A PHOTOGRAPHIC METHOD FOR D E T E R M I N I N G SMALL DIFFERENCES I N SPECIFIC YOLUME ROBERT TAFT Department of Chemistry, University of Kansas, Lawrence, Kansas .4XD
LLOYD E. RIAL31 Department of Chemistry, Utah State Agricultural College, Logan, I'tah Received A p r i l 90, 1998
I n a study of the electrical conductance of sols and gels of gelatin and of agar, it became necessary to determine whether there is a n appreciable difference in the density, or specific volume, in the sol and gel state, Le., whether or not any contraction or expansion in volume occurs when the solidification of the sol takes place. A search of the literature gave very little information on this point, most authors tacitly assuming no change in specific volume during the gelation process. The usual methods of determining densities, especially of the material in the solid (gel) state are not satisfactory, because of the difficulty of removing and measuring the mass and volume of a given quantity of gel. Furthermore, we were primarily interested in deterting differences in density, rather than the actual density itself. Our problem was solved by photographing a specimen of gelatin (or agar) sol in a suitable container before and after it had jelled. A comparison of the resulting negatives enabled us to determine that a slight contraction occurred in passing from the liquid state to the gel state. Further, the method permitted an approximate determination of the difference in density. The actual procedure involved making a negative of the narrow neck of a 50-cc. pyknometer possessing a diameter of 3.7 mm., whirh contained the sol in question. To prevent changes in density occurring aq a result of temperature difference, the pyknometer was placed in a constanttemperature bath provided with walls of plate glass. The negatives were made with a view camera of long bellows extension, fitted with a lens of 2" focal length. With this arrangement the neck of the fiask way projected on the negative a t a magnification of 11 diameters. The camera v a s focussed on the meniscus of the sol, the field including also the defining mark on the neck of the capillary, as will he seen by an inspection of figure 1. 1187
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ROBERT TAFT AND LLOYD E. MALM
FIG.1 Fxo. 2 Fro. 1. Capillary ani1 meiiiscu8 (npproximately times four). 7.80 per rent gelatin sol a t 30°C. FIG.2. Cspillary and meni8cus (approximately times four), 7.80 per rent gelatin KPI a t 30'C.
0 EL
SOL
FIG.3. Diagrammatic illustration of method employed in cdculatiog density change. C corresponds to the defining mark on the capillary of the pyknometer; the areas A $ ,A * and A a t A. are so labeled for convenience in counting squares. ( A i + A 4 ) - ( A I +A,)givesthedeereaseinverticaleross-sectional areaof thesol-gel transformation, measured from the bottom of the gel meniscus. This derrpase in area can be converted into its corresponding volume decrease; if the total volume of the pyknometer is known, the percentage contraction can be computed. Illustration of actual rase (figures I and 2): A , A2 225 squares; A2 .1, = 321 squares; the contraction is therefore 99 squares. Since, by measurement, 0.37 em. was the linear equivalent of 32 squmes (each square would thus have an equivalent side of 0.116 em.), the decrease in volume ='as approximately B rylinder 0.37 em. in diameter and 99/32 x 0.0116 cm. high. The volume derrense i n w h i r wntimeters is therefore (3.112) (0.37/2)'(0.035) 0.0038 C C . ThQ total vnlume of the pyknometer to B WBB found t o be 50.071 ee. The contraction on gel formntion was therefore (O.W1/50.071 0.012) X 100 = 0.008per Pent (0.012 w. is the Y d U m P of sol above thc line E ) .
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DETERMINATION OF SMALL DIFFEREKCES IN DEKSITY
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The specimen under observation in figure 1 was a gelatin sol of 7.80 (weight) per cent gelatin and had a density of 1.0190 at 30"C., as determined b y the usual pyknometric method. It was allowed t o remain in the constant-temperature bath for an hour a t 3O"C., by which time it had set t o a firm gel. It was then rephotographed, neither containw nor camera having been changed from its original position. The print obtained from the second negative is shown in figure 2. A comparison of figures 1 and 2 shows that the meniscus in the gel state is very noticeably pointed; the meniscus in figure 1 shows the familiar form of all liquids. I t is apparent that some contraction has occurred in passing from the liquid state to the gel state. To determine the extent of the contraction, the negatives of figures 1 and 2 were placed on squared paper; then the areas bounded by the meniscus, the walls of the capillary, and the defining mark on the wall of the capillary were carefully traced. From a comparison of these two tracings the change in volume was calculated. The actual method of calculation is shown in figure 3. For the case described it was found that 50 cc. of the liquid underwent a contraction of 0.004 cc.; or the density of the solid (the gel) waq 0.008 per cent greater than that of the liquid. It is recognized, of course, that such a determination is based on the assumption that the volume of the pyknometer is the same before and after gel formation. It is possible that gel formation contracted somewhat the volume of the container, owing to the cohesive forcw between gel and glass. No cracks, or other evidences of strain, however, appeared between the glass walls and the gel. I n addition to the determination described in the present paper, other measurements were made, all showing that for gelatin and agar the density of the gel was always slightly greater than that of the liquid form at the same concentration and temperature.
