M.DOLE,M. FALLGATTER, AND K. KATSUURA
62
polystyrene a,nd other polymers as well. 9 surprising fea,ture is the sensitivit’y of the kinetic quantities in certain situations to the transfer mechanisms,
Acknowledgment. The authors thank Mrs. Maxine ?lockoff for her assistance in programming the equations for the computer.
The Mechanism of Decay of Vinyl Unsaturation during the Radiolysis of Marlex-50 Polyethylerre
by Malcolm Dole, M. B. Fallgatter, and K. Katsuura Dejvartment of Chemistry and Materink Research Center, Yorthwest~rnUniversity, Eoanstoii. Illirioie (Received April 6 , 1966)
60901
The vinyl group decay during the y-ray jrmdfntion of Marlex-50 polyethylene has been rcirivestigated by studying the distribution of vinyl unsaturation bctween sol and gel. Equations liavc been derived for the theorelicdly expected distribution. I t is shown that the initial number-average molcculnr w i g h t of the molecules incorporated into the first bit of gel to br forined should be equal to t ~ i initial r over-all weight-average molecular weight. ’The expeIinients1 results are in good agreenent with iheory provided that the vinyl groups in the gel decayed at the same mte aq vinyl groups in the sol. This fact, as well as the results c,f ICitarnarii, Mandellrern, anti Fatou, rule out the end-linking mechanism of vinyl decay. Calculations indicate that the disappearance of unsaturation is too rapid to be explained on the basis of scavenging by thermal hydrogen atoms, and it is concluded that vinyl decay is mainly the result of ion-molecule clirnerization reactions.
I. Introduction h s reported 1Jy Dole, ?tIilner, and Williams,’ foliowing earlier work of Miller, Lawton, and Balwit,2 the vinyl groups initially present in Marlex-50 polyethylenc to the extent of about 0.9 X mole g.--’ rapidly decay at room temperature during y-ray irradiation with the very high (i value of 9.6 groups/lOO e.v. at zero dose. A possible explanation is that the vinyl group? disappear by reaction with atomic hydrogen. Many people, hut especially H a r d ~ i c k ,].lave ~ shown that 5ubstances f hat contain unsaturation, such as hexene-1, scavenge atomic hydrogen. Charlesby, Gould, and Ledburyl hswe adopted this point of view in explaining the greater limiting yield of trans-vinylene groups a t high doses in a-ray-irradiated polyethyleiie as compared to -pray-irradiated polyethylene. The theory The Journal of Physical Chemistry
advanced by these authors is that during y-ray irradiation the linear energy transfer (LET) is suEciently low to allow “hot” hydrogen atoms produced in the track or spurr to diffuse out to become thermalized and to react with unsaturated groups before the hydrogen atoms recombine. With an LET 400 times greater in the a-ray irradiation, the primary concentration of hydrogen atoms in the spurs would be greater, and Inore recombination would occur. Charlesby, (1) 11. Dole, I). C. hXilner, and T. 80, 1580 (1958).
F. Williams, J. Am. Chem. SOC.,
(2) A. A. Miller, E. S. Lawrou, and J. S. Balwit, J . Phys. Chem., 60, 509 (1956:. (3) T. J. Hardwick, {bid., 64, 1623 (1960). (4) A. Charlesby, A. R. Gould, and K. J. Ledbury. Proc. Roy. SOC.
(Londou), AZ77, 348 (1964).
DECAYOF VINYLUNSATURATION DURING RADIOLYSIS OF POLYETHYLENE
et al., also observed that the first-order rate constant for vinyl decay decreased approximately by the same ratio as the constant for trans-vinylene decay in passing from y to CY irradiation. Another possibility is that vinyl decay occurs after activation of the vinyl group, either through charge transfer to produce polymer as suggested by Collinson, Dainton, and Walker5 and by Chang, Yang, and Wagner,6 mho studied low molecular weight 1-olefins, or through the transfer of excitation energy with the formation of end links as suggested by Dole, Milner, and Williams. Other possibilities which may be imagined are that the vinyl group disappears by freeradical polymerization processes or by isomerization to %olefins or by an internal cyclization process as recently suggested by Seam7 It is the purpose of this paper to consider these various possibilities in the light of new experimental data given below and new calculations. The elucidation of reaction mechanisms in high polymers is helped by comparison with low molecular weight analogs, by studying the effect of concentration, change of phase, and temperature on the reaction rate constants, by deriving equations for the expected changes in weight- and number-average molecular weights and comparing the predictions with experimental observations, by observing the effect of additives on the G values of the products formed, and by measuring the distribution of unsaturation between the sol and gel phases for radiation doses beyond the gel point. One offshoot of the v-ork described below is the formulation of a new rule regarding the initial number-average molecular weight of the first polymer molecules to be incorporated into a gel phase.
