ISOTES
Feb., 1963 TABLE I Salt
LiF LiCl LiBr LiI NaF NaCl NaBr XaI KF KC1 KBr
KI RbF RbCl RbBr RbI
AH" (kcal./moie)*
E0 (ergs./om.Z)fl
1:
51 .O 36.0 38.4 40.8 50 40.8 38.7 38.2 41.3 38.8 37.1 34.7 39.51 36.92 37.12 35.96
169 209 197 181 209 188 177 16 1 195 163 18 1 136 186 155 144 130
44.9 15.7 14.3 14.9 28.1 116.6 14.8 13.7 17.9 14.6 13.7 12.3 16.1 13.2 13.2 12.4
theory in the first place and it depends on essentially unknown quantities. The main purpose of this note was to show that a surface tension equation derived from the cell model obeys the law of corresponding states of Reiss and Nayer and also to indicate the usefulness of Stephan's constant in fuged salt studies, as indicated in Table I. (8) "American Institute of Physics Handbook," McGraw-Hill Book Co., New York, N. Y., 1957, Table 4-j.
REACTIONS O F RADICALS. 111. l\ilEhSUREMEP\'T OF T H E TRANSFElR CONSTANT OF &BUTYL PEROXIDE USING RADIOACTIVE PEROXIDE'S' BY WILLIAMA. PRYOR Department of Chemzstry, Purdue Unzzersity, Lafayette, Indzana Recezved J u l y $0, 1968
Peroxides decompose both by a unimolecular process and by a bimolecular process in which the decomposition is induced by radicals. The first of these is an S H l reaction, and the second an S H r~e a ~ t i o n . ~The S H ~ reactions of peroxides are of great theoretical interest since they are examples of bimolecular radical displacements, and the mechanism of these displacements has not been e l ~ c i d a t e d . ~ - ~ The rates of the induced decomposition of several aroyl peroxides have been r e p ~ r t e dbut , ~ the induced decomposition of only one aliphatic peroxide, namely, propyl peroxide, has been the subject of a kinetic study.2 I n this paper, the transfer constant for t-butyl peroxide (TBP) will be reported. The technique involves polymerizing styrene in the presence of a constant amount of radioactive TBP plus a varying amount of an inactive initiator and measuring the rate of incorporation of radioactivity into the polymer a8 a function of the (1) This work was supported in part by grant AT(11-1) 1168 from the United States Atomic Energy Commission. Grateful acknowledgment is made to the donors of that fund. ( 2 ) Part 11: W. A. Pryor and E. P. Pultinas, .I. Am. Chem. Soc., 86, 133 (1963). (3) W. A. Pryor and T. L. Pickering, ibzd., 84, 2705 (1962). (4) W. A. Pryor, "Mechanisms of Sulfur Reactions," McGraw-Hill Book Co., Inc., New York, N. Y., 1962, pp. 48-57. (5) (a) K. Naeaki a n d P. D. Bartiett, J. Am. Chem. Soc., 68, 1686 (1946); (b) P. D. Bartlett and K. Nazaki, ibid., 69, 2299 (1947); (0) F. R. Mayo, R. A. Grefig, and RI. S. Matheson, ibzd., 73, 1691 (1961): (d) W. Cooper, J . Chem. Soc., 3106 (1981); (e) 2408 (1952); (f) J. C. Bevington and T. D. Lewis, Polymer, 1, 1 (1960).
