Effect of the Extent of Hydration on the Motion of Interlamellar Water: A

motion about the CB2 axis of the interlamellar water is now no longer present. We propose a ..... and the CB* axis, δ is the angle between the CB* ax...
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J. Phys. Chem. B 2000, 104, 9091-9098

9091

Effect of the Extent of Hydration on the Motion of Interlamellar Water: A 1H NMR Study of the Ion-Exchanged Layered Hydrates Cd0.75PS3Na0.5(H2O)y, y ) 1, 2 N. Arun and S. Vasudevan*,† Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore, India

K. V. Ramanathan*,‡ Sophisticated Instruments Facility, Indian Institute of Science, Bangalore, India ReceiVed: February 17, 2000; In Final Form: July 6, 2000

Hydrated Na ions have been ion-exchange intercalated into layered cadmium thiophosphate to give Cd0.75PS3Na0.5(H2O)y. Two stable phases with y ) 1 and 2 are obtained with lattice expansion 2.8 and 5.6 Å, respectively. The former phase is formed from the y ) 2 phase either by evacuation or heating. The effect of the extent of hydration on the motion of interlamellar water has been investigated by analyzing the dipolar splittings observed in the 1H NMR spectrum as the system transforms from the y ) 2 phase to the y ) 1 phase. In the y ) 2 phase the water molecules rotate about the interlamellar normal, C B*, as well as about their C B2 symmetry axis. On formation of the y ) 1 phase there is partial loss of rotational freedom; rotational motion about the C B2 axis of the interlamellar water is now no longer present. We propose a simple electrostatic model to explain these results.

1. Introduction The layered cadmium thiophosphate CdPS3 undergoes an unusual ion-exchange intercalation reaction in which hydrated alkali cations from an aqueous solution insert into the interlamellar space with an equivalent loss of cadmium ions, leaving immobile vacancies in the layer.1 The host lattice, cadmium thiophosphate, is formed by the stacking of CdPS3 sheets, built from edge sharing CdS6 and P2S6 polyhedra (Figure 1). The van der Waals gap is 3.2 Å.2 Intercalation occurs with a dilation of the lattice along the interlayer axis, the extent of which depends on the nature of the guest cation and the extent of its hydration. The intercalation reaction may be written as

CdPS3 + 2xNa+(aq) f Cd1-xPS3Na2x(H2O)y + Cd2+(aq) x ) 0.25, y ) 2 where the guest species, hydrated Na ions, reside in the interlamellar space. The lattice expansion on intercalation, ∆d, is 5.6 Å; this is twice the van der Waals diameter of a water molecule. The projected electron density as calculated from the X-ray diffraction 00l peaks shows that the water molecules in the galleries form a bilayer with Na ions probably located in the octahedral interstities3 of the bilayer, a geometry very similar to that proposed for interlamellar hydrated ions in mica-type silicates.4 The density of the interlamellar water, as calculated from the stoichiometry and lattice parameters, indicates that the two-dimensional bilayer is not infinite but broken up into islands or clusters. Alternatively these clusters may be viewed as being formed by edge sharing Na(H2O)6 octahedra. This model accounts not only for the density of the interlamellar water but also the average Na to H2O stoichiometric ratio of 1:4, which is between that of an isolated Na(H2O)6 and the infinite †

E-mail: [email protected]. ‡ E-mail: [email protected].

Figure 1. Structure of CdPS3. (a) The in plane structure in which CdS6 and P2S6 polyhedra are linked to form CdPS3 sheets. The P-P bond is collinear with the trigonal axis of the P2S6 polyhedra. (b) Perspective view of the structure viewed along the b axis showing the stacking of CdPS3 layers. The a axis is horizontal to the center of the figure. The circles represent P, Cd, and S with increasing size.

