J. MATER. CHEM., 1991, 1(4),685-689 Reorientational Motions of Hydrogenic Species in 12- Tungstophosphoric Acid 14-Hydrate: A Neutron Scattering Studyt Robert C. T. Slade,* Gillian P. Hall, Helen A, Pressman and Ian M. Thompson Department of Chemistry, University of Exeter, Exeter EX4 4QD, UK Variable-temperature incoherent quasielectric neutron scattering (QENS) measurements have been used to investigate motions of hydrogenic species in 12-tungstophosphoric acid 14-hydrate (H3PW120,,* 14H20). Reorien- tational motions are classifiable as those of H20 (free and coordinated to hydrated protons) and H,O+ [free and in non-centrosymmetric H+(H20), units]. Scattering spectra are satisfactorily modelled assuming quasielastic broadening to arise from a three-fold reorientation of H,O+ about an ionic C, axis with a (model independent) €,= 19+ 1 kJ mol-'.Slower reorientation of H20 and H self-diffusion would not give discernible broadenings on the instrument used. Keywords: 12-Tungstophosphoric acid 16hydrate; Quasielastic neutron scattering; H30+ Reorientation Hydrates of the heteropolyacid 12-tungstophosphoric acid (TPA, H3PW12040) provide a range of related structures and Hf/H20/H30f environments. Heteropolyacids have the highest protonic conductivities reported for inorganic mater- ials at ambient temperat~re'~~ and are potentially important in a range of devices including H2/02 fuel cells4 and electro- chromic displays. The stable TPA hydrate is a function of temperature and relative h~midity;~ TPA 6H20, TPA.14H20, TPA.21H20 and TPA*29H20 are all known single phases. The dominant structural feature in these hydrates is the a-Keggin type [PW,20,0]3- anion of overall tetrahedral symmetry,6 the acid protons being associated with a permeating Hf(H20), network. TPA. 14H20 has a triclinic unit cell.7 Structural studies have been made of the related triclinic (Pi) structure of H3PMo12040~(13-14)H20.8In that case the anion is of the p-Keggin type with reduced pseudosymmetry (C3J. A range of 'water oxygen' environments was observed (H atoms not being detectable by X-ray techniques) and the presence of H20, H30+, H50z (and possiblyH,O,+) inferred. At Exeter a systematic study of ion-molecule dynamics of hydrogenic species in TPA hydrates is in progress, probing both bulk (protonic conductivity) and atomic-level (reorien- tational, diffusive) phenomena.In the case of TPA*6H20 (correctly formulated as [H50~]3[PW120~;]) at the atomic level, we have reported (i) inelastic neutron scattering (IINS) vibrational spectra and normal coordinate analyses for H502f ion9*'O and (ii) a quasielastic neutron scattering (QENS) study of internal reorientation in the H,OZ ion." For TPA 14H20 we have reported the separation of contributions to the temperature dependences of 'H NMR relaxation times into those arising from diffusive and reorientational processes, the latter having been detected in preliminary variable tem- perature QENS st~dies.~ We now report investigation by neutron scattering techniques of reorientational processes in TPA.14H20. Experimental Sample Preparation 12-Tungstophosphoric acid 14-hydrate (TPA 14H20) was prepared via hot filtration of TPA -xH20 (Ventron) dissolved t Neutron scattering experiments carried out at the Institut Laue- Langevin (Grenoble, France) and at the Rutherford Appleton Labora- tory (Oxfordshire, UK). in a minimum of deionised water. The solution was then heated until the first signs of crystallisation were apparent and then allowed to cool with continuous stirring to form a damp paste. This was then equilibrated over 47% (by mass) aqueous sulphuric acid (relative humidity 45%) for 48 h. The powder X-ray diffraction pattern (Cu-Kcr radiation, Philips diffractometer) was fully indexed (0<28/"<25) in terms of a triclinic unit cell [a= 14.38(4)A, b = 14.46(8)A, c= 13.97(4)A, a = 112.07",p= 110.85",y =61.93"].Thermogravimetric analy- sis (Stanton-Redcroft STA-780, flowing air) confirmed the formula TPA*(14+0.5)H20. IINS Spectrum This spectrum (Fig. 1) was recorded using the spectrometer TFXA at the ISIS pulsed neutron source (Rutherford Appleton Laboratory). The sample was contained in a rectangular cross- section aluminium slab can (window thickness 0.1 mm) and maintained at T <20 K using a closed-cycle refrigerator. The energy-transfer resolution of TFXA is 2-3%. QENS Spectra Samples for QENS studies were mounted in circular cross- section aluminium slab cans (window thickness 0.1 mm, sealed with indium gaskets) to give <lo% scattering of the incident beam.Spectra were recorded on the focussing time-of-flight spectrometer IN6 at the Institut Laue-Langevin (ILL). 