1762
D. E. O’REILLY AND CHARLES P. POOLE, JR.
Vol. 67
NUCLEAR MAGNETIC RESONANCE OF ALUMINA CONTAINING TRANSITION METALS BY D. E. O’REILLY AND CHARLES P. POOLE, JR. Gulf Research & Development Company, Pittsburgh 30, Pennsylvania Received January 11, 1963 The aluminum-27 nuclear magnetic resonance of high surface area alumina has been studied as a function of the concentration of adsorbed metal oxides of Cr, Ni, and Co. Cr was studied in the reduced and oxidized states as well as coprecipitated with alumina. Proton relaxation times of water molecules adsorbed t o monolayer coverage mTere measured for reduced chromia-alumina. Changes in intensity of AlZ7n.m.r. signals with metal concentration are interpreted in terms of changes in AlZ7spin-lattice relaxation times induced by the adsorbed oxides. Magnetically quasi-isolated clusters of metal ions on the alumina surface are shown to be effective in reducing the relaxation time of AlZ7nuclei near the surface and thereby to produce a measurable decrease in the T out-of-phase component intensity of the AlZ7resonance. A quantitative theory is given for chromium. Proton spin-lattice relaxation times of water molecules adsorbed to monolayer coverage on alumina change by a factor of 40 between pure alumina and 0.5 wt. % ’ of Cr. These relaxation times are interpreted with the aid of the modified Bloch equations, involving protons coordinated with isolated Cr +* ions and protons interacting with quasi-isolated clusters of chromic ions via the dipolar interaction. Both AlZ7and proton n.m.r. yield information on the surface configuration of adsorbed ions.
I. Introduction The technique of nuclear magnetic resonance (n.m.r.) provides a unique method for the study of the surfaces of solids with large specific surface areas. In the present work, data have been obtained on the A127 n.m.r. intensities of high surface area aluniina with adsorbed metal oxides of chromium, cobalt, and nickel as well as the proton n.m.r. relaxation times of water adsorbed on these solids. Recent investigations by electron paramagnetic resonance1 of the chromia-alumina1~2system and by static susceptibility3 of the cobalt-alumina4 and nickel-alumina5 systems have sliowii the transition metal to be present in an oxidized state which coiisists of two types or phases: a dispersed (6) phase in intimate contact with the alumina support aiid a bulk (6) phase consisting of clumps of transition metal oxide. The present results further support this view and yield additional information on the nature of the 6and P-phases. Results of AlZ7and H1n.m.r. measurements are given in section 111. A discussion of the significance of these results comprises section IT,wherein a theory of the AlZ7n.m.r. phenomena and proton relaxation times is presented. 11. Experimental Samples.-Samples of chromium, nickel, cobalt, and zinc supported on high area alumina were obtained by impregnation of r-alumina with a solution of the corresponding metal nitrate. Samples were dried a t 100” for 1 hr. and subsequently calcined in air a t 500’ for 5 hr. Samples of chromia-alumina were reduced in hydrogen a t 500’ for 1 hr. Further details of the technique of sample preparation are described elsewhere.4-6 N.m.r. Apparatus and Technique.-AlZ7 and H1 n.m.r. signals were observed with a Varian Associates V-4200A n.m.r. spectrometer, 12-in. electromagnet, and power supply. A BC-221-D Bendix Radio Corporation frequency meter was used to calibrate the helipot used to vary the magnetic field. All resonances were obtained a t 7.20 Me. and the field strength was 6490 gauss for A127 and 1691 gauss for H1measurements. An audio modulation “sweep” frequency of 40 C.P.S. was used in all measurements (1) D. E. O’Reilly, Advan. Catalysis, 12,31 (1960).
(2) D. E.O’Reilly and D. S.MacIver, J . Phgs. Chern., 66,276 (1962). (3) P. W. Selwood, “Magnetochemistry,” Interscience Publishers, Inc., New York, N. Y., 19.56. (4) J. R. Tomlinson, R. 0. Keeling, Jr., G. T. Rymer, and 5. M. Bridges, “Seoond International Congress on Catalysis,” Paris (July, 1960). ( 5 ) G. T. Rymer, J. M. Bridges, and J. R. Tomlinson, J . Phys. Chem., 65, 2152 (1961). ( 6 ) J. M. Bridges, D. S. MacIver, and H. H. Tobin, Paper No. 110, "Set. ond International Congress on Catalysis,” Paris July, (1960).
