COMMUNICATIONS TO THE EDITOR
3370
(27.6 dynes cm-l) was assumed and a value for A * (25 A2) was calculated from the C02 transport results of H a ~ k e . These ~ approximations give E* a value of 11 f 2 kcal mole-’ which is in good agreement with the activation energy for water transport through hexadecanol monolayers found by Barnes and La Mer.? Thus, the activation energy for gaseous transport through monolayers appears to be the energy required to form a hole in the two-dimensional monolayer “lattice” as predicted by the energy barrier theory.? The value of the activat,ion energy found here is in marked contrast to that of 2.0 kcal mole-’ found by Blanks for the absorption of COz into alkaline buffered solutions through a hexadecanol monolayer. This may be due to the presence of water molecules in the monolayer. Further studies are being carried out on the effect of chain length and the composition of the polar head group on the permeability of monolayers to C02. A detailed account will be published elsewhere.
0
“ 3.5 1 / T X 108.
3.4
1
3.7
3.6
Acknowledgment. We wish to thank the U. S. Public Health Service for financial assistance under the terms of Grant WPOO877-01.
Figure 1.
method described by Hawke and Parts,6 allowing a transmission coefficient to be assigned to the monolayer. Transmission coefficients were calculated for the monolayer at the temperatures of 0.1, 5.1, 10.0, and 15.0” and these are shown in Table I. Barnes and La Mer,’ by considering that the monolayer acts as an energy barrier to gas transport, have applied the transition state theory of Eyring to the permeability (or transmission coefficient) of a monolayer by
- IIsNoA*/RT
T, = c’ exp[S*/R
- E*/RT]
T,
=
*
c”exp[AS*/R
*
- II,NoA*/RT - E*/RT]
(2)
where E* is the experimental activation energy and is a constant. By plotting In T , against 1 / T (Figure l ) , values for E*) were obtained c“ expAS*/R and (II,NoA* for COz transport through hexadecanol monolayers. These values were, respectively, lo7 cm sec-’ and 12 f 2 kcal mole-’. I n order to obtain an approximate value of the activation energy, E*, a mean value of II,
C”
+
The Journal of Physical Chemistry
N.’.,
1962. (8) M. Blank, ref 7, p 75. (9) J. G. Ifawke and I. White, t o be published.
PHYSICAL CHEMISTRY
L - ~ B O R A W ~ E ~
OF
J. G. HAWHE I. WHITE
UNIVERSITY OF SYDNEY SYDNEY, AUSTRALIA
RECEIVED JULY 18, 1966
(1)
where T, is the monolayer’s transmission coefficient, c‘ is a constant, S and E are the entropy and energy of activation, and NoA is the increase in area per mole of activated state caused by the formation of “holes” in the monolayer “lattice.” For measurements made a t constant surface pressure, eq 1 becomes
*
(6) J. G. Hawke and A. G. Parts, J . CoEZoid. Sci., 19,448 (1964). (7) G. T. Barnes and V. K. La Mer in “Retardation of Evaporation by Monolayers,” V. K. La Mer, Ed., Academic Press, New York,
Comments on the Effects of the Nonbonded Electrons on Barriers to Internal Rotation
Sir: Over the past several years, there has been considerable interest in barriers to internal rotation. Perhaps most of this interest stems from t,he lack of any adequate theory describing the origin of such barriers. One very recent theory worked out by Parr and co-workers using the integral Hellmann-Feynman theorem’ has had considerable success. These workers describe a very simple, semiempirical electrostatic model for calculating barrier heights in molecules. (1) H. Kim and R. G. Parr, J . Chem. Phys., 41, 2892 (1964). (2) J. Lowe and R. G . Parr, ibid., 44, 3001 (1966).
COMMUNICATIONS TO THE EDITOR
Table I:
v3g(M-H)
Molecule
CHSCH~~ CHaNH: CHaOHc
3371
Contribution to Barrier Heights in CHaMHs, CH~MHI,and CH3MH Molecules VS(M-H)~
338
343 375
LC-M-H
Molecule
logo 37' 112" 3' 108" 52'
CH3SiH3d CHaPHa* CHaSH'
Va(XI-H)
LC-M-H
194
108" 15' 97" 30' 96" 30'
430
444
Molecule
v3 (X-H)
GHaGeHao 145 C H ~ A S H ~ ~ -340 350 CH3SeHi
LC-M-H
109" 35' (-94") 95" 15'
' W. Lafferty and E. Plyler, J . Chem. Phys., 37, 2688 (1962). * D. R. Lide, Jr., ibid., 27, 343 (1957). P. Venkateswarlu and W. T. Kojima, J . Phys. Soc. Japan, 15, 1284 Gordy, ibid., 23, 1200 (1955). Kilb and L. Pierce, ibid., 27, 108 (1957). 'See ref 4. (1960). ' V. Laurie, J . Chem.Phys., 30,1210 (1959). A. B. Harvey and M. K. Wilson, ibid., 44,3535 (1966). A. B. Harvey and M. K. Wilson, ibid., 45, 678 (1966); C. Thomas and E. B. Wilson, Jr., private communication. Barrier in cm-1.
