Oct., 1958
NUCLEAR MAGNETIC RESONANCE OF ADSORBED WATERON SILICAGEL
1157
Magnetic and X-ray diffraction measurements have been used to calculate spinel cationic distribution in the cobalt oxide-alumina series
It has been shown that, as the series approaches low cobalt concentrations, the cobalt exists only as Co2+ions on A or tetrahedral sites. Furthermore, X-ray diffraction intensity measurements favor the case with lattice vancancies on B sites only. Acknowledgments.-The authors wish t o acknowledge the assistance of Mr. R. C. Damron in making the magnetic measurements, Mr. A. E. Walters for the cobalt analyses and Miss Virginia Harleston for X-ray diffraction measurements. DISCUSSION L. W. VERrioN.-In
Richardson and Vernon's pa er no explanation is given for the Weiss constant curve in &g. 5. Arguments are presented to explain the variation of the Weiss constant in the system cobalt oxide-alumina with the cobalt concentration. The Weiss constant 0 is a measure of the average exchange energy (expressed in degrees temperature) of the unpaired electrons of a given cobalt ion with those of neighboring cobalt ions. This energy depends on the magnetic environment around each cobalt ion and will, therefore, vary in some systematic way with the cationic distribution. To obtain the average magnetic exchmge energy, we sum over all possible interactions in the crystal latt,ice and divide by
ATOMIC FRACTION OF Go, mJ7.
the total number of cobalt atoms. (The details of this treatment will be published later.) After performing this summation and simplifying, this treatment gives the result p2e =
+ - z)%RB + ~
x Z ~ R A (1
(1 ~ ) ~ K A B
The constants K A , K B and K A B are evaluated from the Weiss c0nstant.s of: (1) CoAl2O4,(2) Co804, and (3) the 60.6ojO cobalt sample in the cobalt oxide-aluminn series. The figure shows the theoretical curve for the variation of the Weiss constant with the atomic fraction of cobalt for the cobalt oxide-alumina system. The circles repi-esent the experimentally determined values. The good agreement between the experimental data and the theoretical curve supports the principles on which the derivation is based, and, furthermore, there is also an indication that the cationic distribution parameters, deduced from other considerations, are correct.
NUCLEAR MAGNETIC RESONANCE RELAXATION STUDIES OF ADSORBED WATER ON SILICA GEL. I11 BYJ. R. ZIMMERMAN AND J. A. LASATER Magnolia Petroleum Company, Field Research Laboratory, Dallas, Texas Received March PI, 1868
A refined experimental investigation of the nuclear magnetic resonance relaxation phenomena of water vapor adsorbed on silica gel is described. Two phase behavior for both longitudinal and transverse relaxation measurements is observed to exist simultaneously. The two adsorbed phases in longitudinal relaxation data are shown to be identical with the corresponding two phases in transverse relaxation data. The adsorption at low coverage is identified only with the short time component; the coverage at which the second adsorbed phase begins can be determined. An accurate relaxation (T2) value for the average lifetime of a hydrogen nucleus in an adsorbed phase for a particular coverage is determined. A minimum value of TIis established; reasonable values of nuclear correlation times are obtained. A new and possibly accurate method for determining the monolayer is discussed.
Previous of adsorbed water vapor on silica gel by means of nuclear magnetic resonanceap4 spin-echo6 techniques have demonstrated in a small way the future role that this physical tool may have in probing the phenomena of molecular sorption on solids. These investigations have pointed out the simultaneous existence of two phase behavior from transverse (T2) relaxation measurements and single phase behavior from longitudinal ( T I ) relaxation measurements. The existence of two phases in Tz measurements was interpreted as proof of two distinct adsorbed phases for the water vapor on the silica gel, whereas the existence of a single phase in T I measurements was explained on the basis that average lifetimes in the adsorbed phases (1) J. Zimmerman, B. Holmes and J. Lasater, THIE JOURNAL, 60,1157 (1956). (2) J. Zimmerman and W. Brittin, ibid., 61, 1328 (1957). (3) F. Bloch, Phye. Rev., 70, 460 (1946). (4) N. Bloembergen, E.Purcell and R. Pound, ibid., 78, 679 (1948). (51 E. Hahn, ibid., 80, 580 (1050).
were so short that only a Tlcav, could be experimentally determined. From a combination of these experimental interpretations and the theory of stochastic processes in relaxation phenomena, the average lifetime of a water molecule in one of the adsorbed phases on silica gel was estimated. Another experimental investigation of adsorbed water on a silica gel sample by spin-echo techniques has been completed. The relaxation measurements and the adsorption techniques are considerably more refined in comparison with previous investigations. The general features observed in the initial studies of water vapor adsorbed on silica gel have been confirmed and further clarified. This paper places special emphases on (a) evidences of multiphase systems and phase transition phenomena, (b) quantitative analyses of relative populations of adsorbed phases, (e) lifetimes of hydrogen nuclei in an adsorbed phase, (d) evaluation of nuclear correlation times, and (e) adsorbed phases and dielectric loss phenomena.