Na(H2O)2 sheet. Cd0.75PS3Na0.5(H2O)2 is conducting with a dc conductivity of 10-6 S/cm at 300 K and Arrhenius activation energy 15.6 kcal/mol.5 It was observed that loss of water from

10.1021/jp000620m CCC: $19.00 © 2000 American Chemical Society Published on Web 09/13/2000

9092 J. Phys. Chem. B, Vol. 104, No. 39, 2000 Cd0.75PS3Na0.5(H2O)y(y ) 2) on heating occurred by a two-step process.5 About half the interlamellar water (9.2%) is lost at 343 K, leading to the formation of Cd0.75PS3Na0.5(H2O)y(y ) 1) with a lattice expansion ∆d of 2.8 Å. The remaining water is lost at 370 K. The y ) 1 phase may also be obtained by evacuation of Cd0.75PS3Na0.5(H2O)y(y ) 2) at 10-2 Torr at 300 K. The loss of water is completely reversible; the y ) 2 phase being recovered on exposure of the y ) 1 sample. The conversion of the y ) 2, ∆d ) 5.6 Å “bilayer” phase to the y ) 1, ∆d ) 2.8 Å, “monolayer” phase is accompanied by a dramatic drop in conductivity.5 In the y ) 2 bilayer phase NMR studies had shown that the Na ions are mobile and consequently the material is conducting whereas in the insulating monolayer phase they are immobile.5 NMR studies6 had also shown that in the bilayer y ) 2 phase conductivity was not due to hopping of Na ions between octahedral vacancies of the H2O bilayer but by an anisotropic sliding motion of the Na ion along with its hydration shell. The motion is such that the orientation of the C B2 symmetry axis of the water molecules of the hydration shell with respect to the interlamellar normal, C B*, is always preserved. The water molecules, however, are not static but B* axis as well as undergo fast rotation (τ , 10-5 s) about the C about their C B2 axis. The water molecules literally acting as molecular ball-bearings allowing the hydrated ion to slide between the CdPS3 sheets. In this paper we report results of our study on how the extent of hydration and gallery dimension affect the motion of water molecules in the interlamellar space. We have carried out a 1H NMR study of Cd0.75PS3Na0.5(H2O)y as the system transforms from the y ) 2 phase to the y ) 1 phase due to heating or partial evacuation. NMR spectroscopy is particularly attractive for studying guest molecules intercalated in layered host lattices.7 In these systems the motion of the guest is usually strongly anisotropic and consequently orientation dependent nuclear spin interactions, e.g., dipolar interactions, are partially averaged. In such situations the NMR spectra can exhibit characteristic features which can provide information on the dynamics and type of motion of the guest molecules. In a number of hydrated layered compounds6,8-10 the proton NMR spectra display a near classical Pake line shape characteristic of the proton-proton dipole-dipole interaction which has been assigned to water molecules undergoing anisotropic motion in the interlamellar space. In Cd0.75PS3Na0.5(H2O)y we find that the conversion of y ) 2 to y ) 1 phase is accompanied by loss in the rotational degrees of freedom of the interlamellar water. We propose a simple electrostatic model to explain these observations. 2. Experimental Section Cadmium thiophosphate, CdPS3, was prepared from the elements following the procedure reported in ref 11. Plateletlike crystals of CdPS3 were grown by chemical vapor transport using sulfur as a transporting agent. Powder as well as crystals of Cd0.75PS3Na0.5(H2O)2 were prepared by stirring CdPS3 with 1 M aqueous solution of NaCl in the presence of EDTA.3 Cadmium and sodium ion stoichiometries were established by atomic absorption spectrometry (AAS) and the extent of hydration by thermogravimetric measurements. The formation of the intercalated compound was confirmed by powder X-ray diffraction (Shimadzu XD-D1; Cu KR). Attempts to solve the structure of the intercalated compounds by single-crystal X-ray diffraction methods were unsuccessful since crystals showed considerable mosaic. Thus the Weissenberg photographs showed spots only for the 00l reflections, while all other reflections appeared as streaks. The one-dimensional electron density of

Arun et al. the intercalated compounds was calculated from the X-ray diffraction data. 00l reflections up to eighth order were recorded for crystals mounted flat on a sapphire disc. The disc occupied the same position as the regular sample holder on the goniometer. The integrated intensities of the 00l reflections, after correction for Lorentz polarization effects, were used to calculate the structure factor

|F00l| ) (I00l/Lp)1/2

(1)

where I00l is the integrated peak intensity and Lp, the Lorentz polarization factor, is Lp ) (1 + cos2 2θ)/sin2 θ cos θ. The projected electron density, F(z), was synthesized from z/L ) 0-1 from the discrete transform

