NOTES
+
data to the form In w = A / T B and find A = 615 ~t 30 and B = 5.10 f 0.8. Using these constants and AH" = 22.4 Incal/~rnol,~~ we compute E, = -9.6 kcall mol, a value which is unreasonable. For the radical displacement reaction
Interpretation of Electron Spin Resonance Evidence for the Mechanism
of Free-Radical-Induced Reactions of M e t h y l e n e c y ~ l o b ~ ~ ~ n ~ and Methylene~yclopentane~
by David H. Volman and hence the line width should be proportional to the concentration of Sz08Fz. We prepared two dilute solutions of SzOaFzin C6FI0(CF&with the concentrations of SaO&'z in the ratio 2:1. The use of dilute solutions minimizes an:y solvent effect on kz. If the radical displacement mechanism dominates the line width, then the widths o l the radicals in these two solutions should e in the ratio 2: 1 Since they have been found to be 1, the chomical mechanism has been eliminated.g y the process of elimination we are led to propose the ;most likely mechanism to explain the line width i s spin relaxation due to motional modulation of the spin-rotational interaction. Line widths of comparable magriitude to those reported in this paper and similar variations with temperature have been found for GIOz and have been ascribed to the spin-rotational ~ n t e r ~ ~ t i o ~A. ~quantitative g'~,~ analysis of the results for SO3%? awaits the availability of additional data in a variety oJ solvents of known viscosity. One other mechanism deserves mention, namely the Ohrbach processa' which ia important for species with nearly degenerate ground states (AE/kT 5 6 ) . Because of the ~ ) ~ o ~ a lsymmetry ole of S08F,Cab'one might expect the possiloilily of a 2Eground state. The results of recent sp~~ctros(~op~c measurements and a CNDO calculation1Qimggebt however that the ground state of SOsF' is prokiably ?A2and that the lowest-lying excited ~ too e tfar~removed y from the states of 2E ~ y ~ ~ are ground state to make a significant contribution via the Ohrbach ~nechaiiism. Finally, w~ should comment on a discrepancy between our wosk and that of Stewart, who reported that the line width of SOSF'. in a mixture of SzOsFz and SzOsFz is i ~ ~ d ~ of~temperature. p ~ ~ ~ l1~ We e xbelieve ~ ~ that Stewart's samples were partially decomposed, as evidenced by hit; obse of boiling of the samples in sealed tubea r a h ~ v ~ . We have observed such ome samples; the line widths measured were not reproducible under thermal cycling, and are discardad .these results. 6
(9) The fact thah the line width is independent of [SzOeFz] is additional evidenre f3c)r eliminating the recombination mechanism. For this mechanism the lire width should vary as [SOaF.]-' or approximately as [S&aF1 I -'/2. (10) G . W. King, 93. P. Santry, and C. I-I. Warren, 1.Chem. Phys., 50, 4585 (1969). (11) R. A. Stewart, ibitl.,
The Journal of Phgsical Chem&utru, Vol. 76,No. 6,1971
Department of Chemistry, University of California, Davis, California 96616 (Received October 8,1-970) Publication costs assisted by the National S C ~ EFoundation ~CE
From esr studies in the frozen state at 77%, Takeda, et ~ l . have , ~ concluded that methylenecyclobutane yields a substituted vinyl radical by reaction with H
1
hydroxyl radicals produced by photolysis of hydrogen peroxide but not by reaction with methyl radicals produced by photolysis of methyl io methylenecyclopentane yields a cyclic substituted allylic radical by reaction with either radical. Ring H
II opening for the four-carbon ring and a stable cyclic radical for the five-carbon ring were attributed to the larger strain energy for the ring with fewer carbon atoms. It will be shown here that the esr spectrum for methylenecyclobutane has definitely been interpreted incorrectly. I n consequence, radical I is not a a product but allenyl radical is formed, and radical I1 is probably not a product but a noncyclic substituted radical may be formed. akeda, et a1.,2 inSubstituted Vinyl vs. AElenyE. terpreted their results with methylenecyclobutane on the basis of radical I locked in the electron orbital cis to the p proton. constant reported by Cochran, A UH(,) = 16 G and aH(B,ois)= 34 6,the theoretical spectrum yields line-to-line spacings of 16, 18, and 16 G and intensity ratios of 1:1:1 : 1.: 1. Although the spacings are in some conformity with the experimental values, the intensities clearly are not. Moreover, in(l), This investigation was supported by a grant from the National Science Foundation. (2) K. Takeda, H.Yoshida, K. Wayashi, and S. OkamYra, Bull. Inst. Chem. Res. Kyoto Univ., 45, 55 (1967). (3) E. L. Cochran, F. J. Adrian, and V. A. owers, J. Chem., Phys. 40, 213 (1964).
