INDUSTRIAL AND ENGINEERING CHEMISTRY
November, 1942
Conclusions
1. The vibration modulus and resilience are independent of the frequency of vibration if the temperature is constant. 2. The internal friction is approximately inversely proportional to the frequency. 3. The modulus decreases as temperature increases. Curves for synthetic stocks at high temperatures are not very different from those of rubber a t low temperatures. 4. Resilience rises linearly with temperature. Rubber shows a transition from one slope to another a t about 25" C. 5. The dependence of the internal friction of rubber and similar materials on temperature follows the same exponential law as the viscosity of liquids. At certain critical temperatures sudden changes occur in the cohesive forces which cause a transition from one curve to another. For the natural rubber sample this occurs a t about 17" C. 6. The amplitude of vibration has a large inverse effect on the modulus and friction which cannot be explained by the temperature rise of the sample due to heat generated in it. The effect may be due to nonlinearity of the stress-strain curves. 7. Modulus and friction are affected by temperature in the same way, indicating the dependence of both on some fundamental characteristic of the molecular structure.
1365
Natural rubber requires two straight lines for representation on the modulus-friction plot, the junction occurring a t about 25" C. Acknowledgment
The writer appreciates the assistance and cooperation of J. H. Fielding and the Compound Development Section of the Goodyear Company for furnishing the compounds used. He also wishes t o thank P. J. Jones for assistance in taking the data, and S. D. Gehman for many helpful suggestions in interpreting the results. Literature Cited (1) Gehman, S.D.,J . Applied Phys., 13, No. 6,402(1942). (2) Gehman, S. D., Woodford, D. E., and Stambaugh, R. B., IND. ENG.CHEM.,33, 1032 (1941). (3) Gemant, A.,J . AppEied Phys., 12, No. 9, 680 (1941). (4) Kimball, A. L.,Trans. Am. SOC.Mech. Engrs., 51, 227 (1929). (5) Kosten, C. W., Proc. Rubber Tech. Conf., London, 1938, 987. (6) Laran, B. J., meeting of Am. 600. Mech. Engrs., June, 1942. (7) Mark, H.,Proc. Rubber Tech. Conf., London, 1938, 978. (8) Naunton, W. J. S., and Waring, J. R. S.,Ibid., 1938, 805. (9) Roelig, H.,Zbid., 1938, 821. (10) Sebrell, L. B.,and Dinsmore, R. P., S. A . E . Jozwnal, 49, 368 (1941). (11) Smallwood, H.M., J. Applied Phys., 8, No. 7, 505 (1937). (12) Ward, A. G.,"Structure and Molecular Forces in Pure Liquids and Solutions", p. 88,Faraday Soo., 1936.
THEORY OF RUBBER ELASTICITY FOR DEVELOPMENT OF SYNTHETIC RUBBERS Hubert
M. James'
Purdue University, Lafayette,
Eugene Guth
Ind.
WO cardinal problems exist in connection with the proT duction of synthetic rubbers: choice of the type of synthetics, necessary raw materials, and methods of production; (a)
(b) evaluation of the products obtained. The most important and characteristic property of synthetics (and of natural rubbers) is their long-range reversible elasticity. This property is the one which distinguishes rubber from wax, chewing gum, etc., and makes possible its widespread use for a variety of purposes. Especially does i t make possible the construction of tires. This property is so characteristic that any material possessing it may be called a "rubber", regardless of chemical constitution. Ip spite of the many attempts directed toward an explanation of rubberlike elasticity, this problem (a problem in the chemical physics of solids) continued to be puzzling for many years. A theory of the typical rubber elasticity will obviously be of great help in the production, processing, and evaluation of desirable synthetics. T o mention a concrete problem of vital interest, Butyl rubber has poor rebound a t room temperature but is as lively as natural rubber a t 100' C. It is obvious that, when more is learned about the mechanics of what makes rubber bounce, a more lively Butyl rubber a t ordinary temperatures may be produced. The statistical theory of rubber elasticity (2, 6) explains in terms of molecular structure why rubber has a long-range 1 On leave of absence, Radiation Laboratory, Massaohuaetts Institute of Technology, Cambridge, Msas.
University of N o t r e Dame, N o t r e Dame, Ind.