'
Their model is based on the experimental data now available for several types of molecules and on more elaborate calculations on ethane. The conclusion reached by these workers was that barriers in molecules like ethane may be regarded as arising primarily from nuclear-nuclear repulsion modified by electron density near the hydrogen nucleus. It is stated2 that s-p hybrids on one end of the molecule, e.g., on the oxygen atom in CH30H, do not contribute to the threefold electron density and hence do not affect the barrier. The threefold component apparently arises from the 1s orbitals of the hydrogen atoms and the overlap of the 1s orbital with the s-p hybrid. If this is so, then nonbonded electrons should not significantly contribute to the magnitude of the barrier in molecules such as CH311!tHn, where 31 is a group IV ( n = 3), V (n = 2 ) , or VI (n = 1) atom which uses only s-p hybrids. Reported here are some conclusions which support this theory. It is possible to estimate the nonbonded electron contribution to the barriers in some of these molecules in the following way. If the total barrier height in a CHJ'IHZ molecule is assumed to be a sum of two M-H barriers, then it is possible to compute an individual barrier height contribution for each ?I-H group, v3(M-H), by the relation v3(M-H)
=
of nonbonded electrons, it can be concluded that nonbonded electrons contribute little to ihe barrier heights. This idea is consistent with Parr's model and was recognized some years ago by P a ~ l i n g who , ~ made the comparison in the first row of Table I . Based on the barriers known for CH3GeH3and CH3SnH3, Lowe and Parr2 conclude that the heavy M atom will have considerably more d and f orbital participation. These orbitals will contribute a threefold component to the electron density and hence the nonbonded electrons will affect the barrier height. However, no significant nonbonded contribution is found from the information available for CH3AsH2 and CH3SeH (see Table I), although it is admitted that the uncertainty in the barrier of CH3AsH2 is large and the structure has not yet been determined. The agreement here may therefore be somewhat fortuitous. (3) R. E. Wyatt and R. G. Parr, J. Chm. Phys., 44, 1529 (1966). (4) T. Kojimn, E. L. Breig, and C. C. Lin, ibid., 35, 2139 (1961). (5) L. Pauling, Proc. Natl. Acad. Sci. U . S., 44, 211 (1958). (6) Address correspondence to U. S. Naval Research Laboratory, Washington, D. C.
DEPARTMENT OF CHEMISTRY TUFTS UNIVERSITY &IASSACH~.SETTS MEDFORD,
ALBERTB. HARVEY~
RECEIVED JULY 21, 1966
- V3(CHaMHd 2 cos 3x/2
where V3(CHaMHI) is the total barrier height in the molecule and 2 is the projected H-M-H angle. This was first carried out for CH3PH2 by Kojima, et aL4 I n Table I are listed the V3(M-H) contributions in CHJIHz and CH3MH3 molecules. I n the latter, V 3 ( ~ - ~ was ) taken to be V J ( C H ~ M Hsince ~ ) / ~ LIT-RI-H is almost tetrahedral in every case. These V ~ ( M - H ) may now be compared with the total barrier heights in the CHsMH compounds. Note that when M is in the same periodic series and L C-M-H angles are alike, the v3(M-H) are remarkably similar. Since the molecules of the same periodic series have different numbers
A 2 :1 Pyrene-PMDA Molecular Complex
Sir: Molecular complexes of aromatic hydrocarbons with pyromellitic dianhydride (PMDA) have been extensively studied recently. 1-4 The stoichiometry of these complexes has been reported to be 1:1 except for o-xylene which forms a 2 : 1 complex, and perylene (1) J. C. A. Boeyens and F. H. Herbstein, J . Phys. Chem., 69, 2153 (1965). (2) J. C. A. Boeyens and F. H. Herbstein, ibid., 69, 2160 (1965). (3) Y. Nakayama, Y. Ichikawa, and T. Matsuo, Bull. C h m . SOC. Japan, 38, 1674 (1965). (4) T. Matsuo, ibid., 38, 2110 (1965).
Volume 70, Number 10 October 1966