9 15
NOTIES version of thab aw hydrogen, with a frequency of at least 1Q8sec-' in .Tiny1 radical at 90°K,4 makes it unlikely that the radical is locked in the cis position. As U E ( ,trans) ~ = 68 G, the trans radical I should yield a fourline spelctrium of equal intensities and with spacings of 16, 52, and 16 6. A mixture of the cis and trans forms or inversion ihetwechn the forms would yield a spectrum which would deviate even more widely from that reported. There is, therefore, no evidence that the radical is substituted vinyl. The spectrum obtained by Takeda, et al., is virtually identical with that attributed to allenyl by Morgan and Whites fmm the reaction of hydrogen atoms with propyne a t X"7.K and by usB from the photolysis of allene and of propargyl alcohol at 77°K. The first derivative spclctrurn obtained in the latter two laboratories consisl s of four lines with peak-to-peak separations of 18, 14, and 18 G and approximate intensity ratios of 1:2:2:1. We have shown that such a spectrum results from incomplete resolution with coupling constants of 18 and 14 G assigned to the CHz and CH From the absorption spectrum constructed on this basis, the theoretical peak intensities are 1 :2.3 : 2 . 3 :1. (It xesy be noted that well resolved spectra of allenyl radical have been obtained in fluid media by ~ C H = ~18.9 G and U C H = Fessenden and E$~Iiuler,~ 12.6 G, and by Kochi and Krusic U C H ~= 18.9 G and ~ C S I = 12.7 C ) . The spacings reported by Takeda, el al., are 18, 15, and 18 G and from an examination of their published spectrum an approximate intensity ratio of 1 :2.2: 1 is obtained. Therefore, both from appearance and analysis the spectrum is undoubtedly that of allenyl free radicals. Cyclic A l l y l v8. .Noncyclic Allyl. The esr spectrum1 from methylenecyc:lopegltane attributed to radical I1 consists of five lineis with an averagc separation of 15 G and intensity ratioa somewhat less than theoretical for four equivalent, protons. The interpretation of this spectrum WAS that of the five protons which might be expected t-u couple, the three allyl system protons and 1 he CHz ring pro tons adjacent, @,to the CH group, one of the p protons does not interact. As the allyl radical system is certainly planar, if it is assumed that the ring system is planar the two /3 hydrogen protons would undergo equivalent interaction with the delocalized electron. Although the ring may not be completely planar, it is probably nearly so. I n any ease the four-carbon system leading to the spectrum would tend 1 0 be planar since the primary cause of puckering in the five-carbon ring, hydrogen-hydrogen repulsion, is eliminated by having the CH hydrogen atom staggered wil h respect to the /3 hydrogen atoms. The spectrum shown is very similar to that reported by a number of workers for free allyl radical in frozen systems a t 7'b"K8 The small splitting expected from the proton on the central carbon atom is not resolvable in the low-temperature glassy systems and consequently
the spectrum approximates that expected from interaction of four equivalent protons with the delocalized unpaired electlron. Thus substitution for the central hydrogen atom would not be expected to affect the spectrum significantly. The spectrum obtained from methylenecyclopentane is, therefore, explicable on the basis of either free allyl or a noncyclic substituted allyl but not by a cyclic substituted allyl.
Discussion The mechanism suggested for the decomposition of methylenecyclobutane2 was
the abstraction of a methylenic hydrogen followed by ring opening and the shift of two hydrogen atoms if R is -CH2-CH=CH2; if R is cyclopropyl, only one hydrogen atom needs to shift. As there is no evidence for the vinyl radical and as abstraction of an allylic hydrogen, of which there are four, is much more favorable than abstraction of a methylenic hydrogen, and as the radical is allenyl, a plausible mechanism is
HZC--C(
/y /CHp 2 m
CHS-C-CH
C CJ&
(2)
CH2
The enthalpy change for reaction 2 may be calculated from the tabulated enthalpies of formation of the hydrocarbonsg and free radicalslO and from the value for alleny1,'l AHfoZgs= 75.0 kcal. For the reaction with OH in which case water is an abstraction product, (g) = - 10 kcal, while for the reaction with CH3 (4) R. W. Fessenden and R. H. Schuler, J . Chem. Phys., 39, 2147 (1963). (5) C. V, Morgan and K. J. White, J . Amw. Chem. Soc., 92, 3309 (1970). (6) D. H. Volman, K. A. Maas, and J. Wolstenholme, ibid., 87, 3041 (1965). (7) J. K . Kochi and P. 3. Krusic, ibid., 92,4110 (1970). (8) K. A. Maas and D. H. Volman, Trans. Faraday Soc., 60, 1202 (1964). (9) 8.W. Benson, F. R. Cruikshank, D. M. Golden, G. It. Haugen, H. E. O'Neal, A . S. Rodgers, R. Shaw, and R. Walsh, Chem. Rev., 69, 279 (1969). (10) J. A. Kerr, ibid., 66, 465 (1966). (11) J. Collin and F. P. Lossing, J . Amer. Chem. Soe., 79, 5848 (1967).
