June, 1963
PHYSICAL PROPERTIES OF TRa4XSITIOK M E T A L
The p H measurements were made with a Cambridge Research Model p H meter. The symbol OL refers to the ratio of equivalents NaOH added to equivalents of carboxyl originally present. Poly-( acrylic acid-maleic acid) 1-1 copolymer stock solution (0.1128 N ) was prepared by dissolving poly-( acrylic acid-maleic anhydride) 1-1 copolymer (6.400 g., 0.1128 carboxyl equivalent) in a 1liter volumetric flask and making up to volume with de-ionized water. The solution was then kept in a 85" bath overnight to hydrolyze the anhydride groups. 314-Neutralized Poly-(vinylmethyl ether-maleic acid) Copolymer Stock Solution (0.100 N).-The anhydride copolymer was dried to constant weight in a vacuum oven and 3.90 g. (0.05 carboxyl equivalent) was placed in a 500-ml. volumetric flask containing 17.53 ml. of 2.139 M (0.0375 mole) sodium hydroxide. De-ionized water (approximately 350 ml.) was added to the flask. The flask was then kept in a 60" bath overnight in order to hydrolyze the anhydride groups. The solution was cooled t o room temperature and filled to volume with de-ionized water. Rate Measurements.-In the case of the cationic esters, release of phenol was followed by the rise in the optical density a t 273 mp on a Beckman DU spectrophotometer. A special waterjacketed cylindrical cell equipped with a mechanical stirrerdesigned to prevent bubble formation was used. The cell was 10 cm. long and had a capacity of 50 ml. An aliquot of the ester stock solution (in the neighborhood of 0.1 ml.) was introduced by means of a blowout pipet to start a kinetic run. Prior to each run stock solutions of esters I and I1 were prepared in 0.01 N HC1 and methanol, respectively. In the 10 cm. cell, esters I and I1 were present in concentrations of 0.6 mg./50 ml. and 0.7 rag./50 ml., respectively. The rate of disappearance of p-nitrophenyl acetate was followed a t 273 mp. The test solution containing 0.64 mg. of the ester in 50 ml. was thermostated and at various time intervals aliquots were removed from the flask. The optical densities were measured in a 1 cm. cell. In all cases the temperature was controlled to a t least 0.05'. Kinetics.-The hydrolysis of I in basic solution may be depicted by
CATALYSTS
1297
For the two consecutive reactions shown above, the fraction of ester groups ( E )a t an,y time ( t ) is given byI4
where CE represents the molar concentration of ester bonds, COthe molar concentration of ( I ) a t t = 0 and y = k1/2 ( k l kz). The fraction of ester bonds a t any time was calculated from the optical density D of the solution
D
=
CEeE
+ (2C0 - CE)e, + I:
where and ep are the extinction coefficientsassociated with the ester bonds, and with phenol, respectively, and U is the optical density due to background which is unaffected by the reaction. The initial slope of a plot of -In (D, - D) against time (where Dm is the optical density a t the conclusion of the reaction) equals k1/2, and the final slope is equal to kz if kl > kz and to kl if kz > kl. Although the initial slopes could be used to give good estimates of k l , the final slopes could not be used for an accurate estimate of kz, because kl/kz was not large enough to observe the disappearance rate of ester bonds in I1 without some contribution from I. Thus, the method of initial slopes was used when only values of kl were desired. In order to calculnte easily both kl and kz a graphical method was employed in whieh the observed dependence of In E on t was compared with curves calculated for various values of y. As expected, the pseudo-first-order rate constants of ester hydrolysis in conventional buffer solutions varied with hydrogen ion concentration according to
In order t o represent the data, the following values were taken for ~ ( H ~ and o ) k ( o ~ ) .At 25.8'
Ester I, ~
( H ~= o )
4.5 X
sec.-l,
1. mole-' sec.-l
k ( ~ ~ ~ =) l1.28 < ~X Ester IV, J Z ~ H ~ O )= l.0 X l o w 4sec.-l,
k(oHjKw = 0.375 X 10-lO1. mole-lsec.-l
IA -t @OH
-
The kinetics of the hydrolysis of esters I1 and I11 in buffer solution were first order. Plots of - ln(Dm D ) were linear in time, and were used to obtain the pseudo-first-order rate constants.
