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The long-term strength of polymeric materials
Letters to the Editor THE LONG-TERM STRENGTH OF POLYMERIC MATERIALS* Y U . 1Vi. I V A N O V
(Received 23 February 19{}5) THE generalized equation (1) for the long-term strength given b y Zhurkov [1] is equally valid for crystalline solids a n d polymers. I t was tested for metals
T= roe,(17°-w)/kT
(1)
*rod orientated polymer fibres. A detailed analysis of experimental data has shown, however, t h a t the long-term strength of tmextended polymers deviates from equation (1) [2]. Bartenov [3] attributes this deviation to ~ usecl i n (1) as a constant which is temperature dependent. The contrast in behehaviour between polymers a n d solid crystals can be the consequence of the larger dimensions of the molecules a n d the supermoleeular structures which are the cause of heterogeneity of polymers [4]. The effect of the last n a m e d is larger in unextended polymers because of greater mobility, still greater when the critical temperature is approached. Primary fissures form more easily at the boundary surfaces of supermoleeular structures a n d destruction, as well as bond fractures, will occur at their surfaces during heat fluctuation and stresses, b u t at different probabilities. Changes of temperature therefore must affect the development of these processes i n different ways. The probability al of bond fracture will depend on the direction of the stress moment while probability az, of reduction, will depend on the collision of active groups with free radicals. The value of/~2 must decrease with decreasing temperature more rapidly t h a n that of/~1 because of the increase of the relaxation time and changes of kinetic factors, a l > P 2 in a n irreversible destruction and ratio p s / a x < l ' 0 . W h e n T-+0, /12-->0 and /~1//,1=0; when a-->a0, az-->0 and /12/al = 0. One can assume that/~x will equal/~t when the temperature approaches the critical, i.e. aa[/Jl-+l. One can assume a linear change of/~l/ax as a function of temperature in a first approximation.
~(T)= ( 1 - ~/~1) ~'o
C2)
T h e above equation will also have a linear dependence on T and ~ = 70 when T = 0, b u t will be 0 when T = T , (the full lines in Fig. la). By inserting (2) into (1), one obtains T = TOe , ( U ' - (1 -- l~t/l~l):,oa)lkT.
(3)
Uo-~,oao when ~-->a0; knowing ~0 a n d a 0, one can determine U 0. E q u a t i o n (3) reverts to (1) when at//~x=const, a n d ~=const. The ~(T) values were calculated for throe polymers from experimental results [5, 6]; they were plotted as a function of T in Fig. lb. Straight lines were drawn through the scattered experimental points and intersect the ordinate at Y0, according to which the activation energies given i n the Table, U0, were calculated. * Vysokomol. soyed. 7: No. 7, 1291-1292, 1965. 1432
Letters to the Editor
1433
ACTZVA~ZON ENER6ZES
~0,
keal x ram" or°' kgs × moles kgs/mm=
Polymer
Polymethylmethacrylate Polystyrene ~elluloid
3.23 5.90 5.57
U°'
"
keal/mole
16,0 [5] 8.8 [6] 11.0 [6]
51.8 51.9 61-3
UO' kc~/molq
54 [6] 54 [5] --
The straigth lines appear to go over into curves on approaching ordinate T (indicated b y dotted line in Fig. lb} a n d show a displacement of the intersects with axis T towards the left a n d T c. The p=/pz(T) a n d 7(T) functions become also more complex as a result, this being shown b y the dotted line i n Fig. lal These functions will be established more
7#)
i
5
~,,\\ a
b
1
°'
o2
2-
0
r-, 3
200
4OO
BOO
7;,°C
FIG. 1. Graphic illustration of functions: a--pt/p z a n d r as a function of temperature; b--7(T) according to experimental d~termination: 1--polymethylmethacrylate; 2--polystyrene; 3 -- celluloid. aceurately 'when more detailed experimental data becomes available as well as the value Of ? at T==79°C for polystyrene (see Fig. lb). E q u a t i o n (3) yields a bundle of straight lines in log ~ - - a a n d log 3 - - 1 / T coordinates. The scatter of this bundle in the log v - - a plane is determined b y the difference az--aa l~tween
1434
Letters to the Editor
the intersect of the extreme lines 1 a n d 4 with the log v-~log v~ line. E q u a t i o n (1) gives a narrow bundle of lines when compared with equation (3), a n d this does not agree with experimental data. The a x - - a ~ difference for log v = 3 . 5 is compared with experimental resuits of nsing (1) and (3) below: Polymethylmethacrylate Celluloid Source of results
6.11 5.95 test
3.52 1.67 eqn. (1)
6.13 5.97 egn. (3)
I t follows from the above t h a t equation (3), which takes into account the effect of temperature on 7, gives a better agreement with experimental results.