11. Experimental Section The materials used, radiation source and cells, and infrared techniques have already been described by Fallgatter and Dole.* The sol-gel distribution of the unsaturation in the films was determined by irradiating the films to doses where the total vinyl concentration fell to about 26 and 15% of its initial value. The soluble component amounting to about 50 and 75% was then extracted with boiling toluene containing O.lyo of an antioxidant,. This treatment left the in weak condition’ so that the infrared estimates of the vinyl and vinylene group concentrations were more difficult and less reliable than those of the unextracted films. The thickness of the extracted films was calculated from the area and after the latter were determined by the flotation method. The gel estimates and vinyl and
63
vinylene group concentrations as calculated from the infrared data are collected in Table I.
Table I : Sol-Gel Distribution of Unsaturation in Marlex-50 Polyethylene Dose, e.v. g.-I
x
10-20
[VU,
Ivll,,
mole g.-1 104
mole g.-’ x 104
% gel
% unsaturation retained in gel
0.029 0.314 0.439 0.957 1.003
0.268 0.423 0.960 1.061
0 51 77 91 90
0 44 74 92 95
,Vinylene
x
r
0 7.6 16.5 47.3 70.5
unsaturation-
% unVinyl unsaturation
0 7.6 16.5
0.86 0.224 0.13
1.00 0.265 0.154
0.052 0.03
saturation retained % gel in gel
0.062 0,036
0 51 77
0 12 18
The effect of recrystallization on the rate of vinyl decay was determined by irradiating the films to a dose of about 4.5 X lozoe.v. g.-I, at which point the vinyl concentration had fallen to about 50% of its initial value; see Figure 1. The film was then heated above the melting point and recooled to room temperature. -4s shown by Dole, Stolki, and Williams19this treatment nearly doubled the amorphous content due to inhibition of crystallization by the cross links produced by the irradiation. The latter effectwas also previously demonstrated by Woodward, et ~ 1 . ~ 0 To study the effect of sorbed benzene on the radiation chemistry of polyethylene the film in the irradiation cell held at 38” (the temperature of the subsequent irradiation) was saturated with benzene vapor kept in a side arm a t 36”. Before the saturation, the whole system was evacuated several times with the benzene a t liquid nitrogen temperature with intermittent thawing of the benzene. During the irradiation, the liquid benzene in
( 5 ) E. Collbson, F. S. Dainton, and D. C. Walker, TTWL~. Fardau Soc., 57, 1732 (1961).
(6) P. C. Chang, N. C. Yang, and C. D. Wagner, J. Am. Chem,. &c., 81,2060 (1959). (7) mi. C. Sears, J. Polymer sci., A2, 2455 (1964). ( 8 ) M. B.Fallgatter and M. Dole, J . Phys. Chem., 68, 1988 (1964). (9) M. Dole, T. J. Stolki, and T. F. Williams, J . Po~t,v” 48, 61 (1961). (10) A. E. Woodward, C. W. Deeley, D. E. Kline, and J. A. Sauer, ibid., 26, 383 (1957).
Volume 70, Number 1 January 1966
M. DOLE,M. FALLGATTER, AND K. KATSUURA
64
I.o
O O i \
I
0.9
I
l
l
2(b)
[VI NYLE NE]
3.8
3.7 0.6
3.5
3.4
3.0-
-
I
I
I
I
IO
3.3
3.2
I
I
I
20
30
40
DOSE ( e v g - ' ) x Figure 2. (a) First-order plot of vinyl decay as a function of dose in 61ms saturated with benzene vapor (open circles) and without benzene (solid line and solid circles). (b) Vinylene double-bond growth in f i k saturated with benzene vapor (open circles) and without benzene (solid line and solid circles).