J. R. ZIMMERMAN AND J. A. LASATER
1158
‘L ”=-
IO
’7
-
10
Q
s
I0
I
IO’SECONOS.
+
,f ’y
3
9
2 1
I
4
12
16
20
24
A ( 2 T ) is proportional to MI. The az’s and p2’s are functions of the P’s, 2’2’s and C’s, where Pi is the fraction of the total spin population present at any time in the ith phase, and where Ci is the probability per second that a spin in the ith phase leaves the ith phase. A graphical plot of the transverse relaxation data for a value of x / m = 0.126 is showninFig. 1. l/pzi = Tzl; l/pzj = T’z; andA’o/(A’o Aol) is the approximate fraction of hydrogen nuclei associated with the short time component (jth) phase. A two phase system is clearly demonstrated. The longitudinal ( T1)relaxation data were obtained from amplitude measurements of the free decay signals which immediately follow each of two successive r-f pulses separated by a time 7 . An analysis of the data was made according to the expression R(T)= (alie-cliT - alj e-wiTI-1 (2) where R(T) = MO/(MO - MII) The ul’s and PI’S are again functions of the P’s, TI’S and C’s. A graphical plot of the longitudinal relaxation data of water vapor adsorbed on silica gel for a value of x / m = 0.126 is illustrated in Fig. 2. l/pli = 2’11; l / p l j = T’I; and C’,/(C’o COI)is the approximate fraction of hydrogens in the short time component (jth) phase. This particular example demonstrates the existence of two distinct adsorbed phases insofar as longitudinal relaxation is concerned. Finally, it should be emphasized that numerical analyses of all the relaxation data in terms of expressions 1 and 2 were performed by means of the Field Research Laboratory’s Datatronc computer. This numerical program, in addition to extending the region of accurate evaluations beyond that of graphical analyses, gave an estimate of the reliability of resulting values of relaxation times and population ratios.
+
0.126
0
Y
spin-echo signals were measured visually on an Electromec Model 2150 oscilloscope. The time between r-f pulses was determined directly from a Hewlett-Packard Model 211A square wave generator. All measurements were at 25”. A high vacuum system was mounted above the magnet on a platform that could be moved both vertically and horizontally. The system had two chambers for 1-g. samples in aluminum buckets mounted on silica springs ( k = 0.05 mm./mg.). The n.m.r. test sample was a spherical bulb containing 9.137 g. (before drying) of silica gel. This bulb was connected to the adsorption manifold with a valve arrangement so that it could be attached to or detached from the manifold without changing the pressure on the silica gel. The silica gel samples (two buckets and the bulb) were dried under vacuum ( mm.) for seven days at 168’. The weight loss of the n.m.r. sample on drying was 7.7%. The amount of water adsorbed on the sample was determined from the gain in weight of the gel in the buckets. Periodic checks by direct weighing of the sample bulb proved the validity of this procedure within experimental error. The water used was distilled under vacuum (at liquid air temperature) three times to eliminate the air. An oil (Octoil-S) manometer was used to measure the water vapor pressure. The water source was thermostated during the time it was open to the manifold. The silica gel was Davisson gel (Specification OOMM). The bulk of the particles passed a No. 35 sieve and were retained on a No. 200 sieve. The surface area measurements of the silica gel were obtained by a standard B.E.T. apparatus. Procedure was similar to that described previously,’ and average surface area was found to be 700 m.a/g. Data Analysis.-The transverse ( Tz) relaxation data were obtained from the spin-echo signal A(2 T ) which occurs at time 2 T after the first of two successive r-f pulses separated by the time 7 . These data were evaluated according to the amplitude expression M I = M i o (uzie-%ir - u z j e - W ~ ] (1)
v ,
Fig. 1.-Transverse relaxation time plot illustrating two phase behavior for x / m = 0.126.
f
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28
v I 10) SECOND.
Fig. 2.-Longitudinal relaxation time plot illustrating two phase behavior for x / m = 0.126.
+
Results Transverse (T2)Relaxation Measurements.Fig. 3.-Transverse relaxation times for protons of HzO Relaxation (Tz) data were obtained over the water adsorbed on silica gel. vapor adsorption range of 0 Ix/m 10.427. In Experimental Fig. 3 a plot of T z vs. x/m is shown, where 0 is the Apparatus.-The relaxation data were obtained from a fraction of monolayer coverage of water vapor. At nuclear magnetic resonance pulse (spin-echo) spectrometer values of x/m I0.053 a single relaxation compoc &.
x
~ m n
operated a t 26.5 X 108 sec.-l and used in conjunction with a Varian V-4007 research magnet. The free decay and
(6) Manufactured by ElectroData Corporation of Pasadena, Calif.
