I
C. D. BOPP, W. K. KIRKLAND, OSCAR SISMAN, and R. L. TOWNS Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tenn.
Radiation Effect on Polymer Vibration Characteristics Cross linking of some elastomers can be induced by radiation changes which are then measured by vibration test methods
D m m m N a on chemical structure, either cross linking or cleavage may dominate radiation-produced changes in the mechanical properties of high polymers (4, 5 ) . Radiation-induced cross linking is usually accompanied by the evolution of hydrogen and hydrocarbon gases, and by increased density; however, the change in mechanical properties is often a more sensitive measure of cross linking. The vibrating reed resonance technique (77) was employed to measure dynamic elastic and frictional properties a t room temperature in the frequency range from about 50 to 500 cycles per second. For the most part, measurements were confined to those polymers for which cross linking is dominant since such polymers retain sufficient strength to test them over a wide exposure range. To describe the time dependence of the strain of viscoelastic materials, the retardation time, T , is defined by y = yo(1 - e - t ' r )
(1 )
where y is the deformation at time, t, after application of stress and y o is the equilibrium value of deformation. T o describe the behavior of actual materials it is often necessary to employ a spectrum of retardation times ( I , 2 ) . At sufficiently low rates of straining when the vibration period is much greater than the retardation times, the dynamic elastic modulus is equal to the static modulus. The static Young's modulus of elastomers is given by the kinetic theory of elasticity as proportional to the concentration of cross links (70). V = AkT/E
(2)
where E is the static or equilibrium modulus, k is Boltzman's constant, T is the absolute temperature, V is the volume per cross link, and A is a constant which is of the order of 1. At periods of the same order or shorter than the retardation times the dynamic modulus is greater than the static modulus. Retardation in viscous plastics largely masks high elasticity a t the temperature and frequency employed. Although a large difference occurs in the mobilities of the molecular segments in elahtomers and glasses, it is well known
71 8
that a n elastomer can be changed to a material with glassy properties either by lowering the temperature or by increasing the frequency of testing. A third method of reducing mobility is by extensive cross linking as in hard rubber. A characteristic of the rubbery-glassy transition is a broad maximum in the internal friction-temperature relationship. O n the glassy side of the maximum in friction the mobility is impeded by van der Waals' forces; on the rubbery side the mobility is high. The softer elastomers lie on the high mobility side of the maximum where a decrease in mobility increases friction; viscous plastics lie on the low mobility side of the maximum where a decrease in mobility decreases friction. The dynamic modulus of elastomers is increased if the retardation times are increased until they are of the same order as the period of vibration. A lesser effect may be expected for a change in the retardation times of viscous plastics than for elastomers, since the mobility is initially lower for plastics. Table 1.
Parameters of Equation 3
-' Elastomer Formulation
Plasticized natural rubber PlS2Cl PlS2C2 PlS2C3 P 1 s2c4 Natural rubber PlSlC9 32A43 Polybutadiene
PlSlCl Silastic 250 PlSlC8 Hycar PA-21 PlSlClO GR-S PlSlC3 324147 Hypalon 5-2 PlSlCll NeoDrene GN pisic4 Hycar OR-15 PlSlC2
~ ( A E C O ) ' ' ~ 'C
(Dynes/Sq. (109 n Crn.)l'"(rad),-' rad)
1.0 1.0 1.0 1.0
1.6 1.6 1.6 1.6
X X X X
lo-'
lo-' lo-' lo-'
... ... ... ... ...
1.3 1.2 X 1.3 7 X
0.4
1.8 1
x
10-4
...
1.8
x x x
10-4
...
x x
10-7
...
10-7
0.5
1
1.8 I
2.9 2.9
4 3
3.7 3
3.7 4
10-4 10-
X
... ... 0.4 ...
6 1 X lo-' Obtained from change in specific volume (5,6).