-
IA
kz
(14) A. A. Frost and 1%. G. Pearson, "Kinetics and Mechanism," John Wiley and Sons, Xew York, S . Y . , 1953,p. 153.
ADSORPTION STATISTICS ,4ND THE: PHYSICAL PROP'ERTIES OF TRAKSITION METAL CATALYSTS BY CHARLES P. POOLE, JR. Gulf Research & Development Company, Pittsburgh, Penntrylvania Receive8 December $6, 196.3 The number of small clusters of transition metal ions formed on an alumina surface by adsorption from solution was calculated from a statistical model, and the resulting variation of clusters with metal content was correlated with electron spin resonance, nuclear magnetic resonance, magnetic susceptibility, and gas adsorption data for alumina impregnated with chromium, cobalt, and nickel salts.
I. Introduction Over the paat fern years several members of this Laboratory ha,ve been studying catalysts prepared by impregnating and with transition metal oxides. For example, chromia on alumiiia was studied by electron spin resonance, (1) D. E. O'Reilly, Adtan. Catalysts, 12, 31 (1960). (2) D. E. O'Reilly and D. 8. MacIver, J. Phys. Chem., 66, 276 (1962).
magnetic susceptibility,3 nuclear magnetic resonance ( n . r n ~ . )and , ~ catalytic techniques5; cobalt on alumina X-ray a bwas studied by magnetic (3) J. R. Tomllnson and G. T. Rymer, preprints, Division of Petroleum Chemistry, American Chemical society National Lfeeting, April 5-10, 1959, Mass. (4) D. E. O'Reilly and IC. P. Poole, Jr., t o be published. ( 5 ) J. 11. Bridges, D. 8 , MacIver, and H. H.Tobin, Paper No. 110, Second International Congress on Catalysis, Paris, France (July, 1960).
CHARLES P. POOLE, JR.
1298
Vol. 67
metal ions are adsorbed randomly on available alumina surface sites during the impregnation process. The theory of random adsorption will be developed in section 11; it will be compared with experiment in section I11 and discussed in section IV. In section V several concluding remarks will be made.
11. Theory
Fig. 1.-Various possible arrangements of three ions (e) around a particular ion ( 0 ) to form the QT cluster.
I
I
I
It is assumed that the base or adsorbent contains N adsorption sites and that PN metal ions are adsorbed randomly on PN of these sites, where P is the fraction of the sites covered by the metal ions. hIultilayer adsorption will not be considered for the present. The probability of a given site being unoccupied is (1 - P ) . In a square plane lattice, each site has four nearest neighbors, so the probabiIity S I N finding a given site occupied by ai1 isolated adsorbed ion is the probability of the site being occupied ( P ) times the probability of the four nearest neighbors being unoccupied (1 - P)4. The number of isolated metal ions S is therefore
s = NP(1 - P)4 for a square lattice, and
I
s = NP(1 - P)6
TOTAL
2 FRACTION
I
I 3
I I
OF S I T E S
4 OCCUPIED,
5
P,
Fig. 2.-Fraction of sites occupied by .single ( S I N ) , double (D/A7), triple (T/IV), and quadruple ( Q / N ) isolated clusters for a plane square lattice.
sorption edge spectroscopy,' nuclear magnetic reson a n ~ e and , ~ chemical kinetics6; nickel on alumina was studied by magnetic susceptibility,* nuclear magnetic resonai~ce,~ and chemical kinetics.8 At low chromium concentrations the electron spin resonance spectra of reduced chromia on aluminal.2 were produced by isolated Cr+3ions (&phase Cr+3)and a t high chromium concentrations the spectra were produced by "clumped" Cr +8 ions (p-phase). Intermediate concentration spectra were superpositions of these two cases. The cobalt on alumina and nickel on alumina catalysts each showed the presence of a low concent'ration 8-phase and a high concentration p-phase; these phases are discussed in detail in references 6 and 8. More recently these phases have been studied in coprecipitated chromia-alumina.9 The purpose of this note is to show that such a twophase behavior is expected if it is assumed that the (6) J. R. Tomlinson, R. 0. Keeling, Jr., G. T. Rymer, and J. M. Bridges, Paper No. 90, Second International Congress on Catalysis, Paris, France (July, 1960). (7) R. 0. Keeling., Jr., J . Chem. P h w , 31, 279 (19SQ). (8) G. T. Rymer, J. M. Bridses, and J. R . Tomlinson, J . Phys. Chem., 66, 2152 (1961). (9) C. P. Poole, Jr., (1962).