,
1159
NUCLEAR MAGNETIC RESONANCE OF ADSORBED WATERON SILICAGEL
Oct., 1958
nent TI2 is observed. Some residual hydrogens (or water vapor) do remain after sample preparation under vacuum which give rise to a resonance signal and which have the same value of TI2 2 X sec. as the adsorbed water vapor. For values of 0.061 5 x / m S0.414, a two-component system (Tzl and T’2) is resolved. In terms of previous experimental interpretations, the short time component T‘2 is to be associated with the more strongly adsorbed phase. Only adsorption values of T2vs. x / m are plotted. With the exception of the data a t very high coverage, both TI2 and Tzl are independent of surface coverage. The high value of TZ1for x / m = 0.427 probably indicates the beginning of “capillary condensation.” The large variation of Tzl values in the region of x / m = 0.07 has no apparent significance, for such a scatter of data is expected from the relatively low populations and the necessarily associated inaccuracy of measurements for the T21 adsorbed phase at this region of coverage. The fraction of hydrogens associated with the TZl adsorbing phase at an x / m = 0.063, for example, is only about 0.11.
-
’
I n Fig. 4 a plot of Ti vs. x / m is shown. As in transverse relaxation measurements, a data point exists a t x / m = 0; residual hydrogens are present after sample preparation. The T1 measurements describe a single phase system except for the small range of x / m values in the vicinity of x / m = 0.126, which is two phase. I n the two phase region the solid and semi-solid circles correspond t o the more strongly adsorbed and less strongly adsorbed Ti components, respectively. The behavior of longitudinal (TI) relaxation times with coverage ( x / m ) is quite different from the transverse (T2) components. A minimum value for TI exists in the range of x/m values studied. An amplified ordinate scale of the TI vs. x / m plot shown in Fig. 5 indicates a minimum value at Ticav) 4 X see., where l/Ti(av) = Pi/Tli Pj/Tlj. This minimum occurs in the two phase region; hence, the solid circles corresponding to the short time component in Fig. 5 are not to be confused with the calculated Ti(,,). The T1 system is single phase at x / m = 0.104; yet it becomes two phase at x / m = 0.106. This is a very abrupt change and cannot be explained from the simple fact that Ti is growing shorter in this region with increasing coverage. This critical transition will be discussed later in the paper in terms of lifetime changes. Evidence of Two Adsorbed Phases.-Past experiments have demonstrated the existence of two adsorbed phases for the case of transverse relaxation measurements of water vapor adsorbed on silica gel. The silica gel sample examined in the present study also shows two distinct phases (see Figs. 1 and 3). An examination of the transition region from a single phase to a two phase system is informative. Transverse relaxation time plots are shown in Fig. 6 for values of x / m in the transition region. At x / m = 0.0346 the system is single I
+
B.I.0
e04
008
36
012
010
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0 TWO P H S E LONG TIME COMPONENT
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-
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.TWO PHASE SHOW TIME COMPONENT
I
28
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I I
32
021
I
-
YI
iI
24-
-
-
i 0
0.04
0.08
0.12
0.16
0.20
0.24
54 Q“%rnSlO,. Fig. 5.-An amplified scale of longitudinal relaxatipn times for values of x / m in the region of the TIminimum.
phase, as evidenced by the straight line plot of log A ( 2 7 ) vs. 7 . The first experimental indication of the long time component (l/pzi = Tz,) of the adsorbed phases occurs a t z / m = 0.0528. The smallest surface coverage, where the fraction of hydrogens associated with the long time component was large enough to permit evaluation of the relaxation times (TI2 and TzJ and the relative abundance of hydrogens, - azj/azi = Ao’/&, occurs at x/m 0.0614.
J. R. ZIMMERMANAND J. A. LASATER
1160
I 0
I
I
a2
04
I 08
1 0.6
,a
I
10
I
I 1.2
14
IO’ SECONDS.
Fig. 6.-Transverse relaxation time plot illustrating single phase to two phase transition region of xlm.