F(z) ) (1/L)

∑lF00l exp(-2πilz/L)

(2)

where L is the lattice periodicity. The phase of the structure factors was assumed identical to that of CdPS3. The assumption is not too drastic since the intercalated compounds crystallize in the same space group as CdPS3, C2/m, with only the c lattice parameter changing on intercalation. Static 1H spectra of the powder and single crystal samples of Cd0.75PS3Na0.5(H2O)y were recorded on a Bruker DSX-300 solid-state FT-NMR spectrometer at a Larmor frequency of 300.13 MHz. The spectra were obtained by a Fourier transform of the free induction decay (FID) following the π/2 pulse. Temperature variation studies on both single crystal and powder samples were carried out using the Bruker variable-temperature accessory (B-VT 2000). Angular variation studies on a singlecrystal sample were performed by using an assembly similar to that in ref 12. 3. Results and Discussion A. X-ray Diffraction. The X-ray diffraction pattern of crystals of Cd0.75PS3Na0.5(H2O)y(y ) 2) is shown in Figure 2. As mentioned in the experimental section only the 00l reflections are observed. The 00l X-ray diffraction pattern of pristine CdPS3 recorded under similar conditions is also shown in Figure 2. The as-prepared Cd0.75PS3Na0.5(H2O)y(y ) 2) shows an interlayer spacing of 12.1 Å, which corresponds to a lattice expansion on intercalation, ∆d, of 5.6 Å. All other lattice parameters, as obtained from the XRD of powders, showed no significant change from that of the host CdPS3. The formation of Cd0.75PS3Na0.5(H2O)y(y ) 1) on evacuation of the y ) 2 phase leads to a reduction in the interlayer spacing (Figure 2). The interlayer spacing of 9.35 Å corresponds to a lattice expansion, ∆d, of 2.8 Å as compared to CdPS3. As in the case of the y ) 2 sample all other lattice parameters remain unchanged. The one-dimensional projected electron densities of the intercalated compounds were calculated from a Fourier transform of the 00l reflections and are also shown in Figure 2. For comparison that of the pristine host CdPS3 is also shown. The one-dimensional electron density map of CdPS3 shows the S atoms located 1.6 Å from the Cd atom, in agreement with the reported single-crystal data.2 The resolution of the present experimental data did not allow the phosphorous atom electron density to be detected, which, according to crystallographic data,2 should have appeared at a distance of 1.17 Å from the Cd atoms. As expected for the pristine host, no electron density is observed between the peaks assigned to the S atoms. The projected electron density of Cd0.75PS3Na0.5(H2O)y(y ) 2) shows the layer structure identical to that of CdPS3 with the electron density of the S atoms (the peaks at z/L ) 0.133 and z/L )

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Figure 2. X-ray diffraction pattern showing the 00l reflections, the projected one-dimensional electron density, and the schematic of the structure of (a) CdPS3, (b) Cd0.75PS3Na0.5(H2O)y(y ) 1), and (c) Cd0.75PS3Na0.5(H2O)y(y ) 2). The water molecules and sodium ions are shown as open circles and dotted circles, respectively.

0.869) appearing at 1.63 Å from the Cd atom. In contrast to pure CdPS3, there is considerable electron density in the center of the gap. In addition, two peaks are observed at z/L ) 0.279 and 0.723, which corresponds to 3.37 Å from the Cd atoms of the layer. These features had been interpreted earlier3 as due to Na ions in the center of the gap and the electron density at z/L ) 0.279 and 0.723 to water molecules coordinated to Na ions probably in an octahedral fashion similar to that reported for hydrated ions in mica-type silicates.4 The projected electron density of Cd0.75PS3Na0.5(H2O)y(y ) 1) is quite different from that of the y ) 2 phase. In addition to the features of the CdPS3 layer, electron density at 3.3 Å (z/L ) 0.35) and 6.13 Å (z/L )

