:, EFFECT OF IRRADIATION OF POLYMER MATERIALS

ON P H Y S I C O M E C H A N I C A L

UDC

678:541.6+539.5

PROPERTIES

A. N. Tynnyi and A. A. Velikovskii F i z i k o - K h i m i c h e s k a y a Mekhanika Materialov, Vol. 3, No. 5, pp. 602-618, 1967 Investigations of the effect of irradiation on physicomechanical properties of polymers are reviewed, and it is shown that studies of physicomechanical properties of irradiated specimens must be regarded as only the first stage of researches directed toward elucidating this problem. C o m p l e t e understanding of the effect of irradiation on the performance of materials of this type can be obtained only by studies of the effects of simultaneous action of irradiation and m e c h a n i c a l loads, especially studies of the l o n g - t i m e strength carried out with a view to determining the range of a p p l i c a t i o n of polymers under these conditions. It is shown also that in studies of this kind it is essential to take into account the effect of working m e d i a . In recent years there has appeared a large number of articles dealing with the effect of high-energy radiation on properties of polymer materials, especially on their relaxation characteristics, diffusion coefficients, e l e c t r i c a l conductivity, m e c h a n i c a l properties, etc. Substantial changes produced in these properties by irradiation are attributed to r a d i a t i v e - c h e m i c a l processes taking p l a c e in irradiated materials. Most of the reported studies of this problem [ 1 - 9 ] were concerned with materials which had been irradiated in the absence of applied stresses; their properties were investigated after irradiation, i . e . , the influence of irradiation was regarded as an after-effect. At the same time, the very first investigations [ 1 0 - 1 4 ] of polymers stressed while subjected to irradiation revealed substantial differences, especially between m e c h a n i c a l properties of specimens treated in this way and those irradiated in the absence of stress. It was established that simultaneous application of irradiation and m e c h a n i c a l loads leads to the onset of both irreversible r a d i a t i v e - c h e m i c a l reactions and reversible kinetic processes. And so, the acceleration of relaxation processes in polymers irradiated under stress was attributed [13] to an increase in the concentration of "hot" molecules whose energy is higher than the activation energy for relaxation, it being considered that a nonchemical mechanism of the a c c e l e r a t i o n of stress relaxation is operating. When polymer specimens are subjected to a simultaneous action of stress and u l t r a - v i o l e t radiation, in addition to the fracture which, in accordance with the Zhurkov fluctuation theory, proceeds at a definite rate, a process involving the destruction of c h e m i c a l bonds due to u l t r a - v i o l e t radiation also takes p l a c e at a different rate [10, 11]. Consequently, results obtained on specimens irradiated in an unstressed state must be regarded as only the first stage of studies of radiation-induced changes in m a t e r i a l properties. In this context, problems of simultaneous influence of stress and irradiation assume a considerable importance from both theoretical and practical points of view. In this article an attempt is made to summarize the a v a i l a b l e information on this problem. To facilitate understanding of the nature of the phenomena involved it was considered desirable to analyze the current views on radiativec h e m i c a l processes in irradiated polymers and their influence on physicomechanical properties of materials, to determine the effect of preliminary treatment of polymers on their resistance to irradiation and the effect of various irradiation parameters on m e c h a n i c a l properties of polymers, to describe the mechanism (physical and chemical) of the a c c e l e r a t i o n of kinetic processes during irradiation, and to discuss the problem of l o n g - t i m e strength of polymers simultaneously subjected to stress and irradiation. I.

R a d i a t i v e - C h e m i c a l Processes in Irradiated Polymers and Their Effect on Physicomechanical Properties

The action of h i g h - e n e r g y radiation on polymers consists m a i n l y in ionization and excitation, since the movement of a fast heavy charged p a r t i c l e or a fast electron in a substance leads to the appearance of relatively slower electrons whose energy, however, is higher than the ionization and excitation potential of atoms and molecules [5]. One of the results of the action of such electrons is the destruction of c h e m i c a l bonds and the appearance of polymer molecules which retain unpaired electrons of broken c h e m i c a l bonds.. Free radicals formed in this way trigger off c h e m i c a l reactiom leading to changes in the c h e m i c a l potential and physicomechanical properties of the m a t e r i a l . As a result of irradiation the principal polymer chains m a y b e c o m e destroyed (i. e . , splitting of polymer molecules into smaller fragments m a y occur) and cross-linked, the latter processes involving the joining of neighbor molecules by transverse bonds and formation of larger molecules [ 1 - 4 ] . The cross-linking reaction in its general form may be represented by the equation 2RCH2CH2R* ~ H 2 + RCH,CH 442

RCHRCH2R,

(1)

where the asterisk denotes an ionized or excited m o l e c u l e and R is an alkyl radical. The degradation process is represented by

(2)

RCaH6 R*-+ R.CHa + CH~ = CHR.

From the point of view of the character of reactions induced in p o l y m e r materials by irradiation, most of the polymers investigated belong to two groups [7]: those that b e c o m e cross-linked in vacuum (polyethylene, polypropylene, polystyrol, p01yamides, potysiloxane, phenolformaldehyde and aminoformaldehyde resins, e t c . ) and those that undergo degradation in vacuum (polyisobutylene, p o l y m e t h y l m e t h a c r y l a t e s , polytetrafluoroethylene, cellulose and its derivatives, e t c . ) . The variation in physicomechanical properties of polymers under the influence of irradiation depends on the ratio of rates of degradation and cross-linking processes, which, in the first instance, is determined by the c h e m i c a l structure of a given p o l y m e r and irradiation conditions (temperature, working m e d i u m , m e c h a n i c a l stresses, e t c . ) .

800

t

X

i

r

}s ,A

,

~

,

- - ~ - ' ~ -

40

80

}:' .~,

,..r

~

600

IOB1~

"-"

"~ qO0

,X

U

/

,

7 2 4 7O 20,~/I ?00 u~ 0 Radiation dose, reactor radiartion units

Fig. 1. Elasticity modulus of polyethylene plotted against r a d i a t i o n d o s e at 20 ~ C: 1) static tests; 2) dynamic tests at a frequency of I kc/s; a) dynamic tests at frequencies of a - 7 kc/s; 4, 8) curves constructed from a theoretical expression for a rubber-like state at q0 = 0.8 x 10 "9 and 0.35 x 10 -3 , respectively.

0

720

160

Radiation dose, Mrd Fig. 2. The UTS {curve 1) and elongation (curve 2) of polyethylene ND with M = = 21 000 plotted against radiation dose.

