On the Crosslinked Structure of Rubber Classroom Demonstration or Experiment: A Quantitative Determination by Swelling L. H. Sperling and T. C. Michael Materials Research Center #32, Lehigh University, Bethlehem, PA 18015 'Early European settlers found the American Indians playing games with ruhber balls. These new materials were made from the c o a d a t e d sao of the Heuea brasiliensis tree. Chemically, the i&ber was H linear, high molecular weight cis-polyisoprene, which has the structure C C H r C ( C H J = CH-CHzj., where n may be as large as about 5,000. A ~ r o b l e mwith this early material was that it flowed. After standing for some time, rubber halls made from it became flat on the bottom. The problem became worse when the Europeans made rain coats and boots out of rubber and tried to dry them in front of a warm fireplace. In 1839,Thomas Hancock and Charles Goodyear found that by adding sulfur and then heating, the flow properties suhstantially disappeared, and a heat stable soft solid was made. T h e new process was called "vulcanization." Today, the ~ e n e r aorocess l is known as "crosslinkine." because the lone chains df polymer are linked together &to a network, (see Fieure 1).Other terms meanine crosslinkine include: "tanning" of leather, "drying" of oil-based paintsyand "curing" of inks. Interestingly, a crosslinked network is actually one giant . atom is molecule. Take a rubber band for e x a m ~ l e Every covalently bonded to every other atom, excluding t h e small amount of impurities usually present. Also, cutting the rubber band in half certainly produces a structure with different properties. (It can no longer hold objects together in the same way as before.) Thus, i t is the smallest structure with the properties of interest. . . In the present experiment or demonstration, we will examine the rrmdinked behavior of ruhher, using a rubber band as an example. Experiment Time: About one hour Leuel: Physical Chemistry Principles Illustrated 1. The crosslinked nature of ruhber. 2. Diffusion of a solvent into a solid. Equipment and Supplies: 1large rubber band 1600-ml beaker (containing 300 ml toluene) 1ruler or yardstick 1long tweezers to remove swollen rubber band paper towels to blot wet swollen rubber band 1 clock or watch 1laboratory bench First, cut the ruhher hand in one place to make a long ruhber strip. Measure and record its length in the relaxed state. Place in the MX)-ml beaker with toluene, making sure the rubber hand is completely covered. Remove after 5-10 min. Blot dry. Caution: toluene is toxic and can he absorbed through the skin. Again, measure and record length. Repeat for about one hour. Optional: cover and store overnipbt. Measure the length of the hand the next day. ~ i p e e t e dResults: The rubber band swells to about twice its orieinal lendh. hut then it remains stable. (Note that swelline to twice its lenkh means a volume increase of alwut a facur 01 right., Also, nole /hat [he sriollon ~
~
r u h b w hond i s n,uch u ~ o k c rlhor, rhe d r y ntormol ond m a ) brcok
if not treatedgently. Chemically, most rubber bands and similar materials are composed of a random copolymer of hutadiene and styrene, written poly(butadiene-co-styrene),meaning that the placement of the monomer units is statistical along the chain length. Usually, this product is made via emulsion polymerization.
A
rubber network. Lines Indicate polymer chains, and doh indicate cross
links.
The Swelling ol a Rubber Band with Time Length, cm.
time, min.
16.5 24.0 26.0 27.0 28.0
0 14 25 36 70
Typical results are shown in the table. Over i period of 70 min, the leneth ~-~~ " of the ruhher band increased from 16.5 cm. to 28.0 cm. for a volume increase of nhmt 4.9. Thip is sufficientlyoh\,iuus to he w e n at the hack of an ordinary clatunnm.'l'he mhber band would runtlnue w * to SWPII aloulg for some hours, or even days, hut tLr the ~ ~ r l n of demonstrationsand classroom calculations,the swelling can he considered nearly complete ~
Theory T h e rubber is a three-dimensional network of randomly coiled chains. Each long primary chain is linked to other chains a t 10 to 20 points, called crosslinks. As the rubber swells with liquid, these chains expand, straightening out. The equilibrium swelling theory of Flory and Rehner (1,2) considers forces arising from three sources: 1. The entropy change caused by mixing polymer and solvent. The entropy change from this source is positive and favors swelling. 2. The entropy change caused by reduction in the numbers of wssible chain conformations on swelline. This is a direct conseauence bf the chains straightening out. The entropy change from this source is negative and opposes swelling. 3. The heat of mixing of polymer and solvent, which may be positive, negative, or zero. For most systems, including the rubber-toluene system considered herein, the heat of mixing is slightly positive, opposing swelling. T h e Flory-Rehner equation may he written:
where un is the volume fraction of polymer in the swollen mass, V1 is the molar volume of the solvent, and XI is the Flory solvent-polymer interaction term. This theory, of course, is Volume 59
Number 8
August 1982
65 1
related to the thermodynamics of solutions, except that the chains are prevented from separating from each other. As a rubber elasticity phenomenon, i t is an extension in three dimensions. The value of eqn. (1)lies in its ability t o calculate the quantity n, the number of network chain segments bounded on both ends by crosslinks. For tetrafunctional crosslinks of the type shown in the figure, there are twice as many chain segments as there are crosslinks. Calculations For the system poly(butadiene-co-styrene),XI is 0.39. Assuming additivitv of volumes. u9 is found from the swelling data t(yt,e0.205. he quantit; 1; is 106.3cm'lmole for tolu': ene. Algebraic 3ubvtitution intoean. (1) yields n equal to 1.55
Extra Credit Two experiments (or demonstrations) can be done easily for extra credit. 1. Obtain some unvulcanized rubber. Most tire and chemical c o m p a n i ~ v c a n ~ ~this.' r ~ ~ lPut y apieceofthismaterial into toluene furm a uniform overnight and observe the results. It should diraolvr I*, solution. 2. The quantity n can be used also to predict Young's modulus (the stiffness)of the rubber band. The equation is E = 3nRT (2) ~
~~
wherc E represents Young's rnodulun, and R in these units is R.31 X Ill7 dynelcmlmole-OK.1-h the present experiment, E is calula~edm be 1.1 X 10- dyneslrm~.typiral ofaurh rubbery products Literature Cited (1) Flory, P. J. and Rehner, J.,J Cham. Phya., 11,521.(1943).
(2) Flory, P. J.. "Principle8 of Polymer Chemistry." Cornell University. Ithaea, NY,
,am
(3) Allcock. H. R. and Lampa.F. W.,"ContemporsryPolymerChemistry."Prentice-Hall. Englewwd Cliffa, NJ. 1981. (41 Seymour. R B.and Carraher,Jr., C.E.,"PoIymeymChemi~yY,An I~trdodctiii."M~I
' Commercial source: Firestone Synthetic Rubber and Latex Co.
Trade name: Stereon".
652
Journal of Chemical Education
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(5) Young.R.J.. "lntrduetion toPo1ymers:'Chapmanand Hall. New York, 1981. (6) Radriguez, F., "Principles of Polymer Systems,"2nd Ed., Mffirslw-Hill. New York, ISSZ.
