Communicationsto the Editor
1471
Figure 2. High-temperature spectra of the 3750-cm- band after outgassing at 800” for 8 h r . T h e pressure on the platelet is (a) 5.13 X l o 5 kgf, ( b ) 1.30 X IO5 kgf, and (c) 1.79 X lo3 kgf.
vious work between the spectroscopic and volumetric adsorption isotherm (ref 2, Figures 3 and 4). Indeed, the spectroscopic isotherm was carried out on type b samples, the volumetric isotherm on powder that has not been pressed previously. The presence of two shoulders on the main band in the original work2 led us to the use of a curve resolver to break down the spectra into three components, the number of the components and their shape being constant. Although some of our assumptions (constant band shape for all temperatures and all components) can be questionable, the procedure is very helpful for a deeper understanding of the spectral changes that have been observed, a t least on a semiquantitative basis. Acknowledgment: P. A. J. acknowledges financial support by N.F.W.O. Belgium. Centrum voof Oppervlaktescheilunde en Colloidale Scheikunde De Croylaan 42 6-3030 Heverlee, Belgium
I
F. H. Van Cauwelaert* P. A. Jacobs
J. B. Uytterhoeven
Received February 27, 1973
Fluidity and Liquid Structure
Sir: Hildebrandl published a paper in 1971 on “Motions of Molecules in Liquids: Viscosity and Diffusivity” in which he altered an equation for the viscosity of unassociated liquids published by Batschinski2 in 1913 7 = c/(v
-w)
(1)
c is a constant for each liquid, Y is specific volume, w is similar to the van der Waals b. Hildebrand reasoned that fluidity, q5 = l / 7 , should be a linear function of the ratio of intermolecular volume to the volume, VO,a t which, as temperature decreases, molecules become too closely crowded to permit either free flow or self-diffusion; he wrote q5 = B(
v - VO)/VO
(2) B is a constant whose value depends upon capacity of the
molecules to absorb momentum because of their mass, flexibility, or inertia of rotation. Plots of q5 against V showed straight lines over long ranges of temperature. Extrapolation to cp = 0 gives values of Vo, and slopes give B/Vo. Hildebrand and Lamoreaux3 later gave values of B and VOfor scores of liquids; they showed that the equation holds for propane for pressures up to 544 atm, that VO values are fixed fractions of critical volumes, and that plotted lines can remain straight nearly to critical temperatures. Early in 1972 Eicher and Zwolinski4 published a paper titled “Limitations of the Batschinski-Hildebrand Shear Viscosity Equation.” On the basis of a “least-squares analysis” they asserted, “It can be seen that the simple form of eq 1 or eq 2 will not satisfactorily represent the experimental data for the four substances, n-hexane, ndecane, n-heptadecane, or 1-propanol over reasonable temperature ranges, within experimental uncertainties.” The question thus raised is far more important than merely one of fitting experimental data; equations of very different kinds can be tailored to fit the same data by introducing adjustable, nonoperational parameters. The basic question is whether a very simple equation, based upon the concept of molecular chaos implicit in the van der Waals equation, is adequate for dealing with transport processes in liquids, or whether it is necessary to imagine the presence of “solid-like” structures. Our objective in studying viscosity has been to compare the validity of different concepts of the liquid state. Let us see whether the conclusion that Eicher and Zwolinski have drawn from their mean squares calculation is correct. In Figure 1 the data for n-hexane by Giller and Drickamer5 are plotted as q5 against V. We see that the four upper points, between -60 and Z O O , surely “a reasonable range,” fall on a straight line. The nine divergent points at the bottom, close to the freezing point -95.3”, lie between -90.3 and -98.5’. Eicher and Zwolenski must have given all points equal weight. In doing this they overlooked what Giller and Drickamer wrote about these points. “There is a small but consistent increase in [free energy of activation] for each compound near the freezing point, which would represent the increased activation energy necessary because of a certain degree of order developing in the liquid.” This sort of divergence in a region of high viscosity is usual with substances whose molecules are so unsymmetrical that they do not gain full freedom of motion till the liquid has expanded a little more after melting. Magill and UbbelohdeG showed that this effect can be increased by using species such as tridiphenylmethane. We found it with (C4F9)3N but never with monatomic molecular species. The second liquid they offer as evidence against eq 2 is n-heptadecane, from measurements by Doolittle and Pet e r ~ o n The . ~ plot in Figure 2 shows a straight line from -0.8 to 6 cP-l, and points diverging near the lower end as in Figure 1. J. H . Hildebrand, Science, 174, 490 (1971). A. J. Batschinski, Z. Phys., Chem., 84, 643 (1913). J. H. Hildebrand and R. H . Lamoreaux, Proc. Nat. Acad. Sci. U. S., 6 9 , 3428 (1972). L. D. Eicher and 8.J. Zwollnski,Science, 177, 369 (1972). F. G. Giller and H . G. Drickamer, Ind. Eng. Chem., 41, 2067 (1949). (6) J. H. Magill and A. H. Ubbelohde, Trans. Faraday Soc.. 54, 1811 (1958). (7) A. K. Dooiittle and R . H . Peterson, J. Amer. Chem. Soc., 73, 2145 (1951).
