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 deduced4that 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.
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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
MARVIN Ross AND J O E L 1%.I~ILDEBRAND
1302
and their mixtures are now a ~ a i l a b l e . ~ I- n~ earlier papers, rather good agreement was reported between observed values of (bE/bV) for mixtures and those calculat'ed from the same function for the pure components when the calculation was based upon the old Bertlielot relation, the geometric mean between the van der Waals a's, a12 = (a1a2)1/2 andia ( b E / d V ) , = a/ vz. Smith and Hildebraiid6 found, however, that the exponent of V , as obtained by coinpariiig ( b E / b V ) , with the energy of vaporization per cc., the "energy density," increases with increasing inolecular size, becoming 2.49 for C i F 1 6 and 2.44 for c-C6FllCF3 (vide infra). Our early value2 of the exponent for CCl,, 2.09, has been confirmed by Benninga and Scott.i It is obvious that the dimensions of the "constant," a, change with the exponent, and that the simple Berthelot relation is no longer appropriate. It seems important, therefore, to express the value of ( b E / b V ) ,for mixtures in terms of the same function for the pure components, and to increase the rigor of the t'est by using components for which the volume dependence is very different. We chose mixt'ures of CC14 and octamethylcyclotetrasiloxane, c-Si404(CH&. The lat'ter consists of a core, c-Si404,well buried under eight methyl groups. It is quasi-spherical in form. We have used it in ot'her studiess-ll of the effects of disparity in molal volumes. Experimental The apparatus was essentially the same as that used by Smith and Hildebrand.6 The temperature of the bath was controlled within 0.1 '; the temperature inside the bomb fluctuated about 0.03'. A P-T point was considered acceptable when four makeThe previously calibrated and-break cycles agreed to 0.01 Heise-Bourdon gage could be read to 1 0 . 1 atmosphere. Metal rings of the sort used in distillation columns were placed in the space between the cell and the walls of the bomb in order to hasten thermal equilibrium. The octamethylcyclotetrasiloxane was from the stock used in previous investigations that had kindly been donated by the General Electric Company. Its purity was estimated from its melting point to be 99.6Yc. The CCL, of C.P. grade, was distilled over Drierite and allowed t o stand over mercury. From 5 to 8 points were determined on the P-T line for each volume. The range was from 1 to from 100 to 140 atm. The root mean square deviation is 0.01'. The observed values of ( A P / A T ) v were corrected in the usual manner for the compression of the glass.
The figures for the compressibility, 0,were obtained by dividing (dP/dT) by the coefficient of expansion. is near The value interpolated for 25.0') 1.343 X the figure obtained by Shiiioda and Hildebrand,b1.56 X 10-4. Results for two niixtures of the siloxane with CC1, of mole fraction x1 are given in Table 11. For the internal pressure of pure CCL, needed for dealing with the mixtures, we use the data of Benniiiga and Scott.' We measured the densities of the two mixtures x i t h the results
(2) W. Westwater, H. W.Frantc, and J. H. Hildebrand, Phys. Rev., 31, 135 (1928). (3) J. H. Hildebrand and J. >I. Carter, J . Am. Chem. Sac,. 64, 3592 (1932). (4) E. J. Alder, E. W. Haycock, J. H. Hildebrand, and H. Watts, J . Cham. Phys., 22, 1060 (1954). (5) E. B. Smith and J. H. Hildebrand, i b i d . , 31, 145 (1959). (6) K. Shinoda and J. H. Hildebrand, J . Phys. Chem., 65, 183 (1961). (7) H. Eenninga and R. L. Scott, J . Chem. Phys., 23, 1911 (1955). (7a) Cf.ref. 1, p. 80. (8) K. Shinoda and J. H. Hildebrand, J. P h y s . Cliem., 61, 789 (1957). (9) J. E. Jolly and J. H. Hildebrand, i b i d . , 61, 791 (1957). (10) K. Shinoda and J. H. Hildebrand, i b i d . , 62, 295, 481 (1958). (11) K. Shinoua and J. H. Hildebrand, ibid., 65, 1889 (1961). (12) C. B. Hurd, J . Am. Chem. Soc., 68, 364 (1946).
0.500, d
Xcci4 =
=
0.7627, d
X C C ~== ~
1.1354 - 1.350 X 10-3c g./cc.
(2)
1.2989 - 1.530 X 10-9 g./cc.
(3)
=
We calculated the excess molal volumes of the mixtures to be 0.8 cc. a t 41 = 0.500 and -0.4 a t $1 = 0.237. TABLE I RESULTS FOR PURE c-Si404(C H B ) ~ v, t , OC.
(bp/bT)v,( b E / b V ) r ,
cc. mole-'
22.26 24.45 25.00 29.56 35.65 44.84
'.
Results The results for pure c-Si404(CH3)8are given in Table I. The values of the molalvolume were calculated from the densities published by Hurd.12 The values of (dP/bT). represent t'lie corrected slopes of the AP-AT lines. The figures for ( b E / b V ) ,were calculated by the equation
1701. 67
311.09 311.93 (312.02) 313.90 316.27 319.91
atm. deg.-l
cal. cc.-l
10% atm.-1
n
8.030 7.905 (7.879) 7.663 7.271 6.726
57.45 56.96 (56.88) 56.19 54.37 51.80
1.511 1.537 (1.543) 1.696 1.691 1.844
1.385 1.385 (1.38) 1.390 1.375 1.350
TABLEI1 RESCLTSFOR MIXTURES OF (1) CC4, ( 2 ) 51
91
1.000 0.763 .763 .500 .500 0
1.0000 0.500 ,500 ,237 ,237 0
t,
oc.
v
25.00 97.09 25.00 148.92 31.76 ... 24.57 204.29 25.00 (204.66) 26.00 312.02
C-&o4(CH3)B
-( b E / b V )T--Calcd. ( b P l b T )7 ~ Exptl.