reversible elasticity and why it exhibits an anomalous thermoelastic behavior. The essence of the statistical theory is based on two conceptions. First, rubber consists of giant long-chain molecules. Secondly, a quasi-free rotation is assumed to exist in a rubber molecule around each carbon-carbon bond. An important consequence of this quasi-free rotation is that the molecules are coiled up in the unstretched state. The retractive force in stretched rubber is then due mainly to the tendency of the stretched chain molecules to change from the stretched, less probable form to the more probable coiled-up form. This is in accordance with the second law of thermodynamics and is not caused by forces. The kinetic motion of the quasi-free rotating groups is the principal cause of the contraction. This semiquantitative theory explained the anomalous thermoelastic behavior of rubber. I n particular, it predicted a direct proportionality between absolute temperature and the stress a t constant length, if the dependence of the internal energy upon the length were separated out. However, no conclusions could be drawn from it as to the nature of a proper stress-strain curve. The reason for this restriction was the following. As a model for bulk rubber, this theory assumed a large number of rubber chain molecules and avoided consideration of the interactions between the strings or chains. However, this interaction must be considered if the model is to possess a finite volume. Obviously, strong forces must exist between the molecules to prevent their slipping bodily past one another. On the
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Vol. 34, No. 11
INDUSTRIAL AND ENGINEERING CHEMISTRY
other hand, the existence of these forces is in apparent contradiction to the postulate of the statistical theory that the molecules are free to coil up into a configuration of maximum entropy or greatest probability. RECENTLY, however, a quantitative theory was developed by James and Guth (3, 4,6, 7). This new theory introduces a clear-cut three-dimensional model for bulk rubber, and it also resolves the dilemma between flexibility (free rotation) of the chain molecules and the steric forces binding them to a network. It yields a single analytical expression for the stress-strain curve which exhibits the characteristic S-shape of the typical rubber stress-strain curves. It also predicts the occurrence of “a thermoelastic inversion point” or critical extension below which rubber shows normal thermoelastic behavior. and above which it is “rubberlike”.
For a unilateral stress in the z direction and for an incompressible material like rubber a unit cube before stretching will be transformed into a parallelopiped of the same volume with the sides La, L,, L,. The equilibrium condition applied, for instance, to the free y-x surface leads to the equation F = KTL,
=
PL,L,
(2)
where P is the internal pressure we wish to determine. K e have the conditions, L,L,L.
hence P
=
=
L,L;
=
1
(3)
KT(l/L,)
(4)
That is, the pressure decreases if the cube is extended and increases if it is compressed. If, now, an external force is applied, the equilibrium condition will be that the inward-acting agents again should equalize the outward-acting agents. The external force represents an outward pull. Assuming that the stretch takes place in the 1: direction, this equilibrium condition is obtained:
F
+ PL.L.
=
KTL,
(5)
Using the values of P and the incompressibility condition, we obtain as a final result the equation,
F
Figure I. Cross-sectional Representation of (A) Random Irregular N e t w o r k and (B) O r d e r e d N e t w o r k In the theory it is proved that A may be replaced by B, in which the flexible chains r u n in the direction of three perpendicular coordinate axes.
Let us consider first a sample of unstretched rubber. What is its molecular structure? It is a random network of flexible chains stretched throughout the mass of the rubber (Figure 1). Each element of this network-i. e., a giant long-chain molecule, tends t o contract because of the intramolecular Brownian motion of these free-rotating rubber molecules. Just as a flexible string thrown up into the air will be more likely t o come down in some curved form other than a straight line, a flexible rubber molecule will, in the unstretched state be more likely to have a coiled rather than a straight form. This contracting tendency of the elements would lead to a collapse of the network-that is, to a more or less closepacked configuration. However, the tendency to close packing is counteracted by steric forces acting in the opposite direction in the chain molecule-that is, in the elements of the network and the joints between neighboring chain molecules. This second agent may be pictured as an outward push due to the outward pressure of a fictitious incompressible liquid through which the network of chain molecules extends. This simulates in effect the intermolecular forces which regulate the volume of the material. For the unstretched state there must be an equilibrium between these two agents-namely, the inward pull due to the contracting tendency of the network and the outward push due to the pressure of the “liquid”. This equilibrium condition selves to determine the pressure of the “liquid” if the contracting force is known. The contracting force may be derived by simple probability considerations of thermodynamics and has the form F = KTL (1) where K = a constant which characterizes the rubber networkT = absolute temperature; L = relative length (that is, extended length divided by original length)
=
KT(L
-
1/Li)
(6)
The first term in the parentheses is due to the contracting force whereas the second term is due to the pressure of the “liquid”. This stress-strain curve has all characteristics of the rubber stress-strain curves up to 200-300 per cent extension. It must be stressed that the quantity L which enters here is the ratio of the extended length of the sample (which is kept the same for all temperatures) and of the original length a t room temperature. Hence Equation 6 is not exactly true if the temperature changes, and it is easy to see that the only change we have to make is to correct the internal pressure, a ( T - To)] l/L:. Then the equareplacing l/L: by [l tion reads
+
(7)
Here the slope of the force will be zero if L
=
l+(a/3)(27‘-
To).A negative slope was discovered by Joule some eighty years ago and shows up both in natural and synthetic rubbers andinother rubberlike materials-for instance, in polystyrenexylene mixtures (1). THE theory shows that, for high extensions only, the contracting force changes its dependency upon extension. The internal pressure remains practically the same. This change of the contracting forces leads to an upward turn of the stress-strain curve and gives the characteristic S-shape of typical rubber stress-strain curves. We have proved that there are rubber compounds which show an S-shaped stressstrain curve in a range of extensions where no crystallization enters. This is the case for Buna types of synthetics particularly. Crystallization is sufficient to produce an S-shaped stress-strain curve, but it is not necessary for it. Experiments on natural and synthetic rubber have revealed that the theory checks better with natural rubber than with synthetics, especially those containing carbon black. A correlation of the changes of the constants of the theory with those of the polymerization conditions should lead to the development of synthetics with more desirable properties. In addition, our theory permits a better evaluation and correlation of the thermoelastic properties of synthetics than the usual testing methods.
