P.Segiichi arid N. Tamura
40
Mechanism of IDecay of Alkyl Radicals in Irradiated Polyethylene on Exposure to Air as Studied by Electron Spin Resonance Tadao Seguchi" arid Naoyuki Tamura Takasaki Research Establishment, Japan Atomic Energy Research lnsfitute, Takasaki. Gunma-ken, Japan (ReceivedJune 30, 1972) Publication costs assisted by the Japan Atomic Energy Research lnstitute
The mechanism of decay of alkyl radicals in the crystalline region of polyethylene has been investigated. ecay of alkyl radicals is observed with various kinds of polyethylene by electron spin resonance. A dose relation is found between the decay rate and the sizes of crystallites. It is suggested that the alkyl radicals trapped in the crystalline region migrate to the surfaces of crystallites through hydrogen abstraction and decay by reaction with oxygen a t the surfaces. The kinetics of the radical decay is well explained by the diffusion theory assuming that the decay rate is controlled by the rate of radical migration in the crystallites. The diffusion constant of alkyl radicals is estimated to be 3.0 x 10-18 cm2/sec at 20". It is shown that the migration of alkyl radicals occur intermolecularly rather than intramolecularly and the activation energy of migration is 18 kcal/mol.
Introduction The free radicals produced in irradiated polyethylene have been investiga.ted by many workers using electron spin resonance (esr). The identification of free radicals has been established. The irradiation of polyethylene a t 7'7°K causes the formation of alkyl radicals, -CH26iH(X2-. When the irradiated sample is warmed up to room temperature or the sample is irradiated at room temperature, the allyl. radicals, -CHzCHCH=CH-, are observed. Thesat radicals are more stable than the alkyl radicals under vacuum but decay more rapidly in reactive gases such as oxygen. Various interpretations have so far been made ci~na:erniingthe kinetics of alkyl radical decay. It seems that di.scus;si,onhas been concentrated on whether the decay kinetics is first or second order. In the firstorder kinetics,l--*the decay is presumed to consist of more than two stages with different rate constants. Other workers have suggested that the decay curve of the radicals can be analyzed by the second-order kinetics,5-8 though the initial and the last stages of the actual decay curve do not coincide with the second-order kinetics. We have also investigated the decay of alkyl radicals under vacuum a t room temperature and suggested that part of the alkyl radicals convert to allyl radicals with first-order kinetics and the rest decay with second-order kinetics.9 However, the kinetics of radical decay under grafting reactions have not been clearly explained by either firstor second-order kinetics. Though the monomers cannot diffuse into the crystalline regions, they can react with the radicals which come out of the inside of crystallites by migration along or ;moss the chains. Since rate of reaction with monomtm at the surface of crystallite is much faster than the rate of radical migration,lO the decay rate should be controlled by the rate of migration. Waterman and Dole* have suggested that the alkyl radicals migrate by hydrogen transfer across the polymer chains. Shimada, Kashiwabara, and Sohmas have argued that alkyl radicals migrate along the polymer chains. Mere, we will repart, that the rate of alkyl radical decay in the atmosphere of reactive gases can be well explained by the diffushn of radicals in the crystallites of polyethylThe Journal of Physical Chemistry, Vol. 77, No. 1, 1973
