Classroom Demonstrations of Polymer Principles IV. Mechanical Properties F. Rodriguez School of Chemical Engineering Olin Hail, Cornell University, Ithaca, NY 14853 In past articles (1) demonstrations have been described for illustrating various features of polymer structure, polymer formation, and polymer physical states. In this artlcle, classroom demonstrations of selected mechanical properties are described that can be used to make quantitative measurements. Stiffness, strength, and extensibility are obvious mecbanical properties that can be used to distinguish one polymeric material from another. End uses make specific demands on each of these parameters. A rubber band is expected to be entensiblrandresilient, a plastic table top muat he stiff, and a plastic shopping bag muat be pliahle nnd tough. The manner in which each of these . orooenies is measured -~~~ . may affect its value. The "strength" is particularly dependent on test conditions. As an example, polyethylene film from a shopping bag can be typified by a tensile strength of about 15 MPa (2,175 psi). A fiber made from the same batch of polymer can have a tensile strength of 70 MPa (10,000 psi). The difference in this case is simply due to a stretching process that changes the reference area on which the strength is based. The energy needed to start a tear in a cellulose acetate film (ordinary photographic negative film base) may he many times the energy needed to propagate the tear. The "tear strength" here depends on the presence of a certain kind of flaw. As a generalization, it can be said that stiffness (or modulus) is usually a reproducible material property hut strength (and elongation a t break) is a sample oronertv that d e ~ e n dstronelv s on test conditions. ~~
~
Tensile Testlng The uniaxial, tensile elongation of any sample (Fig. 1) requires a force, f. In engineering terms, the tensile stress, o
Figure 1. Tensile elongation
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is defined as the force, per unit original (undeformed) area
Aa. r = flA0
(1)
The change in length can be described in terms of the strain for which either of two parameters is commonly used where is the elongation and a is the extension ratio: c+l=o=LILo
(2)
In a typical test, a sample is elongated at aconstant rate, and the force is recorded as a function of the elongation. Among the many stress-strain patterns that can emerge, three will he considered here since they typify the behavior of polymers in three common physical states. A polymer glass is brittle, that is, it breaks with little elongation (Fig. 2A). For some common glassy polymers (polystyrene, poly(methy1 methacrylate), cellulose acetate), the stress a t break (also called the tensile strength or ultimate tensile strength) can be on the order of 70 MPa (10,000 psi) with an elongation at hreak of less than 10% (r < 0.10). The ordinary commercial window envelope provides an example. The transparent window usually is biaxially oriented polystyrene. This crisp, stiff plastic can be flexed easily only because i t is so thin (about 40 rm). A polymer "rubber" (a cross-linked melt), often shows an elastic nonlinear pattern (Fig. 2B) that can bedescribed (2, 3) by a theoretical equation as: where N is the moles of chain segments per unit volume, Tis the absolute temperature, and R is the gas constant per mole. At high elongations (a > 3), some rubbers (natural rubber and polybutadiene, for example) exhibit an increase in the slope of the stress-strain curve and are no longer described by eq 3. This is due to a self-reinforcing action involving crystallization on orientation of the chains.
Figure 2. Typical stress-strain diagrams for A, brittle glass; 8, resilient rubber; and C, ductile plastic.
r(
Figure 4. Stress-strain diagram for loading (0) and unloading (a)a rubber band. Stress is in increments of mass added to pulley system. Figure 3. Overhead projector table with pulley arrangement for elongation of rubber band.
Semicrystalline materials are actually polymeric crystallites embedded in a ruhbery, amorphous matrix of the same polymer. The polyethylene in trash can liners or shopping hags is a good example. On stretching this kind of material, the stress may go through a maximum. Continued elongation may require a lesser stress (Fig. 2C). This material is "plastic" or "ductile" in that it can he elongated or "drawn". Unlike the ruhber, it does not retract to its original dimensions on release of the stress. The change in crystallite orientation brought about by stretching ("drawing") is not reversible. The area under any stress-strain curve represents energy/ volume. At the breaking point, the cumulative area is the total energy (joule = newton X meter) absorbed by the sample. This total energy is used as a measure of "toughness". The area under the curve has the dimensions of the product of stress (pascal = N/m2) and strain (mlrn). Thus, stress X strain = N m/m3 = J/m! A "strong" glass with a tensile strength of 70 MPamay have absorbed only about 3.5 MPa-m/m by the time it breaks a t r = 0.10, that is an energy of 3.5 MJ/m" Put another way, that is less than 1cal/cm? A plastic with a modest strength of 14 MPa but an elongation of 6 = 6.0 a t break may have absorbed about 70 MJ/m3 by the time i t hreaks.