11.22 9.69 9.19 8.82 (8.786) 7.879
81.04 . . . 69.97 68.96 ... 67.87 63.60 ... 63.46 62.60 56.88 ,..
Discussion (a) The Pure Siloxane.--We begin by analyzing the data for the pure siloxaiie in the way first proposed by FranklS and applied by Smith and Hildebrand.6 The potential energy of the liquid is assumed to vary with volume in accord with the expression E -a/V" z -AEv (4) where AEV is energy of vaporization. If n is constant, differentiation gives ( b ~ / b ~=) na/P"+l .
(5)
and, for molal quantities, v and E" n = V(~E"/~V>/AE" (6) We may obtain a value of n by means of eq. 5 from the slope of a line obtained by plotting log ( b E / b B ) , us. log v. The interval is not large enough, in view of some scatter of the points, to fix the elope accurately; we find n = 2.3 f 0.2. (13) H .
S.Frank, J .
Chem. Phys., 13, 495 (1945).
June, 1963
13103
E S E R G Y VOLUME RELL4TIOSS O F OCTAMETHYLCYCLOTETRASILOXAXE
In order to obtain n by aid of eq. 6, we use the values ~ at of (bE/bV),in Table I with values of A E calculated the corresponding temperatures from the expression for the heat of vaporization given by Osthoff and G r ~ b b , AHvap ’~ = 20.7 - 0.02462’ kcal. mole-l. This procedure yields the values of n given in the last column of Table I. We see that the value of n obtained from eq. 5, 2.3, is rnuch larger than that obtained from eq. 6, 1.38, indicating that n is far from constant, but diminishes with increasing v. The nature of the discrepancy is to be seen in Fig. 1. The curve AC is drawii with n = 1. I n this case both the slope a t point A and the area under the curve between VI and VZ would yield the value n = 1. The curve BC represents what may be expected for a liquid such as our siloxane, where intermolecular attractive forces depend mainly upon the distances between the peripheral, inethyl groups, arid V. increase as volume diminishes more rapidly than they Fig. 1.-Illustrating why eq. 5 and 6 yield different values of n. would if they were radial and central. The greater slope ai, B yields a larger value for n, from eq. 5 , but since V tis but little altered from A to B, the area under the curve BC tlrould give nearly the same value of n as the area under AC. This substance is obviously one for which a Kihara-type of potential is appropriate. (b) Mixtures-The question we set for this investigation was how the internal pressures of the mixtures are related to those of the pure components in a case where the latter show very different dependence upon volume. We found long ago that n = 1.09 for CCL, a value since reconfirmed. Obviously, values of attraction eoiistants dependeht upon such different powers of n%F14 v as 2.38 aiid 2.09 have such different dimensions that they cannot be properly included in the simple Berthelot relation. We must therefore seek to relate the thermodynamic quantities themselves. We find, first of all, that the values of (dE/dV), are nearly additive with respect to volume fraction ?. (but of course, very far from additive with respect to mole fraction) as shown in the last column of Table 11. ‘0 02 0.4 06 08 IO This accords with the symmetry of the curves of volume fraction vs. temperature for many noii-polar liquid mixtures.15 This fact, the near additivity of volumes, Fig. 2.-Coinparing the mixture CCl, + c-8i40a(CH3)8 with the mixture of the two hexanes investigated by Dunlap and and the solubility parameter for the siloxane obtained from its solutions with iodine8 and c - C ~ F ~ ~ C 8.2, F ~ , ~Scott. close to the parameter of CCL, 8.6, all combine to indicritical point. The components of the latter system cate that the present mixture is probably nearly ideal. differ less than those of the former in “internal presWe have undertaken a study of vapor pressures. sure,” (bE/dV)T, but very strongly in their solubility It is jnstructive to compare the behavior of our mixparameters, 6 = (AE“/V)’”, 5.9 and 7.3, for n-Ca1Fl4 ture with that of the mixture of n-CtiF14and n-CsHL4, and n-CeHv, respectively. As Duiilap and Scott investigated by Dunlap and Scott.16 Iiistead oE being point out, the excess free energy of mixing of this sysnearly ideal, this one deviates very strongly, separating tem, like other mixtures of paraffins with perfluorointo two liquid phases at 22.65’. In Fig. 2 the values paraffins, is much greater than predicted froiii difof (dE/dV)T are plotted against volume fractions; ferences in their 2,olubility parameters. our mixture a t 2 5 O , the mixture of the two hexanes at Acknowledgment.--KTe express our appreciation to 35’ instead of 25’, in order be a little farther from the the General Electric Company for the supply of siloxane (14) R. C. Osthoff and W. T. Grubb, J . Am. Chem. Soc., 76, 399 (1954). and to the Natioiial Scieiice Foundation for the support (15) Reference 1, pp. 140-141. of the investigation. (16) R. D. Dunlap and R. L. Scott, J . Phys. Chem., 66, 631 (1962).
‘Oo I
L
U
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