INDUSTRIAL AND ENGINEERING CHEMISTRY
Discussion of Results The increase in the dynamic Young's modulus of elastomers as a function of radiation exposure may be fitted to the empirical equation
where AE1 is the increase in the dynamic modulus, A E , is the limiting increase approached after long exposure, R is the exposure, and n and c are adjustable parameters. The parameter, c, has about the same value for nearly all of the formulations, and indicates the saturation value of exposure beyond where there is little change in modulus. The parameter, n, is indicative of the increase in retardation which has been produced by radiation-induced cross linking. I n the absence of retardation, (assuming that cross linking is proportional to exposure) n should equal 1. This is the value obtained (Table I) for the highly plasticized elastomer formulations for which retardation is expected to be small. For formulations without appreciable retardation cross linking efficiency can be estimated by using Equation 2. For the plasticized elastomers a value of 20 electron volts per cross link is obtained, nearly the same as determined by Charlesby (8) for crepe rubber both by swelling and modulus measurements. Evidence that n is characteristic of the base polymer is given by the several formulations based on natural rubber and by the two formulations based on GR-S (butadiene-styrene copolymer). Estimates of c are more reliable from the change in specific volume (6) than from the change in modulus, since data at larger exposure were available for the former. I t was possible to estimate c from the modulus for only two of the polymers-Hycar OR-1 5 and Neoprene GN. For neoprene the two estimates are in agreement, but for Hycar OR-15 earlier saturation is indicated for the modulus than for the specific volume. Lack of agreement for Hycar OR-15 is probably associated with its exceptionally high value of n.
The ratio of the viscous modulus E2 to the dynamic modulus El is proportional to the ratio of energy dissipated by internal friction to the elastic energy. The initial decrease in the ratio for elastomer formulations with low values of n (Table 111) corresponds to constancy in the viscous modulus, Es, at low exposure, but after extensive exposure E2 is increased. For elastomer formulations with high values of n, E2 is increased at lo^ exposure, but decreased at greater exposure-an indication that the mobility has been decreased beyond the value which gives maximum friction. I n Table 11, E2 is decreased for plasticized poly(viny1 chloride) forrnulations. The dynamic Young's modulus of the more highly plasticized of the poly(viny1 chloride) formulations is increased uniformly with exposure; the less highly plasticized formulation is little changed at low exposure, but is changed after long exposure. A similar induction period before the onset of hardening is found for elastomers compounded by mixing natural rubber (which is cross linked) and butyl rubber (which is cleaved) ( 6 ) . Cross linking and cleavage are likely to occur together for both the mixed elastomers and the plasticized poly(viny1 chloride) formulations. Initially, softening is caused by reduction in molecular weight; later, after the identit)- of individual molecules is lost through gel formation: the further knitting of the gel is predominant. Cleavage is dominant for rigid poly(viny1 chloride) formulations (7). The difference in radiation effects for plasticized and rigid formulations agrees with the observation that the rate of cross linking is low for highly rigid polymers which are initially uncross linked (5).
Method of Test Two ways of inducing vibrations were used, and are shown schematically in Figure 1. In one method vibration is induced by shaking the clamp (77), but this proves satisfactory only for very flexible materials; since, for more rigid materials, a coupling interaction occurs between the resonant frequencies of the specimen and the driving clamp. To eliminate this interference another method was developed and was used in later work. I n this method the clamp is stationary, and a separate driver is placed in contact with the specimen. The driver is designed so that its own resonance is of low amplitude and of high frequency in comparison with the resonance of the specimen. A magnetostrictive device presents a very compact arrangement (Figure 2 ) . The contact pressure between the driver and the specimen is adjusted by tilting the block so as to change the position of its center of gravity with respect to its pivot. The specimen may be placed in a slot in the
SHAFT FITS IN RECORD-CUTTINGHEAD DRIVER
a OF DRIVER
Figure 1.
Methods of vibration
ternatively, the amplitude may be measured by observing the motion of a minute piece of glass, which is placed on the free end of the specimen, with a microscope at about 500X. The amplitude may also be measured photoelectrically (72). Vibration pickups which must be placed in mechanical contact with the specimen prove less successful because the mechanical impedance of the pickup may be of the same order as that of the specimen. If vibration is induced by shaking the clamp, the nodes move continuously
block so that the driving pressure serves also to clamp the specimen or for nonrigid materials it may prove better to clamp the specimen to the block, Figure 1. For nonrigid materials the driver must be placed very close to the clamp in order to obtain a low amplitude of vibration. 'The amplitude of vibration is measured by the variation in capacitance between the specimen and a charged metal surface which is placed very near the specimen. The specimen is made conductive with a coating of graphite. Al-
Table 11.
Irradiation Effects of Vibration Characteristics of Poly(viny1 Chloride) Formulations
Formulation Plasticized formulations 80770 (25 parts dioctyl phthalate) 2042 (52 parts dioctyl phthalatej Rigid formulations 8700 8750 400 X 75
Dynamic E2lE1, Irradiation Young's Modulus Ratlo of T-iscous Exposure (109 Dynes/ l\iIodulus to (10'8 n l S q Cin.)' Sq. Cm.) Young's Modulus 0
6
0.6 3.6 0 0.6 3.6
5
0 0.6 0 0.6 0 0.6
0.30
...