INDUSTRIAL AND ENGINEERING CHEMISTRY
November, 1942
It appears to be better, when studying synthetics, to use a higher speed of stretching than the usual 20 inches per minute. At higher temperatures and higher extensions synthetics flow at a rate depending upon the speed of the stretching. The rate of flow differs for each particular compound. Therefore fast stretching is necessary to eliminate the plastic flow. A detailed discussion of this new theory will be published elsewhere.
Henry
F. Palmer and Robert H. Crossley
WITH
the increasingly important role being played by reclaimed rubber in the war effort, it seems desirable to examine this raw material more closely than heretofore from the standpoint of maintenance of quality during natural aging. Some lots of reclaimed rubber in certain consumers' plants have attained greater age than usual because of unforeseen changes in production schedules, occasioned by the present situation. Moreover, the creation of a stock pile of reclaimed rubber from excess production, as an emergency supply, has been and may again be considered by the Government. Also, substantial amounts of reclaimed rubber have been exported and thereby have acquired more age than usual before use. Finally, certain manufacturers have desired that reclaimed rubber have a definite age from the standpoint of processing advantages; in some cases, an age of 6 months has been requested if possible. Reclaimed rubber undergoes certain changes upon aging. It becomes drier, nervier, and less tacky on the mill, and requires more mastication to achieve the desired workability. Palmer and Kilbourne (8) commented on this tendency and showed that these changes are accompanied by a reduction in the chloroform extract of the reclaim. The purpose of this paper is to show the effect of these changes in properties of reclaimed rubber during aging upon the quality of products in which it is used. Periodic Testing of Different Types of Reclaim Approximately one ton of each of three commercialproducts (Table I) was set aside from regular production. Five slabs of each reclaim were chosen, and samples obtained by cutting a strip across the cut end of each slab so that the entire cross
Table 1.
Mfg. process
Analyses of Reclaims
A B Black passenger Black passenger inner tube inner tube Open-steam pan Alkali digestion
Analysis", % Acetone extract 7.32 6.37 Ash 26.32 22.87 Alkalinity 0.79 0.14 Total sulfur 1.75 1.66 6.70 Carbon black 4.67 Rubber content (by difference) 59.00 64.84 1.12 Specific gravity 1.17 0 Teats run when reclaims were two weeks old.
Literature Cited (1) Ferry, J. D., J. Am. Chem. Sac., 64, 1323 (1942).
(2) Guth, Kautschuk, 13, 201 (1937). (3) Guth and James, IND.ENG.CHEM.,33, 624 (19411. (4) Guth and James papers at Dii.isions of Rubber and Colloid Chem. of A. C. S.,Detroit, 1940. (6) Guth and Mark, Monatsh., 65, 93 (1934). (6) James and Guth, Phys. Rev., 59, 111 (1941). (7) Ibid., to be submitted for publication (1942).
ots of three typical reclaims w e r e set aside to age, and at intervals acetone and chloroform extracts, alkalinities, milling tests, reclaim-sulfur tests, and tests i n typical test formulas w e r e obtained. As the reclaims aged, they became less tacky and harder to break d o w n during milling. This appeared to be less true of reclaims of high alkalinity than of those w i t h l o w alkalinity. The acetone extracts remained constant w i t h increasing age, but the chloroform extracts decreased. These changes w e r e accompanied by small variations i n physical properties in test formulas, but no significant changes in quality were observed in the reclaims u p to 18 months. A p i l e of scrap tires was set aside, and from them four separate lots of w h o l e tire reclaim w e r e manufactured a t such intervals that fresh and aged reclaim could be tested simultaneously; these tests w e r e made in the laboratory in a typical tread formula and i n the treads OF tires which w e r e roadtested. No significant difference was found in quality between tires containing reclaim 1 5 months or 3 months old.
L
Xylos Rubber Company, Akron, O h i o
Reclaim Type
1367
C
whole tire Blend of alkali digestion and opensteam 8.87 18.67 0.09 1.91 14.56 ~~
~~
56.00 1.18
section of the slab was included. These five strips were blended before testing to make one composite and representative sample of each reclaim. The same five slabs of each reclaim were periodically tested as they increased in age. Acetone extracts and chloroform (uncured) extracts were obtained by the method of Palmer and Kilbourne (8). Milling tests were made by the procedure suggested by Palmer, ' Miller, and Brothers (IO) and later described in detail by Palmer and Kilbourne (8). It consists in milling a sample of the reclaim on a laboratory-size mill under standardized conditions with respect to batch size, roll temperature, roll speed, and roll setting. The times necessary for the reclaim to knit to the slow roll, reach a definite degree of smoothness, and leave the slow roll and adhere to the fast roll are recorded. The alkalinity of the sample was determined by the benzenealcohol-water digestion method described by Palmer and Miller (9). Tensile tests of the reclaims were obtained in test formulas I and I1 (Table 11); these are the same as formulas IV and 111, respectively, proposed by Palmer and Crossley (7). The reclaim-sulfur tensile tests were obtained by using