3.15
0
4
8
12
16
20
24
DOSE (ev g-'1 x Figure 1. First-order plot of vinyl group decay in the irradiation of Rlarlex-50 polyethylene: upper curve, polymer maintained a t ambient temperature; lower curve, after melting and recooling to ambient temperature; dotted line, drop in vinyl group concentration on melting and recooling.
the side arm was maintained at about 36", but outside the zone of intense irradiation. Considering the low hydrogen yield during the irradiation of benzene, any molecular hydrogen coming from the benzene was cdculated to be negligible. It was found that the film absorbed about 8.5% of its weight of benzene vapor, but in the G-value calculations the dose received by the film was calculated on the basis of its dry weight. Thus, the energy absorbed by the benzene was neglected except that the small yieId of hydrogen from the benzene dissolved in the polymer was subtracted from the total hydrogen yield, assuming that the polyethylene had no effect on the benzene. This was a small correction, 0.05 from a total G(H2) of 2.45 leaving a net G(H2) of 2.40 molecules of hydrogen evolved from the polyethylene/lOO e.v. of energy absorbed by the polyThe Journal of Phy8kal Chemistry
Figure 3. Vinyl group concentration in the gel fraction of irradiated polyethylene: dotted line, average vinyl group decay in the whole polymer as a function of the gel fraction beginning at the gel point; solid line with open circles, calculated vinyl group concentration in the gel fraction assuming no vinyl decay; solid line with closed circles, calculated vinyl group concentration in the gel fraction assuming relative vinyl decay in gel fraction to be equal to that of the whole polymer; squares, experimental.estimates.
ethylene. The data of the benzene experiments are plotted in Figure 2 while Figure 3 illustrates observed and calculated relative vinyl group concentrations in the gel as a function of the gel fraction. In some of the theoretical treatment given below, the weight- to number-average molecular weight ratio,
65
DECAY OF VINYLUNSATURATION DURING RADIOLYSIS OF POLYETHYLENE
12.7, is an important parameter of the theory. This was calculated from the weight- and number-average molecular weights given to us by the polyethylene manufacturer. We also assumed one vinyl group per initial molecule. Using this assumption and our infrared estimate8 of the initial vinyl group concentration (Table I), the number-average molecular weight can be calculated to be 11,620 as compared to the manufacturer's estimate of 12,300.
111. Discussion A. The Hydrogen Atom Scavenging Theory. We consider first the possibility that the vinyl group decay could have been the result of reaction with thermal hydrogen atoms, in other words, that the vinyl groups acted as hydrogen atom scavengers. IlIolecular hydrogen yields would be reduced by such scavenger action, so we ask first, for comparison purposes, what should be the hydrogen G value in a semicrystalline polyethylene containing no doublebond scavengers. The theoretical yield can be estimated by extrapolation from lower molecular weight n-paraffins. €Iardwickll found about 6.0 for liquid n-heptane, n-octane, and n-nonane at 23". This is also approximately the value for liquid cyclohexane and the value for liquid Marlex-50 polyethylene at 142". Unfortunately. there do not seem to be any good G(H2) values for solid n-paraffinic hydrocarbons extrapolated to zero dose. In the case of solid n-octacosane at a dose of 56.5 Mrads the average G(H2) value as calculated by Chapiro12 from the data of Miller, Lawton, and Balwit2 was 3.8, exactly equal to that of Marlex-50 polyethylene (hereafter referred to as PE). However, Miller, Lawton, and Balwit in the same work obtained 4.7 for linear polymethylene and 5.0 for a low-density polyethylene. It is hard to reconcile these numbers, but in any event our G(H2) of PE equal to 3.8 is close to these values. In the presence of vinyl unsaturation in low molecular weight liquid olefins such as 1-hexene, 1-octene, and n-hexadecene-1, G(H2) is 0.8, 0.6, and 1.4, respect i ~ e l y . ~Thus, ,~ the presence of vinyl unsaturation markedly reduces G(H2). For first-order vinyl decay, the first-order vinyl decay constant calculated from G( -Vi)/lOONn [vi], where N A is Avogadro's number and [Vi] the vinyl group concentration in moles per for l-hexeneJ6 0.12 X 10-21 gram, is 0.022 X for n-hexadecene-1,' and 1.61 X g. (e.v.)-I for PE,' all at 25". Hence, it appears that the vinyl decay constant is much greater in PE than in 1-hexene or in n-hexadecene-1, despite the higher G(H2). Actually, the G(--Vi) values of these three different investigations are all equal within a factor of about 2,