Among the cross-linking polymers, polyethylene has been studied most. This is one of the simple polymers, which becomes cross-linked under the influence of irradiation, so that r a d i a t i v e - c h e m i c a l phenomena taking p l a c e in it [8, 9] and changes in its physical, m e c h a n i c a l , and other properties are characteristic of other polymers which become cross-linked when subjected to irradiation, The radiation-induced cross-linking of polyethylene is manifested by changes in its m o l e c u l a r weight and solubility, swelling, reduction in the degree of crystallinity, and changes in the c h e m i c a l and m e c h a n i c a l properties. It is known that the tensile strength of solid polymers depends on the degree of polymerization P [18, 1~]. For the case of certain polymers whose m o l e c u l a r weight changes under the influence of irradiation, the following relation was e x p e r i m e n t a l l y established:

Consequently, the variation in the m o l e c u l a r weight under the influence of irradiation not only indicates whether the degradation or cross-linking process predominates, but m a y also be used as a qualitative characteristic of strength The m o l e c u l a r weight of cross-linking polymers increases with increasing absorbed radiation dose [ 1 - 4 , 18]. the case of polyethylene, this relation is described by 1/Mabs= IO-SGD

-1- 1 / M i n i t i a 1 ,

In

{4)

where G is the r a d i a t i v e - c h e m i c a l cross-linking efficiency and D denotes the absorbed dose (Mrd).

443

The extent of radiation-induced chemical changes in polymers is measured in terms of the quantity of the gas liberated [20]. According to [4], hydrogen evolution G(Hz) in the case of polyethylene iriad~ated at temperatures ranging from - 1 9 6 ~ 100~ is equal to about 3.1; it was found also that in the case 0fX-rays.the magnitude of G is independent of the absorbed dose (up to 350 Mrd). Mechanical properties of polyethylene depend on the size and number of crystallites and on the length of amorphous chains linking them. In the case of large radiation doses, the crystalline constituent of polyethylene may disappear even at room temperature [4, 5, !9, 21]. Some experimental data on the elastic properties, elongation, tensile strength, and creep streng.th: Of irradiated polyethylene is available. Figure 1 shows the dependence of the Young modulus (measured by both static, and dynamic methods) of polyethylene on the radiation dose [4]. In the small radiation dose range (up to four reactor radiation units) the elasticity modulus of polyethylene does not change very much. As the radiation dose is increased, the degree of crystallinity is reduced; the effect of this reduction on the elasticity modulus is larger than the effect of the simultaneous increase in the cross-linking strength. The elasticity modulus continues to decrease until a radiation dose 0f 10 reactor radiation units is reached, at which stage the crystallinity of polyethylene is almost completely destroyed; further increase in the radiation dose produces sharp increases in the elasticity modulus [4, 19]. This data is in good agreement with the results of a study [22] in which a vibration method was used to measure the young modulus of polyethylene subjected to ?,-radiation. The UTS of irradiated polyethylene increases (at room temperature) UP to radiation doses of about 10 Mrd (Fig. 2 ) , a f t e r which it slowly decreases. Elongation also initially increases with ipcreasing radiation dose and then sharply decreases [4, 6, 20, 22, 23]. A similar reduction in the elongation due to increased cross-linking density was observed in the case of many other cross-linking polymers [1, 2, 4, 6, 24-26]. The presence of transverse bonds in amorphous regions of polyethylene has a considerable'effect on its creep resistance. The creep strain E of polyethylene under a stress o is reduced under the influence of'irradiation [27] in accordance with the following expression [28]: E

--

~

e ~~[kl + k,, (1 - - e - g 9 + k3 tl,

(5)

where g is the radiation dose, t denotes irradiation time and k 1, k 2, k 3, and 3 are coefficients. !.

The above general picture of the variation in properties of polyethylene under the influence Of irradiation is typical for many cross-linking polymers (rubber, polystyrol, polyamide, etc.). i

Polymethylmethacrylate (PMMA) is a polymer of the degrading polymer group whose behavior under the influence of irradiation was most extensively studied. The degradation of PMMA under the influence of reactor irradiation was observed and described on several occasions [29-31]. The dependence of the molecular weight M v of PMMA on the radiation dose, which is reproduced graphically in Fig. 3, is described by

I/M~ =

38.5.10-6 (r + r0),

(6)

where } is the: radiation dose (in reactor radiation units) and r 0 denotes a correction coefficient depending on the initial molecular weight. The linear Character of the dependence of I / M v on r in a wide radiation dose interval shows that the number of broken links is proportionaI to the radiation dose and that these links are randomly distributed (Fig. 3). IdentiCal results were obtained by other workers [32]. Later studies [33] carried out with the aid of :a cobalt source led to the formulation of a similar relation:

I---- 1.16 ( 1 v

1 )for Mvo

1>10

andA'Ivo>2.10*.

Here I is the radiation dose in megaroentgens and My0 the initial molecular weight. The action of irradiation consists in the destruction of bonds in both principal and side chains, the degradation products remaining in the form of separate atoms and molecules [36]. A direct relationship was established in [34] between mechanical properties and molecular weight of PMMA (Fig. 4), while a study [35] of the degradation of supermolecular structures of PMMA under the influence of ]~-radiati0n revealed a sharp reduction in the strength of this material. Measurements of the UTS and elongation of PMMA irradiation at elevated temperatures with ?,-rays from a cobalt source were made in [$5]; however, the results of this work are of little significance because the test temperatures were above the softening point. Irradiating PMMA with y-quanta in doses smaller than 3 Mrd produces a certain increase in strength [37, 38], but specimens irradiated with doses of about 15 Mrd become very brittle; polaroscopic examination of these specimens revealed the presence of considerable stresses. Specimens of this kind crack spontaneously, sometimes several months after exposure to irradiation [36, 39].

444

Irradiation of PMMA at temperatures above 70* C with doses of up to 100 Mrd is accompanied by intense gas evolution [40, 41], no such effect being observed at lower temperatures [31].

$" 7#" [N I" ~.roel Ox_l

Neutron flux

I III' I I II

2 70 15

.,I I- I]I

"

7

I I I I11%1 e,~,[ !ii] Ill ~

I fU I I IJ

II1

S

I

0.1 0,2

~-

la5

[

i I111 I 11 0.03

S,?otsM 17

"7"-

. [ ii21N

0~07

;0 ~6

i i] i

a~

2.70s J'70* tO* Molecular weight

r + r0, reactor radiation units Fig. 3. Mean viscosimetrie molecular weight of PMMA plotted against radia9 tion dose

Fig. 4. Variation in the UTS (curve 1) and elongation (curve 2) of irradiated PMMA.