5 19
rate of polymerization. Azobisisobutyronitrile (AIBS) was used as the inactive initiator. The unimolecular decomposition of TBP has been the subject of a large number of studies.6 However, no report of the rate of the S Hreaction ~ has been published. This probably is because it was felt that the induced rate would be slow in this hindered peroxide. The early report by Raley, Rust, and Vaughaneethat TBP decomposed a t the same rate in the vapor phase and in solution suggested that the induced path was unimportant in both phases. Recently, however, Batt and Benson6hand McMillan and Wijnen6' have shown that some induced decomposition occurs even in the gas phase. Raley, Rust, and Vaughan also had reported that TBP decomposes a t essentially the same rate in cumene and in tributylamine, in sharp contrast with the behavior of benzoyl peroxide. Kozaki and Bartlettja had reported that benzoyl peroxide decomposes a t a moderate rate in hydrocarbon solvents but undergoes an explosively fast decomposition in amines. The S Hreaction ~ of benzoyl peroxide, which consumes an appreciable fraction of the involves radical attack on the 0-0 bond.' Radicals derived from an amine solvent apparently are extremely effective in this attack, probably because of a polar resonance contribution to the transition state in which a positive charge is localized on nitrogen and a negative charge on oxygen. I n TBP, the 0-0 bond is very hindered, and transfer reactions probably occur largely by hydrogen abstraction. If this is true, amines n-ould not be expected to exert any marked rate effect. These considerations led to the expectation of a measureable rate of induced decomposition in TBP, and this report confirms tha,t expectation. Experimental TBP was prepared by the method of Milas.* The t-butyl alcohol was prepared from acetone-2-C-14 (Volk Chem. Co., 0.2. mc. diluted to 11.9 g.) via a Grignard reaction in butyl ether solvent. The yield of t-butyl alcohol is 9.1 g., 60 mole %, and g.p.c. analysis shows no unreacted acetone. The final distilled TBP is obtained as 7.9 g., 83 mole 70, and is diluted t o 11.1 g. Analysis by g.p.c. shows this material is 71 wt. % TBP in butyl ether and no impurities can be detected. The infrared spectrum is identical with that reported.n Runs were prepared by weighing A I B S into ampoules, adding 1 ml. of the radioactive TBP, inactive TBP if necessary, and 7 ml. of styrene, degassing, and sealing in the usual manner.3 Runs were worked up by transferring the reaction solution t o a beaker using 5-7 ml. of benzene and precipitating the polymer with 200 ml. of methanol. The polymer then was dissolved in benzene and reprecipitated twice. Controls showed that two reprecipitations removed all the TBP-C-14. The polymer was (6) (a) L. Herk and M. Szwarc, J . Am. Chem. Sac., 82, 3558 (1960); (b) J . K. A411enand J. C. Bevington, Proc. Roy. Soe. (London), A262, 271 (1961); (0) J. A. Offenbaob and A. V. Tobolsky, J . Am. Chem. Soc., 79, 278 (1957); (d) A. V. Tobolsky and B. Baysal, J . Polymer Sci., 11, 471 (1953); (e) J. H. Raley, F. R. Rust, and W. E. Vauahan, J . Am. Chem. Soc., 70, 88 (1948); (f) 70, 133F (1948); ( g ) E. R. Bell, F. F. Rust, and W. E. Vauahan, ibzd.. 72, 337 (1950): (h) L. Batt and 9. W. Ben,on, J. Chem. Phys., 56, 895 (1962): (i) A. N. Bose and C. Hinshelwood. Proc. Roy. Soc. (London), 8249, 173 (1958): (j) G. Archer and C. Hinshelwood, ibid., A261, 293 (1961); (k) F. W. Birss, ibzd., A274, 381 (1958); (1) J. Murawski, J. 9. Roberts, a n d M. Szwarc, S. Chem. Phys., 19, 698 (1961): (m) F. P. Lossing and A. W.Tiokner, ibid., 20, 907 (1952); (n) P. L. Hanst and J. G . Calvert, J . Phys. Chem., 63,104 (1959); (0)C. Walling and G. Metzger, J . Am. Chem. SOC.,81, 5365 (1959); (p) G. 0. Pritchard, H. 0. Pritchard, and A. F. Trotman-Diokenson, J. Chem. Soc., 1425 (1954); (9) R. K. Brinton and D. H. Volman, J . Chem. Phys., 20, 25 (1952); (r) G. MoMillan and & H. !I J.. Wijnen. Can. J . Chem., 36, 1227 (1958). (7) E. H. Drewand J. C. Martin, Chem. Ind. (London), 926 (1959); D. B. Denney a n d G. Feig, J . A n . Chem. SOC.,81, 5322 (1959); W. Doering, K. Okamoto, and H. Krauch, ibid.. 82, 3579 (1960). (8) S. A. Milas and D. M.Surgenor, J . Am. Chem. Soc., 68,205 (1946). (9) 3'. Welch, H. R. Williams, and H. S. Masher, zbid., 77, 551 (1955).