The Journal of Physical Chemistry, Vol. 77, No. 7 7 , 1973
1472
Communications to the Editor
3-
-
2-
a, d I-
I
01
I IO
1
I
I I30
I20 V,
cm3 mol-'
Figure 1. Fluidity against molal volume of n-hexane, showing divergence near melting point.
Figure 3. Values of 5
4 against V for propane from V Oto V,.
,
I
I
v, cc Figure 2. Fluidity
against molal volume for n-heptadecane.
TABLE I:Constancyof d / ( V High Pressures for n-Decane P, atm
@, cP-'
- 184.0) at 171' up to V. om3
@ / ( V - VO) I
125
13.6 27.2 54.4 68.0 204.0 340.0 408.0
4.725 4.640 4.505 4.264 3.450 2.989 2.801
232.2 231.0 229.9 227.9 220.4 214.8 212.3
0.0098 0.0099 0.0098 0.0097 0.0095 0.0097 0.0099
Their third liquid is n-decane, whose viscosity was measured by Lee and Ellingtons over ranges of 250" and 408 atm. At 1 atm, the plot is quite like those for n-CsHl4 and n-C17H3~. To test the applicability of eq 2 a t different pressures, we give in Table I values of @ / ( V- VO) a t 171" and seven pressures up to 408 atm: VO = 184 cm3. The virtual constancy of the ratio shows that fluidity is uniquely determined by values of V - VO, irrespective of whether changes in volume result from changes of temperature or of pressure. Their fourth example is an alcohol, an associated liquid, and therefore not pertinent to the validity of eq 2. It has been asserted that viscosity is not a function of liquid volume alone, that it decreases with increasing temperature a t constant volume, We reply by referring to Figure 3 of ref 3 and the accompanying discussion, where variations of V for C3H8 and GO2 are shown from VO to The Journal of Physical Chemistry, Voi. 77, No. 7 7, 7973
135
I30
I
2
140
v , cm3 mal"
Figure 4.
Linearity of @ / ( V - V o ) for five isomeric hexanes.,
1000 cm3. We reproduce here in Figure 3 a plot of fluidity against molal volume of propane from Vo to its critical volume, V,, using data by Starling, Eakin, and Ellingtong obtained at 378, 444, and 5ll"K, and at pressures up to 544 atm. The points for 4 from 0 to 5 cP-1 are at I atm, and below the boiling'point, the usual range of viscosity data. The points for @ from 5 to about 18 cP-1 were determined at various values of pressure and temperature within the range stated above. It can be seen that values of @ over this enormous range depend upon values of V only. As V increases further, however, the single line splits increasingly into three, with fluidity at any value of V largest a t the lowest temperature; in other words, viscosity increases with temperature. As we explained in ref 3, mean free paths at boiling points are very much shorter than molecular diameters. In the case of propane, (Vb - Vo)/Vo is only 0.23. At its critical point, Vc = 203.2 and the fractional expansion is 2.32, ( 8 ) A. L. Leeand R . T. Ellington, J. Chem. Eng. Data. 10, 346 (1965). (9) K . E. Starling, 8. E. Eakin, and R. T. Eliington, AlChE J., 6, 438 (1960).
1473
Communications to the Editor TABLE II: Evidence for Strict Linearity of the Line for 2-CH3C5Hll in Figure 3
4 , cP-'
V , 01113 mo1-l
126.27 126.92 128.03 130.85 131.27 133.82 135.48
2.447 2.528 2.723 3.236 3.308 3.771 4.070
$/(V
- 113.0)
0.1814 0.1816 0.1812 0.1813 0.1815 0.1811 0.1810
where molecules can acquire some momentum between collisions. We have explained that the parameter, B , of eq 2, depends upon the capacity of the species to resist externally imposed momentum by reason of mass, softness, or rotational inertia, or their own thermal momentum, which is, for molecules in free space, (3mkT)1/2. This is approached as length of mean free paths increases. We turn finally to data on five isomeric hexanes measured by Eicher and Zwolinskilo themselves, Their figures for viscosity and density at different temperatures yield the values of and V plotted in Figure 4. All points fall on straight lines except one, which is off by only 0.3 cP-l. The excellence of the fit we illustrate in Table I1 for 2CH3CsHl1, whose line is the longest of all. The intercept gives VO= 113.0 cm3. The ratios in the last column show that the line is even straighter than could be inferred from a good plot. We summarize the foregoing evidence by asserting that (a) the data are accurate, (b) they all conform closely with eq 2, (c) the concept of molecular chaos that served as foundation for it is adequate, and that no highly structured model of the liquid state is required for dealing with transport processes.
