Communications to the Editor
1736
TABLE I: Sublimation behavior of Pure and Doped AP
Fraction sublimed Doped AP Temp,a "C Pure AP ( 320 335 350
0.383 0.685 0.973
Ca2+ S042c1mol %) ( mol %) (10-2 mol %) 0.294 0.555 0.868
0.304 0.546 0.875
0.341 0.631 0.957
%
sublimed 50
'Temp ("C) for 50%sublimation 326
332
332
329
This is the temperature at which the fraction sublimed ( a ) has been calculated. a
chloride) were taken in an aqueous solution in definite proportions and the coprecipitation was done by cooling the saturated solution at 70 "C to room temperature. The particle size of doped and undoped AP was kept constant. The exact amount of the dopant in the AP crystal was not analyzed and therefore the amount to which we are referring is in the solution. so42-doped samples were subjected to usual conduction measurements and the enchancement in conduction is indicative of the incorporation of S042- in the crystal lattice resulting in vacancies.11 Figure 1represents typical sublimation endotherms of pure and doped ammonium perchlorate. The fractional areas at different temperatures and the total area of the endotherm were measured with a planimeter. The fraction sublimed ( a ) at different temperatures could then be calculated from the ratio of the respective areas. This yielded a plot of a vs. temperature which was then used to calculate (i) the fraction decomposed at a particular temperature and (ii) the temperature for 50% sublimation. The results are given in Table I. It is evident from the data in Table I that the sublimation rate is desensitized by Ca2+,S042-, and C1- doping. The behavior of the Ca2+and S042-dopants (in the low concentration range) in the thermal decomposition of AP has been explained on the basis of an ionic diffusion mechanism.6 In thermal decomposition, the Ca2+doping desensitizes and the S042- doping sensitizes the process. This shows that the mechanism of sublimation is different from that of the decomposition of AP. Considering the proton-transfer process on the surface to be the rate-controlling step, the sublimation mechanism can be explained for S042- and C1- doped AP in terms of a proton trap.12 A similar explanation based on Herrington-Stavely's (HS) molecular defects13 can also be given, according to which the defects which are formed via sublimation reactions will dominate near the surface. Although the above explanation can very well explain the sublimation mechanism of S042-and C1- doped AP, it cannot explain the desensitization observed in case of Ca2+doped AP (Table I). This shows that, although the proton-transfer basically remains the rate-controlling process, the overall mechanistic path through which the sublimation occurs may be more than one. Sublimation mechanism can also be explained in the following ways: (I) Higher bond strength of the dopant ion (i.e., Ca2+ and S042-) with counterion on the surface compared to the bond strength between NH4+ and The Journal of Physical Chemistry, Vol. 80, No. 15, 1976
c104- ions. (11)The presence of the dopant ion makes the surface non~toichiometricl~ with respect to the number of NH4+ and C104- ions. When the surface becomes nonstoichiometric then obviously the NH4+ or C104- has to come from the immediate next layer for compensation and thus the sublimation process is slowed down. (111) The strain in the crystal, caused by doping, may also control the sublimation process. Lester and Somorjai have shown that strain in the crystal desensitizes the sublimation rate.9 Proof of the strain in AP due to doping has been shown from the broadening of infrared peaks.15 Further work is in progress to throw more light on the mechanism of the sublimation process. References and Notes (1) G. A. Somorjai, Science, 162,755 (1968). (2)S. H. Inami, W. A. Rooser, and H. Wise, J. Phys. Chem., 67, 1077 ( 1963). (3)V. R. Pai Verneker, M. McCartey,Jr., and J. N. Maycock, Thermochim. Acta, 3,37 (1971). (4)P. W. M. Jacobs and A. Russel-Jones, J. Phys. Chem., 72,202 (1968). (5) C. Guirao and F. A. Williams, J. Phys. Chem., 73,4302 (1969). (6)J. N. Maycock and V. R. Pai Verneker, Proc. R. SOC.,Ser. A, 307,303-315 (1968). (7) G. A. Somorjai and D. W. Jepsen, J. Chem. Phys., 41,1394 (1964). (8) H. Bethge, Phys. Status Solidi, 2,3,775 (1962);Surf. Sci., 3,33 (1964). (9)J. E. Lester and G. A. Somorjai, J. Chem. Phys., 49,2940 (1968). (IO) S.W. McBain and A. M. Baer, J. Am. Chem. SOC.,48,600 (1926). ( I 1) V. R. Pai Verneker, unpublished work. (12) P. W. M. Jacobs and W. L. Ng, J. Solidstate Chem., 9,315,(1974). (13)G.P. Owen, J. M. Thomas, and J. 0. Williams, J. Chem. Soc., Faraday Trans. 1, 70, 1934(1974). (14)D.L. Howlett, J. E. Lester, and G. A. Somorjai, J. Phys. Chem., 75,4049 119711 '(15) V. R. Pai Verneker and K. Rajeshwar, Thermochim. Acta, 13, 333 I . - .. I .
(1975). High Energy Solids Laboratory Department of Inorganic and Physical Chemistry Indian Institute of Science Bangalore 560 0 12, India
V.