The general features of radiation,induced degradation of PMMA, i . e . , the reduction in the molecular weight, intense gas evolution, deterioration of mechanical properties with increasing radiation dose [42, 49], etc., are common to all members of the group' of polymers prone, to degradation [42, 44]. Similar extensive studies of the behavior of polymers were carried out at a later date on rubber, polystyrol, polypropylene and polyvinylchloride [46-49]. A great deal of attention was devoted to studies of the radiation resistance of polymer materials in a wide range of absorbed doses (up to 101~ rads) and radiation intensities, changes in the m e c h a n i c a l properties of these material s as a result of irradiation serving as a measure of their radiation resistance [6, 44, 45, 50.--55]. Studies of this kind are of a great practical value; however, their ultimate objective should be the determination o f the radiation resistance of polymers directly in a radiation field and, since We are concerned with the 9mechanical strength, they should include long-time strength tests because only data of this kind makes it possible to determine the range of application of a given material. In this context, studies of the effect of irradiation on the post-irradiation time and temperature dependence of ' the strength of polymers are of special interest. The first investigations of this kind [56, 57] were concerned with the effect of ~,-radiation on the time and temperature dependence of the strength of nitrocellulose (FT-30), oriented polystyrol (styroflex) and polycaprolactam. The tests, during which the molecular weight was measured, were carried out in a wide temperature interval (from - 1 9 6 " t o 140" C); the radiation dose ranged from 0 to 400 Mrd. In every case a linear relation 9 r(o) was obtained. Increasing the radiation dose shifted the straight line log r(o), without changing its slope, toward the lower stress range in accordance with relations U.--'f ~

.x =

A e -~

and z

=

zo e

kr

,

(7)

where r is time.to-rupture, and A, ce, u 0 and y denote constants determining the material strength, it was established that irradiation produces changes in the activation energy U 0 and structural coefficient ),. The anomalous variation of coefficient A [56] is attributed todegradation and cross,linking processes Characteristic of the materials tested; this view is supported by data on the variation in the molecular weight. The: question of the effect of ionizing radiations on the time and temperature dependence of the polymer strength remains practically open, very little research directed toward elucidating this problem having been done. When an answer to this question is eventually found, it will facilitate formulating an explanation of various aspects of fracture of polymers and developing methods of controlling properties of these materials, since irradiation can be used as a means of producing far-reaching structural changes in materials under consideration. Moreover, investigations of this problem will assist in estimating the contribution of radiation-induced irreversible changes to the long-time strength of polymers exposed to a direct influence of ionizing radiations. II. Effect of Preliminary Treatment of Polymer Materials on Their Radiation Resistance In the preceding chapter we discussed the general features of the influence of radiation on polymers without taking account of changes taking place in these materials as a result of intermediate mechanicochemical processes under the

445

influence of stress or as a result of m e c h a n i c a l processing. It is known that when polymer chains are forcibly displaced relative to each Other under the influence of applied stress, they lose their initial relative orientation; as a result the packing density is reduced and many intermolecular bonds are distorted so that there is a sharp increase in the free energy of the m a t e r i a l . This leads to a substantial increase in the a c t i v i t y and reactive power of polymers and facilitates their interaction with various reagents [ 5 8 - 6 t ] . An important part is played by internal stresses which m a y lead to polymer (e. g. PMMA) degradation e v e n in the a b sence of irradiation [4]. : One of the i m p q r t a n t f a c t o r s determining the radiation-sensitivity of poiymers i s t h e degree of preliminary straining in tension. It was established as early as in 1958 that oriented polyethylene films are more susceptible to radiation d a m a g e than nonofiented m a t e r i a l [62]. A study of the effect of preliminary tensile straining and y - i a d i a t i 0 n on the strength of uni- and b i - a x i a l l y oriented polyethylene specimens showed that both the UTS and Young modulus E monot o n i c a l l y increase with increasing degree of preliminary stretching [63]. Increasing the absorbed radiation dose above a certain level produces an increase in E and a reduction in UTS. This is evidently due to the f a c t that the molecular orientation produced 9 preliminary straining is destroyed during irradiation and transverse cross-links are formed, as a result of which UTS is reduced and E increased. At higher radiation doses the molecular orientation is c o m p l e t e l y destroyed. Similar studies were carried out o n polyethylenetetraphthalate [64]; they led to a concllasion that some crosslinking takes p l a c e in this case in the initial straining stages, but that degradation predominates in the high tensile strain range, leading to a reduction in the ductility of polymer fibers and to the formation of carboxyl groups. Investigations discussed above were concerned with crystalline polymers in the case of which the formation of oriented structures is accompanied by changes in the degree of crystallinity, which m a y have a Stibstantiai effect on the radiation resistance of a given m a t e r i a l . Promising in this respect are results of studies of amorphous Oriented polymers. It was established [38] that amorphous polymers (plasticized and nonplasticized PMMA and its copolymers) oriented by stretching and then irradiated have better physicomechanical properties: than in the initial state, t h e effect becoming more pronounced with increasing degree of orientation. Changes in the physicomechanical properties of oriented p o l y m e r s (.including partially c r o s s - l i n k e d ) t a k e p l a c e at larger radiation doses than in the case of nonoriented materials; in other words, degradation of polymers of this kind is inhibited by the formation of oriented structures. All the above discussed experimental data indicates that the behavior of polymers is to a Considerable extent determined by its technological history. III. Effects of Various Irradiation Parameters on Mechanical Properties of Polymers. 1. Radiation form and intensity. The influence of the form of radiation on the r a d i a t i o n - d a m a g e susceptibility of polymers was studied by many workers. Opinions on this subject are dividedl though the majority view is that r a d i a t i v e - c h e m i c a l effects in polymers do not depend on the kind of radiation (y-rays, X-rays, electron and neutron bombardment) but are determined m a i n l y by the c h e m i c a l structure of a given polymer and quantity of absorbed energy [40, 6 5 - 6 8 ] . This view is supported by the fact that similar data on the r a d i a t i v e - c h e m i c a l efficiency of ciossrlinking and degradation processes and on the strength characteristics of numerous p01ymers exposed to various kinds of irradiation are obtained. At the same time, the results of some investigations [69-73] showed that the r a d i a t i v e - c h e m i c a l efficiency in the case of polymers irradiated with heavy particles m a y differ from that recorded for materials irradiated with light particles. The role Of the radiation intensity has not yet been elucidated. The effect of this factor was observed in studies of m e c h a n i c a l properties of irradiated PMMA [36] and polymonochlorotrifluoroethylene [74]. The dependence of m e c h a n i cal properties of irradiated polymers (polyethylene, polyvinylchloride) on radiation t i m e was established in [75]. Under short exposure conditions (several hours or days), polyvinylchloride becomes brittle only after absorbing doses of hundreds of megarads, while a dose of 15 Mrd is sufficient to halve the strength of:this m a t e r i a l exposed t o radiation for several years. The effect of radiation intensity on the formation of cross-links in Lavsane was studied in [76]; the intensity of irradiation with y-quanta and fast electrons ranged from 0.25 to 1.4 Mrd/min. It was found that the ratio of the number of cross-links formed to the number of broken bonds increases with increasing radiation intensity (due to a reduction in the number of broken bonds). According to some workers [6, 66, 67], changes in properties of irradiated polymers are not related tO radiation intensity when irradiation takes p l a c e in vacuum or a neutral atmosphere (N2). A t the same time, the influence of the radiation intensity becomes quite evident when irradiation takes p l a c e in the presence of oxygen; this effect is especially marked in the low radiation intensity range under long exposure conditions, when oxygen can diffulse to the specimen interior. Thus, the radiation-induced processes i n polymers are affected by oxidation degradation and by the formation of peroxide "bridges" which d e l a y the cross-linking process.

