NOTES
1151
The friction coefficients r+-, r+,-, r++, and r++f, where means the solvent cation, is the tracer cation, and - is the anion, have been calculated in Table 11, following the formalism of Laity.lO At this moment no theory provides a calculation of these basically macroscopic coefficients starting from microscopic concepts.11s12 For ions equal to or larger than the solvent ions, the experimental data for the self-diffusion coefficients are represented rather well by the Stokes-Einstein equation
+
+‘
0.4 0.5[
ICT D.- I -
6a77ri
Figure 1 shows that the slopes of the Di-l/ri curves in NaN03 and KN03 agree remarkably well with the expected values. Ionic radii are those given by Ketelaar.I3 For tracer cations smaller than the solvent cations, the diffusion coefficients are, within experimental accuracy, found to be equal to those of the solvent cations. This is in agreement with a suggestion of Cohen and Turnbull, based on the free volume theory of diffusion. l4 Acknowledgment. The present investigations have been carried out under the auspices of the Netherlands Foundation for Chemical Research (S.O.N.) and with financial aid from the Netherlands Organization for the Advancement of Pure Research (Z.W.O.) . (10) (11) (12) (13) (14)
R. pi. Laity, J, Chem. Phys., 30, 682 (1959). R. J. Bearman, J . Phys. Chem., 6 5 , 1961 (1961). B. Berne and 9. A. Rice, J . Chen. Phys., 40, 1347 (1964). J. A. A. Ketelaar, Chemical Constitution, Amsterdam, 1957. M. H. Cohen and D. Turnbull, J . Chem. Phys., 31, 1164 (1959).
Stepped Isotherms on Carbons
by E. Greenhalgh and E. Redman’ Morganite Research and Development Ltd., London (Received November 7, 1966)
Smith and Fordzain their paper, “Adsorption Studies On Heterogeneous Titania . . . ,” show a typical stepped isotherm for argon on Sterling MTG carbon black. This is stated to be typical of the behavior found with other gases ( 0 2 , Nz,and CO), emphasizing the extraordinary uniformity of the surface. They further state that the extent of surface homogeneity may be associated with the area of exposed graphite
I
Pmm. I .o
1
I
2.o
Figure 1. Krypton isotherm (-195’) for PVDC carbon (2500’).
planes on the surface of the black and that for MTG and FTG, the boundary of the planes represents only a small fraction of the exposed surface, and the heterogeneity introduced cannot be detected on the isotherms. This may be true for readily graphitizable carbon blacks, but we present evidence to show that stepped isotherms on carbon are not always due to the presence of extensive graphite basal planes. Figure 1 shows the 77.95”K isotherm for krypton on the carbon obtained from polyvinylidene chloride after heat treatment to 2500’. The isotherm exhibits pronounced steps, but the carbon is far from graphitic (La = 60 A, L, = 20 A, d = 3.42-3.48 A). The adsorbate used was krypton, while that used by Smith and Ford was argon. It could therefore be argued that the comparison is invalid. However, Crowell and Young2b show isotherms for both adsorbates on graphitized P33 carbon black. The only difference appears to be that krypton gives more pro~~
~~
(1) To whom all correspondence should be addressed a t Department of Chemistry, State University of New York at Buffalo, Buffalo,
N. Y. (2) (a) W. R. Smith and D. G . Ford, J . Phys. C h m . , 69, 3587 (1965); (b) A. D. Crowell and D. M. Young, “Physical Adsorption of Gases,” Butterworth and Co. Ltd., London, 1962, p 174.
Volume 71, Number .G March 1967
NOTES
1152
0.E
0.1
0.:
0.:
0.
o--o0002QD-04d I
P mm. I 1 .o
I
1
2.0
Figure 2. Krypton isotherm (-195')
for PVC carbon (2500").
nounced steps than argon, possibly reflecting the higher heat of sorption. Figure 2 shows the 77.9"K isotherm obtained with krypton and the carbon prepared at 2500" from polyvinyl chloride. This carbon is more graphitic (La = 570 A, L, = 690 A, d = 3.37 A), but the steps are not much more pronounced than those in Figure 1. Both isotherms exhibit hysteresis and this would normally be taken to imply that the samples were porous. Further, if this were so, it might possibly invalidate the interpretation of the isotherms in terms of whether the steps which we have observed correspond to those obtained on materials which are normally considered to be nonporous. However, the observed hysteresis cannot arise from capillary condensation in pores since the equivalence of the mercury and helium displacement densities4 indicates that both samples were nonporous. At atmospheric pressure, mercury will penetrate all pores with an entry diameter above approximately 15 pm. These pores are outside the range of capillary condensation as detected by hysteresis in adsorption-desorption cycles. The hysteresis must therefore result from condensation in the interparticulate voids of the powdered sample. Similar effects must be present for sorption on carbon blackss but few workers appear to have studied the Ths Journal of Phusical Chsmistry
complete sorption cycle. Polley, Schaeffer, and Smith6 have observed hysteresis a t p / p o >0.75 and they attributed this to either interparticulate condensation or slow pressure equilibration. Joyner and Emmett' claim that the adsorption and desorption curves were superimposable for nitrogen on Graphon, but they did not carry out a complete sorption cycle nor did they reach saturation. Bonnetain, Duval, and Letorts have reported stepped isotherms for methane on natural graphite and other nonporous solids, which exhibit hysteresis almost identical with that shown here. Finally, we feel that even if capillary condensation is a complicating factor on the adsorption half-cycle, it would be unlikely to produce regular well-defined steps of the type shown. The structure of polyvinylidene chloride (2500") carbon is not certain, but provided that one accepts that an energetically homogeneous surface is required for stepped isotherms, then whatever the heterogeneities in the surface are, they must be either (a) so small that they cannot be detected by the krypton atom, or (b) so numerous that they form the homogeneous surface. The disappearance of the pore structure of this material on heat treatrnentJ4resulting in the equivalence of the mercury and helium displacement densities, would tend to support model (a) above.
Acknowledgment. The authors thank the Directors of Morganite Research and Development Ltd. for permission to publish this note. ~
~~~~
~
(3) E. M. Barrer, Nature, 181, 176 (1958). (4) E. Greenhalgh, B. M. Miles, E. Redman, and S. A. Sharman, Second Industrial Carbon and Graphite Conference, Society of Chemical Industry, London, 1965. (5) C. Pierce, J. Mooi, and R. E. Harris, J. Phys. Chem., 62, 656 (1958). (6) M.H.Polley, W. D. Schaeffer, and W. R. Smith, ibid., 57, 469 (1953). (7) L. G. Joyner and P. H. Emmett, J. Am. Chem. Soc., 70, 2353 (1948). (8) L. Bonnetain, X.Duval, and M. Letort, Compt. Rend., 234, 1363 (1952).
Surface Tension of Binary Liquid Mixtures
by Raymond L. Schmidt Department of Chemistry, Emory University,Atlanta, Georgia 3032.2 (Received September 96,1966)
Current interest in the surface tension of binary liquid mixtures has resulted in new equations which