0.649) is observed. These may be assigned to Na ions, and its off-center location suggests that the Na ions are probably coordinated on one side to sulfur atoms of the layer and on the other to water molecules. The fact that the electron densities at z/L ) 0.35 and 0.649 are identical suggests that within the interlamellar region sodium ions have equal probability of being bound to either the top or bottom Cd0.75PS3 layer. A schematic cartoon of the arrangement of Na ions and water molecules in the interlamellar region of Cd0.75PS3Na0.5(H2O)y(y ) 1 and 2) phases, based on the projected electron density, is shown in Figure 2. The observed electrical behavior of Cd0.75PS3Na0.5(H2O)y(y ) 1 and 2) may be rationalized on the basis of

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Figure 3. 1H NMR spectra of Cd0.75PS3Na0.5(H2O)y(y ) 2) powder for different periods of evacuation time: (a) 0, (b) 20, (c) 30, (d) 60 min.

structural information inferred from Figure 2. The negligible DC conductance of the y ) 1 phase5 is a consequence of the fact that the Na ions are coordinated on one side by sulfur atoms of the layer and hence immobile. In the y ) 2 compound, in contrast, where DC conductivity is appreciable, Na ions are coordinated only to water molecules. B. NMR. The room temperature 1H NMR spectra of Cd0.75PS3Na0.5(H2O)y(y ) 2) (Figure 3a) shows a well-resolved Pake powder pattern characteristic of an isolated, dipolarcoupled pair of spins. The separation between the inner singularities and between the outer shoulders are 6.7 and 13.4 kHz, respectively. The 1H NMR spectra of Cd0.75PS3Na0.5(H2O)y(y ) 2) for various periods of evacuation at 10-2 Torr (300 K) is shown in Figure 3. The formation of Cd0.75PS3Na0.5(H2O)y(y ) 1) on evacuation is characterized by the appearance of a second doublet with a separation of 40 kHz. This feature is just about discernible in the spectra recorded after 20 min of evacuation but is quite prominent after 30 min of pumping. After about an hour of evacuation the features due to the y ) 2 compound are completely absent and the spectrum now shows a new Pake powder pattern with a separation of 40 kHz between the inner singularities and 80 kHz between the outer shoulders. (The spectra shown in Figure 3 are not typical powder patterns since the Cd0.75PS3Na0.5(H2O)y powders were packed prior to evacuation leading to a pronounced preferred orientation of the flaky crystallites.)

As mentioned in the introduction the y ) 1 phase may also be obtained by heating the y ) 2 phase. The proton NMR spectra of a single crystal of Cd0.75PS3Na0.5(H2O)y(y ) 2) as a function of temperature are shown in Figure 4. The spectra shown in Figure 4 are for crystals oriented such that the interlamellar normal C B* of the crystals is at an angle (δ) of 0° with respect to the applied magnetic field H B o. The room temperature spectrum of Cd0.75PS3Na0.5(H2O)y(y ) 2) shows a well-resolved doublet of 13 kHz. The variation of the doublet separation, ∆, as a function of the angle, δ, was measured and found to follow the relation ∆ ) 13(3 cos2 δ - 1)/2. On heating the intensity of the 13 kHz doublet decreases and a new doublet with a separation of 80 kHz starts appearing. At 330 K the 13 kHz doublet is completely absent and only the 80 kHz doublet is seen. On cooling back to room temperature the 80 kHz doublet is retained as long as the crystals are not exposed to the atmosphere. The doublet separation in the 1H NMR spectra of Cd0.75PS3Na0.5(H2O)y(y ) 1) was also found to a show a (3 cos2 δ - 1)/2 angular dependence; the separation obeying the relation ∆ ) 80(3 cos2 δ - 1)/2. To summarize the 1H NMR spectra of crystals of both Cd0.75PS3Na0.5(H2O)y(y ) 1 and 2) phases are characterized by a well-resolved doublet with a (3 cos2 δ - 1)/2 angular dependence. The magnitude of the doublet separation for the two are, however, quite different. The splitting for the y ) 1 phase for δ ) 0° is 80 kHz, while for the y ) 2 phase for the

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Figure 4. 1H NMR spectra of Cd0.75PS3Na0.5(H2O)y(y ) 2) crystal for δ ) 0° at 300, 320, and 330 K.