despite the large differences in G(H2). In other words, if all of the vinyl decay were due to scavenging by H atoms, G(H2) for PE would be expected to be nearly as low as it is in 1-hexene and n-hexadecene-1. If the H atoms added to the double bonds to produce a vinyl-type polymerization, the vinyl decay (polymerization) per unit dose should be an inverse function of the square root of the radiation intensity, but this is not the case. In this work no change in kl, the vinyl decay constant, could be detected for a 10-fold change in the y-ray intensity. Collinson, Dainton, and Walker6found none for n-hexadecene-1, nor did Chang, Yang, and Wagner.6 Dainton, et al., found that it was impossible to polymerize n-hexadecene-1 by freeradical initiators; Chang, Yang, and Wagner also rejected a free-radical dimerization mechanism because the major portion of the dimers produced contained only one double bond, whereas in the free-radical dimerization of allylic free radicals, two double bonds should have been formed. If a free-radical dimerization occurred in PE to yield one double bond per dimer 4 y-ray by the sequence of reactions ( ~signifies irradiation) 4
C2H2,+iCH=CH2 -+H
+ CzH2,CH=CH2 (R, CHcCH2)
H
+ C,H~,+ICH=CHZ -% CZ+2H2(,+2)+l &+2
R,*CH=CH2
1
+ R,+z* + kt
R,-(,+I,CHC,Hz,CH=CHz Rz+2 then the vinyl decay would be zero order in the vinyl group concentration, contrary to observation. In their study of squalene Danon and Golub13 found that G(H2) was reduced from 3.4, the value in squalane to 0.58 in squalene, but they also rejected the hypothesis that the major decay of double bonds was by hydrogen atom scavenging because the loss of double bonds occurred only in the gel fraction, and the G value for double bond decay, 4.6, was too great to explain by H atom scavenging. On a quantitative basis the production of thermal hydrogen atoms is insufficient to account for the vinyl decay. Letting G(Ht) represent the G value for thermal hydrogen atoms G(HJ is estimated to be in the range (11) T.J. Hardwick, J . Phya. Chem., 65, 101 (1961). (12) A. Chapiro, "Radiation Chemistry of Polymeric Systems,'! Interscience Publishers, Inc., New York, N. Y., 1962,p. 75. (13) J. Danon and M. A. Golub, can. J . Chem., 42, 1677 (1964).
Volume 70, Number 1
January 1966
66
3.16 (liquid hexane) to 2.0 (liquid cyclohexane)14 or lower.15 If each vinyl group decayed by reaction with a thermal hydrogen atom, G(Ht) in P E would have to be the high value of 9.6 in the solid at 25" or 12.5 in the liquid at 142". In the work of Collinson, et aL,6 the discrepancy is even greater because their G(-Vi) values in pure n-hexadecene-1 varied from 16.4 in the liquid at 20" to 33.1 in the solid at 0". Williams and D 0 l e l ~ 3irradiated ~~ P E in which 5% of polybutadiene (PB) was mechanically mixed. At room temperature PB had no effect on G(H2) in polyethylene, but at 142" in the liquid state G(H2) was reduced from 6.0 to 4.6 by trans-PB and from 6.0 to 5.5 by 5% cis-PB. At the same time the vinylene double bonds in PB were decaying at the high initial G value of 50 for trans-PB and at a value almost as great for cis-PB. The very high rate of vinylene decay led Williams and Dole1' to postulate decay of vinylene groups by an intramolecular cyclization process similar to the suggestion of Danon and Golub13 for squalene. Thus, on the basis of investigations of others as well as on our own, the hydrogen atom scavenging theory cannot account quantitatively for the very high G values for double-bond decay. Another quantitative aspect of the insufficiency of the H atom scavenging theory for vinyl decay is that the evolution of hydrogen remains constant despite the initial rapid drop in vinyl concentration; see Figure 1. In previous work in this laboratory using a sensitive Pirani pressure gauge1 it was found that the evolution of hydrogen was linear from the beginning of the irradiation and that, if the hydrogen was intermittently pumped off so as to prevent the hydrogen from accumulating in the radiation cell, G(H2) remained constant to high doses.I8 If vinyl groups decayed by reacting with thermal H atoms, the hydrogen evolution might have been expected to increase as [Vi] decreased. It is true that the concentration of vinylene double bonds, [VI], increased with irradiac tion but the total unsaturation fell to 0.58 of its initial value before beginning to increase. Although the rapid vinyl decay which is followed also by vinylene decay after the irradiation has produced these groups, cannot be explained quantitatively by reaction with thermal hydrogen atoms, data of Williams and Dolei7 on polyethylene slabs held tightly between aluminum plates showed that molecular hydrogen probably back reacted during the irradiation to accelerate the vinyl decay. We ask ourselves then: why do not vinyl groups completely scavenge the thermal hydrogen atoms? From the deuteriumhydrogen exchange data of ~ r a c c o and Dole" it could be deduced that the thermal hydrogen atoms The Journal of Physical Chemistry