and the peak to peak modulation amplitudes employed were about 4 gauss for AlZ7and from 50 to 200 milligausv for H1spectra. Ala?resonances were measured in a radiofrequency field strength H I of 300 milligauss on the dispersion mode as described previously7; H1 resonances were measured with values of HI ranging from 5 to 800 milligauss. Each sample was enclosed in a 15-mm. 0.d. Pyrex tube equipped with a stopcock and taper. The width and shape of the (1/2 t* - 1 / z ) component of the resonance envelope did not vary with metal concentration for impregnated catalysts and hence the vertical maximum of the absorption envelope was taken to be directly proportional to the total intensity of the ( ‘ / z t-) - 1/2) component. The phase of the phase-sensitive detector was adjusted before each series of measurements to give a maximum signal from the pure alumina support. To ensure phase and amplitude stability of the n.m.r. spectrometer, each spectrum was calibrated before and after recording by means of a calibrator circuit similar to the one described by Redfield.s Thus the signal component out of phase with the modulation was measured for all samples. The measured n.m.r. amplitudes were corrected for the relative amounts of sample in the sample tubes. The proton spin-lattice relaxation time ( T I )was determined by the saturation technique and the spin-spin relaxation time ( T z ) was calculated from the peak to peak line width a t low radiofrequency power. The radiofrequency magnetic field H I was measured by inserting a small coil of several turns into the probe and measuring the maximum induced voltage a t the sample position by means of a Hewlett-Packard Model 410A vacuum tube voltmeter. From the known radiofrequency, geometry, and number of turns of the test coil, the radiofrequency field a t the sample position was computed for various radiofrequency power settings. Water Adsorption.-Distilled, degassed water was adsorbed in a vacuum manifold on chromia-alumina catalysts which had been reduced in hydrogen a t 500”. After pumping the manifold to 10-6 mm. pressure, water was allowed to evaporate to equilibrium a t 20’ into a calibrated bulb attached to the manifold. Xext, the bulb was closed off from the manifold by means of a stopcock, and the manifold was evacuated. The water vapor in the bulb then was adsorbed on a chromia-alumina sample a t -195O. After a known amount of water had been adsorbed on the catalyst sample in this fashion, the sample was warmed to room temperature and proton n.m.r. measurements were performed.
111. Results The intensity of the ( l / 2 tt - l / z ) component’ of the XIz7 resonance absorption envelope of oxidized and reduced samples o f chromia impregnated on alumina us. chromium concentration is shown in Fig. 1. The intensity of the resonance attains a minimum near 2 wt. % Cr for reduced samples aiid near 3.6 wt. % Cr for (7) D E. O’Reilly, J. Chem. Phya , 28, 1262 (1958)~ (8) A. G.Redfield, Rei, Scz. In&., 27,230 (19.56)’
NUCLEAR XAGNETIC RESONANCE OF ALUXINA CONTAINIBC TRANSITION METALS
Sept., 1963
oxidized samples. For comparison, the AIz7 n.m.r. intensity of copreieipitated samples calcined a t various temperatures is plotted. As is apparent from the figure, the intensity of these samples decreases monotonically with increase in metal concentration. The error involved in intensity measurements for the impregnated samplet; mas found to be .t3 units out of 100. Similar data for samples of Co and Ni impregnated on alumina and calcined a t 500' are given in Fig. 2. Data for the oxidized chromia-alumina samples also are given for comparison. It is of interest to note that the maximum in the concentration of the Cr &phase as determined by e.p.r.l and the maximum in the concentration of the Co &phase as determined by magnetic susceptibility measurements4 each occurs a t the metal concentration which corresponds to a minimum in the AIzi intensity. Six samples of zinc nitrate impregnated on alumina were prepared in precisely the same way as the Cr, Co, and Ni impregnated samples. Within experimental error (*3%), these samples showed 110 significant decrease in AlZ7n.m.r. intensity per gram of Al2O3in the concentration range studied (0 to 8 wt. % Zn) . The amount of water corresponding to a monolayer coverage was computed for each Cr impregnated sample from the measured B.E.T. surface area by assuming an area of 11 A.z for a water molecule, and this amount of water was adsorbed on the sample after dehydration and reduction a t 500'. The measured proton relaxation times for water monolayers on the impregnated chromia on alumina are given in Table I. TABLEI VARIATIONOF PROTON RELAXATION TIMESTIAND T z OF ADSORBEDWATERWITH CHROXIEMCOXTEXT OF REDUCED CHROMIA-ALUMINA Wt. % Cr
TI,psec.
T2,paec.
240 0.0" 2720 239 0.07 1460 55 0.55 67 37 37 1.2 30 30 2.0 40 40 3.5 47 47 5.8 10.3 160 125 a The blank alumina was similar to the one used in the other samples.
. I)
o
1.4
2
4
I
I
WEIGHT PERCENT Cr. 6
0
10
I
1
0
1763
-
1
RED. IMP.
/---
/---
OXID. IMP
w >
0.2 4
0
0.02
0.04 W/Al
I 0.08
0.06
l
I
l 0.10
ATOMIC RATIO
Fig. 1.-Relative A127 n.m.r. intensity for reduced (red.) and oxidized (oxid.) samples of impregnated (imp.) and coprecipitated (cop.) chromia-alumina. All blank aluminas gave the same AI27 signal except the 900" coprecipitated blank.
