214 LETTERS TO THE EDITORS

Initiator Eficiency in Radical Polymerization Absolute rates of chain initiation are important in polymer kinetics, par-

ticularly in determining rate constants of the individual steps of chain propagation, transfer, and termination. Often these have been evaluated by using initiators with known rates of decomposition, either considering that every radical formed starts a chain, or making some assumption about radical efficiencies. In such work azonitriles such as azobisisobutyronitrile are frequently used since they decompose unimolecularly at convenient rates which vary little from solvent to solvent, are generally effective in producing polymerization, and appear themselves resistant to induced de- composition by participation in the resulting chain reactions.lP2 The rate of decomposition of azobisisobutyronitrile (AN) itself has been deter-

Fig. 1. Decomposition of azobisisobutyronitrile in aromatic solvents. By Nz evolution: (0) Lewis and Matheson' (xylene) (including unpublished data at 70 and 90"); (A) Overberger et aZ.2 (toluene); (B) Arnett3 (xylene); (0) Breitenbach' (sty- rene); (---) least squares line through collected data. (0) By DPPH (benzene)5; (-) least square line through data. (+) Rate in CCI, (Nz evo1ution)l; (x--x) in CCl, (DPPH).b Ordinate: log k + 7, set.-'. Abscissa: 1/T X lo3.

LETTERS TO THE EDITORS 215

mined by two methods: by nitrogen evolution, and by the fading in color of diphenylpicryl hydrazyl (DPPH). However, when results of the two methods are compared, an interesting observation may be made. Thus, in Figure 1 all available data on decomposition rates in aromatic hydrocar- bon solvents are plotted, and it is evident that the two methods appear to measure two processes with quite similar activation energies, but with the DPPH reaction measuring a reaction occurring approximately 70% as fast as the other at 60 ’.

Additional data supporting this conclusion have recently been reported elsewhere, see J. N. Sen, G. S. Hammond, and E. C. Boozer, Abstracts of American Chemical So- ciety Meeting, March, 1954, p. 14Q.

The following seems a reasonable explanation of this observation, which has important implications for polymerization and other radical chain ki- netics.

The initial act in AN decomposition is either simultaneous or successive cleavage of both C-N bonds to yield two isobutyronitrile radicals and nitrogen:

CH3 CN NC CHI cI& CN

\C/ - + Nz (1) /“’ \ /

CH3 / \

\c/ / \

CH3 N-N CHj

This is then the reaction measured by nitrogen evolution and is essentially quantitative.

The resulting radicals may either recombine or diffuse out into the solu- tion. As has been pointed out by Flory,6 any loss of radicals by pair re- combination (the so-called “cage effect”) must occur within perhaps 10-9 sec., since after that time a pair of radicals will have, on the average, sepa- rated so far that rediffusion back together is highly improbable.

Reaction with DPPH, presumably: CH3 CN CH3 CN

+ *N-N& ‘c’ \ / / \ (2)

CH3 N--N+2 I

I picryl

/c’ CH3

picry1 is a subsequent reaction, and, if we take 1010 l./mole sec. as a maximum rate constant for a bimolecular reaction in solution (about the rate of diffusion), with &I DPPH will occur, on the average, after not less than 10-7 sec. In other words, DPPH will count only those radicals which have es- caped from the initial cage (in fact, as Flory has pointed out,6 reaction of one of a pair of radicals with any other species in the system except its part- ner before they separate is kinetically unlikely). Accordingly, the differ- ence in the rates measured by nitrogen evolution or DPPH fading yields a (maximum) value for the fraction of radicals lost by recombination with their initial partners and accordingly unavailable for polymerization initi- ation. If it is assumed that the rate constant for reaction of isobutyronitrile radicals with DPPH is comparable to their rate constant for recombination,

216 LETTERS TO THE EDITORS

as long as the DPPH concentration is large compared to the expected steady-state radical concentration in its absence (lo-’ molar in typical systems) it should be an efficient scavenger, a result in accord with its ob- served zero-order disappearance.

First, because DPPH (or any similar indicator) measures the rate of production of avail- able radicals, it should give a direct measure of the maximum rate of chain initiation by initiators such as AN. Since the isobutyronitrile radicals produced are structurally similar to typical polymer radicals, in a poly- merization reaction giving long chains this measured rate is probably the actual rate of chain initiation, although this is not necessarily true in other radical systems (for example, AN is apparently rather inefficient in attack- ing the (O=) C-H bond of aldehydes’).

