Stretched Elastomers A Case of Decreasing Length upon Heating S. 6. Clough University of Lowell, Lowell, MA 01854 I t is widely known that objects generally increase in length when their temperature is raised, this increase accompanying the volume expansion. The change in length can he used to measure temperature. The bimetallic-strip oven thermometer is an example. An idea of the magnitude of expansion can he seen in the following calculation^ A copper rob 8.0 cm long will undergo the small increase in length of about 0.04 mm when the temperature is increased bG30 "C. The linear expansion is given by A1 = &AT, where or, the coeffifor cient of linear expansion, is equal to 16.6 X 10-"eg-' copper ( I ) , and lo is the original length. A cross-linked polymer, held elongated under a constant load in the rubbery state, however, decreases in length as the temperature is increased (2). and bv a sienificantlv. larzer amount than the copper rod ekpanded. ~ h l ' was s easily qualitatively demonstrated as follows. A rubber band originally 5 cm in length was placed over a clamp on a ring stand and a mass was attached as shown in Figure 1. Then the system was placed in a cold environment (out of doors in January in New England) for several hours and both the sample length and temperature were allowed to equilibrate. he-temperature was about -10 "C. The height of the clamp was then lowered to allow the weight just to touch the base of the stand. Upon bringing the system indoors where the temperature was about 20 "C. the length of the rubber hand decreased by several millimeters for this 30 "C temperature increase, and the weight was raised off the base of the stand. A more quantitative exercise was performed in the laboratory. A similar system was placed in an oven. A millimeter scale was plared Iwhind theiuhber band in order to measure it5 irngth. The orig~nulunstretrhed length of the rlastomer was 6.0 cm. A 200-g mass was hooked through the rubber band, and the stretched band was allowed to stand several hours a t room temperature. Themass needed to elongate the elastomer a given amount will depend on the rubber's crosssectional area as well as the extent of cross-linking of the material. The data in the table were then collected to the nearest degree and nearest half millimeter. The length decreases because the force of retraction increases with increasing temperature. Why is this the case? The rubber band consists of long polymer molecules attached to each other a t long intervals by chemical bonds (cross-links). In the relaxed state prior to stretching, the molecules are randomly coiled (and undergo rapid changes in the exact shape of the coil). When the sample is elongated, the molecules are stretched somewhat in the same direction that the sample is stretched. See Figure 2. The molecules in the original coil have a higher entropy S (i.e., are more random, less ordered) than in the stretched state. The entropy decreases upon stretching. This is hecause there are fewer ways to arrange the molecules when their ends are a t a greater distance apart than when their' ends are close together. In this case the entropy can be thought of as a measure of the number of ways of arranging the molecules with their ends a certain distance apart. The tendency of entropy to increase as the molecules coil back up (return to their original, less-ordered state) causes the force of retraction. This force is greater at higher temperatures, where there is more rapid motion of the molecules, and a more random, chaotic state (3).
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Journal of Chemical Education
Figure 1. A simple method to demonstrate the decrease in length of a stretched elastomer upon heating.
Length Changes of an Elastic Band with a Constant Load as a Function of Temperature Temperature (OC) 20 35 45 48 57
Length (mm) 163.0 158.5 155.5 154.0 151.0
Figure 2. Polymer chain molecuies coiled ( a ) before stretching and (b) after stretching. The cross-iinkr are not shown.
A review of the thermodynamics of rubber elasticity was presented in this Journal by Nash ( 4 ) .The equilibrium force of retraction can be presented as force = -T(ASIAl). The force is seen to he directly proportional to absolute temperature. The increase in force on elastomers with increased temperature has been used to build an engine. One side of a wheel with elastomeric spokes is heated. The difference in force on opposite sides of the wheel causes an imbalance resulting in a rotation of the wheel (5,651.Speeds of 1000 rpm have been obtained when a large AT was employed ( 5 ) . Two points must he mentioned. An "ideal elastomer" is one in which the energy contrihution of retractive force is equal to zero, and the force is due only to entropy changes. In a real rubber the energy contrihution may account for up to 50% of the force and may make a positive or a negative runtrihutio~~ depending un the strurtureoithe polymer mol6.r ulrs ( 3 ) .Further, therr is n slight increase in the volume of the sample no r h ~temperature . is raised. The volume increase
is caused by increased amplitude of vibrations of the seaments of the molecules, and increased "free volume", unoccupied space between the molecules (7). The above discussion is in contrast to the force needed to stretch a copper rod a small amount. This force is due to energy changes, not entropy changes. As the distance hetween copper atoms increases when the rod is stretched slightly, the energy is raised while the entropy remains nearly unchanged. In this case, the force is due to the way the energy changes with increasing length.
1. Hondbook
d Chemistry and Physics, 52rd ed.: CRC: Cleveisnd. OH. 1972.
2. Bsder.M. J. Chem.Educ. I981,5R, 285. a. ~ ~J. E ~' ' ~k~h" b~b, * ,wartic state: in ~ Chemical Society: Washineton. DC. 1984. I hr.h I K J & ' a . c 1879.:,i 40. ' birr.. H .I P , . . m Di .