ene and the diffusion constant is estimated from the experiment with various crystallite sizes of polyethylene. Experimental Section Samples used are high-density polyethylene (Sholex 6050) and radiation-polymerized polyethylene (Takathene). Sholex 6050 samples were prepared in various forms. Powder samples were prepared by boiling the pellet of polyethylene in 3% xylene solution and cooling to room temperature; the xylene was replaced by acetone and the resulting solution was allowed to dry at room temperature. Single crystal samples were prepared in 0.1% xylene solution at 75 and 85" for 48 hr. Annealed samples were prepared by heat treatments of single crystals at 110, 120, and 125" for 24 hr. The thickness of lammelae in single crystal samples was determined by measurement of the long period of X-ray small-angle scattering. Takathene was used in powder form as polymerized in gas phase of 400 kg/cm2; sample P3 was polymerized a t 30"; and sample P12 was polymerized at 70". The percentages of crystallinity are 83, 77, and 63% for the powder samples of Sholex 6050, Takathene P3, and Takathene P12, respectively. Samples were packed in esr quartz tubes of 10 mm 0.d. The samples were irradiated with electrons of 2 MeV from a resonant transformer type of electron accelerator in (1) E. J. Lawton, J. S. Balwit, and 8. S . Powell, J. Chem. Phys., 33, 395, 405 (1960). (2) M. Dole and F. Cracco, J. Phys. Chem,, 66, 193 (1962). (3) F. Cracco, A. J. Arvia, and M. Dole, J . Ctiem. Phys., 37, 2449 (1962). (4) D. C. Waterman and M. Dole, J. Phys. Chem., '14,1913 (1970). (5) M. G. Ormerod, Polymer, 4, 451 (1963). (6) A . Charlesby, D. Libby, and M. G. Ormerod, Proc. Roy. Soc., Ser. A, 262, 207 (1961). (7) S. Nara, S. Shimada, H. Kashiwabara, and J. Sohma, J. Polym. Sci., PartA-2, 6 , 1435 (1968). (8) S. Shimada, H. Kashiwabara, and J. Sohma, J. Polym. Sci.. Part A-2, 8, 1291 (1970). (9) T. Seguchi and N. Tamura, "Large Radiation Sources for Industrial Processes," IAEA, Vienna, 1969, p 353. (IO) Diffusion constant of oxygen in the amorphous region of polyethylcm2/sec, G. A. Bohm, J. Polym. Sci.. Part ene is D = 1.5 X lO-~.? A-2, 5, 639 (1967).
Mechanism- of Decay of Alkyl Radicals
41
1.O
h
-4 v
0.5
Figure 1.
spherical.
Models of the crystallite form: (a) plate-like and (b)
air a t room temperature up to the dosage of 3 Mrads. The dose rate was 0.1 IMrad/sec. Esr spectra were repeatedly recorded immediately after irradiation with Varian V-4502 Si-band spectrometer using 100-kHzfield modulation.
0.5 Figure 2.
2.0 X
1.o t ( x 109, sec.
1.5
Calculated curves of U ( t ) : (a) from eq 8 for D / R * = sec-I. sec-I, (b) from eq 6for D / L 2 = 1.0 X
Diffusion Equation A diffusion equation is expressed as
where D is the diffusion constant of radicals, and u(x,y,z,t) is the concentration of the radicals at point ( x , y , z ) and a time t In case (case I) the crystallite form of polyethylene i s plate-like as shown in Figure l a , eq 1 becomes
aurx,t ) / a t = D( a2u(x,t)lax2)
(2)
In case (case 11) the crystallite is spherical as shown in Figure l b , eq e is reduced to
auir, i!) _ I _ _
at
(3)
where r is radius oi" the sphere. In case I the direction of radical diffusion is perpendicular to the surface of plate ( x direction in cq 1,. The equation is solved with the following conditions: (a) the distribution of initial radicals is homogeneous in the crystalline regions, u(x,t) = uo a t t = 0; (b) the corzcentration of radicals at the surface of crystallite is always zero, u(x,t) = 0 at x = 0 and L, where L is the thickness of the crystallite plate. Equation 2 can be written by Fourier transformation as
where n = 2,b -. I (odd number) and An2 = n24D/L2. Concentration of the total radicals in the crystallite after time t is determined by integration of eq 4 from x = 0 to n = L as
where A is the area of the cross section. Substitution of eq 4 into eq 5 yields
(6) The relationship between U(t) and t can be calculated when A12 =: 71-2D/L2,isknown. Equation 6 can be also applied when the diriection of diffusion is isotropic if the area of crostr section is much larger than the thickness. In case 11, the form of crystallite is spherical and the
spectrum at 20" for polyethylene (Sholex 6050) immediately after irradiation in air. Broken line shows a component of peroxy radicals.