(1)
W.L. Kehl, and D. 9. XacIver, J . Catalysis, 1, 407
(2)
for a plane triangular lattice which has six nearest neighbor sites. Similar expressions may be obtained for the number of ions in isolated pairs D, triplets T, and quadruplets Q, and these are listed in Table I. As ail illustration of how a complicated formula from this table is derived, consider QT for the square lattice. The probability of occupying a particular lattice site with an ion is P and the probability of occupying three more previously designated sites to form this cluster is P3. The probability that the eight nearest neighbor sites to the cluster are empty is (1 - P)E,so P4 (1 P ) Eis the probability of finding this particular cluster. Nom once the site under consideration is occupied there are sixteen ways in which three nearby sites may be occupied to form QT, as shown in Fig. 1, so the probability must be multiplied by 16, as shown in Table I. Figure 2 shows a graph of the fraction of ions in single, double, triple, and quadruple sites for the plane square lattice. Similar graphs have been given for three dimensional lattices by Behringer. lo The formulas in Table I were checked by observing that the sum of all possible clusters is N P , and therefore T Q cannot contain terms in P 2 , the sum S D P3, and P4. This check ensures that no clusters are omitted. It will be useful to notice that these formulas may be used for the number of unoccupied sites by interchanging P and (1 - P ). All of the formulas in Table 1 are of the form KPm. (1- P)" where K is a constant, so the value of P = P,, which corresponds to a maximum in the number of sites occupied by a given cluster is obtained by the formula
+ + +
d dP
- [KP" (1 - P)"J = 0 with the solution P
=
(3)
P,, given by
P,,
=
m
-
m + n
(10) R. E. Behringer, J . Chem. Piws., 29, 537 (lQ58).
(4)
June, 1963
PHYSICAL P R O P E R T I E S OF
TRANSITION METAL
1299
(2ATALYSTS
TABLE I NUMBER O F ADSORBED ATOMSIS S I N G L E 8, DOUBLE D,TRIPLE T , AND QUADRUPLE Q ISOLATED GROUPS
. e. e*.
..' .:
.... .". .*.a
'*..
...'
,'.
.s .. D
Plane triangular lattice
- P)4 4SP2(1 - P ) 6 = 4P(1 - P)*S :, T~ = 1 2 ~ ~ 3 -( 1~ ) =7 ~ P ( -I P ) D Ti = 6 N P S ( 1 - P)' = 1/2(1 - P ) T L 1' = 2'1 TL :: Qo = 41VP4(l - P ) 8 = 2/3PTl
S = NP(l - P)6 D = 6hrP2(1- P ) 8 To = 6NP3(1 - P ) @= P ( l - P ) D 2'1 = 9NP3(1 - P)" = 3/2(1 - P)To T< = 18NP3(1 - P)1° = 2Ti 2' = To Ti 2'< Q~ = 1 2 ~ ~ 4-( 1P ) ~ =O@T1/3 = 1 2 ~ ~ 4-( 1P ) ~ = Z( I P ) ~ Q ~ Q,.= 48NR4(1 - P)" = 4(1 - P)Qo &, = 24NR4(1 - P ) l Z = 2&1 QN = 24NP4(1 - P)12 = 2Q1 Q< = 48NR4(1 - P ) l Z = 4Qi Q,, = 8NP4(1 - P ) l 2 = 2/3 QI
-
=
QO -t- Qi -I- Q,
=
...
+ +
Q
Plane square lattice
= NP(1
+
':' QT = QL = Q1 = *:. QN =
:., ...