M. DOLE,M. FALLGATTER, AND K. KATSUTJRA
could not diffuse very far in PE before reacting to abstract hydrogen atoms from the CH2 groups. In P E the ratio [CH2]/[Vi] is about 700; hence, the probability of a thermal H atom colliding with a methylene group is about 350-fold greater than its probability of collision with a vinyl double bond. Darwent and Roberts,20as well as Back,21give estimates of the ratio of hydrogen atom addition to propylene at room temperature in the gas phase to that of hydrogen atom abstraction. Although their results do not agree very well, 0.19 as compared to 0.048, taking Back's result, we can multiply 350 by 0.048 and obtain 26 as the relative rate of H atom abstraction to H atom addition to vinyl groups in polyethylene. Because of the difference in phases, this result must be only a rough estimate; nevertheless, it indicates one order of magnitude greater probability of H atom abstraction than H atom addition. Even at liquid nitrogen temperature the reactivity of H atoms is so great that their presence, subsequent to the irradiation, has never been detected by e.s.r. measurements, despite the considerable production of molecular hydrogen which is frozen in the lattice. At liquid nitrogen temperature G(H2) is probably about 3.1,22 yet the vinyl decay has been almost completely suppressed.l Thus, once again we see no correlation between vinyl decay and hydrogen yield. As mentioned above, benzene sorbed by the P E lowered G(H2)from 3.8 to 2.40. The PB experiments at 142" also demonstrated a lowering of G(H2) by the double bonds present,ls and this is in agreement with the work of many other people. Some of the reduction of G(H2) by the double bonds may be due to H atom scavenging; however, there has yet been no definite proof of this in PE. In the well-known experiments on mixtures of cyclohexane and benzene the marked reduction of G(H2)by small concentrations (1 to 3%) of benzene is thought by Toma and Hamill15 to be partly due to positive charge exchange as well (14) C. E. mots, Y . Raef, and R. H. Johnsen, J . Phys. Chem., 68, 2040 (1964). (15) S. 2. Toma and W. H. H a d , J . Am. Chem. SOC.,86, 1478 (1964). (16) M. Dole and T. F. Williams, Discussions Faraday SOC.,27, 74 (1959). (17) T. F. Williams and M. Dole, J . Am. Chem. Soe., 81, 2919 (1959). (18) F. Cracco, A. J. Arvia, and M. Dole, J . Chem. Phys., 37, 2449 (1962). (19) F. Cracco and M. Dole, J . Phys. Chem., 66, 193 (1962). (20) B. de B. Darwent and R. Roberts, Discussions Faraday SOC., 14. 65 (1953). (2;) R. A. Back, Can. J . Chem., 37, 1834 (1959). (22) See ref. 12, p. 408.
DECAY OF VINYL UNSATURATION DURING RADIOLYSIS OF POLYETHYLENE
as to H atom scavenging. Dyne, Smith, and Stonez3 state, “It is our opinion that the larger part of the interaction is nonchemical.” Thus, the reduction of G(H2) by benzene or by P B can be explained by mechanisms other than thermal H atom scavenging. The data of Figure 2 demonstrate that the benzene dissolved in the polyethylene had no measurable effect on the vinylene double bond yield but that the vinyl decay was reduced somewhat. The G value for cross linking8 was also reduced. Without further studies the benzene experiments cannot be completely understood, but, if the reduction in G(H2) by the benzene was due to complete scavenging of the thermal hydrogen atoms, then the vinylene yield should have increased and the vinyl decay should have been brought to zero if double-bond decay occurred solely by reaction with thermal hydrogen atoms. This is further evidence of the lack of correlation between hydrogen yields in polyethylene and double-bond decay. B. The End-Linking Theory. Dole, Milner, and Williams1 suggested that vinyl groups decayed by end linking, i t ? . , by a direct addition of the vinyl end to the saturated paraffinic chain after activation of the vinyl group by the radiation to an electronically excited state. If this were true, one might expect to find a lower concentration of the vinyl groups in the gel fraction of irradiated polyethylene than in the sol fraction because, as end linking occurs, the molecular weight increases and the largest molecules have the greatest probability of being cross linked. To test this possibility -the vinyl concentration was determined in the whole polymer and then in the residue (gel) after extraction of the soluble component as described above. The results are given in Table I along with the sol-gel distribution of vinylene groups where [Vila and [Vi] represent the vinyl group concentration in the whole polymer a t zero dose and dose r, respectively, and [Vi], represents the vinyl concentration in the gel as measured after extraction of the soluble component. [Vl] and [Vl], represent the vinylene group concentration in the whole polymer and in the gel, respectively. At first sight, the low concentration of vinyl groups in the gel seems to bear out the prediction of the endlinking theory. However, assuming one vinyl group per molecule, the concentration of vinyl unsaturation in the gel per gram would be expected to be less than in the sol because the large molecules preferentially cross link as mentioned above. At the gel point, if no chain scissions occur, the number-average molecular weight of the initial molecules that have become part of the gel should be equal to the initial over-all weightaverage molecular weight. The validity of this last