Acknowledgment. Acknowledgment is made to the donors of The Petroleum Research Fund, administered by the American Chemical Society, for support of this research. (10) L. D. Eicher and B. J. Zwoiinski, J. Phys. Chem , 76, 3295 (1972) Department of Chemistry U n i v e r s i t y o f California B e r k e l e y , C a l i f o r n i a 94720
J. H. Hildebrand" R. H. Lamoreaux
Received December 6. 1972
Infrared Frequency Shifts Due to Hydrogen Bonding of Surface Amino Groups on Silica
Sir: There have been numerous H-bonding studies of hydroxylic compounds by means of infrared spectroscopy.1 The occurrence of H bonding is observed as a perturbation of the free OH stretching vibration band to a lower frequency and an increase in the integrated intensity of the perturbed band. Often, more fundamental information can be obtained in the absence of interfering solvent effects by observing the H-bonding interactions between surface hydroxyl groups and various gaseous adsorbates which form H bonds with these hydroxyl groups. Surface silanol groups have been extensively studied for this purpose. Attempts have been to correlate the observed frequency
shifts with polarizability,2 quadrupole moment,3 ionization potential,4-6 and heat of adsorption.5~~ To a much lesser extent, the H-bonding behavior of other surface M-OH groups has been studied.8.9 Despite the number of studies, there is still controversy concerning the origin, and thus the quantitative treatment, of the hydroxyl band frequency shifts. Less attention has been paid to H-bonding interactions involving -NH groups10 and apparently no studies have been carried out in the absence of solvents. With a view to determining if the H-bonding behavior of surface -NH groups shows any essential difference from the behavior of surface -OH groups, the frequency shifts of the free -NH group band were measured when various gaseous adsorbates interacted with these groups. A silica surface can be covered with amino groups.11J2 Peril2 reacted cc14 with surface silanol groups above 350" and obtained a surface covered with Si-Cl, groups. At these temperatures NH3 reacts with the Si-C1 groups leaving Si-NH2 groups on the surface, and NHbC1 sublimes to cooler parts of the vacuum system. Such an aminated surface was prepared, using pressed silica (Cab-0Sil, Cabot Co., Boston, Mass.) disks. A compensated infrared cell for holding sample disks, equipped with a side arm, was connected to a vacuum rack. The silica disk, preheated to 800" in air, was placed in the side arm, around which a furnace was mounted. The silica was treated with CC14 vapor at 420" for 15 min, evacuated, and then treated with NH3. Deposited NH4C1 was observed on the cooler parts of the side arm after this procedure. By tipping the cell, the silica disk dropped from the side arm into the infrared cell. The spectra were recorded on a Perkin-Elmer Model 621 infrared spectrophotometer. Bands due to the surface amino groups are observed a t 3444(s), 3530(w), and 1555(s) cm-1, which arise from the symmetrical stretching, asymmetrical stretching,ll and bending frequencies, respectively. The band due to the free OH stretching frequency at 3747 cm-1, present before reaction, is completely absent. When various gases are admitted to the aminated sample a t 30" the N H bands are perturbed, due to the hydrogen bonding interaction. Very dry adsorbate gases are necessary, since even traces of moisture result in rapid hydrolysis of the Si-N bond to produce Si-OH groups. Some typical spectra are given in Figure 1. The frequency shift due to the perturbation of the 3444-cm-l symmetrical NH stretching band is readily measured. The 3530cm-1 asymmetrical NH stretching band is low and broad, and for most of the adsorbates the perturbed band was also too broad to obtain an exact measure of the frequency shift. The perturbations of this asymmetrical NH band (1) G. C. Pimentel and A. L. McClelian, "The Hydrogen Bond," W. H. Freeman, San Francisco, Calif., 1960. (2) R. S. McDonald, J. Amer. Chem. SOC..79, 850 (1957). (3) G. J. C. Fronsdorff and G. L. Kington, Trans. Faraday Soc., 55, 1173 (1959). (4) M . R . Basiia, J. Chem. Phys., 35, 1151 (1961). (5) W. Hertl and M. L. Hair, J. Phys. Chem., 72, 4676 (1968). (6) F. H. VanCauweiaert, J. B. VanAssche, and J. 8.Uytterhoeven, J. Phys. Chem., 74, 4329 (1970). (7) G. A . Gaikin, A. V . Kiselev, and V. I . Lygin, Russ. J. Phys. Chem., 41, 20 (1967). (8) M. L. Hair and W. Herti, J. Phys. Chem., 74, 91 (1970). (9) J. A. Cusumano and M. J. D. Low, J, Phys. Chem., 74, 1950 (1970). (10) S. Mukherjee, S. R. Palit, and S. K. De, J. Phys. Chem.. 75, 2404 (1971), (11) M. Folman, Trans. FaradaySoc., 57, 2000 (1961) (12) J. B. Peri, J. Phys. Chem., 70, 2937 (1966). The Journai of Physical Chemistry, Vol. 77, No. 1 1 , 1973