.
Apparatus
the demonstrator should wear safety glasses to protect against flying ruhber hands or springs. Rubbery Polymer
Rubber hands and balloons usually are made from natural rubber (1,4-polyisoprene) or synthetic materials withsimilar properties. I t is worth the while to have on hand a number of relatively similar samples so that one can he substituted for another without having to change conditions in the test. Nonlinearity of the Stress-strain Curve The rubber hand is anchored on a stud or a clip (Fig. 3) and attached to a hook and strine a t the free end. A erid drawn on a sheet of plastic or celloGhane is added so thatthe changes inlength can he plotted. This sheet can be areplaceable item so that the acrylic sheet does not get mixed up. The vertical axis is arbitrarilv laid out in increments of the masses t o be used. Examule 1: The rubber band was 7.0cm hv0.10 cm hv 0.20 4.0 X m2 (There were two 710-cin strands in cm. Ao ; parallel). Each mass of 0.100 ke represents a force of 0.981N. Thus each mass added an increment of stress = 0.245 MPa (35 psi) according to eq 1. The diagram that resulted on adding the masses is shown in Figure 4. The nonlinearity is obvious. Replotting of the more data as stress versus (a- a-2)would result in a much -~~~ linear plot (3) as predicted by kq 3. The area hounded by the loadine and unloadine curves is the hvsteresis. that is. the energidissipated as i e a t in the system during a cylicprocess. Although possibly aggravated by friction in the pulley, the major contribution to hysteresis is internal friction (viscoelasticitv) within the rubber hand. Repeated stretchine and relaxing would result in a measurable increase in temperature. For example, when an automobile tire rotates it is alternately stressed and unloaded. This causes the tire to heat up. As one might imagine, racing car tires become exceedingly hot due to this internal friction. ~
The overhead projector is useful when properties are to he illustrated for a eroup of more than iust a few soectators. An acrylic plastic s;eet;about 'I4-in. t k c k servesBs a table on which samples are displayed (Fia. 3). Near one corner, a plastic or metal pulley $ &untedrlf the shaft for the p l i e y is small in diameter, friction will be minimized. Then the force exerted by mass on the end of a string will be transmitted almost entirely to the sample. Sample grips can he made from a variety of materials. Paper clips can he fashioned into hooks for rubber bands or strines. For flat samales of alastic or ruhber. electrical allieator clips are useful. A set of five to 10 masses, say in 0.100-kg increments, is adequate for most samples and is unlikely to overstress the pulley arrangement. A common shop micrometer is useful for measurin~the thickness of materials in the range of a few thousandtLs of an inch. A heat gun is needed to show the changes in mechanical poperrie; with temperature for glassy and ruhhery materi81s. h 500-w model usuallv is sufficien~.Ordinary hair dryers do not give a high enough temperature with materialslike polystyrene. One does need to take care not to oveheat the acrylic table. Although there is very little hazard involved,
Temperature Dependence According to eq 3, when stress is held constant, an increase in T should result in a decrease in a. Since we know that materials expand on heating, the contraction in length (although accompanied by the increase in volume) can he rather unexpected. Mild heating of a rubber band that i s a t 2 or 3 times its relaxed length will give a detectable, but not dramatic shrinkage when seen on the overhead projection. Rather than using the overhead projector, a separate apparatus can be constructed using the lever arm principle to Volume 67
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Figure 5. Device for magnilying the change in elongation with temperature for a rubber band.
