R. C.
1904
Ireton, An-Nan KO, and B. S.Rabinovitch
rational Energy from Highly Excited Butyl Radicals. Structural Effects on of Relative Collision Diametersla R. C, Ireton,IbAn-Nan KO, and B. S. Rabinovltch* Q
~
~
~of Chemistty, i ~ ~ University ~ n t of
Washington, Seattle, Washington 98 195 (ReceivedMay 2, 1974)
Relative collision diameters for energy transfer have been measured at room temperature in the butyl-2 radical chemical activation system for various substituted and cyclic fluorocarbon molecules. Three generalizations are supported and illustrated by the data. (1) Branching of fluoroalkanes causes a decrease of the collision diameter relative to the straight chain perfluoroalkane of the same carbon number. (2) Cyclization of the gluoroalkane chain decreases the effective size of the molecule. (3) Introduction of EL terminal double bond decreases the size relative to the straight chain perfluoroalkane. A simple equivalent sphere model based on the strongest end-to-end carbon chain systematizes the relative collision diameters of related molecules. These results support similar considerations for hydrocarbon bath molecules found previously in the thermal methyl isocyanide system.
Introduction Intermolecular vibrational energy transfer during the collision process in a gas-phase reaction is the primary mechanism of activation in thermal unimolecular systems, and of deactivation of vibrationally excited species. A knowledge of relative collision diameters of bath gas molecules for the energy transfer process in systems of highly vibrationally excited polyatomic molecules is of importance. For the most part, assumed collision diameters derived from transport properties (viscosity measurements, usually) have been used in the literature for the calculation of gas kinetic collision diameters, of rate constants, and for the evaluation of energy transfer data. In some cases, errors or irregularities in g~ are carried directly into the corresponding &(MI values, the efficiencies for transfer of vibrational energy upon collision between substrate and bath molecule. It is apparent, then, that a consistent set of collision diameters is important for the determination of &(M) and for comparison with theoretical predictions when applicable. Previously, we have made an extensive investigation of this phenomenon for the thermal low-pressure unimolecular isomerization of methyl isocyanide in the presence of several homologous series of hydrocarbon and fluorocarbon polyatomic bath m o l e c ~ l e s .It ~ *was ~ possible to determine relative values of effective hard-sphere collision diameters for substrate-bath molecule pairs, SAM; incremental changes A s A were ~ ~ also determined with increase in the number of structural units, i.e., AsAM(CHZ)and AsAM(CF~) were measured.:! The relation between the molecular geometry of structural isomers and their effective collision diameters for energy transfer was also examined in this thermal system. In particular, it was €owid that increased branching of alkanes having constant carbon number entailed a progressive decrease in the collision diameters; cyclization of the alkane also decreased the effective size of the bath molecule. In order to broaden the experimental basis of this phenomenon, we have previously reported4 a study of vibrational energy transfer in the chemically activated butyl-2 system and have measured the collision diameters of some fluorocarbon bath gases. In particular, a simple method The Journalof Physical Chemistry, Vol. 78, No. 20, 1974
was devised for measuring the increments, AsgM(CF2), and the relative collision diameters, SgM, of bath molecules for a homologous series of perfluoroalkanes (e,to CS); aiso, by comparison of apparent collision diameters a t 298 and 195'K, the relative collisional energy transfer efficiencies, /3,(M), could be surmised for the less efficient gases. The experimentally determined values of &# forV inefficient I) bath gases are dependent directly on the choice of the equivalent hard-sphere collision diameter for the collider species. In the present study, we extend our earlier studies on use of the nonpolar butyl-2 species in a chemical activation system. A series of perfluoro-1-alkenes, as well as selected cyclic fluoroalkanes and cyclic fluoroolefins, has been studied for comparison with the corresponding alicyclic compounds.
Experimental Section The fluorocarbon compounds were obtained from P.C.R. Inc. and were further purified by gas chromatographic techniques until free of impurities. The cis-butene-2 was Phillips Research Grade, and was also chromatographically purified until the impurity level was less than 0.001%. Mixtures of the fluorocarbon with cis-butene-2 were made in the ratio of 20:l on a pressure basis for all but the CzF4-butene (1O:l) system. The reactants were subjected to a vessel. The details of the run procedure and analytical techniques are given in ref 2 and 4. Results Description of the calculation of the effective hardsphere collision diameters, s BM, has been given earlier and need only be described briefly here. The relevant quantities measured in chemical activation systems are the ratio of stabilization to decomposition, S D , and the collision frequency, w = Zp. The apparent rate constant for decomposition is k , = &(M)w(D/S). Then, S/D = & ( M ) w / k , = P,(M)Zp/k,, and plots ofS/D us. p yield a linear relation whose slope is P,(M)Z/k,; the specific collision rate 2 is a function of S B M ~ ,and a ratio of the slope of the butyl-M collision pair relative to the butyl-butene reference pair yields a relation for SBM in terms of SBB
Energy Transfer Collision Diameters for the Butyl-2 Radical
1985
TABLE I: Experimental Quantities and Lennard-Jones Constants a t 300°K
0.620 rt 0.037d 5.757 s 0.033 i -CdF10 0.894 rt 0.060 1.092 i 0.082 czs -CdF, C5F10 1.284 s 0.089 c -CdF, 0.896 i 0.110 1.040 t 0.040 c-CSF~ c-C6FlZ I. 195 i 0.064 c-c6F10 1.148 k 0.020 CsF6 1.245 i 0,114 c - C F ~ C ~ F ' ~1.325 ~ .t 0.038 c~s-C~H, 1.00 C2*,
G3F6
5.52 5.88 6.35 7.02 7.61 6.36 6.85 7.35 7.20 7.50 7.74 6.72
5.83 6.18 6.69 6.69 7.67 6.69 7.67 8.43 8.43 8.43
0.31 0.30 0.34 -0.33 0.06 0.33 0.82 1.08 1.23 0.93
157 176 185 189 202 187 201 212 212 224 222 259
1.178 1.193 1.200 1.204 1.214 1.203 1.214 1.220 1.220 1.230 1.230 1.251
4.14 4.62 5.35 6.43 7.31 5.32 6.06 6.82 6.57 6.97 7.36 5.51
4.81 5.16 5.89 5.89 7.39 5.81 7.39 8.58 8.58 8.58
a Collision diameter obtained using Bc(CzF4) = 0.88, Pc(C3F6) = 0.99, and &(M) = 1.0 for M 2 C4F8. Collision diameter from ref 5 for the corresponding straight chain alkanes. Decrement between the collision diameter SBM and the corresponding straight chain diameter. d Standard deviation.