! METALICr,Co.OR
I
10 0.12 N i l / A l ATOMIC RATIO
J
I 0.14
Fig. 2.-Relative A127 n.m.r. intensity for oxidized samples of alumina impregnated with cobalt, chromium, and nickel oxides.
the first two layers of the alumina surface. As a result only AIz7nuclei below the first two surface layers contribute to the observed spectrum. This was demonstrated experimentally1 by the slope of a plot of AlZi intensity us. B.E.T. surface area for samples ranging between 100 and 376 me2/g. AlZ7intensity was observed to decrease linearly with increase in B.E.T. surface area. Let us consider, for the present, a single paramagnetic ion M situated on the surface of the alumina support. This situation is illustrated schematically in Fig. 3 . AlZ7nuclei below the surface will experience a magnetic field Up due to the magnetic dipole moment ji of M. However, due to the constant reorientation of Z in space caused by spin-lattice interactions, H, will fluctuate rapidly in time. Such fluctuations may be characterized by a time T~ = T I M , the correlation time (or spin-lattice relaxation time) of a component of the moment M~ in the x direction which is chosen as the direction of the applied field H,
A very large change in T1 occurs between the pure support (TI = 2720 psec.) and the 0.55 wt. % Cr sample (Tl = 67 psec.), while a less abrupt change occurs for T z . As is evident from Table I, the Tl and T z values reach a minimum ( T I = T z )near 2 wt. % Cr. The error in Tl values is estimated to be *lo% and that in Ti?*3%. IV. Discussion A127 N.m.r. Data.-The dispersion mode AIz7nucIear magnetic resonance signal obtained from a-alumina was i p z ( t ) p L . ( t 711 = (pz2)e-T'TP reported previously.? The resonance recorded at high power (HI 300 mgauss) is asymmetric in shape due (h2) = 1/8s(s l)gzpBZ (1) to the quasi-random distribution of aluminum nuclei ~ ~ ~ where S is the total electronic spin of the ion M, g is in the octahedral sites of the oxygen n e t ~ o r k ,althe spectroscopic splitting factor of M (which is presthough the presence of some AlZ7nuclei in tetrahedral ently considered to be isotropic), and pB is the Bohr sites is not excluded. Strong crystalline electric field gradients near the surface of the alumina interact with magneton. The time T~ is in the range of to 10-12 the large AlZi quadrupole moment and thereby broaden sec. for Cr+3, Wi+2, and C O +in ~ solids a t room tembeyond detection the resonance signal of AI2?nuclei in perature. T~ is short compared to the dipolar spin-spin 4
-
-
+
+
D. E.O'RI:IT,T,YAND CIIARLES P. POOLE, ,JR.
1701 H O
SURFACE L A Y E R
H 0
H 0
1st CRYSTAL L A Y E R
AI*
0
M
0
AI*
0
2nd C R Y S T A L LAYER
0
AI*
0
!:I
0
AI*
3rd
CRYSTAL LAYER
:3
0
AI
0
AI
0
4th
CRYSTAL LAYER
0
AI
0
AI
0
[I
AI 0 1: 0 AI 0 CRYSTAL LAYER Fig. 3.-Schernatic representation of parctmsgnetic ion h l in the surface layer of yA1203. The Aln nuclei marked with an asterisk arc in sulficiently strong electric field gradients so as not to contribute to the measured AI2' n.m.r. signal. Possible AI2; vacancies are indicated by [3.
for thc absorption cnvrlopc of tlw quadivpolar po\\-drr liiic shapci of .UZ7 uith II i l l uiiits of gauss. 0 1 1 t l i otlicr ~ Iiaiid, if lllh(0) < w , , ~7'1 < I , Ilic sigtial is a/2 oiit-of-phase I\ ith t hc niodulation I'iwluciicy pliaw and proportioiial to h(ZI - I I o ) (raw 2).' 111 our cxpcbi.inic>iitsIll = 0.6 gauss, w,,, = 2.5 X l o L s w . I, uiid w,,,?" \ I = :300 >> I . ll'IlPl1
5th
relaxation time T2.41of AIz7,which is equal to about 3 X lop5 sec. iii alumina. I n a singlc preccssional pcriod of AlZ7(v0-l = 1.4 X lop7sec.), H , will average essentially (neglecting Boltzmann population difference between energy states) to zero arid hcnce cannot appreciably broaden an Aln resonance component in comparison with thc broadening duc to the dipolar interaction between AIz7nuclci. II, can, however, contribute quitc significantly to tlic spin-lattice relaxation time Tl*l of AIz7. The relaxation time of Aln rcsultiiig from the nuclear-electron dipolar intcraction may be written as -4