same orientation it is 13 kHz. The 1H NMR spectra of powders of the y ) 1 and 2 phases exhibit powder patterns with the separation between the inner singularities and outer shoulders being different. Pake doublet-like spectra have been reported in a number of hydrated layered intercalates but are usually observed in association with a central component which is assigned either to isotropically tumbling water molecules which lie outside the hydration shell and/or to proton exchange.7,9,10 The absence of a central component in the 1H NMR spectra shown in Figures 3 and 4 clearly rules out the existence of either of these two processes in both Cd0.75PS3Na0.5(H2O)y (y ) 1) and -(y ) 2) and also indicates some similarity in the motion of interlamellar water molecules in the two cases. The 1H NMR spectra (Figures 3 and 4) correlate fairly well with the spectra expected of a solid in which nuclear spins occur in isolated pairs. In the case of isolated water molecules it is well-known13 that intramolecular dipolar interactions give rise to a doublet with separation 3 ∆ ) R(3 cos2 θ - 1)/2, where R ) 3γ2p/rH-H , θ is the angle between the interproton vector and the magnetic field, and rH-H the interproton distance. For rH-H of 1.58 Å, corresponding to water molecules in their equilibrium geometry, Requil ) 91 kHz. The fact that the ratio of the splitting for δ ) 90° and 0° in the crystal spectra is 1:2 and these values are close to that for the inner singularities and outer steps, respectively, of the powder spectrum (Figure 3) implies that the orientations of the intramolecular H-H vectors of all the interlamellar water molecules with respect to the C B* axis, averaged over all possible molecular motions, have the same value. Assuming that rH-H of the intercalated water molecules is 1.58 Å, i.e., the water molecules maintain their equilibrium geometry even after intercalation, the observed dipolar splitting can be interpreted based on the motion of water molecules. The proton NMR spectrum of Cd0.75PS3Na0.5(H2O)y(y ) 2) has been previously analyzed6 and the interlamellar water molecules have been shown to undergo fast rotational motion about the interlamellar normal, C B*, as well as about their C B2 symmetry axis. Corresponding to this motion the dipolar splitting may be expressed as

∆) Requil((3 cos2 ψ - 1)/2)((3 cos2 δ - 1)/2)((3 cos2 γ - 1)/2) (3) where ψ is the angle between the C B2 axis of the water molecule

and the C B* axis, δ is the angle between the C B* axis and H B o, and γ is the angle between the H-H vector and C B2 axis of the water molecule (the definition of angles is indicated in Figure 5a). The observed angular dependence of ∆ has been shown to be satisfied for ψ ) 67.8°, which is similar to that obtained for hydrated ions in mica-type silicate clays (ψ ) 65°)8 and corresponds to Na(H2O)6 octahedra being trigonally compressed. A motional model has also been postulated in which the C B* axis, about which rotation occurs, passes through the water molecule, i.e., a spinning motion of individual water molecules along with a rotation about the C B2 axis. This motion allows the water molecule to maintain an identical orientation toward neighboring Na ions, while at the same time satisfying requirements for the observed 1H Pake doublet splitting and its angular dependence. The larger magnitude of the dipolar splitting in Cd0.75PS3Na0.5(H2O)y(y ) 1) clearly indicates that dipolar interactions are averaged to a lesser extent as compared to the y ) 2 compound. As in the preceding analysis the magnitude of the observed dipolar splitting may be arrived at by considering the position of interlamellar water molecules in the immediate vicinity of a Na ion in Cd0.75PS3Na0.5(H2O)y(y ) 1). If the C B2 axis of the water molecules rotates about the interlamellar normal, C B*, then the function (3 cos2 θ - 1)/2 must be averaged for this rotation. The function (3 cos2 θ - 1)/2, which is the second degree Legendre polynomial P2(cos θ), may be expressed as P2(cos θ) ) P2 cos(δ)P2 cos(β), where β, the angle between the C B* axis and the H-H vector, is the same for all the water molecules. The experimentally observed angular dependence of the dipolar splitting in Cd0.75PS3Na0.5(H2O)y(y ) 1), ∆ ) 80(3 cos2 δ - 1)/2 then requires that β be 16°. Correspondingly B*, the angle between the C B2 axis and the interlamellar normal, C will have a value of 74°. Any further averaging of the dipolar interaction leads to unphysical values for the geometrical parameters. Other types of motion may also be ruled out, e.g., rotational motion exclusively about the C B2 axis would lead to a maximum splitting of 45.5 kHz, half of Requil, much less than the experimentally observed 80 kHz separation. Thus in this case the only motion possible for the water molecule is rotational motion about the C B* axis. As in the case of y ) 2 compounds, the rotational motion could be one involving a collective motion of the hydration shell as a whole or an “individual” spinning motion in which the C B2 axis rotates about an axis parallel to C B* and passing through