15 1.3 4 14
0.07 0.7
30
42 40 38
0.025 0.025 0.025 0.025 0.025
36
0.025
30
0.6 0.09
0 An integrated flux of 1018 neutrons/sq. em. is, for poly(viny1 chloride), approximately equivalent t o from 2 X 109 to 5 X 109 rads (4).
VOL. 49,
NO. 4
01 APRIL 1957
719
Figure 2. along the reed as the frequency is varied ( 9 ) . In this case resonance occurs f o r . the node a t the clamp. If the reed is driven a t a point other than a t the clamp, resonance occurs a t the frequency when the node coincides with the position of the driver. Experimentally, it agrees with the mathematical analysis, that the resonant frequencyis a function of the position of the driver and is increased as the driver is moved from the clamped end toward the free end. The resonant frequency is not very sensitive to the contact pressure of the driver; however, the amplitude of resonance increases with increasing pressure. A minimum pressure is necessary to maintain a steady state vibration which is insensitive to room noise. To avoid amplitude dependence of the modulus, very low amplitude was employed. At low amplitude heating effects were negligible. [At higher amplitudes, a n appreciable temperature gradient must be built up in the specimen so as to dissipate the energy result-
Apparatus
ing from internal friction ( 2 ) ] . A high amplitude was employed initially to locate the approximate resonant frequency; the amplitude was then reduced. Surface friction with air is negligibly small for specimens of the present thickness (about 0.1 inch). The limit on sensitivity is usually set by uniformity of dimensions. Best results were obtained for specimens cut with a die similar to that commonly employed for tensile dumbbells except that the shape is rectangular. Specimens were cut before irradiation since after irradiation the materials may be very hard.
curves
Analysis of R~~~~~~~~
The resonant frequency v' (cycles per second) was taken as the frequency which gives maximum amplitude; the band width, as the difference in the two frequencies which give 0.7 maximum amplitude, Av0.7, or the difference in the two frequencies which give 0.9 maximum
amplitude, AVO+ The former is advantageous for sharp resonances; the latter for broad resonances. Using these shape parameters of the resonance curve and the physical properties of the test specimen, the dynamic Young's modulus, and the viscous modulus may be read from Figures 3 and 4, which were prepared in the following manner. The equation of motion of the free end of a viscoelastic reed which is clamped at the driven end is Y '
= Yf(q)eiwt
where q = (rnw2/E*I)l/*l cos J. cosh J. 1- 4, cns - _ _d ~cneh - - -d- -
'(*)
and where Yei0' represents the sinusoidal motion of the clamped end, y is the motion of the free end, E" is a complex function of frequency, Z is the moment of inertia of the cross sectional area (I = ( b a 3 ; / 1 2 for a rectangle of width, b , and
10
4
3
:-It
2
- PRESENT ANALYSIS
1
lU%0 0
01
0 AV -
v'
A
Figure 3. Relation of Young's modulus to band width
0 01
0 01
Figure 4.
720
Relation of modulus ratio to band width
INDUSTRIAL AND ENGINEERING CHEMISTRY
b
01
Au Y'
EFFECT O F P O L Y M E R R A D I A T I O N Table 111.
A series of resonance curves \vas plotted for the fundamental mode of vibration. Figures 3 and 4 were plotted from values of the shape parameters read from these curves. In the previous analysis referred to in Figures 3 and 4 the friction was taken as small ( 7 7 ) . This analysis shows good approximation even if the friction is not small.
Irradiation Effects of Vibration Characteristics of Elastomers
Dynamic
Elastomer Formulation (43 6
Base Polymer
Young’s Modulus El, 108 Dynes/
Exuosure 10; Rads
Sq.
Cm.
Modulus Ratio, E2/E1
Group I Natural rubber
32A43
GR-S
0.19 1.4
2.3 2.8 9.2
0.07 0.05 0.15
0 0.19 1.4
1.8 2.6 270
0.07 0.07
0
32A47
0.07
Composition of Plastic and Elastomer Formulations
Major constituents of the elastomer formulations are polymer, carbon black, and plasticizer (4, 6). O n the basis of 100 parts of polymer, the unplasticized Group I formulations contained about 20 parts of carbon black; the plasticized Group I formulations, about 30 parts of carbon black; the plasticized Group 1 formulations, about 30 parts of carbon black and 30 parts of various plasticizers. Group I1 formulations contained 70 parts of carbon black. Of the poly(vinyl chloride) formulations, two were plasticized; three were rigid. The plasticized formulations contained 52 and 25 parts of dioctyl phthalate, respectively, in addition to stabilizer. HoM’ever, the concentration of stabilizer is probably an insignificant variable for this study when compared to earlier work ( 4 ) .