1 I I 11 1 0 10 20 30 10 50 60 70 80 90 100 energy transfer/ rneV Fig. 1 The incoherent inelastic neutron scattering (IINS) spectrum of 12-tungstophosphoric acid 14-hydrate at Tc20 K Measurements were made in the range 230 < T/K <300 (con- trolled using a standard ILL cryostat, the upper limit chosen to avoid sample dehydration) using an incident neutron wavelength A. of 5.9 A, elastic energy resolution (FWHM) AEo of 70peV and an elastic scattering vector magnitude range 0.25 <Qe,/k <1.75 (at scattering angle 8, Qel= 4.n sin 8/lo).The sample was inclined at 135" to the incident beam.Data acquisition times were typically 2 h. The exper- imental Qel-dependent resolution function was determined using a similarly mounted vanadium sheet sample and empty- can scattering was also determined (both at 300 K). Qel values corresponding to diffraction peaks were known from X-ray diffraction and confirmed using the local program CSUM (following elastic peak heights as a function of Qel). Spectra at these values were removed from further data analysis. Sample spectra were corrected (after subtraction of back- ground and empty-can scattering) for absorption and slab geometry, normalised by comparison to vanadium spectra and then converted to the symmetrised scattering law S(Q, w) form (all steps using standard ILL procedures).Results Vibrational Spectra These spectra were recorded to yield any further information concerning H +(H20), (hydrated protons) present. The infra- red spectrum is dominated by modes for H20 and heteropoly- anions present, these obscuring any information on hydrated protonic species. In the IINS spectrum (Fig. 1) only three bands were discerned (the experimental range was 50-5000 cm-I), these being at ca. 100, 160 and 330 cm-'. These features may arise from H20 molecules in an ice-like state, IINS and IR spectra of ice and sorbed water having features in this Information on hydrated protonic species such as has been obtained for TPA*6H209-12 and HUP (HU02P04*4H20)15is not available in this case, where there is a disordered hydrogen-bonded network and nearly all H atoms will be present in discernible H20 molecules (coordinat- ing H+ and otherwise).Quasielastic Scattering (IN6) Spectra were initially fitted individually to a simple analytical form, consisting of a simple scattering law S(Q, a)=Bo(QP(w)+F(Qy0) (1) convoluted with the instrumental resolution function. The quasielastic component F(Q, w) was taken to be adequately represented by a single Lorentzian (L). The empirical elastic incoherent structure factor [EISF(Q)] is the ratio of the elastic to the total (elastic +quasielastic) intensity in the incoherent scattering spectrum EISF(Q) =Bo(QNBo(Q)+JF(Q, w)dwl- =Bo(Q)for normalised S(Q, w) (2) and is a measure of the time-averaged spatial distribution of the proton (incoherent scattering being dominated by the 'H present), while the time-dependent proton position is in the quasielastic term F(Q, w).Spectra at T<270 K were indistinguishable from the instru- mental resolution function (no discernible quasielastic broad- ening). At higher temperatures the half-width for the Lorentzian (quasielastic) component was found to be Qel-independent at each temperature, indicating that rotation/ reorientation of hydrogenic species is being detected. Empiri- cal EISFs are shown in Fig. 2 as a function of temperature, along with the predicted variations for various dynamical J. MATER. CHEM., 1991, VOL. 1 models (see below). It is expected that EISF+l as Qel+O.The observed small deviations from this behaviour arise from unavoidable incomplete removal of multiple scattering effects in data reduction. A temperature dependence of the EISF is apparent at the highest temperatures and could arise in two ways: (1) the broadenings at the lowest T values are narrow and difficult to determine accurately, (2) a change in the motion@) detected may occur (see below). Discussion Protonic Species and Reorientational Motions Protonic