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Figure 6. Schematic of the simplified electrostatic model of Cd0.75PS3Na0.5(H2O)y showing a coordinated water molecule trapped between two insulating, negatively charged discs of radius X with uniform surface charge density, σ, and separated by a distance Z.

Figure 5. (a) Definition of the angles used in the analysis of the 1H NMR spectra of Cd0.75PS3Na0.5(H2O)y(y ) 2). The C B3 axis of the Na(H2O)6 octahedra and the C B2 axis of the water molecule are shown as dotted lines. (b) Definition of the angles used in the analysis of the 1H NMR spectra of Cd 0.75PS3Na0.5(H2O)y(y ) 1).

the water molecule as shown in Figure 5b. For reasons mentioned in the preceding analysis, an individual motion is favored since it would allow the water molecule to maintain an identical orientation toward neighboring Na ions, between which stoichiometry dictates that it be shared. The analysis of the dipolar splitting in the 1H NMR spectra of Cd0.75PS3Na0.5(H2O)y(y ) 1 and 2) thus indicates that in both

compounds the orientation of the C B2 axis of the water molecules with respect to the interlamellar normal is almost identical (68° and 74° for the y ) 2 and 1 compounds) and that the C B2 axis rotates about the interlamellar normal. It is also clear that the dipolar interactions are averaged to a lesser extent in the y ) 1 compound, which implies reduced degrees of freedom. The only difference is that in the y ) 2 compound the water molecules rotate about their C B2 axis but in the y ) 1 compound they do not. The spectra at intermediate stages of evacuation and temperature shown in Figures 3 and 4, respectively, arise out of the presence of both the type of phases in the transformation from y ) 2 to y ) 1. C. Rotation of Interlamellar Water. The loss of rotational freedom about the C B2 axis of the interlamellar water in the y ) 1 phase is rather puzzling since the interlamellar expansion of 2.8 Å on intercalation would provide sufficient space to allow for such a motion. In fact the expansion is sufficient even for an isotropic tumbling motion; space constriction may therefore be ruled out as the cause for the absence of rotational motion. The major difference between the y ) 1 and y ) 2 phase is, of course, the fact that the distance between Cd0.75PS3 sheets in the former is considerably smaller. Additionally, as may be seen from Figure 2, the disposition of the interlamellar water vis-a`vis the top and bottom layers is very different in the two phases. In the monolayer y ) 1 phase the protons of the water molecule are almost equidistant from the top and bottom layers, whereas in the bilayer y ) 2 phase they are closer to one of the layers. It may be recalled that the Cd0.75PS3 sheets are negatively charged. In addition the protons of the water molecules coordinated to the Na ions are likely to bear a partial positive charge. The change in electrostatic potential energy during rotation about the C B2 axis of the interlamellar water may be expected to be quite different in the two phases and could be the reason for the absence of such a motion in the y ) 1 phase. To test this hypothesis we construct a simplified model of Cd0.75PS3Na0.5(H2O)y by considering a water molecule trapped

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Figure 7. Variation of (U(0) - U(90)) as a function of X/Z and (Z - R)/Z.