Figure 3. Esr
direction of diffusion is isotropic. Equation 3 is solved with the same conditions of plate-like crystallite, u(r,t) = uo at t = 0 and u(r,t ) = 0 a t r = R, where R is a distance from center to surface. The solution for eq 3 can be written as m
(7) where A,2 = m2+D/R2 and m = 1,2,3, . . . The concentration of the total radicals U ( t )in the crystallite after time t is determined by integration eq 7 from r = 0 to r = R as
Equation 8 can be calculated with computer when X12 = +D/R2 is given. Figure 2 shows the changes of U ( t )with time t in the case of DIR2 = 2 x 10-5 in eq 8 and D / L 2 = 10-5 in eq 6.
Results (1) Radical Species Trapped in Air at Room Temperature. When polyethylene is irradiated in air at room temperature, the esr spectrum obtained immediately after irradiation consists of a six-line component with a slight amount of an asymmetrical component as shown in Figure 3; the six-line spectrum is assigned to alkyl radicals and asymmetric line spectrum to peroxy radicals as is well known. Allyl radicals or dienyl radicals are not observed and are presumed to rapidly react with oxygen. From the experiment with the oriented mat of single crystals, it was found that the radicals trapped immediately after irradiation in air consist mainly of alkyl radicals trapped in crysThe Journal of Physical Chemi.stry, Vol. 77, No. 7 , 7973
T. Seguchi and N. Tamura
42
(a)
1.0
(a)
e 15
20 (b)
5 6 7 8 9 Time, hr. Figure 4. Decay of alkyl radicals in air at 20": (a) Sholex 6050 (O), observed; (--I-), calculated from eq 8 for Q / R 2 = 9.6 X sec-I; (---.----), calculated from eq 6 for D / L 2 = 4.6 X sec-I: (b) Takathene, (A),P3; ( O )P12 , observed. Solid lines are calculated from eq 8 : D / R z = 1.4 X l o n 5 sec-' and Q / R 2 = 2.5 x 1 0 . 4SeC-i. 1
2
4
3
talline regions; a t room temperature. (2) Decay of i l l k y l Radicals in Air. The decay of alkyl radicals with the powder samples of Sholex 6050 in air at 20" and that with Takathene P3 and P12 is shown in Figure 4. Here .the concentration of alkyl radicals is measured from the height; of outermost peaks of six-line spectrum, since the outerimost peaks do not overlap with the peaks due to radicals such as peroxy or allyl radicals and the shape of the outermost peaks does not change with the radical concentration. The initial concentrations of radicals are 9.8, 2.1jt, and 5.3 ( l o 1 7 spins/g) for Sholex 6050, Takathene E'3, and Takathene P12, respectively. The decay rate in air is much faster than that observed under vacuum; the half-life of the radicals is about 20 hr under vacuum and about 3 hr in air. The behavior of radical decay does not agree .with the formula, dcldt = Kcn ( n = 1,2, 1.5, etc.). Assuming that the d k y l radicals can migrate in the crystalline regions of polyethylene and rapidly react with oxygen a t the surface of crystallites, the rate of decay is controlled by the radical migration. Then the diffusion theory would be applied to the analysis of the decay curve in Figure 4. 'The migration of alkyl radicals in the crystallites suggests proton transfer either intramolecular
-
- c H ~ ~ M c ' H ~--CH&H~CHCH~-
(a)
or intermolecular -C>M2&ICH2-(X2CH2CW2-
-CH2CH2CH2--CH$HCH~-
(b)
Two assumptions are made, namely, that the distribution of alkyl radicals immediately after irradiation is homogeneous and that theire :we no radicals a t the surface of crysThe Journal of Physical Chemistry, Vol. 77,No. 1, 1973
5
10 15 20 Time, hr. Figure 5. Decay of alkyl radicals in air at 20" in polyethylene crystallized at 75" (a) and 85" ( b ) : (a),observed: (-), calculated from eq 8; (-------), calculated from eq 6.
