THE STRUCTURE O F GELATIN SOLS AND GELS Part IV. Fluidity and Hydrolysis* BY 5. E. SHEPPARD AND R. C. HOUCK
I n a previous paper' there was presented an extended study of the effect of temperature change on the fluidity of gelatin sols. Using a de-ashed gelatin, fluidity-time curves a t different pH values were obtained a t 4ooC., so°C., 60"C., 7ooC., and 85OC. Initially the curves sufficiently approached straight lines for their slopes to be taken as measures of the rate of change of fluidity. The slope, A@/At,plotted as function of pH, gave at each temperature a curve showing a flat minimum. These curves sufficiently resembled the logarithmic form of the catalytic catenary2of Hudson to allow the conclusion that @k, the fluidity change constant, was proportional to log K, where K was the actual velocity constant of hydr~lysis.~On the other hand, if @k is considered as proportional to the actual velocity constant of hydrolysis, then it is found that the comparison of the family of log @k pH curves with Northrop's pH curves is somewhat closer. Fig. I shows the actual curves. log K Plotting the data in this manner indicates more clearly that the slopes of the straight line on the acid side and on the alkaline side of the flat portion of the log @k p H curve are practically the same for all the temperatures employed. Further, it appears to be probably the better method of plotting since by considering @k the velocity constant, the usual methods employed in chemical kinetics for studying a reaction can be employed. Further evidence, pointing to hydrolysis of gelatin molecules as the main cause of the decrease in viscosity with time, has been found by calculating the heat of hydrolysis from the @k values a t constant p H and at different temperatures. The heat of hydrolysis is calculated by application of the van't Hoff expression dealing with the relation of the velocity constant and temperature, This expression is as follows:
-
-
in which
k
= velocity constant
T = absolute temperature Q = heat of reaction R = gas constant expressed in calories A study of this relation indicates that a linear relation should exist between the logarithm of the velocity constant and the reciprocal of the absolute temperature. *Communication No. 493 from the Kodak Research Laboratories.
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S. E. SHEPPARD AND R .
C. HOUCK $0 0 a
0 1
s 4 5 2
'eo '1 6
b 4
3
t
f 7 E 8
4 b
I
I
2
S
4
6
0
1
0
I
10
FIQ.I
Accordingly, log & values a t the same pH, but different temperatures, were plotted against the reciprocals of the absolute temperatures. The results obtained are shown by Figs. 2 to 3. With pH's up to 5.4, fairly good straight lines were obtained, provided the results at 85OC. were excluded. The #k values at this high temperature appear to be too low, possibly due to a change in the reaction products. A very satisfactory straight line was obtained over the pH range 5.6 - 6.8, in which the velocity constant is practically independent of pH at all temperatures studied. At pH 8.0 and above, straight lines were not obtained, indicating that probably there are other disturbing factors in this region as well as hydrolysis. Inspection of the van't Hoff equation, particularly in the integrated form:
shows that the heat of the reaction is obtained by multiplying the slopc of the log +k I/T curve by 2.303 R, where R is the gas constant expressed in calories and is equal to 1.98. This was done for those cases where the log 4 I/T graph was a straight line. The results obtained are shown by Table I.
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THE STRUCTURE O F GELATIN SOLS AND GELS
FIG.3
FIQ.4
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S. E. SHEPPARD AND R . C. HOUCK
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TABLE I Heats of Hydrolysis of Gelatin No. 36 Heat of Hydrolysis of Gelatin
PH
Slope
4 4 4 7
5258 5522
2 j,zoo
5
5825
26,540
(calories)
2
j 6 - 6 8
4735
24,000
19,920
(Mean 23,915 cal.) These values appear to be significant when comparison is made with the value for the heat of hydrolysis of gelatin calculat,ed from velocity constants determined chemically. Greenberg and Burk4 determined the velocity of hydrolysis of gelatin at high t'emperatures by autoclaving and measuring the amino-acid content by the Van Slyke method. They calculated a constant, ICs, involving the activity coefficient. By plot't'ing log K, against I/T, a fair straight line is obtained, as shown by Fig. 4. The authors preferred to plot log I