\.()I. 07
Wl,l
4 X I O p R wr.
((i)
tlic c~pc'iiiiwiital contlit ioii rorrcqpoiids to ('as(' 2 . .Uz7iiuclvi satisfyiiig c a w 2 aiv iiot o l w r v i d , siiice thc phase scnsiliw dctcctor is tuiicd to rejcct a signal ~ / 2 c ut-of-phasc ilith Ilic main signal (T1.il = 7'lo.il). I lencr, in o d c r that .UZ7nuclci iii thc viciiiity of ,1I br iiiiobsci*vablc in our i1.m.r. expcrimrnts, it is nccc'ssary I hat i Iicw
-
I\ hcre Tloalis thc spin-lattice relaxation timc of ,Uz7 in the abscncc of ill (lop2sec. 1the AIz7resonance signal is T out-of-phase with the modulation field where is the phase and proportional to h(l1 - Ho), angular frequency of the modulation ficld and h(H H o ) is the normalized absorption eiiwlopc shape function defined by (4) For y-.4Ia03 (case 1) we have'"
Xctually tlic relaxatioii timc of ai1 illz7 nucleus a distance IZ from 11 ran hc somcvliat lcss than that given by cq. 2 and 3 as a rcsult of spin diffusion.10 Due to the rclativcly strong quadrupolar interaction in yA1~03,~ mutual spin cxchangc is possible only bctwcen nuclei with mI = * l / * . Furthermore, due to the inhomogeneous naturc of the ( l / ~ t-) - l / J components, spin exchange can occur only bctwen nuclei n ithin the samc spin packet. l 1 For polycrystallinc a-.1l2O3, a11 are in the same spin packet spins uith nzr = vithin a single crystalline particle and different m1 = I / * spin packets corrrspond to differcnt oriciitations of t hc particle c-axis relative to the applicd magnetic ficld. I n y-.ilz03, cven n ithin thc same particlc, mI = =I= ' / ?spin packets may not be the same duc to a random variation of the electric ficld gradient from one h l u site to ailother. This is in contrast to the rcgular distribution of AIz7 sites in o-AlZ3O. Thus, in -pA120aspindiffusion may bc strongly inhibited \\ ithin a particle. Owing to lack of detailed knowlcdgc about the variation of ficld gradicnts from site to site in y-A&O3, the spindiffusional contribution12 to T1 nil1 not bc cstimated, but instead the experiincntal data on coprccipitatcd rliromia-alumina catalysts XI ill be examined. From thc initial slopc of the decrease of Aln intensity of the coprccipitated catalysts calcined at 900°, one finds that about 200 AIn nuclci per Cr+3ion disappear from observation. These nuclci correspond to case 2 and are contained in a sphere of average radius 10.3 A. However, from inequality 7 one may compute the maximum possible value of R for which the inequality may be satisfied by placing r p = w0-l = 2.2 X sec. This value of R is 10.2 A., which corresponds to about 190 Aln nuclei per Cr+3 ion. The agreement between this estimate and the experimental value is excellcnt, although perhaps fortuitous. It does indicate, howcvcr, that effects duc to spin-diffusion are small. Unfortunately, rP = Tlcr could not be measured directly with presently available radiofrcqucncy micro-
*
(IO) N. Bloembergen, Phyeca, 15, 386 (1949). (9) A. Abragam, "Tlie Princii,lrs of Nuclear Magnetism,'' Oxford University Press, New York, N. Y.,1961.
(11) A.M. Portis, Phys. Reo., 91, 1071 (1953). (12) W.E.Blurnberg, tbzd , 119,79 (1960).
KUCLEAR MAGXETIC RESONAKCE OF ALUMISACOXTAINIXG TEANSITIOS METALS
Sept., 1963
wave power. However, some other sources of data of T1 for Cr+3 are available. LO+^ reports the line width of very dilute solutions of Cr+3in MgO to be 1.5 gauss a t room temperature. Hence one may conclude that Tlcr 2 4.5 X 10-8 sec. for C r i 3 in MgO a t 25'. Blurnbergl2 finds by an indirect method that Tlcr = 1 X 10-8 sec. for Cr+3 in NH4HS04a t room teinperaassumed above ture. Thus the value Tlcr = 2.2 X is not unreasonable and will be tentatively retained in the following. One may incorporate in the inequality 6 any effects of spin-diffusion in yA1203 by multiplying ius2 times an enhancement factor LYDso that the first part of (7) beconies
This results because the effective range of a paramagnetic ion in causirtg a definite relaxation time by spindiffusion12 is proportional to just as is the case witheq. 3. Returning now to the impregnslted chromia-alumina, if an ion Cr+3 is situated in the surface phase as depicted in Fig. 3, Allz7nuclei marked with an asterisk will experience a very large magnetic field H , due to Cr+3. However, as discussed previously, these nuclei are in the first two cation surface layers and hence will not contribute, on the average, to the AlZ7resonance studied even in the absence of Cr+3. Such a double layer will be approximately 6.9 A. in depth. Since the angular dependence of (l/Tl)a, is sinZ B cosz B the number of AlZ7nuclei effected by the surface paramagnetic ions is dependent on the angle between the normal to the surface and the magnetic field direction. However, the A127nuclei affected according to inequality 7 are contained in a volurne V , which may be calculated by averaging over-all orientations of Ho relative to the surface, from the following expression for the volume of a segment of a hemisphere, of radius R, and height Rc - 6.9 A.