species in TPA. 14H20 include H20 and hydrated protons H+(H20), (one or more of H30+,H50;, H703f; see above). In the case of TPA*6H20 (all H in centrosymmetric H5O;), reorientations of 'terminal waters' were characterised by QENS studies [residence time, r,,,(300 K)=2 x 10-'os].In the case of the related protonic conductor HUP (HU02 Po4*4H2O), QENS data were interpreted in terms of an H30+ reorientation occurring more rapidly [z,,,(303 K) = 4 x 10-l2 s] than H20 reorientations [zreS(303K)= lo-'' s, comparable to that in TPA*6H20].'6 That observation was explained in terms of H30+ reorientation being possible without changes in H-bond distribution, while H20 re-orientations are likely to be coupled. consideration of those results and formulation of TPA*14H20 as [H30+]3[PW12040]3-1 1H20 suggests that: (i) motions described as H20 reorientations may be monitored for recog- nisable H20 molecules [both 'free' and coordinated to acid protons i.e. for H20 and 'terminal waters' in H+(H20),, where n >I], (ii) motions described as H30+ reorientations may be monitored for recognisable H30+ ions ('free', in non- centrosymmetric H50; and in more hydrated groupings).The H-bonded network itself will prevent concerted reorien- tation of larger groupings. The geometries of protonic species present are not known. In order to generate predicted EISFs for various possible motions, it is therefore necessary to choose appropriate bond lengths and angles (EISFs are insensitive to small variations in these parameters). For H20 a bond length of 0.951 A and a bond angle of 118.7' (as found in TPA*6H20 and typical of crystal hydrate^'^) were taken. For H30+ examination of the literature18-20 and assumption of C3" symmetry led to the choice of 1.01 8, and 118'.While possible motions are likely to be classifiable as characteristic of H20 or H30+ (see above), it is possible that within each class crystallographically inequivalent species will have differing residence times zres (and reorientational activation energies and prefactors). Reorientational Models A simple approach to modelling reorientational dynamics in the H-bonded region (following from previous work on HUP16) is to consider separate H20 and H30+ populations and all H atoms within a given population to be dynamically equivalent (or very nearly so). Theoretical EISFs can then be calculated for motions of each population, assuming the other to be reorientating more slowly (contributing only an 'elastic' component to the spectra, no corresponding quasielastic broadening being discernible) and hence describable as a 'static fraction' of the H present.Reorientations of H20 and H30+ can be discussed in terms of jumping of H atoms between equivalent sites on a circle (following Barnes21) or on the surface of a sphere (isotropic rotational diffusion, following Sears22). For a population reorientating about a single axis (Barnes model) the scattering law is then in the form of eqn. (1) (convoluted with the instrumental resolution J. MATER. CHEM., 1991, VOL. 1 0.6-LL v,W 0.4-0.21 ~~ I,,,, QeIlA-' Oa2I to.21 I I I 1 0.00 0.50 1.00 1.50 2.00 2.50 0.00 0.50 1.00 1.50 2.00 2.50 Qe,/A-' QdlA-' Fig. 2 Comparison of empirical Q,,-dependent elastic incoherent structure factors (EISFs) for 12-tungstophosphoric acid 14-hydrate with the predictions of various reorientational models involving hydrogenic species present (see text): at (a)270, (b) 280, (c)290 K, (d) 300 K.Error bars for empirical points are < the diameter of the symbols (0)used function) with where n Bn(Qa)=N-' j0[2Qa sin (np/N)] cos (2nnplN) (4) p= 1 and jo(x)=(sin x)/x for a powder sample, a is the radius (of gyration) of the circle, N is the number of sites and zn= z1 sin2(n/N)/sin2(nn/N).z1is the half-width at half maximum (HWHM) in angular frequency for the first Lorentzian and is related to the mean residence time on a site z,,, by zre,=z'[l -cos(2n/N)] (5) In the case of observation of distinct reorientating and 'static' populations, the predicted EISF(Q) for QENS spectra is simply related to EISFrof(Q) appropriate to the dynamic population [calculated via eqn. (1) and (3)] by EISF(Q)=[Patic +Pro']+Pr0'EISFro'(Q)]/[PStatiC (6) where Paticand Pro'are the (relative) magnitudes of the static and rotating H populations.In calculating theoretical EISFs the