APPENDIX 9.3 DETERMINATION OF THE CROSS-LINK DENSITY OF

RUBBER BY SWELLING TO EQUILIBRIUM†

The present experiment is based on the rapid swelling of elastomers by organicsolvents. Application of the Flory–Rehner equation yields the number ofactive network chain segments per unit volume, a measure of the extent ofvulcanization (C1,C2).

Experiment

Time: About 1 hour

Level: Physical Chemistry

Principles Illustrated:

1. The cross-linked nature of rubber

2. Diffusion of a solvent into a solid

Equipment and Supplies:

One large rubber band

One 600-ml beaker (containing 300 ml toluene)

One ruler or yardstick

One long tweezers to remove swollen rubber band

Paper towels to blot wet swollen rubber band

One clock or watch

One lab bench

First, cut the rubber band in one place to make a long rubber strip.Measure and record its length in the relaxed state. Place in the 600-ml beakerwith toluene, making sure the rubber band is completely covered. Removeafter 5 to 10 minutes. Blot dry. Caution: toluene is toxic and can be absorbed

through the skin. Again, measure and record length. Repeat for about 1 hour.Optional: Cover and store overnight. Measure the length of the band the nextday.

Expected Results

The rubber band swells to about twice its original length, but then it remainsstable. Note that swelling to twice its length means a volume increase of abouta factor of 8. Also, note that the swollen rubber band is much weaker than the

dry material and may break if not treated gently.

APPENDIX 9.3 DETERMINATION OF THE CROSS-LINK DENSITY OF RUBBER 503

† Reprinted in part from L. H. Sperling and T. C. Michael, J. Chem. Ed., 59, 651 (1982).

Chemically most rubber bands and similar materials are composed of arandom copolymer of butadiene and styrene, written poly(butadiene–stat–

styrene), meaning that the placement of the monomer units is statistical alongthe chain length. Usually this product is made via emulsion polymerization.

Swelling of a Rubber Band with Time

Length, cm Time, min

16.5 024.0 1426.0 2527.0 3628.0 70

Typical results are shown in the table. Over a period of 70 minutes, thelength of the rubber band increased from 16.5 to 28.0 cm, for a volumeincrease of about 4.9. This is sufficiently visible to be seen at the back of anordinary classroom. The rubber band would continue to swell slowly for somehours, or even days, but for the purposes of demonstrations and classroom cal-culations, the swelling can be considered nearly complete.

Calculations

For the system poly(butadiene–stat–styrene) and toluene, c1 is 0.39. Assumingthat additivity of volumes v2 is found from the swelling data to be 0.205. Thequantity V1 is 106.3 cm3/mol for toluene. Algebraic substitution into equation(9.92) yields n equal to 1.55 ¥ 10-4 mol/cm3. (Compare result with Appendix9.2.)

Extra Credit

Two experiments (or demonstrations) can be done easily for extra credit.

1. Obtain some unvulcanized rubber. Most tire and chemical companiescan supply this. Put a piece of this material into toluene overnight andobserve the results. It should dissolve to form a uniform solution.

2. The quantity n can be used also to predict Young’s modulus (the stiff-ness) of the rubber band. The equation is

(A9.2.1)

where E represents Young’s modulus, and R in these units is 8.31 ¥ 107

dynes·cm/mol·K. For the present experiment, E is calculated to be 1.1 ¥ 107

dynes/cm2, typical of such rubbery products.

E nRT= 3

504 CROSS-LINKED POLYMERS AND RUBBER ELASTICITY