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Short time component
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Previously reported longitudinal relaxation measurements of water vapor on silica gel have been single phase, even though the transverse measurements were two phase. In other words, for each x / m there was associated a single relaxation time TICav). An interpretation of this experimental fact was presented on the assumption that two phases did exist but that the average lifetimes, t’s, of the hydrogens were too short compared with the Ti's, t o allow resolution of the two phases. In the present study (see Fig. 4) the TI measurements a t very low coverage are again single phase. However, as coverage increases, the system becomes two phase. In Fig. 7, longitudinal relaxation plots are given for x / m values which demonstrate the transition from single phase t o two phase and back to single phase. The Tl data for both x / m = 0.104 and x / m = 0.160 give typical single phase plots; however, the plot of log R ( r ) us. r for s / m = 0.106 definitely demonstrates a two phase system. This very critical transition region will be considered later in terms of abrupt lifetime changes. Relative Population of Adsorbed Phases.-In a nuclear relaxation two phase system, the relative population Pi/Pj of the hydrogen nuclei associated with the phases can, in principle, be determined. In reality, however, the quantity which can be measured is - q/aj; and this quantity is equivalent to Pi/Pj only if ti > > Ti and tj > > Tj, where ti and tj are the average lifetimes of the hydrogen nuclei in the ith and jth phases. The data described are good approximations to this limiting case and are sufficiently accurate to justify the quantitative conclusions. From transverse relaxation data the distribution of water vapor in the two adsorbed phases is shown in Fig. 9. The water vapor is associated only with the short time (Tz’) component a t low coverage. This phase logically can be described as the one corresponding to the greater heat of adsorption. If a straight line is the best fit to the long time (T2J component data, then the coverage a t which equilibrium adsorption first occurs for the Tzl phase 0.044. Once two phases have been esis x / m tablished, the population of each phase increases with x/m. The fraction of bound hydrogens associated with the short time (T’z) component vs. x / m is plotted in Fig. 10. At a coverage of 6’ = 2, approximately 62% of the hydrogens are associated with this phase. The longitudinal relaxation measurements shown in Fig. 4 give three values of x / m which illustrate two phase behavior. It is particularly informative to compare the relative populations of the two adsorbed phases obtained from transverse relaxation measurements with those relative populations evaluated from longitudinal relaxation data. Such a comparison is made in Fig. 8. The quantity &’I(&‘ Aol) is the fraction of hydrogens in the short time component phase. The agreement between transverse and longitudinal measurements is convincing, especially so since the data were analyzed by numerical procedures rather than by graphical foresight. Therefore, it can be concluded that the two phases in longitudinal relaxation measurements are identical with the corre-
-
Fig. 7.-Longitudinal relaxation time plot illustrating single phase to two phase transition region of x/m. X/M
Vol. 62
T Imeasurements
0.106
0.80
,126
.79
1
Ao’ AD‘ ADI
+
Ti measurements
0.78 .76
+
?
NUCLEAR MAGNETIC RESONANCE OF ADSORBED WATERON SILICAGEL
Oct., 1958
sponding two phases in transverse relaxation measurements. Lifetime of Hydrogen Nuclei in an Adsorbed Phase.-The average lifetime of a nuclear spin in a given phase which is characterized by a relaxation time Ti is simply ti = 1/Ci where Ci is the probability per second that a spin in the ith phase leaves the ith phase. Since multiple phase (i and j) systems have been observed in both longitudinal and transverse relaxation measurements, it is relatively easy to calculate a limiting range for the average lifetimes of the hydrogen nuclei in the adsorbed phases. It can be shown from either equation 1 or 2 that 1
1
Pj
PI
- I Tj I T ( a v ) I T I Ti
(3)
Ti and Tj are defined as the actual relaxation times which would be measured under very slow exchange conditions (ti > > Ti and tj > > Tj); l/pi and l / p j are the apparent relaxation times evaluated from the experimental data; and T(,,) is the single relaxation time which would be ohserved under very fast exchange conditions (ti < < Ti and tj < < Tj). Also, the limits of the amplitude factors ai and aj in equations 1 and 2 are given by 1 2 ai 2 Pi 0 2 aj 2 -Pj (4) where Pi and Pj are population fractions of hydrogens associated with the ith and jth adsorbed phases, and where - &/aj is the apparent population ratio determined from the experimental data when the limiting conditions of fast exchange do not exist. Hence, as ti and t j become long 1
1
+Ti, Pi - +Ti,ai +Pi,aj +-Pj (5) Pi As ti and tj become short 1 1 titi +T(nv), pj - +ai +1, aj +0 (6) Pi ti tj'
+
With the aid of these limiting expressions, an approximation to the average lifetimes, ti and t j , of the hydrogen nuclei in the adsorbed phases is possible. An examination of Figs. 3 and 4 shows that a value of x/m = 0.104 is a logical coverage region for computing the average lifetimes. At this value of x/m, the TI system (Fig. 4) is still single phase; the T2 system (Fig. 3) is two phase. A rough estimate of the lifetimes can be made immediately, for from equation 3 Tzcsv)