67
statement can be seen intuitively; it also follows from eq. 8 given below. I n the case of Marlex-50 polyethylene used in this work, the weight-average molecular weight was 1.56 X lo5. The reciprocal of this number is 0.064 X mole g.-l which should be the concentration of vinyl groups in the first bit of gel that forms if no vinyl groups decayed a t all. However, a t the gel point of this work, the dose was 1.81 X lozo e.v. g.-l, a t which dose the over-all vinyl concentration had fallen to 0.75 of its initial value. If the vinyl groups in the gel decayed also to this extent without increasing the molecular weight in so doing, then the vinyl concentration in the gel should have been 0.048 X mole g.-’. We consider below the effect of changes in molecular weight. We do not have any values for the vinyl concentration in the first bit of gel to be formed, but we can calculate the expected vinyl concentration in the gel for the 51 and 77% gel experiments in the following way. CharlesbyZ4has shown that the sol fraction, s, can be expressed by the equation (assuming a constant G value of cross linking with dose and no chain scissions) U
U
and the fraction, f, of the initial molecules remaining in the sol is expressed by the equation U
U
where u is the number of monomer unit,s per molecule, q is the fraction of monomer units cross linked, and g is the gel fraction. If we adopt an initial distribution of the generalized Poisson type as Inokutiz5has done, namely
where uois the initial number-average degree of polymerization and /3 expresses the broadness of the molecular weight distribution through the equation
--
MW.0 a r
M n,O
-I+:
1 P
(4)
where M,,o and Mn,o are the initial weight- and numberaverage molecular weights, respectively, then replacing the summations in eq. 1 and 2 by integration over u it follows that (23) P. J. Dyne, D. R. Smith, and J. A. Stone, Ann. Rev. Phys. Chem., 14, 324 (1963). (24) A. Charlesby, “Atomic Radiation and Polymers,” Pergamon Press Inc., New York, N. Y.,1960,p. 636. (26) M.Inokuti, J . Chem. Phys., 38, 2999 (1963).
Volum 70,Number 1
January 1966
M. DOLE,M. FALLGATTER, AND K. KATSUURA
68
P
-
-s = - - -
f
Mn,o
P
+rg
(5)
where M , ,s is the initial number-average molecular weight of molecules left in the sol at any dose and y is equal to uoq. Now from Inokuti's eq. 12 it can be shown that in case of no chain scissions -8-1
s = (1
+$)
Introducing eq. 6 into eq. 5 1M n,O
(7)
From material balance eq. 7 can be converted to
where Mn,, is the initial number-average molecular weight of molecules incorporated into the gel at any dose. C h a r I e s b ~had ~ ~ previously shown that in the case of an initially random molecular weight distribution (P = 1)
Mnfg - - - 1 + &.1/1 Mn,o
(9)
in agreement with eq. 8. Inasmuch as Mn,o/Mn,gequals [Vi],/ [vi], assuming no decay of vinyl groups during the irradiation, it is possible to calculate the latter ratio from eq. 8. This was done taking /3 to be 0.085, the value for the Marlex50 polyethylene used in this research. The results of the calculation at several G values are shown in Figure 3 (open circles). Note the rapid rise in this ratio as the gel fraction approaches unity, 75% of the rise of this theoretical curve occurring over the gel fraction range, 0.97 to 1.0. This is the result of the very broad distribution of molecular weights in the initial polymer, and the fact that it contained many molecules of low molecular weight which are incorporated into the gel structure only at the highest gel fractions. However, the vinyl groups of the whole polymer decayed according to the dotted line of Figure 3. If the vinyl groups in the gel decayed in the same ratio without changing significantly the weight-average molecular weight, then by multiplying [vi],/ [vi], as calculated from eq. 8 by the values of the dotted line, the line represented by the solid circles is obtained. These are the [vi],/[vi], ratios which the gel should exhibit provided that the vinyl groups in the gel deThe Journal of Physical Chentistw