The Journal of Physical Chemistry, Vol. 76, N o . 6, 1.971
7 16
NOTES
yielding methnne, ANOzRs (g) = +5 kcal. This difference in enthalpies can explain the formation of aUenyl OH. but not with CHa. Thaenthalpy of formation of XI1 may be estimated by assuming that the resonance stabilization energy of I11 is approximatelgr equal {JO that of the allyl I%dical and that the ring strain energy in I11 is intermediate between that for cyclobutane, 26.5 kcal, and that for cyclobutene, 3Q.Qkcal,12 AHf 11) then should exceed AHf (methylenecyclobutme) y the difference in strain energies, 1.8 kcal, plus ilhe difference between the enthalpies of formation of propene and allyl radical, 33.1 kcal. These values yield L@f0298 (111) 2i 65 kcal and for reaction 2b, A ~ ” ~ ~ 26 8 kcal. ~ ~ ) Despite the approximations, this value ii3 not likely to be in error by more than A 5 kcal. Therefore, unless I11 receives energy liberated in step 2a it is not likely to be the precursor of the products, allenyl and ethene. It is not, however, necessary that 1x1be formed as the reaction may occur y a concerted’ mechanism accompanying free-radical abstraction of an allylic hydrogen atom
Measurement of the Isothermal Piezoopeic Coefficientwith the Ultracentrifuge
by Ibbert JosePhs* and Allen p*R!hton Polymer Department, Weizmann Institute of Science, Rehovoth, Israel (Received October 1% 1970) Publication costs borne completely b;y The .Tourna! Phyaicaz
Of
The isothermal piezooptic coefficient, (bn/bP)TI,,A [hereafter abbreviated as ( ~ T L / ~ Pis ) a~ ]physical , quantity of interest in the theory of light scattering of pure liquids1 and, in conjunction with PVT data, as a measure of intermolecular interaction in a pure liquid.2 The only reported measurements of this quantity for liquids other than water and methanol are those of Coumou, et U Z . , ~ who have determined (bn/dP), at 23O, 5460 d, and 1 atm for a number of organic liquids using a specially adapted Rayleigh interferometer. ~ measured the refractive index of Waxler, et U Z . , ~ ? have water, benzene, and carbon tetrachloride as a function of pressure at several temperatures an but only at pressure intervals of several hundred atmospheres, necessarily rendering imprecise any evaluation of the differential quantity from their reported data. For ~rnet~h~lenecycl~opentane an analogous mechanism In view of the lack of corroborating data for organic yielding allyl radical and allene seems attractive, but liquids it was felt that another set of measurements by a the calculated enthalpy changes yield 14 and 29 kcal different method entirely would prove useful. Furtherendothermicity for the reactions with hydroxyl and more, the method presented here is of interest as a novel methyl. Howevers as observed earlier, any centrally application of the ultracentrifuge. Finally, this substituted allyl radical should yield the same esr specmethod, in distinction to that of ~ o ~ etma&*~ will u ~ trum as allyl. It is not possible to choose between be shown to provide information on the pressure deseveral alternatives but a possible one is pendence of (bn/bP),. Basis of the Method. In a liquid-filled rotating cenR% trifuge cell there exists a radially directed pressure ir gradient @P/dr), in the liquid, from 1 atm at the I meniscus to up to several hundred atmospheres at the centrifugal edge of the cell, depending on the quantity of the liquid, its density and compressibility, and the rotor speed. Since the refractive index of the Iv (4) liquid is a function of the pressure, a radially directed AHfo29A(1V) may be estimated in the same way as for refractive index gradient (dn/br),also exists which may y goupcontribution methods for the parent be measured using the schlieren optia:al system built into the ultracentrifuge. The isothermal pieBooptic rbon of IQI, AH~~~~(2-methyl-lJ3-pentadiene) coefficient is readily obtained €rom (dn/dr)T = 11 f 2 kea1 yielding AHf ‘288 (IV) Z 44 kcal. With and (bP/br)T as shown below. OW, A ~ * ~ ~ -25 * ~kcal ~ and ) with CHa, AHoZ9*(g)= -10 kcall, and foamation of IV from the reaction with (1) M. Kerker, “The Scattering of Light and Other Electromagnetic ical LB exothermic, As for methylenecycloRadiation,” Academic Press, New York, N . Y., 1969, Chapter 9. butane, thermochemical calculations indicate that a (2) H. Eisenberg, J. Chem. Phys., 43, 3887 (1965). concerted process rather than the formation of an in(3) D. J. Coumou, E. L. Maokor, and J. Hijmans, Trans. Faraday t e r ~ e d ~isa favored. t~ Soc., 60, 1539 (1964). I ;
(12) J. 13. Cox and G . Pilcher, “Thermochemistry of Organic and Organometallic Conipountls,” Academic Press, New York, N. Y., 1970, pp 671 and 580.
The Journal of Phgskal Cherni%try/,Vol. 76, No. 6, 1871
(4) R. M. Waxler and C. E. Weir, J . Res. Nat. Bur. Stand., Sect. A , 67, 163 (1963). (6) R. M. Waxler, C. E. Weir, and H. W. Soharnp, ibid., 68, 489 (1964).