obtain easily seen motions (Fig. 5). In a film made over 25 years ago, Winslow used such a device where the rubber band was immersed successively in hot and cold water (4). The heat rmn allows for a somewhat simoler arrangement. In " either case, the room temperature position of the arrow can be adiusted bv movina a mass alone the lone arm of the lever. The iever a r k magnkcatiou really is needed when more than a few people wish to see the effect a t the same time (5). Various mechanical devices have been proposed to use the temperature effect in engines (6). Cross-Link Dependence
The term N in eq 3 is the chain density, the moles of chain segments that form the 3-dimensional network of the crosslinked polymer. With no cross-links, a polymer melt flows (as when a glassy polymer is heated above its transition temperature in part 2, below). When cross-links are removed from a network, the segments are longer and there are fewer of them per unit volume. In fact, N = 2C, where C is the moles of cross-links per unit volume. The cross-links in rubber bands and toy balloons often are made of polysulfide links. One classical way of reclaiming rubber from tires is to break the sulfide bonds with alkali and thus convert the elastic rubber into a plastic melt. Example 2: Two strips, a and b were cut from a rubber balloon so that each was 5.0 cm X 1.5 cm with a thickness of 0.015 cm. Strip b was placed in a test tube filled with triethylamine. TEA for 24 h. TEA should be used with adeauate ventilation. On removal from the TEA, the strip was swbllen to about 1.3 times its oriainal - leneth. .. . but washine in warm water restored it to its original dimensions. However, the cross-link densitv was reduced hsreaction of the amine with the sulfide bonds. When a mass of 0.12 kg was used to elongate each strip a t 22 O C , the stress applied in either case was 0.52 MPa, but the extension was no longer the same as shown in the table. In eq 3, we used R = 8.314 J/K. mol and T = 295 K to calculate N. The alkaline treatment of strip b removed 40% of the cross-links.
Figure 6. Rubber catapult. Velocity of projectile (a) is given by ratio of distance x to time of fall through distance y.
Example 3: A catapult was made from a rubber band by stretchingit across two posts 6.5 cm apart and retracting the center 2.8 cm. Using this "slingshot", a projectile weighing kg was propelled horizontally a distance of 0.98 m 9.0 X from a height of 43 cm (start of trajectory being horizontal). The catapult was made from two nails in a wooden board (Fig. 6). The time it takes for any object to fall through a vertical distance of y is given by t = (2ylg)'" where g is 981 cm/s2. When y = 43 cm, t = 0.30 s. Thus the constant horizontal velocity of the projectile must have been u = 0.981 0.30 = 3.30 mls. If all the potential energy stored according to eq 4 were converted into kinetic energy, the chain density can be calculated from the experimental data. Volume of rubber band = 1.04 X 10-6 m3 Temperature = 27 "C = 300 K rr = 1(6.5/2)2+ (2.8)211'2/(6.5/2) = 1.37 Kinetic energy = mui/2 = 0.0090 X (3.30)2/2 = 0.049 J R T = 8.314 X 300 Jlmol W = 0.049 Jl(1.04 X 1 0 - h 3 ) = 47 X 1 o 3 ~ m 3 W = N (8.314 X 300)(0.168) Jlmol N = 110 mol/m3
Glassy Polymer
A simple molecular model for many common polymers is a string of atoms (mainly carbon with some oxygen or nitrogen) connected by single bonds (Fig. 7). The model is an
Energy Storage
The energy, W stored as a result of straining an ideal rubber sample is obtained by integrating the stress over the total strain:
Extendon ol Rubber Balloon Sir@ Unbeated a
Amine-treated b
\I\,
i
-0 '
Figrne 7. Polymer chain modelled as a series of atoms linked by bonds at constant bond angle 8'. Above To,rotation like that shown for the last bond is possible for all bonds. Below Tg,rotation ceases.
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Journal of Chemical Education
sme ASTM tests of rubber. Instead of adding masses to the pulley arrangement, a coil spring can he used as a measure of force. The spring can he calibrated by extension with weights. Extension of most metal springs is almost linear in force. When the equivalent of 0.20 kg mass was used the crescent scarcely deformed. However, when a tiny (1 mm) slit was cut in the concave side, the sample failed a t the equivalent of about 0.02 kg mass. The size of the flaw is important. In a "trousers" tear test, a rectangular sample is pulled apart as shown in Fig. 9B.Large ro&d holes wire mehe in a Diere of 35-mm ~hotocraphirfilm (develuped film that has been washed free of &&ion) (cellulos~acetate)using a notebook punch. A tiny razor notch was made a t the bottom of the first .~--~ - and - ~ second holes. Now. when a mass of 0.20 ke was applied, the sample failed rapidly, but the tear stoppei when it reached the un-notched hole. For the tear to propagate, i t is necessary that the stress he concentrated in small leadine " area and not spread out over the circumeference of a large circle. ~~~~~
..