following motions were considered. (i) Reorientation of H30+ (H20 Molecules taken as Static) Model A: Three-fold reorientation of H30+ ions about the ionic C3axis (N=6, a= 1.00 A). Model B: Six-fold reorien- tation of H30+ ions about the ionic C3 axis (N=6, a= 1.00 A). This allows for a possible higher order axis at the H30+ site. Model C: Rotational diffusion of H30+ ions about the ionic C3axis (N =co,a = 1.OO A).Model D:Isotropic rotational diffusion of H on a sphere (radius 1.00 A) centred on the 0 atom. Such descriptions correspond to nine of the H atoms in the chemical formula participating in reorien- tation, with 22 H atoms (71% of those present) being 'static'. (ii) Reorientation ofH20 (H30+Ions taken as Static) Model E: Two-fold reorientation of H20 molecules about the molecular C2 axis (N =2, a =0.818 A). Model F: Four-fold reorientation of H20 molecules about the molecular C2 axis (N =4, a=0.818 A). This allows for a possible higher order axis at the H20 site. Model G: Rotational diffusion of H20 molecules about the molecular C2 axis (N =00, a =0.818 A. Model H: Isotropic rotational diffusion of H on a sphere (radius 0.951 A) centred on the 0 atom.Such descriptions correspond to 22 of the H atoms in the chemical formula participating in reorientation, with nine H atoms (29% of those present) being 'static'. EISFs calculated for these models are shown in Fig. 2. Over the experimental Qel range, the predictions of H30+ models 688 A-C are indistinguishable and differ little from model D (H30+ isotropic rotational diffusion). The predictions of H20 models F and G are likewise indistinguishable. Agreement between empirical and theoretical EISFs is best for the naive reorientational models involving a population of dynamically equivalent H30+ ions (models A-D). The possible temperature dependence of the empirical data could then be assigned to dynamic inequivalences within that popu- lation.The separation of populations is simplistic. The pos- sibility that some of the H20 molecules can rotate more freely than others (with H30f as a static species) and hence that a higher static fraction should be included in models E-H (leading to closer agreement with experimental EISFs) cannot be ruled out. Interpretation of the data in terms of observation of the effects of H30+ reorientation is, however, in agreement with earlier studies of TPA*6H2O1' and HUP16 in which H20 reorientations [zre,(3O0K) z10-lo s] were too slow to produce quasielastic broadenings of the magnitude observed in this study. Modelling the Scattering Law The '(Q,O) data were fitted to the form corresponding to model A (three-fold reorientation of H30 + ion).The hydrogen-bonded network discourages further con- sideration of models involving rotational diffusion (uniaxial or isotropic) and there are no grounds for preferring model B (six-fold reorientation), the predictions of which are very similar in the experimental Qel range. Spectra were initially fitted individually as a function of Qel to yield the temperature dependent HWHMs of the first Lorentzian in the Barnes model [eqn. (3)-(5) with N= 31 and the z,,, values given in / I I 10 i 0a 7 0 0-7 E/meV # 1 1 1 I 1 J. MATER. CHEM., 1991, VOL. 1 Table 1. Fig. 3 presents final fits of S(Q,o)as a function of Qe, and temperature (HWHM now fixed to the mean value at each temperature), which appear satisfactory at all tempera- tures and Qel values.Naively assuming an Arrhenius temperature dependence for qes,it follows that the pre-exponential factor z,OS= (3.0& 0.2) x 10-l2 s and the (model-independent) activation energy E,= 19+1 kJ mol-'. Relationship to Previous (IN5) Data In the spectra reported previously (obtained using instrument IN5 at ILL), quasielastic broadenings were discerned only at 280 and 290 K.7 The Qel-dependent EISFs were compatible with those we now report (from IN6 data), but the poorer counting statistics of IN5 lead to considerably large errors and more scatter in the data. Refitting of individual IN5 spectra to the theoretical form used for the IN6 data (above) led to large uncertainties in HWHM values at each tempera- ture.IN5 spectra (summed in groups of four for each detector angle to improve counting statistics) were therefore remodelled Table 1 Reorientational parameters for H,Of reorientation in 12- tungstophosphoric acid 14-hydrate T/K HWHM/peV" Tres/lo-lls 270 16+4 6.17 f0.28 280 26k4 3.75 k0.45 290 47+4 2.10 k0.45 300 83k2 1.19f0.03 aFor the first Lorentzian in the Barnes modelz1 (see text). 