April, 1957
MECHANISM OF HIGHENERGY RADIATION EFFECTS IN POLYMERS
the W value for percentage mixtures of acetylene with benzene as a function of the percentage mixture. The curve appears to be a straight line which extrapolates to a value of 27.5plus or minus 0.3 e.v./ ip. for the IV value of benzene. Discussion I n all mixtures studied, except Ne-C2H2, it is found that eq. 2 accurately represents the W values for a-particles losing their entire energy in the gas mixture. Table I shows that appreciable errors would be made by assuming eq. 1. It is fur-
425
ther emphasized that the constant ((d’ appearing in eq. 2 has, to this date, no correlation with other physical constants of the gases comprising the mixture. Acknowledgments.-The authors wish Do express their thanks to Dr. Robert L. Platzman of Purdue University for his interest in and suggestion of these mixtures. We also wish to thank Dr. S. C. Lind and Dr. P. S. Rudolph of the Chemistry Division, Oak Ridge National Laboratory, for stimulating discussions on the subject.
MECHANISM OF HIGH ENERGY RADIATION EFFECTS I N POLYMERS BY ROBERTSIMHAAND LEOA. WALL Department of Chemical Engineering, New York University, New York, N . Y . Polymer Structure Section, National Bureau of Standards, Washington, D. C. Received September 18, 18.56
A series of elementary processes for cross-linking and scission reactions based on free radical intermediates in a homogeneous system are proposed. The kinetic evaluation under several approximations leads to expressions for the amounts of volatiles, unsaturation, cross-links and scissions as functions of time and intensity of radiation. The dependence of the rates on intensity is linear only in special cases. Isotopic substitution with deuterium should decrease the roduction of unsaturation. Hydrogen yield, on the other hand, can remain constant if certain conditions are fulfilled. !he observed isotopic differences in polystyrene may indicate an additional step for the capture of atoms. This is suggested to occur through the phenyl ring. Qualitative considerations that seem to favor free radical over ion intermediates in polymere are mentioned.
Introduction A number of investigations of the effects of atomic radiation on solid polymers have been reported during recent The most obvious changes are either predominant cross-linking or predominant scission. These are accompanied by an evolution of volatiles such as hydrogen and the formation of double bonds. The results are not only sensitive to the structure of the repeating unit but also depend on the method of sample preparation. Formulation of possible mechanisms and their kinetic evaluation are necessary for a quantitative description of the observed over-all effects and for a comprehension of the basic processes. Most efforts in this direction have dealt with gross over-all e f f e ~ t s . ~ JRecently a series of elementary mechanisms have been postulated and the ensuing kinetics developed by Okamoto and Isiham6 Some of . the steps to be proposed here are similar to theirs. Others, however, are significantly different and hence the over-all results are different. One may think of the development of a theory which gives, in terms of elementary processes, overall rates as well as information about changes in molecular weight and molecular weight distribution, similar to that which has been done7,* for free (1) K. H. Sun, Modern Plaatics, 83, 141 (1954). A. Wall, Conference on Effects of Radiation on Dielectria Materials, Naval Research Laboratory, Washington, D. C., Deo. 14-15, 1954, ONR Symposium Report ACR-2, page 139. (3) R. Simha and L. A. Wall, Chapter to appear in “Catalysis Series,” edited by P. H. Emmett. (4) A. Charlesby, Proc. Roy. Soc. (London), 232A, 60 (1954). (2) Leo
(5) A. R. Schultz, Nuclear Engineering and Science Congress, Dec. 12-16, 1955 (Cleveland, Ohio). (6) H. Okamoto and A. Isihara, J . Polymer Sei., 30, 115 (1956). (7) R. Simha. L. A. Wall and P. J. Blatz, dbid., 6 , 615 (1950).
radical thermal depolymerization. This is more difficult, particularly when simultaneous build-up and breakdown processes are to be considered. Moreover, basic knowledge of the steps is much more limited and hence we are bv necessity, here, more speculative. We shall therefore deal only with rates of production of double bonds, volatiles, unstable species such as H atoms, radical “sites” along a chain, cross-links and scissions. A number of fundamental assumptions will be made. First, ionic processes will be entirely disregarded and only certain selected free radical processes considered. Second, the kinetics considered will be that appropriate to a homogeneous system, such that spatial coordinates do not appear in the rate equations and diffusion rates do not enter the picture. Third, actual integrations are performed under steady-state conditions with respect to atomic species and all types of radicals. Since the processes take place in the solid state, this can be a questionable assumption as we know from free radical polymerization. It will nevertheless be used in this first attempt, to facilitate the mathematical operations. For the same reason several further simplifying approximations will appear in the treatment. Some of these can be justified on a chemical basis; others may well have to be revised. In any instance, where a term has been discarded, only the zero approximation with respect to this term has been pursued. However, we believe that the elementary processes proposed here will have to appear in any kinetic treatment of radiation effects on polymers, provided the first two assumptions are reasonable. (8) R. Simha and L. A. Wall, THISJOURNAL,56, 707 (1952).
ROBERT SIMHAAND LEOA. WALL
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Kinetics without Main Chain Scission For simplicity we consider first the cross-linking process in the prototype vinyl polymer, polymethylene or linear polyethylene. The following postulated reactions are expressed both chemically and symboljcall y.
---
-CH~CH~CH~H. + H a +
ki
k [HI
~~CH,CHCH~+ H.
z (kz[H]
+k
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On substitution into kixZ
+ (kzfH1 + k
d ) =~ ktyS
+ [ ( k s + k’s)/21S2
a quartic in S results. Manageable relations are obtained by inaking the following alternative approximations (kz[Hl k d ) 5~ 5 k1x2 (a), (a’)
+
P+S+Z
+
>
J
assuming that the diverse abstraction processes are all governed by the same factor J , and that the remaining constants are not affected. Now in (4a,k',s)'/z constant b,c), B , a constant.k,(ks (ksk2[H]). Hence a sharp reduction in B, occurs by a factor of the order of J 2 = 6-9. The rate dB/dt is less diminished, particularly if the &term is not negligible. We can express the dependence of y on J by means of the equation, following from (4a,b,c).
+
+
0
1.0
2.0
3.0
4.0
5.0
T.
Fig. 1.-Product concentrations as function of time in re, 1: duced variables; Equations 4a, b, c, for k z [ H ] / k ~ B= 1, hydrogen, y/B,; 2, cross-links, v/B,; 3, double bonds, BIB,. Dashed lines correspond to 1 and 3, for eq. 4a', b, with k,'S2/(2C2)= 1; curve 2 is unchanged in this special case.
Wall and Browng found that the gas evolution from y-irradiated polyethylene remains practically unchanged on complete deuteration of the polymer. kB(dy/dt) = Kl(kz[HI kBBm)/(kz[HI ~BB) I n polystyrene, on the other hand, deuteration reWhence, for k's
