisorbed species (methanol, methane). References and Notes (1) Hayashi, H.; Moffat, J. B. (a) J. Catal. 1982, 77, 473; (b) J. Catal. 1983, 81, 61; (c) J. Catal. 1983, 83, 192. (2) Keggin, J. F. Proc. R. Soc. (London) 1934, A144, 75. (3) Spirlet, M. R.; Busing, W. R.; Levy, H. A. Acta Crystallogr., Sect. B 1978, 34, 907. Brown, G. M.; Spirlet, M. R.; Busing, W. R. Acta Crystallogr., Sect. B 1977, 33, 1038. Clark, C. J.; Hall, D. Acta Crystallogr. ,Sect. B 1976, 32, 1545. Allman, R.; d’Amour, H. Z. Kristallogr. 1975, 141, 161. Strandeberg, R. Acta Chem. Scand. 1975, A29, 359. (4) Erofeev, L. N.; Shteinberg, V. G.; Atovmyan, L. O.; Korosteleva, A. I.; Leonova, L. S.; Ukshe, E. A. Dokl. Akad. Nauk SSSR 1986, 286 (5), 1162. (5) Dus, R.; Lisowski, W. Surface Sci. 1976, 61, 635. (6) Misono, M.; Sakata, K.; Yoneda, Y.; Lee, W. Y. Proceedings of 7th International Congress on Catalysis; Kodansha: Tokyo, and Elsevier: Amsterdam, 1981; p 1047. (7) Chidichimo, G.; Golemme, A.; Imbardelli, D.; Santoro, E. J. Phys. Chem. 1990, 94, 6826. (8) Chidichimo, G.; Golemme, A.; Imbardelli, D.; Iannibello, A. J. Chem. Soc., Faraday Trans. 1992, 88 (3), 483. (9) Hodnett, B. K.; Moffatt, J. B. J. Catal. 1984, 88, 253. (10) Cohen, M. H.; Reif, F. Solid State Physics; Academic Press: New York, 1947; Vol. 5, p 322. (11) Waldstein, P.; Jackson, S. W. J. Chem. Phys. 1964, 41, 3407. (12) Abragam, A. The Principles of Nuclear Magnetism; Oxford University Press: London, 1962. (13) Kustanovich, I.; Fraenkel, D.; Luz, Z.; Vega, S.; Zimmermann, H. J. Phys. Chem. 1988, 92, 4134. (14) Amm, D. T.; Segel, S. L.; Bostow, T. J.; Jeffrey, K. R. Z. Naturforsch., Phys. Chem., Kosmophys. 1986, 41A (1, 2), 305. (15) Brown, G. M.; Busing, M. R.; Levy, H. A. Acta Crystallogr., Sect. B 1977, 33, 1038. (16) Woessner, D. E.; Snowden, B. S.; Meyer, G. M. J. Colloid. Interface Sci. 1970, 34, 43. (17) Davis, J. H.; Jeffrey, K. R.; Bloom, N.; Valic, N. I.; Higgs, T. P. Chem. Phys. Lett. 1976, 42, 390. (18) Photinos, D. I.; Bos, P. J.; Doane, J. W.; Neubert, M. E. Phys. ReV. A 1979, 20, 2203. (19) Rance, M. A. Ph.D. Dissertation; University of Guelph, 1981. (20) Pimentel, G. C.; McClellan, A. L. The Hydrogen Bond; Freeman: New York, 1960. (21) Pole, C. P.; Farach, H. A. Relaxation in Magnetic Resonance; Academic Press: New York, 1971. (22) Slichter, C. P. Principles of Magnetic Resonance; SpringerVerlag: Berlin, 1980. (23) Chuvaev, V. F.; Yaroslavtseva, E. M.; et al. Koord. Khim. 1987, 13 (1), 80.
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