446

2. Radiation temperature. It was shown in [20, 31] that the value G for breaking the principal chains depends on radiation temperature. This effect was observed during the degradation of PMMA and polyisobutylene and also during the formation of cross-links in polyethylene and silicones [40, 77, 70]. T e m p e r a t u r e effects during irradiation were studied in [79] on several materials at various temperatures and radiation levels. Changes taking p l a c e in polymers were reflected in a sharp reduction produced in the mobility of long m o l e c u l a r chains by lowering the temperature, this being a c c o m p a n i e d by an increase in strength and a reduction in ductility. Some of the reactions triggered off by irradiation ( e . g . , the formation of trans-vinyl nonsaturation, e t c . ) do not appear to be t e m p e r a t u r e - d e p e n d e n t . Turner [80], investigating the effect Of temperature on the formation of polymer networks, observed that, in the case of rubber, the efficiency of radiation-induced cross-linking and hydrogen evolution does not depend on temperature. Evidently, the temperature effect is characteristic only of certain specific kinds of radiation-induced reactions. 3. Working m e d i a . Like most reactions in which free radicals are involved, radiation-induced degradation and cross-linking processes are considerably affected by the presence of oxygen, which m a y increase both degradation and cross-linking rates [81]. In some cases this effect is so pronounced that, in the presence of oxygen, degradation becomes the predominant process in polymers (polystyrol, polyvinylchloride) which are known to be cross-linking materials in vacuum [7. 46, 48, 82-84]. When polymers are irradiated in the presence of oxygen, the extent of radiation damage depends on radiation intensity and specimen thickness [26, 27]. The degree of cross-linking of polyethylene is considerably higher in vacuum than in air; as the thickness of specimens irradiated in air increases, the degree of cross-linking decreases. Irradiation in air produces a marked deterioration in the m e c h a n i c a l properties and wear resistance of p o l y ethylene [29,]. Isotactic polypropylene becomes cross-linked when irradiated with doses larger than 3 • 107 rads in vacuum and undergoes intense degradation in air, the former process being accompanied by the formation of an insoluble fraction and the latter by a sharp deterioration in m e c h a n i c a l properties of this polymer [46]. There is evidence [ ~ ] that the aging of nylon, mailar, teflon and dacron subjected to ultraviolet radiation is affected by the working atmosphere; the aging rate is faster in oxygen than in nitrogen. The degree of aging is estimated from the deterioration in the m e c h a n i c a l properties of a given polymer and from the reduction in the proportion of cross-linked m a t e r i a l . The aging in vacuum is slower than in oxygen or nitrogen; the aging rates of films and fibers are approximately the Same. Working m e d i a have no effect on a p o l y m e r NT-1 of the aromatic p o l y a m i d e t y p e ; m e c h a n i c a l tests on 1.0 mm thick PMMA specimens i r r a d i a t e d in vacuum and in air revealed no differences either. Evidently, in these cases 0nly the surface layers are affected by oxidation. Published data on the mechanism of the action of oxidation during irradiation of polymers are contradictory; the only certain fact is that no chain reactions are involved. Irradiation of polymers in air m a y be accompanied by the accumulation of considerable quantities of ozone in the ambient atmosphere so that in some cases the possibility of polymers reacting with ozone should be taken into account. This effect is especially pronounced during irradiation of certain deformed resins which are subject to intense ozoneinduced cracking [85, 86]. The combined effect of irradiation and moisture on m e c h a n i c a l properties of polyethylenetetraphthalate under dynamic loads was studied in wide ranges of temperature (80-5,~0" K) and of loading frequency (8-1300 cps) in [49]. It was found that increasing the absorbed radiation dose to 1000 Mrd produces a considerable reduction in the vitrification temperature and a deterioration in the m e c h a n i c a l properties of this m a t e r i a l . A marked influence of adsorbed moisture, especially under conditions of a simultaneous action of irradiation, strain, and working medium, was observed; this effect was noted also by other workers [87, 88]. 4. Mechanical stresses. All the above discussed r a d i a t i v e - c h e m i c a l and physical changes in polymers, including changes in their m e c h a n i c a l properties, were observed on specimens irradiated in the absence of stress. Studies of the influence of stress applied during irradiation on properties of polymers were first carried out on r u b b e r q i k e materials [86, 8 9 - 9 a ] . The total number of radiation-induced defects in rubber is noticeably increased under the influence of applied stress, and there is a 10-fold increase in the rate of variation in the deformation characteristics of this m a t e r i a l . It was postulated that i f rubber is subjected to alternating loading-unloading cycles, there should be corresponding cycles of breaking and linking of chains under the influence of ionizing radiation. As a result therefore of the opposite effect of these two factors on the density of transverse bonds in elastomers, rubber exposed to radiation should last longer under dynamic than under static loads [90]. Especially interesting in this connection is a study [11] of the effect of ultraviolet radiation of capron fibers, in which the contribution of stress to the variation in the coefficient y was experimentally d e t e r m i n e d . The dependence of y on t i m e t at small radiation doses was taken to be linear: ~=y0+kt,