Fbure 8. A. A blaxiallv oriented oolvsMena strlo Is cut Into a dumbbell rhaoe " . w ln IS ends remtorcea by tape. 8. On caulio~ohealong, me sample relaxer to become thocker. snoner, an0 narrower.
accurate description for 80% of the 30 billion or so kilograms of polymers used in the United States in 1986. Only the tight network materials like the epoxies and phenolics are exceprotation is tions. Above a characteristic temperature, Tg, possible around single bonds and the chains are flexihlethe material is a melt or rubber. Below that temperature, rotations cannot occur and the material is a glass. For polystyrene, T,is about 100 *C. As mentioned earlier, the transnarent windows from the ubiquitous envelopes that appear in our bills and in various junk mailings provide an almost endless source of ~olvmericclass. The usual material has been hiaxially orientkd by stretching in the plane of the film at a temperature ahove T,. The orientation is "frozen" in because the film is well below T,a t room temperature. ~~~
~
High Mcdulus Example 4: A sample (Fig. 8) was cut out with scissors to he about 7.0 cm X 1.5 cm X 0.0040 cm. Thus Aa = 6.0 X m2. An added mass of 0.10 kg represents an increment of stress = 1.7 MPa (250 psi). Each end of the sample was reinforced with tape (almost any kind of cellophane or plastic tane will do). The sample was mounted on the overhead proj&tor table.' When force was applied, say as much as 0.400 kg, almost .. no elongation was observed, confirming the rigid nature of the polymer. The modulus, the ratio of stress to strain, is about lo3 times higher for a glass compared to a typical rubber hand or balloon. Thermal Effects Example 5: Cautious heating of the sample to about 80 OC under minimal load (0.050 kg) allowed the sample to relax from its oriented state back to a chaotic, random state (Fig. 8). In this relaxed state the sample is shorter, narrower, and thicker than i t was before heating. Further heating ahove T, changed the sample to a melt and flow occurred. These effects can also be analyzed with the help of polarized light ( 1 , 7). Tear Strength Anyone who has attempted to open a plastic hag of potato chips or similar product can appreciate the importance of a stress-concentrating flaw. Wrestling with the package can be of no avail until a tiny tear is started. Then the tear propagates very easily. Example 6: The polystyrene window envelope material was cut in the shape of a crescent (Fig. 9A) and reinforced a t the ends with tape. This is a standard configuration used in
~~~~
a
Semlcryslalllne Polymer Almost any polyethylene packaging material is suitahle. Most material used for packaging magazines and other mail is in a suitahle range of thickness. The behavior of Figure 2C usually is more pronounced when the sample is cut perpendicular to the "machine" direction. This is because the extrusion of polyethylene into the film form orients the crystallites somewhat in the direction of flow (the machine direction). The rearrangement of crystallites with localized deformation is more dramatic than the more uniform deformation in the pre-oriented direction. Example 7: The polyethylene cover from a mailing was chosen because it is pigmented and is easily seen when projected. If polarized light is used ( I , @ , a transparent sample should he used. The s.~ r i -n awas again used to characterize force. The sampledimensions werP7.0 cm X 1.0cm X 0.0040 cm. The i m ~ o r t a n lenrth t is that of the uniform width section only. A; the assembly was stressed (shown by the spring extension), there was very little sample deformation until a sudden localized strain (the "neck") occurred (Fig. 10). The deformation then continued and the length of the sample increased by a factor of 5 or more with the stress slightly less than the maximum needed to start the neck (the yield stress). The adjective "ductile" is quite appropriate since it
razor notch
B.
/r
razor notches
Figure 9. Tear tests. A. Crescent type. 8. Trousers type.
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coil spring
grip
polyethylene dumbbell
neck
.
. . .