V, =
3 (R, - 6.9)2(2Rc+ 6.9) L3 ?T
(9)
From the initial slope of the plot of AlZ7intensity vs. chromium content in Fig. 1for the impregnated samples reduced in hydrogen a t 500', one estimates that 15 f 7 AIz7 nuclei disappear from observation per Cr+3 ion present. This number of A127nuclei corresponds to a volume of 340 + 160 A.3in A1203. Placing this volume in eq. 9 and solving for R,, one obtains R, = 10.3,in good agreement with the previous estimate of the range of Cr+3 in the coprwipitated samples calcined a t 900'. Thus it is likely that the proposed mechanism is correct. Values of (pE2), N(AI/M) (the number of A1 nuclei removed from obaervation per M ion a t low concentrations of M), R,, and the lower limit of r p , T,,-, as derived from eq. 9 are given in Table 11. The value of T ~ -derived for Crf3 is reasonable as already noted. The value for Ni+' is not unlikely, since nickelous ion in dilute solution i n a host crystal gives fairly sharp resonance lines a t room temperature, although specific data do not appear to be available in the literature.14 The (13) W. Low, Phys. Rev., 105,801 (1957). (14) 1%'. Low, %bad.,109 247 (1958).
1765
predominant symmetry type assumed, Le., either octahedral or tetrahedral, is indicated for each ion, Co+2 in tetrahedral symmetry would behave as Cr+3 in octahedral symmetry and vice versa. The value of 7,derived for Co+' in octahedral symmetry appears to be too long by a t least three orders of magnitude, since ~ is generc.p.r. of octahedrally coordinated C O + salts ally too broad to be observed a t room temperature. It is possible that an inordinately distorted octahedrally coordinated Co + 2 ion, however, would have longer relaxation times. Another possibility is that the C O + is ~ tetrahedrally coordinated, in which case the derived value of 7,- is reasonable since tetrahedrally coordinated C O +may ~ be observed by e.p.r. a t room temperatures. Still another possibility is ~ diffuse into the second or third that some C O + ions surface cation layer and thus become more effective in observationally annihilating AIz7nuclei. TABLE I1 A127 N.M.R. RESULTS FOR VARIO~~S METALIONS M IN OCTAHEDRAL (OCTAH)AND TETRAHEDRAL ( TETRAH) SYMMETRIES Included in the table are the g-value, the spin S , the mean square component of the magnetic moment ( ( p z / p ~ ) 2 )the , number of A127 nuclei per ion relaxed beyond detection N(Al/M), the ion's relaxation range Bo, and the correlation time Q. Sym-
N (Al/ M)
Ro,
-3.5
16 7 12 * 2
10 3 10 0
-25 -6.6
15 i 1 1 0 . 4 15& 1 1 0 . 4
((pa/
M
metry
S
B
PB)$
Cr+8 Ni+2
Octah Octah
3/2 1
2 0 2 3
C o + l Octah Co+g
Tetrah
3/2{An:i2p1c) 3/2
2 3
5
*
A.
TP,
pseo. 0.022 0.021
(~~~~~ to
-0,018
Let us now consider the state of affairs a t high metal ion concentrations. The situation is schematically illustrated in Fig. 4. For simplicity, we consider the alumina surface to be covered with a slab of thickness h of Cr203. At 25' this chromia is entirely paramagnetic with essentially no short range antiferromagnetic ordering. Thus one may consider the spins free to orient relative to the applied field and readily compute the relaxation time of 41 a t a point 0 in the alumina due to Cr+3ions in the slab of chromia. The point 0, furthermore, is considered to be several lattice spacings away from the interface and likewise the distance h is also considered to be equal or greater than several lattice spacings, so that we may replace a summation over lattice sites of M ions by an integral. In evaluating the relaxation time of AlZ7nuclei due to Cr+3ions in the slab of Cr203, we may either perform the integration over Cr+3 sites using eq. 2 and then average 0 over a sphere or simply use eq. 3 for v h i c h the 0 averaging has already been performed. Both methods will give the same answer and since the latter procedure is more expedient, we shall use it. The integration over the slab is most readily performed in cylindrical coordinates ( p , x , 4 )
(10)
where N is the number of C1-+3ions per unit volume in the slab of Crz03. The integral is easily performed to yield eq. 11.
D. E. O'REILLYASD CHARLES P. POOLE, JR.
1766
tI
T~
Vol. 67
= 6 X 10-l2 sec.
(T2M)d is derived by application of Van Vleck's formula16 to Crz03and re from the observed2 line width of the 0phase. Hence
rP
At 10 wt.
= 5 X 10-l2 sec.
% Cr, one sixth of the entire surface of
&03 is coveredBby Crz03 and so h = 5.7 X 10-8 cni. (with N = 4.1 X loz2cm.-a) and
Fig. 4.-Coordinate system used for calculating the 9 1 2 7 spin lattice relaxation time due to a slab of Cr203 on an A1203 surf ace.