R. Pal Verneker K. Kishore.
M. P. Kannan
Received December 18, 1975
Vibration to Translation Energy Transfer from Excited Cyclobutane Chemically Activated by Nuclear Recoil Reaction Publication costs assisted by the United States Energy Research and Development Administration
Sir: Intermolecular energy transfer studies from thermally and chemically activated molecules provide information of fundamental and practical importance in chemical dynamics. Of particular interest are highly vibrationally excited species which transfer relatively large amounts of energy on collision.1-6 Previous reports for conventional chemical activation systems have shown that the average energy transferred per collision is on the order of a few kilocalories per mole, while the relative energy transfer efficiencies generally range over no more than an order of magnitude in going from simple monatomic to complex polyatomic c o l l i d e r ~ .The ~ , ~ detailed mechanism for vibrational energy transfer, however, as yet is not understood in complex molecular systems. We have measured the vibration to translation energy transfer efficiencies from nuclear recoil chemically activated cyclobutane-t to the homologous series of noble gases He, Ne, Ar, Kr, and Xe in order to further clarify the mechanism for inter-
1730
Additions and Corrections
with mass through Xe to be observed, the coflision of the inert gas must occur with a fragment at least as large as two methylene groups. In fact, for the case of mass division as CzH4CzHsT, if the 120 kcal/mol average vibrational energy of the cyclobutane is partitioned uniformly among 22 of the 30 vibrational modes14 and the translational temperature in the system is 300 K, the amounts of energy transferred from vibration to translation per collision in kcal/mol are calculated to be, He, 0.5; Ne, 1.4; Ar, 1.8; Kr, 2.0; and Xe, 2.1. Whereas these values are reasonable, such an idealized model is surely an over-simplification of the energy transfer process. It does, however, suggest that insofar as the collision is impulsive, interaction between the inert bath gas and the cyclobutane is not localized but involves at least one-half of the molecule. Nonlocalized collisions also enhance the probability of forming transition modes which can serve mechanistically as a nonimpulsive channel for statistical redistribution of vibrational energy. Such energy transfer through transition modes has been suggested previously as a model for high energy systems since it naturally allows for the relatively large amounts of vibrational energy transferred per c01lision.l~If transfer of vibrational energy through transition modes is considered for the cyclobutane-t studied here, it is apparent that the total efficiency is dependent on both the number of transition modes formed and the magnitude of the attractive branch of the collision potential. It appears reasonable then that relatively efficient vibration to translation energy transfer results from nonlocalized collisions which are influenced significantly by long-range intermolecular forces.
Contract No. E(l1-1)-2190. N.N. wishes to thank the Phillips Petroleum Co. for a graduate research fellowship during the course of this work. The cooperation of the Washington State University Nuclear Radiation Center in performing irradiations is also acknowledged.
References and Notes (1)G. H. Kohlmaier and B. S.Rabinovitch, J. Chem. Phys., 38, 1692, 1709 (1963);S.C. Chan, B. S. Rabinovitch, J. T. Bryant, L. D. Spicer, T. Fujimoto, Y. N. Lin, and S.P. Pavlou, J. Phys Chem., 74, 3170 (1970). (2)4.W. Setser and E. E. Siefert, J. Chem. Phys., 57,3613,3623(1972). (3) M. G.Topor and R. W. Carr, J. Chem. Phys., 58,757 (1973). (4)M. Volpe and H. S. Johnston, J. Am. Chem. SOC.,78,3903 (1956).
(5)W. Forst, "Theory of Unlmolecular Reactions", Academic Press, New York, N.Y., 1973. (6) P. J. Robinson and K. A. Holbrook, "Unimolecular Reactions", Wiley-lnterscience, New York, N.Y., 1972. (7)D. W. Setser, MTP Int. Rev. Sci., Phys. Chem., 9, I(1972). (8) N. S. Nogar, J. K. Dewey, and L. D. Spicer, Chem. Phys. Left., 34, 98 (1975). (9)E. K. C. Lee and F. S. Rowiand, J. Am. Chem.nSoc.,85,897 (1963);A. Hosaka and F. S.Rowland, J. Phys. Chem., 75,3781 (1971). (IO) J. 0.Hirschfelder, C. F. Curtiss, and R. 8. Bird, "Molecular Theory of Gases and Liquids", Wiley, New York, N.Y., 1967,p 1 1 10:uncorrected uovalues were used. The collision diameter for c-C4HBwas taken as 5 A.
(11)P. G. Miasekand A. G. Harrison, J. Am. Chem. SOC., 97,714(1975). (12)J. W. Slmons, B. S. Rabinovitch, and D. W. Setser, J. Chem. Phys., 41,800 (1964). (13)S.W. Benson, "The Foundation of Chemical Kinetics", McGraw-Hill, New York. N.Y.. 1960.D 166. (14)This excludes parkipation of the C-H stretches in energy equilibratlon. Such an arbitrary cholce is based generally on the number of "active" oscillators involved in energy randomization for thermally activated cyciobutane decomposition and does not affect the trend in the calculated results. (15) Y. N. Lin and B. S. Rablnovitch, J. Phys. Chem., 74,3151 (1970);R. G. Bhatachargee and W. Forst, Chem. Phys. Lett., 28,395 (1974). (16) Camille and Henry Dreyfus Teacher-Scholar 1971-1976.
Department of Chemistry University of Utah Salt Lake City, Utah 84 112
Acknowledgment. This work was supported by the U.S. Energy Research and Development Administration under
N. S. Nogar Leonard D. Spfcer' j 6
ReceivedMarch 29, 1976
ADDITIONS AND CORRECTIONS 1976, Volume 80
Frederick Peter Sargent and Edward Michael Gardy: Radical Yields in Irradiated Methanol and Ethanol. An Electron Spin Resonance and Spin Trapping Method. Page 856. Equation 10 should read as follows:
-G(I)
kz[CH30Hl G(I1) - k4[t-BuNO]
[
+
Go(C"OH)] Go(CH30.)
+
GGo(CH30.) ~(WOH) (10)
-F. P. Sargent
The Journal of PhysicalChemistry, Vol. 60, No. 15, 1976