(8)

where )/0 is the initial value of y of nonirradiated specimens, and k is a coefficient depending on temperature and radiation i n t e n s i t y . The experiments consisted in exposing a series of specimens to a simultaneous action of radiation and a

447

constant stress without, however, fracturing t h e specimens. It was found that under these conditions k increases with increasing stress; at o = 22.5 k g / m m 2 k = 0.7 x 10 -s mm2/kg sec, and at o = 45 k g / m m z !4 = 1 . 2 • 10 -4 mm2/kg sec. This indicates that irradiation under stress produces more far-reaching irreversible changes:in the~polymer structure than irradiation of unstressed materials. IV. Physical and Chemical Mechanisms of the Acceleration of Kinetic Reactions During !tradiation in Relation to Creep Properties of Polymers. The irreversible changes produced in polymers by irradiation are, in an overwhelming majority of cases, studied at a certain time after the exposure to radiation. Data Obtained in this way can only partially characterize the radiation resistance of materials which, Under actual service conditions, are almost always subjecte d to a simultaneous action of radiation and stress. Mechanical stresses as such may activate various reactions in materials of this kind, and t h e very first studies of this problem [18, 94-96] showed that there is a large difference in the way properties of polymers change under the influence of irradiation alone and in the presence of applied stresses. An important fact established by these investigations is that the action of stress on a polymer in a radiation field accelerates m e c h a n i c a l relaxation processes, lowers the forced elasticity limit, e t c . The acceleration of relaxation processes is intensified with increasing radiation intensity, and is no longer observed when irradiation ceases; this is known as the reversible r a d i a t i v e - m e c h a n i c a l effect. In this context, a distinction is made between playsical and chemical mechanisms of acceleration of kinetic phenomena in materials exposed to irradiation [9q]. In several articles [12, 18, 94, 95] there was described a physical mechanism according to which the acceleration of these processes is due to an increase in the number of "hot" particles in an irradiated material and due to a consequent increase in the number of elementary acts (jumps of atoms, molecu!es or chain segments) Whose occurrence involves overcoming inter- and intramolecular forces nonchemical in character. The rate of kinetic processes in an irradiated material is described [18] by the following expression:

n = No ~2(7") ,v ( U ) = N O2 (T) [w, (U) + wj (U)l.

(9)

Here No is the number of molecules in 1.0 g of the material; f~ is the frequency factor; w(U) denotes the overall probability of finding in the material a particle with an energy larger than U. If the material is in a radiation field, w(U) consists of two parts N0w(U) and N0wj (U) representing the numbers of particles whose energy is larger than U due, respectively, to goltzmann distribution of particle energy and absorption of the radiation energy. Approximate calculation of oJj (U) gives the appropriate expression for the creep rate at o = const, and for the relaxation time at low stress levels

[1.~]. The concept of thermal activation of kinetic processes by irradiation is used also [13] in solving the problem of t i m e - t o - r u p t u r e of m a t e r i a l s u n d e r stress. In this case, the time-to-rupture Tbr of a material stressed in a radiation field is given by

B =

rbr (o) I.

where U - - - U 0 - - ' r o ;

B " e

.

,

(IO)

kT e-u/kr + 2. l O-2jNo 1q't, U-'I, h

/d'e---[a

k/"

is an expression for ~-br at } = 0.

kr

Criteria of the creep rate of materials in a radiation field [19] show that the observed effects cannot be explained by breaking of chemical bonds [96] (chemical mechanism). These criteria are applicable only to hard materials since the volume relieved as a result of breaking of one chemical bond is small, of the order of atomic volume. Resins represent a, different case. The acceleration of m e c h a n i c a l relaxation in resins (and, generally, in reticular polymers in a highly elastic state) exposed to radiation may probably be explained by the radiation-induced break, down of chemical bonds [96]. It is assumed in this case that the breakdown of one chemical bond is equivalent to the destruction of one network node. With the aid of formulas of the kinetic elasticity of resins, an expression was obtained relating the rate of creep in a radiation field to the number N of bonds broken in one second in 1.0 cm s of the irradiated specimen:

1 dN N dt

--

lda

(II)

a dt "

where N is the number of network nodes in 1.0 cm s of the material (calculated from the equilibrium value of the Young modulus E = 3NkT), and c~ denotes elongation of the specimen.

448

Calculations in which experimental values of G for a resin SKN-18, natural rubber and polyisobutylene had been used showed [13] that creep and relaxation of resins exposed to radiation are, basically speaking, r a d i a t i v e - c h e m i c a l in character.

"~

b

t7

t8 76

76

15 151

0

700

2o0

200

6 00

tOOO

0

T i m e , rain

4O

O0

o, k g / m m 2

Fig. 5. Creep curves of capron fibers at o = 69 k g / m m 2 : a) t I = 80 min: b) tl = = 360 min.

Fig. 6. Stress dependence of t i m e - t o - r u p t u r e of capron fibers at 25~ C: 1) without irradiation; 2, 3, 4) irradiated at j = 0.01, 0.03, and 0.07 c a l / c m 2 rain, respectively.

The view [13] that kinetic processes under consideration become accelerated in a radiation field was not supported by the results of the determination [98] of elastic constants of polymer materials irradiated with 7-rays and fast electrons; the effect of reversible changes in the shear and elasticity m o d u l i predicted in [13] was not observed [98]. Consequently, reversible effects reported in [13, 95, 96] have a different mechanism, and the theory itself must be regarded as the first tentative attempt to solve the problem in question. An important contribution to the development of concepts relating to laws governing the fracture of polymers exposed to a simultaneous action of irradiation and stress was made by investigations [10, 11] in which Zhurkov's fluctuation theory was used as a basis for elucidating the problem of interdependence of steady-state creep rate and the rate of polymer degradation [10]. According to this theory, to understand the laws of creep it is necessary to take into account the fact that flow and fracture processes develop simultaneously in a specimen under load. The creep strain may therefore be conditionally regarded as consisting of two components e, and as determined, respectively, by the laws governing the progress of flow and fracture: = ~1 + e~.

(12)

In t h e first approximation it is postulated that the strain s 2 due to fracture is a linear function of time while s 1 rapidly reaches a constant level, so that the steady-state creep rate is determined entirely by the rate of fracture processes. An indirect proof of the correctness of this view is provided by experimental data on the relationship between t i m e - t o , r u p t u r e r and steady-state creep rate [10]: s sscx = COllSt.