1 f II\. I 1 0 I 0-7 I 0 0.7 ElmeV I \ 0 0-7 0 J. MATER. CHEM., 1991, VOL. 1 (as a function of temperature and Qel)assuming model A and fixing the HWHM to the values predicted from IN6 data analysis (above). The consequent fits were similar in quality to those reported previ~usly.~ The poor statistics characteristic of the IN5 spectra combined with the small broadenings observed prevented reliable modelling with IN5 data alone.Other Motions While conductivity studies support conduction via crystallite surfaces as the most rapid H+ conduction pathway in a pelletised ample,^ it is evident from NMR studies that self- diffusion of H occurs within the crystallites3 and the H20 present will also be capable of reorientational motions. Direct measurement by pulsed field gradient (PFG) NMR of the H self-diffusion coefficient gave D (300 K)zl x1OP6 cm2 s-'.~ At low Qel values the quasielastic broadening (HWHM) due to self-diffusion r(Q)= DQz1.23It follows that the correspond- ing maximum quasielastic broadening (at Qel= 1.75A-') is < 1 peV (calculated value 3 x Hz =7 x lop8eV) and is too small to discern with the instrumental resolutions used.As discussed above, broadenings due to slow H20 reorien-tations are also too small to detect at the resolutions used. The above considerations could suggest further measure- ments on instruments of higher resolution such as the back- scattering spectrometers IN10 and IN13 at the ILL. The shorter wavelengths then used and the low (triclinic) symmetry of the unit cell preclude such studies, contamination of spectra by coherent scattering (diffraction) occurring in all detectors. It has been possible to correct data for such prevalent Bragg ~cattering,~~but only with prior assumption of a particular reorientational model.NMR studies3v7 detect both H self-diffusion (by 'H PFG NMR and high-temperature variations in 'H relaxation times TI and T2)and a reorientational contribution (deconvoluted as a lower temperature minimum in Tl). The 'reorientational Tl minimum' is likely to be the sum of separate minima, one arising from H20 reorientations and another (at lower tem- perature) arising from H30+ reorientation. The deduced E, (15fl kJ mol-') and 7: (1 x s) are therefore not directly comparable to values obtained in this study. Conclusions The proton-conducting solid electrolyte 12-tungstophosphoric acid 14-hydrate (TPA. 14H20) contains a range of protonic species [H,O and H+(H20),]. Vibrational spectra do not allow further characterisation of hydrated protons present.Reorientational motions can be classified as those of H20 (free and coordinated to hydrated protons) and H30+ [free and in non-centrosymmetric Hf(H20), units]. Incoherent QENS spectra of H30+ ions can be satisfac- torily (if naively) modelled assuming three-fold reorientation H30+ ions about the ionic C3 axis with a (model-independent) activation barrier E, = 19f1 kJ mol -'. Quasielastic broaden- ings that would arise from a slower reorientation of H20 and from H self-diffusion (both evident in NMR relaxation stud- ie~~.~)are too small to be discerned with the instrumentation used. This interpretation is in line with previous studies of hydrated proton-conducting solid electrolytes,"~'s but the possibility that a fraction of the H20 present rotates more freely than other hydrogenic species present (with the quasi- elastic broadenings observed then arising from that motion) cannot be ruled out.We thank the Institut Laue-Langevin for access to the spec- trometers IN5 and IN6 and the ISIS source (Rutherford Appleton Laboratory) for access to the spectrometer TFXA. We thank SERC for grants in support of the Exeter neutron scattering programme and studentships for G.P.H., H.A.P. and I.M.T. We thank Drs. G.J. Kearley, C. Poinsignon, J.Tomkinson and R.C. Ward for practical assistance and helpful discussions. References 0. Nakamura, T. Kodama, I. Ogino and Y. Mikaya, Chem. Lett., 1980, 1, 231. A. Hardwick, P.G. Dickens and R. C. T. Slade, Solid State Zonics, 1984, 13, 345. R. C. T. Slade, J. Barker, H. A. Pressman and J. H. 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