Second, even though AN and similar initiators may decompose at the same rate in a variety of solvents, its initiator efficiency may vary from system to system. As an example, the DPPH method indicates that it is quite inefficient in carbon tetrachloride (crosses and dashed line in Fig. 1). Accordingly, an initiator’s “ availability” may have to be separately eval- uated in every solvent system, and changes in availability may account for complex kinetic orders in respect to monomer which have sometimes been observed in polymerizations. The significance of this variation is at pres- ent somewhat obscure, but it may be noted that the quantum efficiency of iodine atom production is also notably lower (0.19) in carbon tetrachloride than in heptane (0.41), indicating that iodine atoms as well undergo a larger amount of primary recombination in the former solvent.* A more ex- tensive comparison of quantum yields has just been reported by Lampe and Noyes$ and leads to a similar conclusion.

Third, similar arguments apply to other common initiators as well. Al- though accurate data on benzoyl peroxide are more difficult to obtain since induced decomposition must be taken into account, a recent summary of published datalo indicates that, in benzene, decomposition rates measured using DPPH5 are only 25-50% of those obtained by measuring the over-all rate of peroxide disappearance and correcting for induced decomposition.

Fourth, it is worth noting that Matheson, et a1.,l1 have concluded that AN is 100% efficient in initiating polymerization of vinyl acetate and some other monomers at 25-60’. However, their values for rates of AN de- composition are obtained by extrapolating measurements of 70-90 O , using Lewis and Matheson’s activation energy of 31.3 kcal./mole for the decom- position. Since this is significantly higher than those of other workers (Fig. 1 indicates the true value is about 29.5-30 kcal./mole), two largely compensating errors have been introduced, and their resulting rate con- stants probably need no correction.

Finally, Tobolsky and Russell12 have shown that DPPH fades rapidly in the presence of thermally polymerizing styrene, and suggest that this disappearance is due to reaction with diradicals which would otherwise cyclize or undergo mutual disproportionation.

A number of conclusions follow from this analysis.

LETTERS TO THE EDITORS 217

This analysis suggests that such cyclization would occur too rapidly for reaction of the diradicals with DPPH to be important, so the fading may be due to some other, as yet unknown, cause.

References

(1) F. M. Lewis and M. S . Matheson, J. Am. Chem. SOC., 71, 747 (1949). (2) C. G. Overberger, M. T. O'Shaughnessy, and H. Shalit, ibid., 71,2661 (1949). (3) L. M. Arnett, ibid., 74,2027 (1952). (4) J. W. Breitenbach and A. Schindler, Monatsh., 83, 724 (1952). (5) C. E. H. Bawn and S. F. Mellish, Trans. Faraday SOC., 47,1216 (1951). (6) P. J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca,

(7) E. F. P. Harris and W. A. Waters, J. Chem. Soc., 1952,3108. (8) R. Marshall and N. R. Davidson, J. Chem. Phys., 21,2086 (1953). (9) F. W. Lampe and R. M. Noyes, J. Am. Chem. Soc., 76,2140 (1954).

N. Y., 1953, pp. 120-1.

(10) A. V. Tobolsky and R. B. Mesrobian, Organic Peroxides, Interscience, New York-

(11) M. S. Matheson, E. E. Auer, E. B. Bevilacqua, and E. J. Hart, J. Am. Chem.

(12) K. E. Russell and A. V. Tobolsky, ibid., 75, 5052 (1953).

London, 1954, p. 18.

Soc., 71,2610 (1949).

CHEVES WALLING

Department of Chemistry Columbia University New York 27, New York

Received May 17, 1954

Viscosity of Dilute Polyelectrolyte Solutions at Low Flow Velocities

We have recently reported some experimental work' involving correla- tion of the viscous and ionic properties of a vinyltoluene-styrene copolymer sulfonic acid in aqueous hydrochloric acid solutions. It was emphasized at that time that our inability to correct the Ostwald-Fenske viscometer flow data for the influence of varying shear gradients might impose serious limitations on the quantitative significance of the results. In an attempt to clarify this issue, further experiments were carried out with a polysul- fonic acid of comparable degree of polymerization (DP = 800). This work involved measurement of dilute aqueous solution viscosities of the polyelectrolyte under conditions of very low shear gradient. Runs required 1000-6000 seconds of flow a t 25°C. at driving pressures in the range 0.3-3 g. cm.-2. The upper limit of pressure produced shear gradients in most of the polymer solutions which were nearly coincident with those encoun- tered previously in comparable measurements with Ostwald-Fenske vis- cometers. Results of the current experiments (see Fig. 1) clearly indicate no dependence of the observed viscosity coefficient on shear gradient with-