Group II Plasticized natural rubber
PlS2Cl
PlS2C2
PlSZC3
0 0.19 0-43 1.0 0 0.19 0.43 1.0
0.33 0.7 0.9 2.0 0.25 0.5
0.19 0.43 1.0
0.8 1.8 0.30 0.4 0.8 2.3 0.47 0.8 1.3 3.8
0
0.9
0
0.19 0.43 PlS2C4
PlSlCl
Polybutadiene
1 .o 0
0.19 0.43 1.0 PlSlC2
Hycar OR-15
1.6 2.3 10 1.2 2.1 80 350
0
0.19 0.43 1.0
PlSlC3
Hycar OS-10
PlSlC4
Neoprene GN
0 0.19 0.43 1.0
1.2 5.6
20 270 1.2 4.0 50 250
0
0.5 1.1 2.5 PlSlC7
Polysulfide
Silastic 250
PlSlC8
PlSlC9
Natural rubbei
Hycar PA-21
Hypalon S-2
4.0 4.0
4.0 6.3
1
1 0.1
0.3 0.06 0.09 0.1 0.08 0.2 0.3 0.03
1.1
0.3 0.02
3.5
0.02
11
0.6
0 0.19 0.43
1.4
1.0
0.7
PlSlCll
0.19 0.43 1.0 0
1.4 3.3 13 3
Group I elastomers and the poly(viny1 chloride) formulations were furnished by the B. F. Goodrich Research Center; Group I1 elastomers, by the Materials Laboratory of the Wright FieId Development Center. literature Cited (1) Alfrey, T., Jr., “The Mechanical Behavior of High Polymers,” Interscience. New York. 1948. (2) Ballow, J. W., Smith, J. C., J . A t @ . Phys. 20,493 (1949). (3) Bland, D. R., Lee, E. H., Ibid., 26,
0.03 0.09 0.04 0.06 0.5
1497 (1955). (4) Bopp, C. D., Sisman, O., Nucleonics 13. NO. 7.28-33 (1955). (5) Zbid.,‘No. 10, pp. 5f-5. ( 6 ) Bopp, C. D., Sisman, O., ORNL1373. Office of Tech. Service. Dept. of Commerce, Washington 25, D. C., 1954. (7) Byrne, J., others, IND. ENG. CHEM. 45,2551 (1953). (8) Charlesby, A,, Atomics 5 , 12 (1954). (9) Elasser. W., Ann. Physik 13, 791 (1904). ‘ (10) Klein, E., Jenckel, E., Z . Naturforsch. 7a, 801 (1952). (11) Nolle, A. W., J. A t p l . Phys. 19, 753 (1948). (12) Robinson, D. W., J . Sci. Instr. 32, 2 (1955).
0.4 1 1
1
0.5
5
0.3 0.4
1.1 2.5
30 200
0.1
0.4
lus, El is the dynamic Young’s modulus, and E2 is the viscous modulus. If Y is constant over the width of the resonance curve, the resonance curve is given by a plot of the modulus of the complex variable 1 f (\k) (which is proportional to amplitude) us. the square of the modulus of Q (which is proportional to frequency).
+
Acknowledgment
0.20 0.20 0.20 0.20
0.3
0
where E* is the complex Young’s modu-
0.5
0
PlSlClO
+ i E2
0.04
0.06 0.12 0.04 0.04 0.06 0.16 0.06 0.08 0.10 0.15 0.06 0.1 0.2
0.19 0.43 1.0
3.1 8.6
thickness, a), I is the length, and m is the mass per unit length (3). For many organic materials it is found that over the Lyidth of a resonance curve approximately E* = EL
0 0.10 0.20 0.50
0.16 0.06 0.06 0.10 0.12 0.06
\
I
I
RECEIVED for review February 27, 1956 ACCEPTED October 10, 1956 Division of Polymer Chemistry, 127th Meeting, ACS, Cincinnati, Ohio, April 1955. VOL. 49, NO. 4
APRIL 1957
721