Q
=
16NP4(1- P)* = 4Qo 32NP4(1 - P ) 9 = 8(1 - P)Qo 8NP4(1 - P)'" = 2( 1 - P)'Qo 16NP4(1- P ) 8 = QT
+ + QL + Qi + QN
00
&T
+ Q, + + Q< + QA QN
On a square lattice, for a given size cluster (given 17%) a single linear chain has the lowest P,, and a square has one of the largest P,, values (a configuration which more closely approximates a circle has a larger P,, than a square) as shown in Table 11. Figure 3 shows the variation with cluster size of these two P,, values and the analogous quantities for a triangular lattice. For each lattice the average P,, for all clusters of a given size will lie between the corresponding limits on the graph, and Fig. 2 illustrates such average maxima for T and Q clusters. The symbols So, DO,. . .will be used to denote the maximum in the number of sites occupied by atoms in the corresponding clusters S , D,.. ., and for isolated atoms we have na = 1, and
80 = NP1,(1 - PI,)" (5) For the square lattice where n = 4 So = 0.082N and PI4= l / 5 while for the triangular lattice where n = 6, we have
0.6
7 I
0.6
-
I
I
I
I
0.4
---
I' O'I
t
5
10
SPUARE LATTICE TRIANQULAR LATTICE
25
20
15
30
NUMBER OF ATOMS IN CLUSTER, m.
Fig. 3.-Variation
of Pm,,with cluster size m for four particular cluster shapes. I
Sa = 0.057 and PIE= 1/7
I
I
I
1
1.0
a t their respective maxima. 0.8
VALUESOF P,,
TABLE I1 FOR FOUR TYPESOF CLUSTERS L0.6
k
The Quantity k is defined by the expression ~n = Lattice type
Plane square
Arrangement of atoms
In single straight line
Plane square
In square
Plane triangular
In single straight line
Plane triangular
I n equilateral triangle
m
J
s
j=L P,,
0.4
m 3m .f 2 Yn
0.2
+ 42/m
m 3m 4 rn m + 3 ( k + 1)
-+
111. Comparison with Experiment A. Electron Spin Resonance and Magnetic Susceptibility Data.--ils mentioned above, the electron spin resonance spectrum from alumina impregnated with a low concentration of chromia originates from isolated Crf3 ions.1~2The present theory may be compared with these experimental data by normalizing the experimental results in such a way that both the abscissa
P/P,.
AND P / P e .
Fig. 4.-Comparison of plane square lattice (- - - - - -) and plane triangular lattice (--) theoretical curves with experimenta,l data from the Cr+3 &phase detected by the e.s.r. of reduced Cr/ALOa (X), from the AlZ7 n.m.r. of reduced Cr/AlzOa ( A ) and from the C O + &phase ~ detected by the magnetic susceptibility of Co/A1203 (0).
and ordinate iii the graph of the number of isolated Cr + 3 atoms against the chromium concentration are set equal to one at the maximum point. For the present case this maximum corresponds to 8.1 X l o J 9 spins/g. and 2.1 weight 70chromium.2 The normalized experimental data are given on Fig. 4, and they are
1300
CHsRLES
P. P O O L E , JR.
( a ) Cr +G e.s.1. from cI/&o~. 1.0
0.6
0.4
a2 PIP1,. 1
PIP,,
.
2
3 ‘ PIP* *
1
5
6
PIP,..
(b) AlZin.m.r. from c r / B l ~ o ~ .( d ) AlZ7n.m.r. from N/A1203. Fig. 5.-Comparison of theoretical curves with Cr +6 ( -/-phase) e.8.r. and AlZi n.m.r. data for oxidized samples. I n the figure A = S/So (-), A = (S D T &)/(A‘ D T &lo ( . . . . ) and A = Q/Qo ( - - - - - - ) where A is normalized to unity a t its maximum and plotted against PIP14 for a square planar lattice.
+ + +
+ + +
Fig. 6.-A comparison of the calculated (-) and measured (x) ratios of CO to 0 2 surface areas. The CO/Oz surface areas are assumed t o be proportional t o the ratio of the number of sites available for double site to that available for single site adsorption.
