Gelatin as a Physically Crosslinked Elastomer G. V. S. Henderson, Jr., D. 0. Campbell, V. Kuzmicz, and L. H. Sperling Lehigh University, Bethlehem, PA 18015 Gelatin is good to eat. Such gels also serve as demonstration material, teaching about rubber elasticity, the physical behavior of proteins, and the influence of hydrogen bonding on stiffness. This paper describes an inexpensive way to count the hydrogen bonds in gelatin as a classroom demonstration or laboratory experiment. Ordinary gelatin is made from the skins of animals by a partial hydrolysis of their collagen, an important type of protein ( 1 , 2 ) .At home, a crude type of collagen can he prepared from the broth of cooked meats and fowl; this material also frequently gels on cooling. When dissolved in hot water, the gelatin protein has a random coil tvne of conformation. On cooline. -. a conformational change takes place to a partial helical arrangement. At the same time, intermolecular hydrogen bonds form, probably involving the N-H linkage. On long standing, such gels may also crystallize locally. The bonds that form in gelatin are known not to be permanent, but rather they relax in the time frame of 1O3-106 s (3-5). T h e amount of bonding also decreases as the temperature is raised. For the purposes of this paper, intermolecular hydrogen bonds will be assumed responsible for the stiffness of the gel.
-
&
Theory By observing the depth of indentation of a sphere into the surface of gelatin, "indentation" modulus is easily determined. The indentation modulus yields its close relative, Young's modulus. The crosslink density and thus the number of hydrogen bonds (simple physical crosslinks) are readily determined by treating the gelatin as a hydrogen-bonded elastomer. Young's modulus may be determined by indentation using the Hertz equation (6),
Principles nlustrated: 1) Hydrogen bonding and physical crosslinking in elastomers. 2) Rubber elasticity in elastomers. 3) Physical hehavior of proteins. Equipment and Supplies: 5 150. X 75-mm I'yrex" vrysmlliamg dishes or suup dishes 5 %cup lnckelk of flavored Srllo* hrnnd pr4alin !8 g p n r ~ i nprr packet) 18 2-cup packets of unflavored Knox' brand gelatin (6 g protein per packet) 1 metric ruler 1 steel hearing (1.5-in. diameter and 0.2256 kg-or any similar snherical obiect) 1 Lb bench 1 knife ~
~
Five concentrations (see Table 1)of gelatin were prepared, each in 6W ml of water, and allowed to set overnight in a refrigerator at 5.0 T.Then, indentation measurements were made by placing the steel hearing in the center of the gelatin samples and measuring the depth of indentation, h (see Fig. 1).Since it is difficult to see through the gelatin to observe this depth, it is desirable to measure the height of the bearing from the level surface of the gelatin and subtract this quantity from the diameter of the bearing (Fig. 1). The measured depth of indentation, the radius of the hearing, and the force due to the bearing are algebraically substituted into eqn. (1). This value of Young's modulus is substituted into eqn. (3) to yield hydrogen bond crosslink density. Results A plot of E as a function of aelatin concentration (Fia. 2) demonstrates n linear increase in Young's modulus a t l o w conrentrations. T h r slight upward curvature at high w n Table 1. Qelatln Concentrations
where E = Young's modulus rdynes/rml), u = Poisson's ratio (-0.5 for elastomers), I.' = forre of spherearainst rheaelatin surface = dynes, h = depth of indentation orsphere (cm), and r = radius of sphere (cm). The hall indentation experiment is the scientific analog of pressing on an ohjed with one's thumb to determine hardness. The less the indentation, the higher the modulus. Young's modulus is related to the crosslink density through rubber elasticity theory (7,8):
Dish
Conc.'
1 3.0
Jeilo GelatinC
1 8
2 2.0 1 5
3 1.0 1 2
4 0.75 1 1.25
5 0.50
1 0.5
M n c . = number of timer the na-1 gelatin concenhatim (each dish contain* 600 ml of water) 4Jello = number of 2cup packets of Jell0 brand black raspberry f~avorsdgelatin 'Gelatin = number of 2-wp pack& of Knox brand vnflsvored gelatin
Assuming a tetrafunctional crosslinking mode (four chain segments emanating from the locus of the hydrogen bond):
E = 6C,RT
(3)
Gelatin c r o s s section
where n = number of active chain segments in network, C, = crosslink density (moles of crosslinks/unit volume), and R = 8.314 X lo7 (dyne-cmlmole OK). For this experiment, the gelatin was a t 278.0 OK,the temperature of the refrigerator employed. Experimental Time: About 30 min, the gelatin prepared previously. Level: Introductory Polymer Science, Physical Chemistry, or Biochemistry.
DEPTH OF INDENTATION.
h(cm) = d- h* Figure 1. Schematic of experiment, measuring the indentations of the ball in the gelatin.