(13)

The authors of [I0] postulated a formal model of the deformation of polymers, in which the influence of fracture on the deformation of polymers is represented by a special "fracture element" in the form of a bundle of flexible fibers. Such a model reflects with a sufficient degree of clarity the view that the creep strain is a result of not only flow but also fracture processes, and that under certain specified conditions it cannot increase unless fracture processes take place. Experimental studies carried out on oriented capron fibers showed that in spite of substantial changes in r and ~ssc under the influence of irradiation, the product ~ssc r is practically constant under all the experimental conditions tested.

The view [10] that radiation-induced changes in the steady-state creep rate are almost entirely due to changes in the rate of fracture ts supported by experimental data reproduced in Fig. 5. Here we have creep curves plotted for two specimens, one of which was irradiated in the initial creep stages (when sl >> s2) and the other during the steady-state creep stage (when ~1 << ~ ) - Test results showed that the radiation-induced absolute increase in the creep rate is approximately the same at any creep stage, being slightly larger in the initial stages. However, the relative increase in the steady-state creep rate is many times larger than that recorded in the initial stages. In tests on nonoriented polymers it was not possible to detect any effects of irradiation on the creep rate; in this case, however, ~, >> ~2 so that changes in the relatively small values of ~ on the background of very large ~1 are difficult to detect. All this proves that ultraviolet radiation accelerates mainly the process of fracture and has little effect on deformation processes which are not associated with fracture.

449

T h e mechanism of fracture of polymers exposed to a simultaneous action of irradiation and stress Was also studied in [11, 99]. The stress dependence of the t i m e - t o - r u p t u r e of capron tested in a radiation field (Fig. 6) was explained in the following way. The combined action of ultraviolet radiation and stress leads to the onset of fracture by Zhurkov's mechanism [59, 61] which proceeds at a certain conditional rate vI and which is accompanied by radiation-induced destruction of chemical bonds taking place at a rate v 2 proportional to the radiation intensity. The rate of fracture of polymers is usually understood as the number of chemical bonds broken in a u n i t time. If the destruction of N chemical bonds is taken as the criterion of rupture and if it is assumed that the same bonds are broken under the influence of irradiation as due to thermal fluctuations under load, the t i m e - t o - r u p t u r e r e due to a simultaneous action of radiation and stress may be determined from a condition

~r (O, -q- 'Us) = 1%/

(14)

I/% = 1/~ + 1/~j.

(15)

Or

Here r denotes t i m e - t o - r u p t u r e as defined by the Zhurkov formula, while rj is time-to-rupture at temperatures and stresses at which the effect of ultraviolet radiation is strong (although rj is less stress- and temperature-dependent than r , experiment shows that both rj and vz are certain functions of o and T). Experimental investigations showed that the t i m e - t o - r u p t u r e r0 of specimens tested under a simultaneous action of stress o and ultraviolet radiation is shorter than the t i m e - t o - r u p t u r e r of a specimen first exposed to irradiation in an unstressed state for a time r c and then tested under a stress in the absence of radiation. It was also shown in [11, 99] that although ultraviolet radiation produces g r a d u a l changes in the structure of capron fibers and, consequently, in the structural coefficient T, the variation in this coefficient cannot fully account for the effect of ultraviolet radiation on time-to-rupture and steady-state creep rate. T h e explanation of this effect was based on the superposition of two processes: fracture taking place in accordance with the Zhurkov formula and fracture induced by radiation. Subsequent studies [99] carried out on other materials showed that the laws of fracture established in [11] are valid for all the materials tested. The marked reduction in the creep strength of polymers simultaneously acted on by stress and X-rays [14] is definite confirmation of the view that irradiation produces changes in the mechanism of fracture. The explanation of this effect proposed in [14] takes into account not only the presence in the material of irradiation products (electrons, ions of excited molecules, free radicals, etc.) but also the increased degree of structure imperfection which increases with increasing absorbed radiation dose; the latter effect is associated with the fact that the re-formation of bonds destroyed in a stressed polymer under the influence of irradiation is less probable than in the case of unstressed polymer chains.

r

(..a"

>X - / ~3' x 4

I

2

~

~

5"

6

o',. k g / m m 2

Fig. 7. T i m e dependence of the strength of PMMA: 1) tests in air; 2) specimens irradiated in air under stress; 8) calculated curve; 4) specimens irradiated in air before the application of stress.

The estimation o{ the effect of irreversible radiation damage on the creep strength of polymers in relation to the absorbed radiation dose showed that up to a c e r t a i n dose (4.8 x 104 joule/kg in the case of PMMA) log r is p r a c t i c a l l y independent of the absorbed dose. When the dose D is increased, the following dependence is obtained [14]:

(16)

9 ~---xo e -~o, where r0 is the t i m e - t o - r u p t u r e of a nonirradiate specimen, and c~ is a coefficient. Using the Bailey principle, the estimated time-to-rupture at D > 4.8 • 104 joule/kg may be described by Xest =

In ( a l % + l ) ad

,

(17)

where ] is the absorbed radiation intensity. The t i m e - t o - r u p t u r e of a specimen that fails only as a result of radiation damage due to a radiation dose absorbed by the material is given by x = ~:*o + Zest,

where r'~ is the t i m e during which a radiation dose not affecting the time-to-rupture is absorbed.

450

(18)

Comparison of e x p e r i m e n t a l results (Fig. 7) with data c a l c u l a t e d from (17) and (18) showed satisfactory a g r e e ment [14]. The discrepancies between curves 9, and 3 (Fig. 7) in the small radiation dose range are evidently due to reversible processes not accounted for in the calculations. Summary Experimental evidence analyzed in this review indicates that irradiation of stressed polymers produces both reversible and irreversible changes leading to a reduction in the creep strength of materials of this kind. The contribution of e~ich b f these processes to the variation in the creep strength depends on the p o l y m e r structure, stress level, radiation intensity, absorbed radiation dose and, to a certain extent, form of irradiation. The success of p r a c t i c a l applications of polymer materials depends to a large extent on solving the problem of their radiation resistance and the effect of working m e d i a on their m e c h a n i c a l properties. The influence o f various factors (including the effect of gaseous and liquid working media) on physicomechanical properties of polymers is at present considered m a i n l y in qualitative terms which makes it difficult to use experimental results in the formulation of general laws. Problems presented by p r a c t i c a l applications of polymer materials should be solved by extensive preliminary investigations simulating the actual service conditions. An important point is that in addition to irradiation and stress the effect of working m e d i a (gases, liquids, vapors, e t c . ) must be taken into account. The combined influence o f these factors on polymer materials, not to mention the radiation-induced changes in the p r o p e m e s of working media and the resulting variation in the character of their interaction with polymers, introduces complications in studies of this problem and makes it difficult to g e n e r a l i z e results obtained. In our view, however, only investigations of this kind are of a p r a c t i c a l value and m a y be used as a basis for formulating universally a p p l i c a b l e laws and theoretical concepts. REFERENCES 1.