NOTES 1
I
In
2
3
Tal. 67
Data and Discusslon The mechanism for polymerization of stvrene, M, by an initiator, AA, includesihese steps
I
4
-
3
a
X
q 2
1
0
1
4
5
log j .
Fig. 1.-Graph of eq. 13: circles represent solutions in which (TBP)/(M) = 0.063 and give C = 8.2 X and kdf = 1.0 X 1 0 - 9 set.-'; squares are for (TBP)/(M) = 0.15 and give C = 9.2 X and kdf = 1.0 X 10-9 sec.-l. 2
1
0
-1
In the specific case where A h is TBP, A . is a t-butoxyl radical and AA. is the radical resulting from hydrogen abstraction from TBP, ie., CsH700C3Ha.. Kote that the rate constant for reaction 1 is written on a per radical basis to conform with conventions in polymerization kinetics.1° We assume that all rate constants are independent of chain length, so AM. = AM,.. Reaction 4a corresponds to transfer by attack on oxygen and 4b by hydrogen abstraction. The sum of the rates of reactions 4a and 4b is equal to the total rate of transfer, reaction 6.
-2
& -3 0 50 e
-4
-5
-6
-7 -8
-9 1.5
2.0
2.5
3.0
10*/T.
Fig. 2.-Arrhenius graph of the decomposition of TBP: 0, gas phase; 0 , gas phase measurements of Batt and Benson; 0 , hydrocarbon solvents; 0 , amine sclvents; A, polymerizable olefins as solvents. Line drawn with activation energy equal t o 37.0 kcal. counted by dissolving a weighed amount in 10 ml. of toluene containing 4.00 g. of PPO and 0.100 g. of POPOP per 800 ml. of toluene (Packard Instrument Company). The scintillation counter employed a silicone oil bath coupled t o a Lucite light pipe and suitable detectors and counters. Efficiency was 53%, determined from a benzoic acid standard purchased from Packard. Controls shokTed that the polymeric product does not affect counting efficiency after dark adaptation.
+
(7) Allen and BevingtonGLhave shown that reactions 1 and 2 lead to the incorporation of one entire molecule of TBP in the polymer. That is, the initially produced tbutoxyl radical adds to the monomer before appreciable decomposition to methyl radicals and acetone occurs. We shall assume that each of the mechanisms for transfer eventually leads to the incorporation of an entire TBP molecule. That is, reaction 4a followed by 2, as well as reaction 4b followed by 5 , are assumed to incorporate an entire TBP molecule. This implies that the t-butoxyl radical and the C3H700C3H6.radical do not undergo appreciable decomposition before they add to styrene. We require an expression for the rate of incorporation of radioactive TBP into the polymer, R’. Note that the rate of incorporation of A’s into the polymer, R.4, is twice the rate of incorporation of TBP. Rtr = R i a
R4b
Ra = 2R’ At the steady state in A . , Rqa
+ 2Rd = Ri
(8)
(9)
( I O ) See, 6.0.. C. Walling, “Free Radicals in Solution.” John Wiley and Sons, Ino., New York, N. Y.,1957, p. 67. This factor results from the faot that two chains are initiated for each peroxide which decomposes: L e . , Ri = Zkdf(TBP). See also ref. 6f. Note, however, that studies of the gas phase deoomposition of T B P use -d(TBP)/dt = ki(TBP). and that 2hd ]01.