compared with the theory by plotting on the same figure S/Sa us. P/P1, for the plane square (n = 4) and plane triangular (n = 6) lattices. It will be noticed that the theory agrees with the experiment except a t high chromium concentrations. The Crf6 (7-phase) e.s.r. data obtained after oxidizing these samples produce a niaximuin a t 2.1 mt. yo Cr, and these data were normalized in the same way and plotted on Fig. 5a. The low concentration magnetic susceptibility data for cobalt on alumina were normalized in a similar way with Sa = 1.17 wt. % Co and plotted on Fig. 4. These data agree with the theory a t low cobalt concentrations and deviate a t high concentrations. B. Nuclear Magnetic Resonance Data.-When alumina is impregnated with a transition metal, the amplitude of the 4lZ7n.m.r. absorption envelope a t first decreases with increasing metal content, reaches a minimum, and then increases for higher concentrations.4 The decrease in AlZ7amplitude was attributed
Vol. 67
by O’Reilly and Poole to the removal from detection of A127 nuclei near small clusters of transition metal ions. The number of aluminum nuclei removed from detection by chromium, cobalt, and nickel ions was normalized to the maximum number and the resulting data are plotted on Fig. 5b, 5c, and 5d for the oxidized samples, and in Fig. 4 for reduced Cr/A1203. The values of SOused were 2.1, 1.17, and 4.3 wt. % Cr, Co, and Si, respectively. The data shorn a general qualitative agreement with the theoretical curves except a t high metal concentrations. C. Gas Adsorption Data.-Bridges, hlacIver, and Tobin have showii that the amount of oxygen adsorbed at 77°K. on a chromia-alumina surface is proportional to the Cr203surface area,6 and the lower areas obtained by CO adsorption were attributed by them to a twosite adsorption In Fig. 6 their experimental points for the ratio of the surface area froin CO adsorption to that from Os adsorption are plotted against the chromium concentration and the data are seen to fit the curve computed for the ratio of the number of chromium ions available for double-site adsorption to the number available for single-site adsorption. This double site calculation was made with the plane square lattice and assumes that cluster D can adsorb one CO molecule, &o can adsorb two, QT can adsorb one, etc. Again the high concentration point deviated from the curve. IV. Discussion The simple assumption that the aluinina surface contains randomly distributed transition metal ions has allowed us to calculate the distribution of various small clusters as a function of the transition metal concentration. The dispersed or &phase Crf3and C O + ~ concentratioiis detected by e.s.r. and magnetic susceptibility correlate quite well except at relatively high metal concentrations with the theoretical curve S/So for isolated ions, as Fig. 4 indicates. The high concentration deviations occur because during the impregnation process most of the metal ions are adsorbed directly from low concentration impregnating solutions, while as the solution concentration increases, more and more of the total number of metal ions originate from the solution which is trapped in the pores and evaporated during the drying process, as previously noted by R ymer, Tomlinson, Keeling, and Bridges.Q This latter mechanism probably results in multilayer adsorption and explains the deviations from the theory a t high metal concentratioiis. Oxidized chromia on alumina samples contain Cr +5 ions (referred to as the y-phase) with a maximum concentration of 1.6 X 1019 spins/g. a t 2.1 wt. % Cr and a coiicentration dependence similar to that of the &phase, but with only a fifth of the number of spins. Because the &phase Cr+3 spins are insensitive to oxidation, while both the bulk or /?-phase and the ?-phase are oxidation dependent, O’Reilly and lllacIver associated the Cr+6 ions with the p-phase1s2 which is most susceptible to oxidation when in rather small clusters. Figure 5a indicates that the Cr+6 ions may predominate in small clusters of chromic ions. Again the 5 wt. % Cr point deviates due to condensation of chromium in the pores. The magnetic susceptibility data of the Si-Aldh (11) D. S. MacIver and H. H. Tobin, J . Phys. Chem., 64, 451 (1960).
June, 1963
ENERGY VOLUME RELATIONS OF OCTBYETHYLCYCLOlrETRASILOXdNE
system did not allow a calculation of the &phase as a function of concentration, but the 8-phase was detected in this work.* It was previously deduced4 that the AlZ7n.m.r. signal from transition metals on alumina is affected by small clusters of metal ions on the surface. The suitably normalized AlZ7results presented on Fig. 4 and on Fig. 5b, 5c, and 6d show a general qualitative agreement with the theoretical curves except a t high concentrations, and this supports the postulated origin of the hlZ7n.m.r. results. The data shown in Fig. 5 scatter much more than those shown in Fig. 4. When the Cr-A1203 sample is oxidized, the maximum in the number of aluminum nuclei relaxed beyond detection shifts to larger chromia concentrations in the manner shown on Fig. 4 and 5b, and this may originate from the partial oxidation of medium size clusters of chromium. Figure 3 shows that for clusters larger than the Q cluster the maximum P,, changes only very slowly with the number of atoms m in the cluster, so the fit of theoretical curves to experimental data becomes insensitive to 7n. The metal concentration So for the maximum in the 8-phase was 1.17, 2.1, and 4.3 for the three ions Co+2, respectively, and this indicates that Cr+3, and Si+2, the amount of surface accessible to each ion is not the same. Part of this difference may result from the use of separate alumina preparations in each series. Sacconi12had discussed the order of adsorption of various cations when their solutions are passed through an alumina chromatographic column, but this order differs from the variation in Xo observed for the three cations discussed above. Gas adsorption studies of chromia-alumina catalysts5 showed that less than 20% of the total alumina area is available for adsorbing chromium. The present treatment assumed random adsorption on those regions of the alumina surface which are accessible to the metal ions. (12) L. Saoconi, Discusssons Faladay Soc., 7, 173 (1949).
