# Gelatin as a Physically Cross-LInked Elastomer

##### Equipment:

5 150*75mm Pyrex crystallizing dishes or soup dishes, 5 2-cup packets of flavored Jello brand gelatin (8g protein per packet), 18 2-cup packets of unflavored Knox brand gelatin (6g protein per packet), one metric ruler, one steel bearing (1.5-in. diameter and .226 kg or any similar spherical object), one lab bench, one knife.

##### Procedure:

Five different concentrations of gelatin were prepared (table below), each in 600 ml of water, and allowed to set overnight in a refrigerator at 5 degrees C. The indentation measurements were made by placing the steel bearing in the center of the gelatin samples and measuring the depth of the indentation, h. As 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 (figure below).

The measured depth of indentation, the radius of the bearing, and the force due to the bearing are algebraically substituted into the equation E = (1-v^2)F/[4h^3.2*r^1/2]. This value of Young's modulus is substituted into the equation E = 6C(sub)x * RT to yield the hydrogen bond cross-link density.

##### Science:

By observing the depth of indentation of a sphere into the surface of gelatin, the "indentation" modulus is easily determined. The indentation modulus yields its close relative, Young's modulus. The cross-link density and thus, the number of hydrogen bonds (sample physical cross-links) are readily determined by treating the gelatin as a hydrogen-bond elastomer.

Young's modulus may be determined by the indentation using the Hertz equation: E = 3(1-v^2)F/[4h^3/2*r^1/2] where F represents the force of the sphere against the gelatin surface = mg (dynes), h represents the depth of the indentation of the sphere (cm), r is the radius of the sphere (cm), g represents the gravity constant, and v is the Poisson's ratio. The ball indentation experiment is the scientific analogue of pressing on the object with one thumb to determine hardness. The less indentation, the higher the modulus. Young's modulus is related to the cross-link density through the rubber elasticity theory. E = 3nRT Assuming tetrafunctional cross-linking mode (four chain segments emanating from the locus of the hydrogen bond): E = 6c(sub)x * RT where n represents the number of active chain segments in network and C(sub)x is the cross-link density (moles of cross-links per unit volume). For this experiment the gelatin at 278.0K, the temperature of the refrigerator employed. [eq]. The plot above, of E as a function of gelatin concentration demonstrates a linear increase in Young's modulus at low concentrations. The slight upward curvature at high concentrations is caused by the increasing efficiency of the network. However, the line should go through the origin. Physical cross-link concentrations were determined using equation E = 6C(sub) x * RT, and the results are shown in the table below.

Remarks:

Measurement of the modulus via ball indentation method allows a rapid, inexpensive method of counting cross-links. Except at the highest concentrations, the number of bonds was shown to increase linearly with concentration. In this experiment, the concentration of sugar was kept constant so as to minimize its effect on the modulus.

Rahul Pinto