tallites. The first assumption is reasonable because a first measurement immediately after irradiation (relative intensity 1.0 at time zero) was carried out within 10 min after irradiation, which is much shorter compared with the decay rate. The second assumption is based on the fact that molecules of oxygen can penetrate into amorphous region to reach the surface of crystallite and react with alkyl radicals. Although the actual form of crystallite is thought to be complex, two simplified forms can be treated: plate-like and spherical crystallites. Equation 6 i's applied to the case of plate-like crystallites and eq 8 to the case of spherical crystallites. Calculated decay curves thus obtained are shown in Figure 4. The solid line and the broken line are for the cases D/R2 = 9.6 x 10-6 sec-1 in eq 8 and D/L2 = 4.6 x 10-6 sec-1 in eq 6, respectively (Figure 4a). The upper line and the lower line in Figure 4b are for the cases D/R2 = 1.4 x 10-5 sec-1 and D/R2 = 2.5 X 10-5 see-1 in eq 8, respectively. These results show that the curve from eq 8 agrees well with the observed plats. When the single crystal samples that crystallized a t 75 and 85" are irradiated, the decays of alkyl radicals are similar to the powder samples as shown in Figure 5. The solid line and the broken line in Figure 5 are calculated using eq 8 and 6, respectively. The solid line shows good agreement with the observed points except the slight deviation at the initial stage. On the other hand, the broken line agrees with the observed points at the initial stage, but then greatly deviates. The decay curves obtained with annealed single crystals are shown in Figures 6a and 6b for the samples crystallized at 75 and 85", respectively; the solid line is calculated from eq 8 and the broken line is calculated from eq 6. It is well known that single crystal sample consists of lamellae crystals and the thickening of lamellae is induced by
Mechanism of Chcay of Alkyl Radicals
43
. 1.06
(a)
I
4 (.J
10
in,
15
20
25
LL
1
4 5 6 7 8 9 Time, hr. Figoure 7. Decay of alkyl radicals in polyethylene crystallized at 85 . Stored in air at 22 (0),30 (El), and 40' ( A j after irradiation. Solid line calculated from eq 8.
C.6
0.4
-9
0.2
. -10
2
3
t -
h
N
5
10
20
15 Time, hr.
25
v
Figure 6. Decay of alkyl radicals in air at 20" in polyethylene crystallized at 75 (a) and at 85" ( b ) , and annealed at 110 ( 0 ) , 120 (a), and 125' (Aj.Solid line calculated from eq 8. Broken line calculated irom ecl 6 for annealing temperature of 125".
annealing of 1 he sample. With thickening of lamellae the decay rate decreases, i.e., D/R2 in eq 8 or DIL2 in eq 6 decreases. The relationship between annealing temperature and the calculated values of DIR2 and DIL2 are presented in Table I; these values are derived from eq 8 and 6 best fitted with the observed points. Changes of lamellae thickness with annealing temperature, measured by X-ray small-angle scattering, are also shown in Table I. If the diffut,ion constants D does not change with samples, the values of DlR2 or DIL2 depend only on crystallite size. In such cases the values 2R and L can ke calculated using the data in Table I. These data are presented in Table I1 fcir the cases D = 4.0 X 10-18, 3.0 X 10-18, and 2.5 X lC-18 cm2,/sec. (3) Temperature Dependence of Decay Rate. The radical decay in air was investigated a t different temperatures above 20" with single crystal samples. As shown in Figure 7, it also obeys eq El and the decay rate depends on temperature. Since the size of crystallite does not change, the TABLE I: 0/R2and D / L 2 for Annealed Samples and the Long Period from &Ray Smiill-Angle Scattering Crystal. lization
Annealing
temp, "(:
temp, "C
75
110 120
I25 85 1'10
120 125
D/R2, sec-'
11.1 6.95 4.33 3.18 8.96 7.93 4.65 3.45
.k a
D/L2. sec-'
4.68 3.04 2.01 1.61 3.76 3.50 2.16 1.76
Long
period, A 113 123 189 265 123 128 171 221
C -
-11
~
-121
,
,
,
,
3.2
3.3
3.4
3.5
I / T x io3, OK-'. Figure 8. Plots of In D vs. 1I T derived from Figure 7.