Fiaure 10. As force f increases. exoandina me coil sorino. > t h e oolvethvlene e l o n g a l e s anmy a ttle Once t h e nocr f o r m % 11g r o w u%a y u In ess force tnan was needed to in loate t h e necr
0.mooell
means "canable of beine drawn out". The drawine nrocess had, in fait, convertedthe typical ductile semic&talline olastic into a tvnical tane or fiber. The area used in calculating the stress could be-the original plastic area or the new, stable, oriented tape area, so what one chooses to call the tensile strength could differ by a factor of 5 or more even though the test is performed on the same sample. A semicrystalline polymer like nylon differs from polyethylene in that the noncrystalline matrix is glassy rather than rubherv as in the case of oolvethvlene. - . Drawine of common nylon is, consequently more difficult a t room temperature, but about as easy as it is for polyethylene if the temperature of the nylon is raised above its T,of about 50 O C . I t is easy to see from this that one should not overeeneralize on the basis of the demonstrations suggested here:
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Conclusions Many variations from the behavior of Figure 2 are seen when real materials are tested. The concepts of stiffness and strength are important in applications as diverse as parachute cords, appliance enamels, garden hoses, shoe laces, glues, and floppy disks. The manner of characterizing the parameters may differ widely. Standard tests abound (8-
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13). For the purpose of classroom demonstrations, the tensile testing of thin samples used in this article differentiates among some major classes of behavior. Several caveats are in order for the demonstrator. Always rehearse the demonstration under conditions as similar to the classroom as possible. Always have duplicate samples in reserve. Choose examples and tailor dimensions to fit the apparatus. Wear safety glasses to protect against springs and flyingsamples. If nothing else, it is needed to impress students with the importance of safety. e. The demonstration is only a means to emphasize'a point. It does not replsce explanation,organization, or enthusiasm. Some convenient sources of materials include: Rubbery polymers: Rubber bands, toy balloons, surgical gloves. Glossy polymers: Envelope windows (polystyrene),negative film base (cellulose acetate). overhead transoarencies (oolvester). .. .
Kraft caramel wrappersicoated cellophane).
Semi-crystalline polymers: Trash bags, sandwich bags (polyethyl-
ene). Llterature Cited 1. Rodriguez, F.: Mathias. L. J.: Kruschwi1z.i.: Carrsher,C. E., Jr. J . Chrm Edur. 1987, M , 72.88fi: 19SS.65,352. 2. Treluar. L. R.G. The Phvrie.%ri/RuhberElorticity. 3rd ed.: Oxlord: New York. 1975. 3. Rodrieua. F.J . ChemEduc. 1973.50.764. ow "Phynical Chemistry oi Polymed'. (16-mm pound lilm. 4. F. H . . w ~ ~ ~(Narrator,. color. 21 mink Reil Telephone laboratories: Murray Hiil. NJ, 1962. 5. Lasvick,P.H. J.ChemEduc. 1972,49.469.andDole,M. J.Cham.Educ. 1971,54,75& 6, Pines.E.: Wun, K. L.: Prins, W. J . Chrm.Educ. 1973.50.758. I. Hudrieuez. F. J. Chem.Educ. 1969.46.456. 8. L ~ ~ ~ ~E.;: wys, A . ,I. A. T ~ ~P & t i r ~ ~ t ~ t i " , n: / ~ ~ o r t i ~c r o h ~ i3 ~ ded.: i ~ . CRC: Cleveland, 1968. 9. Shah. V. Handbod n/Plorlrcs T ~ i i n T~chnnlrrpl.: p Wlley: New Ynrk. 1984. 10. B C O W ~ R. . P., Ed. Handboob o(Plostirr Teat Mrthods.2ndod:Gdwin: London. l98I. 11. Hndiey,D. W.: Ward, I. M. In E n ~ i l P u l y mSii.4 Enp.:Kioachwifx, J. L..Ed.;Wiley: New York, 1987: Vol 9, p :119. ~ . ~ ~ ~ h ~ nTwin(: i e o lo / ~ o s r i c r :wiiey: ~ e ~wo r k1984. , 12. T U ~ E S. 13. Kampf, G . Chornrlrriiotion of Plaslicr by Phwiral Melhoda: Oxiurd IHanser): New York. 1987