F. Bovey, The Influence of Ionizing Radiations on Natural and Synthetic Polymers [Russian translation], IL,

1959. 2. T. S. Nikitina, E. V. Zhuravskaya, and A. S. Kuz'minskii, The Influence of Ionizing Radiations on Polymers [in Russian], Goskhimizdat, 1959. ~. I. V. Vereshinskii and A. K. Pikaev, Introduction to Radiation Chemistry [in Russian], Izd. AN SSSR, 1963. 4. A. Charlesby, Nuclear Radiations and Polymers [Russian translation], IL, 1962. 5. S. Ya. Pshezetskii and V. A. T a l ' r o z e , Proceedings of the 2nd All-Union Conference on Radiation Chemistry [in Russian], Izd. AN SSSR, 1962. 6. R. O. Bolt and I. G. Carrol, Effects of Radiation on Organic Materials [Russian translation], Atomizdat, 1965. 7. V. L. Karpov, Session of the AS USSR on the Peaceful Uses of Nuclear Energy [in Russian], OKhN, Izd. AN SSSR, 1965. 8. N. A. Slovokhotova and V. L. Karpov, A Collection of Articles on Radiation Chemistry [in Russian], Izd. AN SSSR, 1955. 9. L. N. Pravednikov and S. S. Medvedev, in "Proceedings of the 1st All-Union Conference on Radiation Chemistry" [in Russian], Izd. AN SSSR, 1958. 10. V. R. Regel and N; N. Chernyi, Vysokomolekulyamye seodineniya, 5, no. 6, 1963. 11. M. P. Vershinina, V. R. Regel, and N. N. Chernyi, Vysokomolekulyarnye soedineniya, 6, no. 8, 1964. 12. M. A. Mokul'skii, Yu. S. Lazurkin, and M, B. Fiveiskii, Vysokomolekutyarnye soedineniya, 2, no. 1, 1960. 13. M. A. Mokul'skii, Vysokomolekulyarnye soedineniya, 2, no. 1, 1960. 14. A. N. Tynnyi, S. I. Mikitishin, A. A. Velikovskii, Yu. N. Khomitskii, and Yu. A. Kolevatov, FKhMM [Soviet Materials Science], no. 1, 1967. 15. T. Alfrey, Mechanical Properties of High-Molecular Polymers [Russian translation], IL, 1952. 16. A. Sippel, Kunststoffe, 49, 626, 1959. 17. S. N. Zhurkov and S. A. Abasov, FTT, 4, no. 8, t969. 18. H. Busch, K o l l o i d - Z . u. Z. Polimere, 2, 186, 1962. 19. Effects of Radiations on Materials and Machine Parts [in Russian], Izd. GU NAE, 1959. 20. A. Shapiro, J. Chem. Phys., 52, 1955. 9.1. V. L. Karpov and B. I. Zverev, in A Collection of Articles on Radiative Chemistry [in Russian], Izd. AN SSSR, 1955. 9,2. Dzebu Abatani and Matsuo Minegaki, Trans. 1apan Soc. Mech. Engs., 29, 203, 1963. 9,3. R. Simcha and L. Wall, I. Phys. C h e m . , 61, 1957. 24. Yu. S. Lazurkin and G. P. Ushakov, Atomnaya energiya, 4, no. 3, 1958. 25. C. G. Currin, Commun. and Electr., no. 4, 1959. 26, T. A. Blokh, V. L. Karpov, and Yu. M. Malinskii, Proceedings of the 9,nd All-Union Conference on Radiation Chemistry [in Russian], Izd. AN SSSR, 1969.