cayed at the same average rate as the vinyl groups in the whole polymer. The experimental results are shown by the squares. These values are slightly higher than the calculated ones but are equal to them within the limits of error. Thus, there is no evidence that the vinyl group concentration in the polymer incorporated into the gel decayed at a greater relative rate than the average for the whole polymer, The exact comparison of the end-linking theory with experiment is also complicated by the fact that chain scission could lead to an increase in the vinyl concentration via the disproportionation reaction 2RCHzCHz. +R C H 4 H 2
+ RCH2CH3
(10) Sears' has recently shown on the basis of much heavier doses than those used in the early work of Dole, Milner, and Williams1 that the vinyl concentration in Marlex-50 polyethylene attains a limiting value of 0.094 times the initial concentration. I n this work our estimate was less than 0.056 X lom4mole g.-'. At a dose of 16.5 e.v. g.-l (Table I), vinyl production by chain scission should be, therefore, practically negligible. Tn the mathematical theory given above, chain scission was not taken into consideration. Another possibility is that end linking occurs intramolecularly, e.g. -CH2CH2CH2CH2CH=CH2
hw+
CHZ-CH2 -CH
/ \
CH2-CH2
\ CH2 /
(11)
as suggested recently by Sears' and Golub.26 If this were the case, vinyl decay would have no effect on the molecular weight, or on gel formation, and the reaction would be nearly impossible to detect. However, the high polymer yield observed by Collinson, Dainton, and Walker6 in the radiolysis of nhexadecene-1 shows that intramolecular end linking is not very important, at least at high vinyl group concentrations. Furthermore, Chang, Yang, and Wagners did not mention the production of any cyclohexane in their radiolysis of n-hexene-1. If vinyl decay occurred solely by intramolecular end linking, it would be difficult to understand why the reduction of crystallinity by melting and recrystallizing an irradiated film restored the first-order vinyl decay constant to its initial value (Figure 1). I n the end linking mechanism in a selected reaction the vinyl group of a molecule of degree of polymeri(26) M . Golub, J. Phys. Chem., 69, 2639 (1966).
DECAYOF VINYLUNSATURATION DURING RADIOLYSIS OF POLYETHYLENE
zation p will become end linked to a molecule of degree of polymerization 1 as schematically represented by
\
+-
+
P 1 P+1 The rate of change in the concentration of molecules of degree of polymerization p as a function of dose T is given by the equation
d d P ) - - k m ( p ) J m lm(1)dl dr 0
k p m ( p ) J m m(Z)dZ 0
+k
c Zm(Z)m(p - 1) dd (12)
in which m ( p ) is the number of moles of polymer molecules per gram each containing one vinyl group with degree of polymerization p, and k is the first-order reaction rate constant. The first term on the righthand side represents the decrease in m(p) due to the addition of molecules of degree of polymerization p to all other possible molecules; the second term represents the decrease in m(p) due to the attachment of the vinyl group of all other molecules to molecules of degree of polymerization p; and the third term represents the increase in the number of molecules of degree of polymerization p due to two smaller molecules end linking to form one of degree of polymerization p . Following the general mathematical methods of Saito* eq. 12 can be solved in terms of the zeroth, first, and second moments, fo, f i , and f2, to yield after normalizing the first moment to unity fo = fo,oe-k' fi
69
of three amorphous Marlex-50 fractionated samples having three different molecular weights is constant without correction for vinyl decay. According to the theory here the Mw,,ygproduct should have changed about 67% over the molecular weight range studied because of the different doses for the gel point for the three samples. Parenthetically, it can be noted that if the vinyl groups decayed by a second-order process to form a dimer, then a treatment similar to that given above yields the following equations for the changes in the weight- and number-average molecular weights as a function of dose at small conversions
where k2 is the second-order decay constant and ~0 is the initial number-average degree of polymerization. Inasmuch as P is very small for Marlex-50 polyethylene, of the order of 0.08, it is obvious from eq. 15 that the weight-average molecular weight would hardly increase on irradiation if the second-order mechanism held. C. Ion-Molecule Reaction Mechanisms. From Collinson, Dainton, and Walker's carbonium ion mechanism6 for vinyl group polymerization during radiolysis the following kinetic equation may be derived
= 1
