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.-'. TABLEI 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 runs contain 0.22 iM butyl ether as diluent. The TUP is 4.73 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 TBP 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
In 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 65OZba t room temperature. At higher temperatures this ratio is greatly diminished-for example, k ~ ~