DIR2 depends only on D. The relation between In D and 1/T is linear as shown in Figure 8, from the slope of which activation energy of radical diffusion i s calculated to be 17.9 and 17.5 kcallmol for the samples crystallized at 75 and 85", respectively. Discussion It was found that the decay of alkyl radicals in air is well explained by the diffusion of radicals in the crystalline regions. Although a part of alkyl radicals would decay by recombination or be converted to allyl radicals through the reaction with double bond in the crystalline region, the relative amount of radicals decaying through such processes is very small in air. Since the decay curve obtained with powder samples obeys eq % well, it is suggested that the presumed initial conditions to solve diffusion equations are reasonable. It should be noted that in the single crystal samples, the decay curve is explained well by using eq 8 rather than eq 6. Since the single crystals of polyethylene consist of lamellae-like crystals, which have thickness of about 100 A and width of a few microns, and the molecular chains are oriented perpendicular to the surface of lamellae, the decay curve should obey eq 6 assuming the alkyl radicals migrate only along the molecular chains or the lamellae consist of perfect crystals even if the migration is random. Therefore, the alkyl radicals must migrate intermolecularly rather than intramolecularly and the lamellae The Journal of Physical Chemistry, Vol. 77, No. 1, 7973
T. Seguchi and N. Tamura
44 TABLE II: Crystallite Sizes L ( W ) and 2 R ( A ) of Annealed Samples for Three Cases of ~ i f ~ u sConstant ~ ~ f l Da Crystallite size, Crystal- Annealing izatton 'e-mp, teomp, C C:
75 110 120 125
85 110 120 125
TABLE Ill: D / R 2 and 2R for Various Samples in the x cm2/sec
A
D I R ~ 10-5 , Sampie
b
9
L
93 :I5 140 157 I03 107 138 15"l
a (a) 4.0 X 1 0 - l 8 , ( b )
2R
3.0 X
120 152 182 224 134 142 186 214
L
80 100 122 137 89 94
118 131
2R
L
104 131 167 194 115 123 161 187
73 91 111 125 82
85 108 119
2R
'
2 ~ A,
Crystal size,aA
95
Sholex 6050
Takathene P3 Takathene PI 2
1.07 2.5 1.4
106 63 92
207 120 180
120 152 177 106 112 146 170
and (c) 2.5 X 10-18cmz/sec.