where 4 is a function of the y r a y intensity, ki is the rate constant for formation of carbonium ions [ViH+] from the initial ion [vi+], k , is the propagation rate M , = Mn,Oekr (13) constant for the reaction between the carbonium ions M , = M,.0e2kr (14) and vinyl groups, and A is equal to ,%,[e], the neutralization rate constant multiplied by the steady-state I n the first stage of the irradiation, the vinyl decay concentration of negative charges. A may also be is first order with the decay constant equal to 1.61 X shown to be equal to fkn4[Vi]]"'. Equation 18 was g. (e.v.)-l. With a dose to the gel point equal derived assuming that the neutralization rate constant to 1.8 X 1020 e.v. g.-l, the M,/M,,o ratio at the gel point is calculated from eq. 13 to be 1.34, and Mw/Mw,O, k n was the same for the carbonium and free-radical positive ions and that termination was by recombinafrom eq. 14, is calculated to be 1.79. These calculation of the monomeric allyl free radical with the polytions indicate that the dose to the gel point should meric free radical formed by neutralization of the be reduced by the inverse of 1.79 if end linking had carbonium ion of the growing chain. occurred. From data obtained in these laboratories, it is impossible to test this prediction, but from the (27) 0.Saito, J . Phys. Soc. Japun, 13, 198, 1461, 1466 (1968). recent results of Kitamaru, Mandelkern, and FatouZ8 (28) R. Kitamaru, L.Mandelltern, and J. Fatou, Polymer Letters, 2, it is evident that the product MW.0rgfor irradiation 611 (1964). From these we obtain the desired results
Volume 70,Number 1 January 1966
M. DOLE,M. FALLGATTER, AND K. KATSUURA
70
The carbonium ion mechanism yields a first-order vinyl decay rate, independent of the radiation intensity as observed, provided that ki[Vi] is greater than and k , [Vi J is less than A. Inasmuch as ki Wi]/A is equal to [ViH+]/[Vi+]and inasmuch as the carbonium ions are probably less reactive than the initial free-radical ions, Vi+, and therefore more abundant, [viH+]/ [vi+] would be greater than unity, and ki [vi] would be greater than A. Similarly, k i w i ] is probably greater than k , [vi] ; consequently, k, [vi] may be less than A. The increase in the weight- or number-average molecular weights expected on the basis of the Collinson, Dainton, and Walker scheme cannot be predicted precisely because of ignorance concerning the rate constants of the various reactions. However, if we make the simplifying assumptions that the mechanism is as stated above, namely, that the polymer free radical does not terminate by coupling with other polymer free radicals and that zeroth, first, and second moments of the intermediate reaction species are constant with time (steady-state approximation), then it is possible to derive the general equations
~M n - eKIcd lvn,o
(19)
and
where
and kl is the qb of eq. 18. The other symbols have been defined above. If k, is equal to zero, then the process reduces to a dimerization reaction, K is unity, and we see again that, for broad distributions, M,/Mw,o changes little with dose. If k,fo is not negligible with respect to kn[e], then the chain polymerization reaction can proceed, and the increase of M w with dose would depend on the number of steps in the chain reaction.
The JOUTVAA~ of Physical. Chembtry
N. Conclusions Any kinetic scheme to be selected a-sthe most nearly valid one must be consistent with the following experimental facts of vinyl decay-namely, decay rate first order in vinyl concentration, dose rate independent, and negligible effect of vinyl decay on dose to the gel point. The sequence of reactions which best fits these facts is an ion-molecule dimerization. For this case k, of eq. 18 would be equal to zero. However, if the dimer produced were a l-olefin polymer, then a similar kinetic treatment would yield the equation
where, as before, A equals (kn+ [Vi])"'. Equation 21 correctly predicts the first-order decay, independent of dose rate, provided that k d , the dimerization rate constant, multiplied by [Vi] is greater than kn[e]. If the reverse were true, then the neutralization of the vinyl ion would proceed faster than its dimerization, and little product would be formed. The dimerization mechanism also correctly predicts the negligible influence of this reaction on the weightaverage molecular weight for doses to the gel point and is thus in harmony with the data of Kitamaru, Mandelkern, and Fatou. 28 Charlesby, Could, and Ledbury4 discovered that the first-order vinyl decay constant was fivefold lower in the a-particle irradiations than in the y-ray experiments. This LET effect could be explained on the basis of the ion-molecule dimerization reaction mechanism if the IC, constant of eq. 21 is much greater in the CYparticle case. As A increases to become much larger than k d v i ] , d [Vi]/dt should approach zero. Acknowledgments. This research was supported by the U. S. Atomic Energy Commission and by the Advanced Research Projects Agency of the Department of Defense through the Northwestern University Materials Research Center. We are indebted to Professor W. W. Graessley and Dr. D. M. Bodily for several stimulating conversations.