between two Cd0.75PS3 sheets separated by a distance Z (Figure 6). The negative charge on the insulating Cd0.75PS3 sheets is considered to be localized and represented by a negatively charged disc of radius X with uniform surface charge density, σ, and is identical for the y ) 1 and y ) 2 phases. Treating the insulating Cd0.75PS3 sheets as a lattice of discrete negative point charges would be inappropriate. Photoemission14 and X-ray absorption spectra15 as well as band structure calculations15 on the MPS3 compounds have indicated strong covalent bonding within the P2S6 moiety and considerable overlap of the S 3p orbitals. The valence band, in fact, originates mainly from S 3p states admixed with P 3p states and has typical band widths of ≈2 eV in these compounds.16 The protons of the interlamellar water bear a partial positive charge qH. The NMR results require that the C B2 axis be at an angle ψ ) 90 - β with respect to the interlamellar normal, C B*. The coordinate bond between the water oxygen and Na ion coincides with the C B2 axis. We calculate the potential energy of the system for various values of η, the angle between the H-H vector and a plane perpendicular to the layer containing the C B* and C B2 axis. When η has a value of 0° the H-H vector is perpendicular to the C B* axis. The interproton distance is designated rH-H and the distance from the center of the H-H bond to bottom layer (disc), R. We consider the change in the electrostatic potential energy, U(η), for rotation of the H-H vector about the C B2 axis for various values of X/Z and (Z - R)/Z. A (Z - R)/Z value close to 0.5 would represent the situation in the y ) 1 phase, while (Z R)/Z greater or less than 0.5 to the y ) 2 phase. The X/Z value for y ) 1 phase would, obviously, be larger than that for the y ) 2 phase. In computing the electrostatic potential energy we ignore all terms that are invariant to rotation of the H-H vector about the C B2 axis. These terms include the proton-proton interaction, the interaction between the protons and the oxygen of the water as well as the Na ion, the interaction between the

water oxygen and the Na ion, and their respective interactions with the layers. As may be seen from Figure 6 the distance associated with these interactions do not change with η. For a single proton with charge qH interacting with a circular disc of radius X and surface charge density σ as in Figure 6, the electrostatic potential energy is given as

U)

qH σ 2 ((X + z2)1/2 - z) 2o

(4)

where z is the distance between the point charge qH and the disc. The η-dependent part of the electrostatic potential energy of the system shown in Figure 6 may be therefore written as

U(η) ) qHσ/(2o){[(X2 + (R - r′ sin η)2)1/2 (R - r′ sin η)] + [(X2 + (R + r′ sin η)2)1/2 (R + r′ sin η)] + [(X2 + (Z - R - r′ sin η)2)1/2 (Z - R - r′ sin η)] + [(X2 + (Z - R + r′ sin η)2)1/2 (Z - R + r′ sin η)]} (5) where Z is the distance between the circular discs, X is the radius of the disc, and r′ ) rH-H sin ψ/2. The first two square bracketed terms represent the interaction of the two protons with the bottom layer, while the last two terms represent that with the top layer. From the derivative of U(η) (eq 5) with respect to η, it may be shown that irrespective of the values of X, Z, and R, U(η) has a maximum for η ) 0° and decreases monotonically for values of η f ( (π/2). The difference (U(0) - U(90)) is therefore the electrostatic potential energy contribution to the barrier for rotation of the H-H vector about the C B2 axis. In Figure 7 the function (U(0) - U(90)) has been plotted for various values of X/Z and (Z - R)/Z. The units of the ordinate are qH/(2o) and the values have been computed for r ) 0.79 Å

9098 J. Phys. Chem. B, Vol. 104, No. 39, 2000 and ψ ) 71°, which is the average of the experimentally observed values for the y ) 1 and 2 phases. It may be seen from Figure 7 that the difference (U(0) U(90)) increases with increasing values of X/Z. For the y ) 1 phase with a larger value of X/Z, the electrostatic potential energy contribution to the barrier for rotation would therefore be more significant as compared to that for the y ) 2 phase. The effect of displacing the water molecules toward/away from the layer given by different values of (Z - R)/Z has also been explored. There is qualitative change in the behavior of (U(0) - U(90)) depending on whether X/Z is greater or less than unity. For large values of X/Z (U(0) - U(90)) has a maximum for (Z - R)/Z ) 0.5, i.e., when the water molecule is equidistant from the top and bottom layers as in the case of the y ) 1 phase, for which not only is the X/Z value larger but also the individual water molecules are almost symmetrically placed between the Cd0.75PS3 sheets. The results of this simple electrostatic model indicate that the contribution of the electrostatic potential energy to the barrier for rotation about the C B2 axis of the interlamellar water in the y ) 1 phase could be very different from that for y ) 2 and thus provide an explanation for the experimental observation of the absence of rotation in the former. 4. Conclusion The nature of motion of interlamellar water molecules in the ion-exchange intercalated Cd0.75PS3Na0.5(H2O)y(y ) 1,2) has been investigated by 1H NMR spectroscopy. In both the monolayer y ) 1 and bilayer y ) 2 compounds, analysis of the dipolar splitting indicates that the orientation of the C B2 symmetry axis of the water molecules with respect to the interlamellar normal, C B*, is almost identical. In both compounds the observed dipolar splittings require that the C B2 axis rotates rapidly about the interlamellar normal C B*. In the y ) 2 compound, in addition, the water molecules rotate about their C B2 axis, whereas in the