crystal must have many defects which behave like surfaces of crystals fcr the reaction with reactive gases such as oxygen. The form of crystallites can be adequately approximated by sphere rather than plate. The slight deviation of the calculated curve from the observed plots at the initial stage of the radical decay may be due to rough approximation of crystallite form. Supposedly the actual form of single crystals i s rectangular rather than spherical forms. The decay rate o€ the radicals in the annealed single crystals is slower than that observed in the original samples. Though the same results have been reported by Ornierodll and Takamatsu and Maibara,12 they have not given clear errplanation for such phenomena. As shown in Table 1, h 2 / x 2 =: D I P in eq 8 or X 2 / r 2 = D/L%in eq 6 decreases with thickening of lamellae. When the migration rate of alkyl radicals or the diffusion constant D does not change by the annealing of sample, X 2 / 4 should be proportional to 1/IP or l/U. Since R or especially L of annealed single crystals can be measured by X-ray smallangle scattering, wle ran estimate D.The values L and 2R are compared with lorig periods measured by X-ray smallangle scattering in Table I. It is found that the values of the long periods agree well with 2R. This result also supports the model of intermolecular migration of radicals in the crystalline "egionc; To fit these values of long periods with I,, diffusion ronstant D must greatly increase with annealing temperature, such phenomena are unlikely to occur Crystallite sizes of 'TakEthene are estimated, as shown in Table 111, assuming that the diffusion constant in Takalhene are the same as in Sholex 6050. The relative values of crystallite Eize derived by this method are in good agreement with the relative values obtained by X-ray diffraction.13 This, result supports the fact that the decay rate of alky1 radicals depends on the crystallite size of polyethylene The most probable value of diffusion constant i s estimated to be D = 3 x 10-18 cmZ/sec at 20" assuming 2R corresponds to long period. Since the decay rate a t a certain temperature depends only on diffusion constants, the linear relation between In D and 1/T is obtained as shown in Figure 8. The activa-
The Journal of Physcai Chemistry, Voi. 77, No. 7, 7973
sec --
C
a The value was measured from a width of the (110) peak of X-ray diffraction.'
tion energy of radical diffusion derived from Arrhenius plot is about 18 kcal/mol. This value is in good agreement with the value 17 kcal/mol obtained by Waterman and Dole4 and the value 18 kcal/mol obtained by Shimada, et aE.,8 although they obtained these values of activation energy using the first-order kinetics. The activation energy for radical migration would be divided into two components, that is, the energy a neighboring proton approaching the radical (Eph)and the energy the radical extracting a proton (Ech).In vapor-phase reactions of low molecular weight compounds the activation energy for alkyl radicals to extract protons is 12-13 kcal/mo1.14,15 Waterman and Dole have reported that the activation energy of alkyl radical decay of polyethylene in hydrogen gas is 13 kcal/moL4 In our experiment Eph becomes 5 kcal/mol, when Ech is taken to be 13kcal/mol. Although the diffusion constant I) of radicals is. presumably dependent upon the molecular motions in the crystallite region of polyethylene, the values of Eph thus obtained are much smaller than the activation energy of the molecular motions such as o( or /3 process to which nmr or dynamic mechanical studies refer.16.17 ~ c t ~ v a t i oenergies n of these processes are reported as 4 0 4 0 and 14-17 kcal/ mol16 for 01 and /3 processes, respectively. The value of Eph is rather near to the value of y process. Since the y process is assigned to the local molecular motions of noncrystalline regions of polyethylene it seems that no correlation exists between the radical migration and the molecular motions. However, the molecular motions of radical sites are supposed to differ with the motions of parent molecules, since the radical sites in the crystalline regions form a kind of defects. Molecular motion must have some role in the radical migration in the crystalline regions of polyethylene.
Acknowledgments. We wish to acknowledge Dr. Waichiro Kawakami for the calculation of diffusion equation using a computer. M . G . Ormerod, Phii. Mag., 111, 681 (1965). T. Takamatsu and M . Kaibara, Rep. ins?. Phys. Chem. Res., Tokyo, 42, 231 (1966). N. Tamura, N. Hayakawa, and T. Fujimura, Rep. Progr. Poiym. Phys. Jap., 13, 339 (1970). M. H. J. Wijnen and E. W. R. Steacie, J , Chem. Phys., 29, 205
(1952). G . H. Miller and E. W. R. Steacie, J . Amer. Chem. SOC..80, 6486
(1958). N. Saito, K. Okano, S. Iwayanagl, and T. Hideshirria. Advan. Solid State Phys.. 14, 462, 343 (1963) M. Takayanagi and T. Matsuo, J. Macrornoi. Sci., Phys., I,407
(1967).