T r a n s l a ~ by K. A. ALLE~
REFERENCES
'
1. S. N. ZHURKOV, Vestn. Akad. Nauk SSSR, No. 11, 78, 1957 2. Yu. M. IVANOV, Zavod. Lab. 27: 455, 1961 3. G. M. BARTENEV and Yu. S. ZUEV, "Strength a n d Destruction of Highly Elastic Materials". (Prochnost' i razrushenie vysokoelasticheskikh Materialov.) Izdat. "Khimiya'" 58 and 87. Moscow 1964 4. V. A. KARGIN, "Contemporary Problems of Polymer Science." (Sovremmenye problemy n a u k i o polimerakh.) Izdat. Moscov. Gos. Univ., 1962 5. S. N. ZHURKOV a n d S. A. ABASOV, Vysokomol, soyed. 4: 1703, 1962 6. S. N. ZHURKOV and B. N. NARZULAEV, Zhur. tekh. Fiz. 23: 1677, 1953
FREE RADICAL FORMATION BY OXYGEN IN POLYMERS* V. K . ~ I I L I N C H U K
(Received 22 March 1965) IT IS known t h a t the ageing of polymers under natural conditions is chiefly the result of exposure to oxygen to and sunlight at one time. The mechanism of the photo-oxidation has not yet been completely clarified [1, 2]. To explain the part played b y oxygen a n d light during natural ageing of polymers, we have studied the formation of free radicals due to the presence of oxygen and sunlight. The light source was in this case a DRSH-250 and DKSSH- 1000 lamp. The tests were carried out at the temperature of liquid nitrogen. The free radicals were studied b y electron spin resonance (ESR) and it was found t h a t U.V. light of 3000 A wavelength caused intense free radical formation when oxygen wis present in different hydrogen containing polymers such as polyethylene, polypropylene, poly-isobutylene, polyvinyl acetate, polymethylmethaerylate, natural rubber etc. The formation of radicals is attributed to oxygen for the following reasons: (1) free radicals are created in polymers although this is not the case in vacuum over the studied wavelength of light; (2) the rate of formation a n d the specific concentration of * Vysokomol. soyed. 7: No. 7, 1293, 1965.
(Received 23 February 19{}5) THE generalized equation (1) for the long-term strength given b y Zhurkov [1] is equally valid for crystalline solids a n d polymers. I t was tested for metals
T= roe,(17°-w)/kT
(1)
*rod orientated polymer fibres. A detailed analysis of experimental data has shown, however, t h a t the long-term strength of tmextended polymers deviates from equation (1) [2]. Bartenov [3] attributes this deviation to ~ usecl i n (1) as a constant which is temperature dependent. The contrast in behehaviour between polymers a n d solid crystals can be the consequence of the larger dimensions of the molecules a n d the supermoleeular structures which are the cause of heterogeneity of polymers [4]. The effect of the last n a m e d is larger in unextended polymers because of greater mobility, still greater when the critical temperature is approached. Primary fissures form more easily at the boundary surfaces of supermoleeular structures a n d destruction, as well as bond fractures, will occur at their surfaces during heat fluctuation and stresses, b u t at different probabilities. Changes of temperature therefore must affect the development of these processes i n different ways. The probability al of bond fracture will depend on the direction of the stress moment while probability az, of reduction, will depend on the collision of active groups with free radicals. The value of/~2 must decrease with decreasing temperature more rapidly t h a n that of/~1 because of the increase of the relaxation time and changes of kinetic factors, a l > P 2 in a n irreversible destruction and ratio p s / a x < l ' 0 . W h e n T-+0, /12-->0 and /~1//,1=0; when a-->a0, az-->0 and /12/al = 0. One can assume that/~x will equal/~t when the temperature approaches the critical, i.e. aa[/Jl-+l. One can assume a linear change of/~l/ax as a function of temperature in a first approximation.
~(T)= ( 1 - ~/~1) ~'o
C2)
T h e above equation will also have a linear dependence on T and ~ = 70 when T = 0, b u t will be 0 when T = T , (the full lines in Fig. la). By inserting (2) into (1), one obtains T = TOe , ( U ' - (1 -- l~t/l~l):,oa)lkT.