C8.60
Q \
cn 0.40
0.20 0.01
0.03
0.05
P~
(torr
i"2)
Q07
Figure 1. Plots of S/D vs. p,, for butyl radical decomposition in the presence of the following bath gases at 300'K: c-C4Fe (0);c-C5F8 (0); C-C~FIO(A); CsFfi (A); C-c~Flp(D); C - ( C F ~ ) C ~ F(0). ~ I Dashed line represents the data for the reference cis-C4H8.
''
= SBB (slopeB,/P,(M)slop@BB)* (1) with the assertion that &(B) is unity.5 Of the present collision partners studied, C2F4 and C3F6 may have PC(M)less than unity. Previ~usly,~ P,(M) for C ~ Fwas G found tQbe 0.8, and P,(M) for C3F8 was 0.9. Chan, et a1.,2 found an increase in PJM) in going from perfluoroethane to perfluoroethylene, from Pc(CzF6) = 0.64 to Pc(C2F4) L 0.71. This represents an increase of 10%. This seems a reasonable choice for the present system, also, and yields PC(C2F4)= 0.88 and Pc(C3F8) = 0 99. For the remainder of the bath gases studied, PJM) equal to unity was used in the evaluation of SBM. The Lennard-Jones constants d k (and the integrals Q B M ~ ~ *were ) found as in ref 5. The results are summarized in Table I and the data are shown in Figures 1 alnd 2. SRM
Discussion Fluoroolefins. Hydrogen atoms add to the olefin to give
0.01
p
P
0.03 (torr S'")
0.05
Figure 2. Plots of S/D vs. pp for butyl radical decomposition in the presence of the following bath gases at 300'K: CpF4 (0);C3Fs (0); i44F10(A);cisC4F8 (A); C~FIO(W).
for the reference cisC4H8.
Dashed line represents the data
the excited fluoroalkyl radical5 For CzF4H., as well as CSF~H.,evidence of radical addition to the stabilized butyl radical was confirmed by mass spectrometric identification. Where mass spectrometric identification was not feasible, chromatographic retention data provided identification of the radical combination products. These products accounted for a maximum of 20% of the stabilization product for the C2F4 system, -10% of S for CSF8, -1% of S for c ~ s - C ~ F ~ , and -5% for C5F10. The C2E4, CsF6, and C ~ F bath ~ O gases show a decrease in collision diameter in comparison with the corresponding alkanes (see Table I), but the cis-C4Fs diameter is larger than that of perfluoro-n- butane. The general trends here are consistent with the findings for hydrocarbon-olefin compounds in ref 2, where contracThe Journal of Physical Chemistry, Vol. 78. No. 20, 7974
1986
tion in diameter occurred on going from alkane to olefinic species, except for interior olefins such as cis-butene-2 where the reverse was obtained. C5F10 data appear to give the smallest contraction. These results apparently reflect the contraction of bond length encountered on going from a single to a double bond in the a position of the carbon skeleton. When interior double bonds are considered, the planar configuration of the fluoromethyl groups seems to lead to a larger effective diameter, as for cis-C4F8-2. Cyclic Fluoroalkanes. The results of Spicer and Rabinovitch3 in the isocyanide system revealed that cyclic hydrocarbon bath gases behaved like straight chain molecules with an effective length equal to the longest end-to-end distance in the ring, and with the remaining CH2 moieties to be taken as CR3 branching substituents; such branching adds an increment to the effective collision diameter which is less than 0.4As(CH2) for the interval in question. On applying this madell to fluorocarbon species, c-CcFg simulates a CBcompound having one CF3 substituent, or effectively has the same size as i-C4F10; likewise, C-CSrepresents an effective chain of four carbons with one side CF3 group; and a c6 cyclic compound is effectively n-perfluorobutane in length with two methyls attached. These considerations are summarized in Table 11, where the equivalent carbon number chain length and side CF3 groups are given. The collision diameter SBM for perfluorocyclobutane is 6.36 A, almost identical with that of perfluoroisobutane, SBM = 6.35 A, as anticipated. Also, the increase in diameter from C3Fs to i-CdF10 was measured as 0.17 A, in agreement with the prediction of S0.22 %, obtained from