451

1954, 27. D. S. Ballantine, G. I. Dienes, and B. Manowitz, i. Polymer Sci,, 9 28. J. Marin and P. B. Griesacker, J. Appl. Polymer Sci., 7, n o . . ! , !963. 29. p. Alexander and A. Charlesby, Nature, 178, 1954. 30. A. Charlesby, Nucleonics, 12, no. 6, 18, 1954. 31. M. Ross and A. Charlesby, Nature, 178, 1954. 32. A. R. Schultz, P. I. Roth, and G. B. Rathmann, 3. Polymer Sci., 25, 495, 1956. 38. H. G. L. B0ttger, Kernenergie, 8, no. 6, 1 9 6 5 . 34. C. D. Bapp and O. Sisman, Nucleonics, 13 (7), 28, 1955, 1B (10), 53, 1955. 35. A. N. Neverov and Yu. V. Zherdnev, Radiation Chemistry of Polymers [in Russian], Moscow, 1966. 36. A. Chapiro, 3. Chem. Phys., 58, 295, 1956. 37. P. K. Kaushal, ~. T. Tahmpy, and B. K. Pamaik, Chem. Age India, 1B, no. 7, 1965. 38. A. N. Neverov, Radiation Chemistry of Polymers [in Russian], Moscow, 1966. 39. B. L. Tsetlin, N. G. Zaitseva, and V. A. Kardin, DAN SSSR, 118, 380, 1957. 40. L. A. Wall and D. Brown, J. Phys. C h e m . , 61, 129, 1957. 41. L. A. Wall and D. Brown, 3. Res. Nat. Bur. Stand., 5'/, (3), 1956. 42. L. G. Gurvich, Proceedings of the 2nd A l l - U n i o n Conference on Radiation Chemistry [in Russian], Izd. AN SSSR, 1962. 48. 3. J . Lohr and J. A. Parke, AIAA Journal, 8, no. 4, 1965. 44. N. V. Mikhailov, L. G. Tokareva, and T. L. Bratchenko, Proceedings of the 2nd A l l - U n i o n C o n f e r e n c e on Radiation Chemistry [in Russian], Izd. AN SSSR, 1962. 45. Sigematsu T o m a m i t i , Eng. Mater., 10, 19, 1962(RZh. Khimiya, 2 2 T l l , 1968). 46. E. E. Baroni, Proceedings of the 2nd All-Union Conference on Radiation Chemistry [in Russian], Izd. AN SSSR, 1962. 47. F. Rybnika[', M. Mo~.'is~ek, and O. Jelinek, Plaste u. Kautschuk, 10, no. 6, 1968. 48. I. D. Aitken, H. Wells, and I. Williamson, Atomic Energy Res. Estab., NR 8381, 45~ 1961. 49. D. E. Kline and I. A. Sauer, Polymer, 186, no. 2, 1962. 50. Adamec, Electrotechn. Obzor, 52, no. 8, 1963. 51. R. Kraub and H. Bannmann, Electronic, 18, no. 12, 1964. 52. I. V. Paschale, D. B. Hermann, and R. I, Miner, Mod. Plastik, 41, no. 2, 1963. 53. W. Schnabel, Glas-und I n s t m m . - T e c h n . , 9, no. 8, 1965. 9 54. L. T. Tokareva, T. D. Bratchenko, and N. V. Mikhailov, Radiation Chemistry of Polymers [in Russian], Moscow, 1966. 55. N. S. Tikhomirova, N. I. Bol'shakova, Z. S. Ustyanskii, and V. I. Serenkov, Radiation Chemistry of Polymers [in Russian], Moscow, 1966. 56. B. N. Narzullaev and S. N. Karimov, DAN Tadzh. SSR, 7, no. 6, 1964. 57. B. N. Narzu!laev and S. N. Karimov, DAN Tadzh. SSR, 7, no. 7, 1964. 58. N. K. Baramboim, Uspekhi khimii, 58, no. 7, 1957. 59. G, M . Bartenev and Yu. S. Zuev, Strength and Fracture of High-Elasticity Materials [in Russian], Izd. "Khimtya, " 1964. 60. V. E. Gul', Strength of Polymers [in Russian], Izd. " K h i m i y a , " 1964, 61. G. Batzer, Introduction to the Chemistry of High-Molecular Compounds[Russian translation], IL, 1960. 62. W. P. Slichter and E. R. Mandell, J . Phys. C h e m . , 62, 334, 1958. 63. C. C. Hsiao and I. W. Iang, I. Appl. Phys., 88, no. 9, 1962. 6 4 . O. Teszler and H. A. Rutherford, Textille Res. L , 796, 1956. 65. A. Chapiro, Compt. Rend., ~89, 703, 1954. 66. C. V. Stephenson and W. S. Wilcox, 3. Polymer Sci., 8, 1963. 67. H. Wilski, Atomwirtsch-Atomtechn., 10, no. 2, 1965. 68. P. K. Kaushal, R. T. Tahmpy, and T. S. Bhardwoj, Chem. Age India, 18, no. 4, 1965. 69. T. I. Sworski and M. I. Burton, Amer. Chem. Soc., 73, n o . 8, 3790, 1951. 70. p. Alexander, I. Litt, P. Kopp, and R. Itzhaki, Pad. Res., 14, 363, 1961. 71. R. Itzhaki and P. Alexander, Pad. Res., 15, 553, 1961. 72. Ya. I. Lavrentovich and A. M. Kabakchi, Radiative Chemistry of Polymers [in Russian], Moscow, 1966. 73. W. W. Parkinson, C. D. Bopp, D. Binder, and I. E. White, J. Phys. C h e m . , 69, no. 3, 1965. 74. I. Goodman and I. H. Coleman, J. Polymer Sci., 2fi, 1956. 75. H. Wilski, Industrie kurier. T e c h n . - u n d Forsch, 18, no. 4 8 , 915, 1965. 76. D. I. Turner, G. F. Perdirtz, and G. D. Sands, I.~Polymer Sci., 4, no. 1, 252-254, 1966. 77. P. Alexander and D. Toms, J. Rad. Res., 9, no, 5, 509, 1958. 78. R. M. Black, Nature, 178, no. 4528, 305, 1956.

452

79. E. C. Kannan and B. L. Gause, Ekspress inf. Atomnaya energiya, no. 47, 1965. 80. D. I. Turner, I. Polymer S c i . , 81, no. 2, 1963. 81, A. Shapiro, I. Chem. Phys., 82, 246, 1955. 89. W, C. Sears and W. W, Parkinson, J. Polymer. S c i . , 21, 3~5, 1956. 8.q, V. M. Anikeenko, K. M. Kevroleva, R. M. Kessenikh, and Y. G. Somikov, Vestnik elektropromyshlennosti, no. 6, 1969. 84. P. Alexander and D. Toms, J. Polymer S c i . , 99, 1956. 85. R. Harrington, in "Chemistry and Technology of Polymers" [Russian translation], IL, 1958. 86. R . G . Baumann, J. Appl. Polymer S c i . , 2, no. 6, 1963, 87. V. I. Likhtman and O. A. Troitskii, Zhurnal fizicheskoi khimii, 3q, no. 8, 1964. 88. O. A, Troitskii and V. I. Likhtman, Atomnaya energiya, 16, no. 6, 1963. 89. A. S. Kuz'miuskii, L. S. Fel'dshtein, E. V. Zhuravskaya, and L, I. Lyubchanskaya, Proceedings of the 2nd A l l - U n i o n Conference on Radiation Chemistry [in Russian], Izd. AN SSSR, 1962. 90. J. W. Born. Report WADC-TR-55-58, part Ill, 1956. 91. R. G. Baumann and J. W, Born, J. Appl. Polymer S c i . , 1, no. 3, 351, 1959. 99. W. E; Shelberg and L. H. Hevantman, Rubb. Age, 87, no. 2, 263, 1960. 93. J. W. Born, Materials Research and Standards, 1, no, 4, 980, 1961. 94. M. A, Mokul'skii, Yu. S. Lazurkin, M, B. Fiveiskii, and V. I. Kozin, DAN SSSR, l~fi, 1007, 1959. 95. M. A. Mokul'skii, Yu, S. Lazurkin, M. B. Fiveiskii, and V. I. Kozin, Vysokomolekulyamye soedineniya, ~, no. 1, 1960. 96. Yu. S. Lazurkin. M. A. Mokul'skii, and M. B. Fiveiskii, Proceedings of the 9nd All-Union Conference on Radiation Chemistry [in Russian], Izd, AN SSSR, 1962. 97. A. T. Koritskii, Yu. N. Molin, and V. N. Shamshev, Vysokomolekulyamye soedineniya, 1, 1182, 1959. 98. O. F. Tatarenko, A. I. Kurilenko, and V. L. Karpov, Radiation Chemistry [in Russian], Moscow, 1966. 99. V. R. Regel' and N. N . Chernyi, Khimicheskie volokna, no. 6 , 1965. 4 M a y 1967

Institute of Physics and Mechanics, AS UkrSSR, L'vov; Institute of Physics, AS UkrSSR, Kiev.

453