CROSS-LINKINQ PROCESS IN QELATIN QELS
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STUDIES OF T H E CROSS-LINKING PROCESS IN GELATIN GELS. I1
STATIC RIGIDITYAND STRESSRELAXATION MEREDITH MILLER,' JOHN D. FERRY, FREDERIC W. SCHREMP,' A N D JOHN E . ELDRIDGES
Department of Chemistry, University of Wisconsin, Madison, Wisconsin Received August 28, 1960
When the rigidity of a gelatin gel is measured under static conditions (12, 18), mechanical equilibrium appears to be maintained for a period of minutes, at least, indicating that the linkages joining the elastic structure do not break or rearrange during this time interval. However, there is evidence from a variety of sources that over longer periods of time these linkages are labile. When a gel is maintained at constant strain, the stress (11, 15) and the strain double refraction (16) decay gradually. Moreover, studies of the swelling of gels in water (13, 14) indicate a distensible structure with cross-links that can rearrange very slowly at 5°C. and within a few hours at 20°C..(7). To obtain more information about this process, a detailed study has now been made of stress relaxation and its dependence on temperature and previous thermal and mechanical history. Because of the complexity of this behavior, measurements have been restricted to a single gelatin concentration and molecular weight. In addition, it is now possible to report a direct comparison between measurements of static rigidity and the dynamic rigidities determined previously by the method of transverse wave propagation (6, 8). MATERIALS AND METHODS
The gelatin employed was the ossein sample P6-20 described previously (8), with a number-average molecular weight of 34,000. The sterile stock solution was stored at O'C., and all measurements were made with this solution, which contained 59.2 g. gelatin per liter and 0.15 M sodium chloride, at pH 7. Before each experiment, the solution was heated at 37°C. for 1 hr. to erase previous thermal history, introduced into the apparatus, and then cooled to the desired temperature as described below. Static rigidity and stress relaxation were measured in an apparatus which is described in more detail elsewhere (17). The gel was contained between coaxial stainless steel cylinders separated by an annular gap of 0.125 in. The outer cylinder was rotated through a small angle O A ; the inner cylinder, which a t the u.pper end w&s machined down t o a diameter of 0.103 in. for a length of 1.75 in. to form in effect a very stiff torsion wire suspension, responded with a very small rotation es. The gel rigidity was calculated from the equation 1 Present address: Film Department, E. I. du Pont de Nemours and Company, Buffalo, New York. 2 Present address: California Research Corporation, La Habra, California. 8 Present address: Polychemicals Department, E . I. du Pont de Nemours and Company, Wilmington, Delaware.
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MILLER, FERRY, SCHREMP, AND ELDRIDOE
G = %b/b(eA
- )0,
(1) where @ is the torque, which in turn is equal to kO,, and b is a constant calculated from the dimensions of the cylinders, following the procedure of Goldberg and Sandvik (10) in evaluating end effects. The torsion constant k was obtained by calibrating the inner cylinder assembly through application of small known torques by flexing thin drill rods attached to the bottom of the cylinder by a collar. The angle e,. was always less than 0.02, and usually less than 0.015 radian, corresponding to maximum shear strains in the gel of 0.09 and 0.07, respectively. It is important that the strain be small not only to avoid risk of rupture but also to insure proportionality between stress and strain; in several caaes this proportionality was confirmed within experimental error. The angle BE was usually less than 0.0005 radian; it waa measured by deflection of a light beam by a mirror mounted on the inner cylinder, with an optical lever of 968.4 cm. Stress relaxation was measured by holding OA fixed and following the change in OB with time. Since the strain was proportional to e,. - 0, and OB