Arun et al. y ) 1 phase, such motion is absent. We present a simple electrostatic model which suggests that the differences in the gallery heights of the y ) 1 and y ) 2 phases could give rise to significant differences in the contribution of the electrostatic potential energy to the barrier for rotation about the C B2 symmetry axis. Acknowledgment. We thank Professor K. L. Sebastian and Mr. D. Srivatsan for useful discussions. References and Notes (1) Clement, R.; Lagadic, I.; Leaustic, A.; Andiere, J. P.; Lomas, L. Chemical Physics of Intercalation II; NATO ASI Ser., Ser. B, 1993; p 315. (2) Ouvrard, G.; Brec, R.; Rouxel, J. Mater. Res. Bull. 1985, 20, 1181. (3) Jeevanandam, P.; Vasudevan, S. Solid State Ionics 1997, 104, 45. (4) Sposito, G.; Prost, R. Chem. ReV. 1982, 82, 553. (5) Jeevanandam, P.; Vasudevan, S. J. Phys. Chem. B 1998, 102, 3082. (6) Arun, N.; Jeevanandam, P.; Vasudevan, S.; Ramanathan, K. V. J. Chem. Phys. 1999, 111, 1231. (7) Mu¨ller-Warmuth, W. In Physics and Chemistry of materials with low-dimensional structures; Mu¨ller-Warmuth, W., Scho¨llhorn, R., Eds.; Kluwer Academic Publishers: Dordecht, Netherlands, 1994; Vol. 17, p 339. (8) Hougardy, J.; Stone, W. E. E.; Fripiat, J. J. J. Chem. Phys. 1976, 64, 3840. (9) Arun, N.; Vasudevan, S.; Ramanathan, K. V. J. Am. Chem. Soc. 2000, 122, 6028. (10) (a) Ro¨der, U.; Mu¨ller-Warmuth, W.; Scho¨llhorn, R. J. Chem. Phys. 1979, 70, 2864. (b) Ro¨der, U.; Mu¨ller-Warmuth, W.; Scho¨llhorn, R. J. Chem. Phys. 1981, 75, 412. (c) Ro¨der, U.; Mu¨ller-Warmuth, W.; Spiess, H. W.; Scho¨llhorn, R. J. Chem. Phys. 1982, 77, 4627. (11) Klingen, W.; Ott, R.; Hahn, H. Z. Anorg. Allg. Chem. 1973, 396, 271. (12) O’Hare, D.; Evans, J. S. O.; Turner, P. A.; Mason, S.; Heyes, S. J.; Greenwood, J. J. Mater. Chem. 1995, 5, 1383. (13) Abragam. A. In Principles of Nuclear Magnetism; Oxford University Press: Oxford, 1961. (14) Piacentini, M.; Khumalo, F. S.; Leveque, G.; Olson, C. G.; Lynch, D. W. Chem. Phys. 1982, 72, 61. (15) Ohno, Y.; Hirama, K. J. Sol. Stat. Chem. 1986, 63, 286. (16) (a) Mercier, H.; Canadell, E.; Mathey, Y. Inorg. Chem. 1987, 26, 963. (b) Kurita, N.; Nakao, K. J. Phys. Soc. Jap. 1987, 56, 4455.