The time T,, however, is in this case much shorter than the spin lattice relaxation time Tlnr of the hI ion. I n the absence of exchange interactions, the field H , will fluctuate in time with a correlation time of the order of the spin-spin relaxation time T 2 R I . The reason for this may be stated qualitatively as follows. The spins which mill contribute the most to the H , at the point 0 n7ill be those closest to 0. If a t t = 0 these spins have a definite orientation (e.g., all with M , = + 3 / 2 ) , in a time t = Tzar this orientation will have changed to another, due to mutual (energy conserving) spin flips with neighboring Kt ions and subsequent spin diffusion. Hence lIp will be changed significantly at t = T2hI. If, in addition, there is significant exchange coupling between spins, of the form J Xi.X,, this coupling will induce an additional time-dependence of H , due to mutual spin precession of M ion spins about the exchange field He. This effect is discussed more fully in ref. 24. As a result of these interactions ( i e . , dipolar and exchange) H , will fluctuate with a correlation time given by
-
-
3
where T , is an exchange correlation time and ( l / T z n ~ ) dis the contribution of the dipolar interaction to l/Tznl) for the paramagnetic ions 31. Hence 7'1 for AlZ7nuclei is given by
where R, is in A. A12' nuclei will not be observed when (TI)A~ I4 X see. as already noted. The above inequality cannot be satisfied for 2.2 A. I R and hence there is no observable effect of the presence of the paramagnetic Cr203 on the AlZ7resonance. Such is approximately the case for 5 and 10 wt. % Cr samples of Cr on alumina reduced in hydrogen at 500' as may be seen by reference to Fig. 1. However, samples oxidized at 500' do exhibit an observable effect at 10 wt. yo Cr. This result will be discussed after the follom-ing considerations on the intermediate concentration range. 4 t intermediate concentrations (e.g., 0.1-5 wt. % Cr) clusters of NI ions will be formed 011 the alumina surface as well as quasi-isolated (&phase) iV1 ions. Let us first consider the quasi-isolated hI ions which are defined to be 31 ions that do not have any first nearest neighbor M ions. We will assume that exchange interactions between these quasi-isolated NI ions and the remainder of the 31 ions may be neglected and consider only the dipolar interactions. The central fact is that spin exchange between quasi-isolated 31 ions and the rest of the iLI ions cannot occur with conservation of energy, and hence will be greatly inhibited. Each 6phase' Cr+3 ion is situated in a strongly asymmetric crystalline field which results in a splitting between which varies magnetic sublevels ( M s = =t3/*) strongly with the relative orientation of the principal axes of the Cr ion and the external field Ho. Since on a real surface next nearest neighboring lattice positions (-4 A.away) cannot be expected to be occupied by Cr ions with the same directions for their principal axes, the appropriate sublevels have significantly different energy separations, and mutual spin flips cannot occur with conservation of energy. A similar argument holds for in distorted octahedral coordination and C O + ~ in distorted tetrahedral coordination. Hence, quasiisolated hI ions [M= Cr t3,S i t2, or Co t 2(tetrahedral) ] may be expected to be quite as effective as truly isolated M ions in causing relaxation of AlZ7nuclei. In a somewhat similar manner we may define a quasiisolated cluster of n metal ions. Such a cluster is defined as a group of 31 ions with interionic spacings equal to the nearest cation neighbor distance. Consider n = 2. For such pairs of Cr + 3 ions there will be a strong exchange interaction and the system may be .-, characterized by energy Ievels with total (XI= (SI 4Xz = 0, 1, 2, and 3 and a dipolar magnetic field pro-+ duced by the magnetic moment gP(& XZ) centered d
4
where T~ > 10, generally will contain ions surrounded on all sizes by other ions. Such ions will yield an exchange-narrowed e.p.r. spectrum symmetrical about H = h v / g p and hence will effectively have all magnetic sublevels separated by hv = gpH. These ions may undergo spin exchange with other, similar ions in other large clusters. If a cluster of size n has, on the average, ne completely exchanged-narrowed M ions which are, on the average, a distance Re from a cluster of size n’ with ne’exchange-narrowed ions, then spin exchange between these clusters miill occur in a time TZnd which is approximately determined by the mean square fieldls “seen” a t the first cluster due to the Cr+3ions of the second cluster, i.e.
with Re in Angstrom units. As Tzndbecomes shorter, the cluster of size n becomes less effective in relaxing AlZ7 nuclei. Consider, for example, a cluster with ne = 10. In order that this duster be half as effective as a completely isolated cluster in removing A12’ nuclei from sec. observation, (T2n)dmust be greater than 1.0 X (using (9) and ( 7 ) ) ,and hence (17) (16) L. Ramai, H. S t s t z , XI. J. Weber, and G . F. K o s t e r . Phgs. Res. Letters, 4, 125 (1960).