Volume 62
Number 3 March 1985
heavy
269
Table 2.
Getattn Indentations Yleld Hydrogen Bond Numbers
bnc.
h (cm).
0.5 0.75 1.0 2.0 3.0
1.50 1.30 1.20 0.80 0.40
C,
(mol/cm3)"
3.5 X 104.4 x lo-' 5.0 x lo-' 9.1 x lo-' 2.6 X 10"
the rubber-like elasticity of these materials. A t greater elongation the sample breaks, however. This is because the gelatin protein chains are much diluted with water.
N~
0.60 0.50 0.50 0.43 0.84
h = IMsntatlon measured at gelatln temp. of 5 C ' = number of hydrogen bonds N = number 01 hydrqlenbonds per molecub
3 C,
(x
NORMAL GELATIN CONC.)
Figrae 2. Modulus of gelatin samples Venus conurnoatim. For camparison. anobar ban0 b r a Young s modulusot snout 1 X lO%ascals(l pascal = 10 dynes/cm2).
centrations is caused by the increasina efficiency of the network. However, the line should go through the origin. Phvsical crosslink concentrations were determined usina eqn. i3), and the results are shown in Table 2. Assuming molecular weight of about 30,000 glmole for the gelatin, there are about 0.60 hydrogen bonds per molecule (see Table 2). Using gelatin as a model crosslinked elastomer, its rubber elasticity can also be demonstrated by a simple stretching experiment. Thin slices of the more concentrated gelatin samples were cut and stretched by hand. On release from stretches up to about 50%, the sample snaps back, illustrating
Discussion Young's modulus is a measure of a material's stiffness. For rubbery materials, Young's modulus is also related to the number of crosslinks in the system. In this case, the crosslinks are of a physical nature, caused by hydrogen bonding. Measurement of the modulus via ball indentation techniques allows a rapid, inexpensive method of counting these hydrogen honds. Table 2 shows that the number of these hydrogen bonds is of the order of 10-I moles/cm3. The number of these bonds also was shown to increase linearlv with concentration. except at the highest conrenrratiuns. Table 2 also demonstrntes that at each gelatin conrentration, the number of hydrogen honds per gelatin molecule is relatively constant.Th~snurnber,of course, is the number of hydrogen bonds taking part in three-dimensional network formation. Not all of the gelatin chains are bound in a true tetrafunctionally crosslinked network. Many danglingchain ends exist a t these low concentrations, and the network must be very imperfect. The gelatin molecule is hasically composed of short a-helical segments with numerous intramoleculz hydrogen honds a t room temperature. The a-helical segments are interrupted by proline and hydroxyproline functional groups. These groups disrupt the helical structure, yielding intervening portions of chain that behave like random coils, and which may be relatively free to develop intermolecular hydrogen bonds. In this experiment, the concentration of sugar was kept constant so as to minimize its effect on the modulus. In concluding, i t must be pointed out that if sanitary measures are maintained, the final product may be eaten a t the end of the experiment. If gelatin five times normal or higher is included in the study, the student should be prepared for his or her jaws springing open after biting down! Literature Clted
a
270
Journal of Chemical Education
52M39.
(61 Sperling, L. H., "lntcrpenetratingPoIym~~ Newor%and RelatedMstcrials,"Plenum Prega,Now York. 1SBI.p. 177. (71 Radriguez,F.,"PrincipimofPolymuSyatems,"2ndd..McGraw-HiU.NewYork.1982. PP. 19?405.
(81 Nick", L., ''Mechaoleal Pmpenim olPolymers and Cmnpasites,"Vol I. M d M u , Inc, New York. 1974.n.176.
Hiah School Advanced Chemlstrv Form 1984-ADV S w i n g Formula-Number Right-60 Items Group A-represents 2 semesters of high school chemistry. Group 8-represents 4 semesters of high school chemistry. Entire Grouo-reoresents 2 to 4 semesters of hiah school chemisbv . . The courser were described variously as regular. advanced, honors, advance3 placement, and the like. NO.of Students NO. of Schools Length of Course
RAW SCORE
Group A
Oroup B
Entire Group
161 7
425 26
566 31
2 sem.
2 *em.
2 sem
% ILE
% lE
% ILE 10 14 22 30 35 36 43
29 30
68 73
46 49 54. 58 63
32 34 36 36 40
60 63 66 93 94
66 72 76 84 88
44 48 54
98 99 100 26.93 26 7.66 0.772 10-51
93 97 100 26.56 28 9.605 0.852 8-56
Median
Mean Median c 7
KR 21 Rel. Range
272
44 47 51
~
Median
~
29.18 28 10.13 0.868 8-56
Journal of Chemical Education
. . Median