NOTES
Feb., 1963 and a t the steady state in AA- , Rhb
NOW,RA is given by
RA = Ri
(10)
= R5
+ + 2R5 R4a
Substitution of eq. 9 and 10 gives
RA = = =
+ 2Rd) -!- Ria $. 2Rab 2Rd + 2Rtr ICkdf(TBP) + 2ktr(AM,*)(TBP) (R4a
(11)
where the factor f represents the efficiency of the radicals produced in reaction 1 initia,ting chains. From eq. 3 Rp = k,(AM,*)(M) =: Rp (12) where Rp is the total observed rate of polymerization. From eq. 8, 11, and 12
521
method, the efficiency of production of radicals from TBP is very high, and its rate of decomposition is very similar in the gas phase and in solution.Rc The elegance of the present method should be emphasized. For each of the lines in Fig. 1, the only variable is the concentration of AIBN. Thus, both the transfer constant and the dissociation constant for TBP can be measured without varying the concentration of either TBP or styrene. It has become increasingly apparent that simple polymerization theory may become inadequate when large variations occur in the concentration of transfer agents.ll (11) See the summary given in footnote 12 of ref. 2.
THE THIRD BODY EFFICIENCY OF MOLECULAR BROMINE I N THE RECOMBIN.ATION OF BROMINE ATOMS I N ARGON BY MICHAEL R. BASILA' AND ROBERT L. STRONG Rensselaer PolVtechnac Institute, Troy,New York Received August 10, 1062
where C = kt,/k,. Equation 13 is equivalent to that of Bevington and Lewis,jf who first suggested the present method. From eq. 13, a graph of the rate of incorporation of radioactivity into the polymer us. the rate of polymerization yields a straight line of slope C(TBP)/(M) and intercept 2kdf(TBP). Table I gives the data, and Fig. 1 is a graph of eq. 13. From the figure, C is obtained as 8.6 X and lcdf as 1.0 X set.-'. TABLE I POLPXERIZATION OF STYRENE AT 60" CATALYZED BY AIBN TBP-C-14 -NolarityAIBN TBP
Sec.
Styrene
x
10-8
RP
x
104
Counts/ min.@
Moles
TBP~
x
AND
R* loae
8.9" 0.12 0.10 1020 0 0.476 7.6 91.3 1.93 372 3.26' 1.13 3.60 0.0667 .476 7.6 600 4.50 2.35 5.26' 1.46 ,0968 .476 7 . 6 4.11 3.87 698 6.72' 2.04 .261 ,476 7 . 6 2 72 4.67 6.72 5.55' 2.55 .380 .476 7 . 6 420 8 . % j d 1.69 6.7 5.82 1.23 .0330 1.03 5.82 1.75 710 15 Od 2.87 ,0672 1.03 6.7 4.50 2.76 715 15.1d 3.71 .167 1.03 6.7 2.72 3.16 570 12.1d 4.91 ,220 1.03 6.7 a Counts per minute incorporated in the polymer. Counted in a liquid scintillation counter with 53% efficiency. Counts per minute (c./m.) in the po1,vmer divided by the activity of the TBP in c./m./mole. The TBP i8 11.4 X lo8 c./m./mole. These The TUP is 4.73 runs contain 0.22 iM butyl ether as diluent. X 10* c./m./mole. These runs contain 0.20 X butyl ether as diluent. e R* is the rate of incorporation of TBP-C-14 into the polymer. It is calculated as (moles TBP)/(l. of reaction solution) (sec.).
The rate of decomposition of T B P has been measured by 12 groups of workerss from 350 to 60'. A composite Arrhenius graph, drawn with an activation energy of 37.0 kcal., gives the value of 2.0 X 10-9 sec.-l for kl a t 60°, in excellent agreement with the value of 2.0 X 10-9 sec.-l for 2kdf found herelo (Fig. 2). Offenbach sec.-l for and TobolskyGchave reported 3.2 X k d f , or 6.4 X for k, a t 60'. This value was not corrected for the contribution to the rate of the secondorder process and is probably high for that reason. Within the precision of the extrapolation of rates using the Arrhenius graph and the accuracy of the present
I n the last decade the recombinations of halogen atoms following the dissociation of gaseous molecular halogens by flash photolysis or shock-wave methods have been under rather intensive study. Of particular interest has been the effect of the nature of the third body upon the recombination rate constant. The recombination of iodine atoms has been the most studied, and it has been shown that molecular iodine itself is a highly efficient third body; the rate constant , the subscript indicates the third ratio, k I z / k ~ rwhere body, has been reported as 2602*and 65OZb a t room temperature. At higher temperatures this ratio is greatly diminished-for example, k ~ ~