1301
When silica is put in an aqueous solution of n'i-F2 it does not appreciably adsorb the nickel, in contrast to the strong adsorption that occurs on alumina.* The magnetic susceptibility measurements of cobalt catalysts6 indicate that the cobalt concentration which produces a maximum iii the &phase on silica is less than one-fifth as large as that which produces a d-pha$,e maximum on alumcna. One may conclude that silica has considerably fewer adsorption sites for adsorbing these transition metals than alumina has. This makes it very difficult to obtain experimental data on a silica base for cornparison with the theory, and at the present time such data are not available. It mould be particularly instructive to study a series of silica alumina-transition metal catalysts from the viewpoint of this paper.
V.
Conclusions By making the amumption that transition metal ions are randomly adsoibed from an impregnating solutioii 011 an alumina surface, and that the distribution of these ions remains random after drying and calcination, it has been possible to explain a large body of experimental data. For example, electron spin resonance, magnetic susceptibility, and nuclear magnetic resonance data give &phase spin concentrations which correlate quantititatively with the number of isolated single ions computed from the theory, and the GO-02 adsorption data agree with the ratio of the number of chromium double sites to the total number of chromium sites on a Cr-A1203surface. The theory breaks down at high metal concentrations due to the condensation from solution left in the pores. Acknowledgment.-The author wishes to thank Dr. D. S. MacIver, Dr. Joanne M. Bridges, Dr. J. E. Tomlinson, Dr. D. E. O'Reilly, Mr. G. T. Rymer, and Mr. H. H. Tobin for helpful discussions of their experimental data.
EKERGY VOLUXE RELATIONS OF OCTAMETHYLCYCLOTETRASILOXhNE AND ITS MIXTURES WITH CARBON TETRACHLORIDE BY MARVIN ROSSAND JOEL H. HILDEBRAND Department of Chemistry, University of California, Berkeley, Calafornia Received January 9, 1963 Values of ( ~ P / ~ Thave ) v been determined for octamethyltetrasiloxane, c-Si404(CH,)8, over the range from 22 to 45". At 25" and a molal volume of 312.02 cc., it is 7.879 atm. deg.-I, and ( ~ E / ~ Vis )56.88 T cal. cc.-I. If, following the suggestion of Frank, we set the potential energy of a liquid E = -a/Vn, then ( d E / d v ) = ~ na/Vn and n = v ( d E / d v ) ~ / A E 'where , AE' is energy of vaporization. The second expression yields n = 2.3 and the third n = 1.38, instead of n = 1 for a van der Waals liquid. Both values are consistent with ~ mixtures of this siloxane with CC14 are an intermolecular potential of the Nihara type. Values ( d E l d V )for only slightly greater than additive on a volume fraction basis, differing as expected from the mixture, n-CEHlz n-CsF,,, investigated by Dunlap and Scott.
+
The purpose of this research is that stated by Hildebrand and Scott1 in their recent book, "for practical purposes," the most useful theory is likely to be the one which is built "close to the ground," and which evaluates its parameters under conditions closely approximating those where they will be applied. For this (1) J. H. Hildebrand and R. L. Scott, "Regular Solutions," PrenticeHall, Inc., Englewood Cliffs, New Jersey, 1962.
reason, we prefer to relate the properties of liquid solutioiis to those of pure liquids, rather than to dilute gases at very different densities and temperatures. Of these parameters, (dE/dV),, which we will call internal pressure, is one of the most significant, and is also easy to determine with precision, because it can be calculated from (dP/dT)V,which is constant over a wide range of pressure. Extensive data for pure liquids
