Table A9.1.2 also demonstrates that at each gelatin concentration, thenumber of bonds per gelatin molecule is relatively constant. This number, ofcourse, is the number of bonds taking part in three-dimensional network for-mation. Not all the gelatin chains are bound in a true tetrafunctionally cross-linked network. Many dangling chain ends exist at these low concentrations,and the network must be very imperfect.

The gelation molecule is basically composed of short a-helical segments inthe form of a triple helix with numerous intramolecular bonds at room tem-perature; see Section 9.13. The a-helical segments are interrupted by prolineand hydroxy proline functional groups. These groups disrupt the helical struc-ture, yielding intervening portions of chain that behave like random coils, andwhich may be relatively free to develop intermolecular bonds. The subject hasbeen reviewed by Djabourov (A7) and Mel’nichenko et al. (A8).

In this experiment the concentration of sugar was kept constant so as tominimize its effect on the modulus. In concluding, it must be pointed out thatif sanitary measures are maintained, the final product may be eaten at the endof the experiment. If gelation five times normal or higher is included in thestudy, the student should be prepared for his or her jaws springing open afterbiting down!

REFERENCES

A1. A. Veis, Macromolecular Chemistry of Gelatin, Academic Press, Orlando, 1964.

A2. E. M. Marks, in Encyclopedia of Chemical Technology, Kirk-Othmer, Interscience,New York, 1966, Vol. 10, p. 499.

A3. J. L. Laurent, P. A. Janmey, and J. D. Ferry, J. Rheol., 24, 87 (1980).

A4. M. Miller, J. D. Ferry, F. W. Schremp, and J. E. Eldridge, J. Phys. Colloid Chem., 55,1387 (1951).

A5. J. D. Ferry, Viscoelastic Properties of Polymers, 3rd ed., Wiley, New York, 1980, pp.529–539.

A6. L. H. Sperling, Interpenetrating Polymer Networks and Related Materials, PlenumPress, New York, 1981, p. 177.

A7. M. Djabourov, Contemp. Phys., 29(3), 273 (1988).

A8. Yu. Mel’nichenko, Yu. P. Gomza, V. V. Shilov, and S. I. Osipov, Polym. Intern. (Brit.

Polym. J.), 25(3), 153 (1991).

APPENDIX 9.2 ELASTIC BEHAVIOR OF A RUBBER BAND†

Stretching a rubber band makes a good demonstration of the stress–strainrelationships of cross-linked elastomers.The time required is about 30 minutes.

APPENDIX 9.2 ELASTIC BEHAVIOR OF A RUBBER BAND 501

† Reproduced in part from A. J. Etzel, S. J. Goldstein, H. J. Panabaker, D. G. Fradkin, and L. H.

Sperling, J. Chem. Ed., 63, 731 (1986).

The equipment includes a large rubber band (Star® band size 107, E. Faber,Inc., Wilkes-Barre, PA, is suitable), a set of weights up to 25 kg, and a meterstick. Also required are hooks to attach the weights and a high place fromwhich to hang the rubber band.

First, the rubber band is measured, both in length and cross section, and thehooks are weighed. Increasing weight is hung from the rubber band, its lengthbeing recorded at each step. When it nears its breaking length, caution isadvised.

A plot of stress (using initial cross-sectional area) as a function of a,Figure A9.2.1, demonstrates the nonlinearity of the stress–strain relationship.Initial values of the slope of the curve yield Young’s modulus, E. The sharpupturn of the experimental curve at high elongations is due to the limitedextensibility of the chains themselves. The number of active network chains per unit volume can be calculated from equation (9.34) as 1.9 ¥102 mol/m3.

A Mooney–Rivlin plot according to equation (9.50) yields a curve that rapidly increases for values of 1/a greater than 0.25; see Figure 9.18.The constants 2C1 and 2C2 are calculated from the intercept and slope,respectively. Values of 2.3 ¥ 105 Pa and 2.8 ¥ 105 Pa were obtained,respectively.

502 CROSS-LINKED POLYMERS AND RUBBER ELASTICITY

Figure A9.2.1 Simple rubber–elastic behavior of a rubber band under increasing load.