1767
TABLE I11 PARAMETERS FOR PLANAR, QUASI-ISOLATED CLUSTERS OF CHROMIC IONS The range within which a clutser of n ions relaxes AlZ7nuclei beyond detection is Ron and the volume of the corresponding segment is VBn. The last column gives the number of A127 nuclei removed from observation per Cr +3 ion in a cluster containing n Cr+3 ions. The second, third, and fourth columns are in h g atrom units van N(Sl/Cr), n R Q ~ VBn n
1 2 3 4 5 10 20 100
10.3 11.6 12.4 13.0 13.5 15.1 17.0 2’2.2
330 680 990 1270 1530 2600 4300 112600
330 340 330 320 305 263 217 125
15 15 15 14 14
IS 10 6
where the sum is over all i clusters of size nei a t a distance Rei from the cluster under consideration. The condition of (17) is quite stringent in that a cluster must be greater than 14(ne)’I68. from a neighboring cluster if it is t o be a t least half as effective as a completely isolated cluster. Since the effectiveness of such a cluster in removing AlZ7nuclei from observation is also a very rapidly varying function of distance, we may consider each cluster to be either quasi-isolated or part of a larger, neighboring cluster. It is clear from the above discussion that as the system of M ions on alumina becomes more connected magnetically, so that spin diffusion may take place over a large volume, the eficiency of the chromia in the relaxation of AlZ7nuclei below the first two surface cation layers approaches zero. For a given arrangement of chromium ions on the alumina, we may estimate the number 61 of AlZ7nuclei removed from observation. However, it is also clear that there are a large number of possible configurations of Cr+3 ions in clusters of various sizes and degrees of connectedness. Let us, nevertheless, group the chromic ions into three types: (1) chromic ions which constitute the socalled d-phase detected by electron paramagnetic resonance’J; ( 2 ) chromic ions which contribute to the socalled p-phase resonance1P2; (3) chromic ions which are not observed by e.p.r. As discussed ions of type 1 are considered to be quasi-isolated clusters of size 1 while chromic ions of type 2 are thought to comprise rather large clusters of Crz03. Finally, the chromic ions of type 3 are regarded as comprising clusters of intermediate size. From the above considerations, one might expect the quantity 61 to be approximately proportional to the difference between the total chromium concentration Ncr and the concentration No of the p-phase chromic ions 61
(Nc, - No)
where the constant of proportioiiaiity is expected to be about 15 A12’ nuclei per Cr+3 ion. The values of 61 and (Ncr - No) shown in Table IV are plotted in Fig. 5 ; the data yield an average value of the constant of proportionality equal to 16 f. 5. In summary, the behavior of the AlZ7resonance intensity may be interpreted in terms of varying degrees of clustering of chromic ions and isolation of the
D. E . O'REILLYAND CHARLES P.POOLE, JR.
1768
Vol. 67
arise from the modulation of intra- and intermolecular proton dipolar fields by rotational and translational diffusion of mater molecules over the surface of the solid. Expressions for relaxation tinies due to such motions of water molecules have been derivedls for three-dimensional diffusion. These results may readily be extended to the case of two-dimensional translational diffusion. The rotational diffusion is, for purposes of estimation, coiisidered to be three-dimensional. One finds 0
3
I 2 ( N C , - N ~ ) . C r IONS PER GRAM X IO2'.
Fig. 5.-Graph of the number of aluminum nuclei 61 removed from observation as a function of the number of non-P-phase chromium ions ( N c , - N o ) .
TABLE IV THEQUANTITIES Kc,, (,Vm - N o ) , AND 6I FOR VARIOUSWT.% OF Cr. UNITSARE @;.-I x 10-20
Wt. % Cr 0.07 0.55 1.2 2.0 3.6 5.8 10.1
NOT
0 08 0.63
1.38 2.30 4.14 6.72 11.61
Ncr
- NP
0.06 0. n50 1.17 1.68 1.47 0.34
*..
61
... 4 1 3 25 f 3 36 f 3 19f3 2 2 ~ 3 3 f 3
clusters that are formed. It is to be noted that the interpretation is sufficient, but not necessary to rationalize the data, since an equally admissible model would involve a gradual withdrawal of Crf3ions from chemical contact with alumina to form a very fine-grained mechanical mixture of Cr203and &03. Elementary considerations of the process of adsorption of Cr+3 ions on the alumina surface from aqueous solution and the subsequent steps in sample preparation, however, indicate that statistically such an end product is not likely to occur. The above considerations may also be applied to Co and Ni on A1203. The minimum in the ?r component of intensity in the Co samples occurs where the 6phase concentration is maximum as determined by magnetic susceptibility measurements4 on the same samples. The persistance of short range anti-ferromagnetic order in COO above the Keel temperature would lessen the magnetic moment of clusters of C O + ~ ions. Co304is ferromagnetic a t very lorn temperatures and may show some ordering at room temperature. Co304has a very low magnetic moment due to the lack of paramagnetism of C O + in ~ octahedral sites." Also, the small value of rp for C O +in ~ cubic octahedral symmetry renders such C O + ~ ions ineffective. The differences in the intensity of the AlZ7resonance between the oxidized and reduced samples may conceivably be due to the oxidation of large clusters of chromia to a smaller magnetic size, making them more effective in the relaxation of A12' nuclei. H1N.m.r. of Adsorbed Water.-Let us consider the relaxation mechanism of a monolayer of water adsorbed on an alumina surface in the absence of paramagnetic ions. Neglecting relatively weak dipolar fields from Al*' nuclei on the solid and any protons present as OH groups rigidly attached to the surface of the solid, the relaxation times TI and T2 may be considered to (17) P. Cossee, X e c . t r a t . chzm , 75. 1089 (1956).