(3)
Uo-~,oao when ~-->a0; knowing ~0 a n d a 0, one can determine U 0. E q u a t i o n (3) reverts to (1) when at//~x=const, a n d ~=const. The ~(T) values were calculated for throe polymers from experimental results [5, 6]; they were plotted as a function of T in Fig. lb. Straight lines were drawn through the scattered experimental points and intersect the ordinate at Y0, according to which the activation energies given i n the Table, U0, were calculated. * Vysokomol. soyed. 7: No. 7, 1291-1292, 1965. 1432
Letters to the Editor
1433
ACTZVA~ZON ENER6ZES
~0,
keal x ram" or°' kgs × moles kgs/mm=
Polymer
Polymethylmethacrylate Polystyrene ~elluloid
3.23 5.90 5.57
U°'
"
keal/mole
16,0 [5] 8.8 [6] 11.0 [6]
51.8 51.9 61-3
UO' kc~/molq
54 [6] 54 [5] --
The straigth lines appear to go over into curves on approaching ordinate T (indicated b y dotted line in Fig. lb} a n d show a displacement of the intersects with axis T towards the left a n d T c. The p=/pz(T) a n d 7(T) functions become also more complex as a result, this being shown b y the dotted line i n Fig. lal These functions will be established more
7#)
i
5
~,,\\ a
b
1
°'
o2
2-
0
r-, 3
200
4OO
BOO
7;,°C
FIG. 1. Graphic illustration of functions: a--pt/p z a n d r as a function of temperature; b--7(T) according to experimental d~termination: 1--polymethylmethacrylate; 2--polystyrene; 3 -- celluloid. aceurately 'when more detailed experimental data becomes available as well as the value Of ? at T==79°C for polystyrene (see Fig. lb). E q u a t i o n (3) yields a bundle of straight lines in log ~ - - a a n d log 3 - - 1 / T coordinates. The scatter of this bundle in the log v - - a plane is determined b y the difference az--aa l~tween
1434
Letters to the Editor
the intersect of the extreme lines 1 a n d 4 with the log v-~log v~ line. E q u a t i o n (1) gives a narrow bundle of lines when compared with equation (3), a n d this does not agree with experimental data. The a x - - a ~ difference for log v = 3 . 5 is compared with experimental resuits of nsing (1) and (3) below: Polymethylmethacrylate Celluloid Source of results
6.11 5.95 test
3.52 1.67 eqn. (1)
6.13 5.97 egn. (3)
I t follows from the above t h a t equation (3), which takes into account the effect of temperature on 7, gives a better agreement with experimental results.
T r a n s l a ~ by K. A. ALLE~
REFERENCES
'
1. S. N. ZHURKOV, Vestn. Akad. Nauk SSSR, No. 11, 78, 1957 2. Yu. M. IVANOV, Zavod. Lab. 27: 455, 1961 3. G. M. BARTENEV and Yu. S. ZUEV, "Strength a n d Destruction of Highly Elastic Materials". (Prochnost' i razrushenie vysokoelasticheskikh Materialov.) Izdat. "Khimiya'" 58 and 87. Moscow 1964 4. V. A. KARGIN, "Contemporary Problems of Polymer Science." (Sovremmenye problemy n a u k i o polimerakh.) Izdat. Moscov. Gos. Univ., 1962 5. S. N. ZHURKOV a n d S. A. ABASOV, Vysokomol, soyed. 4: 1703, 1962 6. S. N. ZHURKOV and B. N. NARZULAEV, Zhur. tekh. Fiz. 23: 1677, 1953
FREE RADICAL FORMATION BY OXYGEN IN POLYMERS* V. K . ~ I I L I N C H U K
(Received 22 March 1965) IT IS known t h a t the ageing of polymers under natural conditions is chiefly the result of exposure to oxygen to and sunlight at one time. The mechanism of the photo-oxidation has not yet been completely clarified [1, 2]. To explain the part played b y oxygen a n d light during natural ageing of polymers, we have studied the formation of free radicals due to the presence of oxygen and sunlight. The light source was in this case a DRSH-250 and DKSSH- 1000 lamp. The tests were carried out at the temperature of liquid nitrogen. The free radicals were studied b y electron spin resonance (ESR) and it was found t h a t U.V. light of 3000 A wavelength caused intense free radical formation when oxygen wis present in different hydrogen containing polymers such as polyethylene, polypropylene, poly-isobutylene, polyvinyl acetate, polymethylmethaerylate, natural rubber etc. The formation of radicals is attributed to oxygen for the following reasons: (1) free radicals are created in polymers although this is not the case in vacuum over the studied wavelength of light; (2) the rate of formation a n d the specific concentration of * Vysokomol. soyed. 7: No. 7, 1293, 1965.