40
(i2 cot-1
e;)
+ 4 cot-] (YO))]
(20)
where ro is the proton-proton distance in an adsorbed water molecule, rr is the rotational correlation time for an adsorbed molecule, N is twice the number of adsorbed water molecules per unit area, D is the translational diffusion coefficient for water molecules on a plane alumina surface, and a is the distance of closest approach of two water inolecules on the surface. Equation 18 and 19 are derived in ref. 9. Equations 20 and 21 were derived from eq. 18 and 19 by placing 7 0 trane
r2 - _ 80
and integrating over r in two dimensions from T = a to infinity. Inserting known values of (YH) and h one coniputes 3iT
10 y H 4 i i 2 =
5.35 x 10-37
Using the assumption
uoa2 ->>1 40 ro = 1.5 K., and a and the values 1/N = 5.4 8. in aiialogy with liquid water, one obtains
(18) R. Kubo and K. Tomita, J . Phys. SOC. Japan, 9,888 (1964).
=
2.8
NUCLEAR MAGNETIC RESONANCE OF ALUMINA CONTAINING TRANSITION METALS
Sept., 1963
($)inter
-
10.5 X D
I
(k)inter
(A 80
- 23.7 X D
(27) (28)
The over-all relaxation times TI, and Tzu.of water on alumina are given by
By neglecting (T1-l)inter relative to (T1-l)intra and employing the experimental value T1, = 2.72 X 10-3sec. one obtains 7,. = 3.05 X IO+ sec., and then the use of sec. gives D the experimental value T2, = 2.39 X = 5.7 X 10-l1 cm.2/sec. Substituting these values of rr and D back into the equations we see that woaZ ~-
4D
156 >> 1
1769
where T 1 and ~ T 2 are ~ the contributions of the dipolar fields of the paramagnetic ions to the relaxation times of the protons which are not coordinated with Cr, Tlh and T2h are the relaxation times of the protons coordinated with Cr+3, t h is the mean lifetime of these protons in this environment, Ncr and N H are the total number of chromic ions and the number of protons of adsorbed water, respectively, and n h is the average number of protons coordinated with Cr+3. An alternate derivation for eq. 34 and 35 is given in the Appendix. For the present only the &phase Cr+3 ions will be considered. Equations 34 and 35 were originally derived for aqueous solutions20-22but they are just as valid for “two dimensional solutions.” The hexaaquochromic complex ion in water a t 25’ is unique among hydrated ions of the iron group since the exchange rate of coordinated water oxygen with bulk water is known to be ~ 1 0 the ~ rate ~ ~for; protons is much faster but still slow compared to that of other sec.21),and this rate iron group ions ( t h = 4 X determines the over-all relaxation time in such solutions. The times T l h and Tzi,may be estimated from eq. 3 and the corresponding expression for TZ, with y.41 replaced by YH. The resulting equations are
and
and
( T I inter ) ___ - 116 >> 1 (TI)intra
(32)
as assumed initially, Considered from the point of view of simple rate theory D corresponds to a jump frequency 4D/a2 of water molecules equal to 2.9 X lo5sec.-l and an activation energy AF*
=
2.3RT log.()
‘4hD a2k T
= 11 kcal./mole
where is the proton gyromagnetic ratio, pLpis the magnetic moment of the paramagnetic ion, and RI-I is the distance of the hydrated proton from the parasolutions, magnetic ion. I n analogy to the Cr(HzO)6+3 RH is estimated to be about 3 A. Using the value of r p = 2.2 X lo-* sec. obtained previously for Cr+3, one computes
Proton relaxation times of water adsorbed on a chromiaalumina catalyst may be discussed conveniently and quantitatively by means of McConnell’s modificationlo of the Bloch equations. The protons are considered to be continuously exchanging between two magnetically distinct environments, namely, the water molecules coordinated with Cr+3ions on the chromia-alumina surface and the remaining adsorbed mater molecules which move about rapidly on the surface. The spin-lattice ( T I ) and spin-spin ( T2) relaxation. times are given by 20--22
and
(19) H. M. MoConnell, J . Chem. Phgs., 28,430 (1958). P.F. Cox and L. 0. Morgan, J . Am. Chem. Soc., 81, 6409 (1959). (21) N. Rloembergen and L. 0. Morgan, J . Chem. Phys.. 54, 842 (1961). ( 2 2 ) R. G. Pearson, J. Palmer, M. XI. Anderson, and A. L. Allred, Z. ElektTochem.. 64, 110 (1960).
1.8
x
10-’SeC.
