INDUSTRIAL A N D ENGINEERING CHEMISTRY
June, 1924
593
Some Unresolved Factors in Jelly Strength Determination'p2 By S. E. Sheppard and S. S. Sweet EASTMAN RODAK Co., ROCHESTER, N. Y.
I
N PREVIOUS papers3 the authors have dealt with the determination of the elastic properties of gelatin jellies as well as with the empirical measurement of jelly strength. Recently, they have discussed the relation of jelly strength to accurately defined elastic constant^.^ In the present paper they propose to deal-incompletely, it is true-with certain of the variable factors in the determination of jelly strength.
ELONGATION IN CM.
FIG.~-LOAD-ELONGATION CURVES
ELASTIC CONSTANTS In the first place, it is necessary to recapitulate briefly the relations between the different elastic constants of an isotropic material. Calling the modulus of rigidity, which expresses the resistance of the material to pure shearing stress, N , and the modulus of stretch, E , we have
where
= Poisson's ratio-i.
e., p = lirn
[y
Presented a t the Gelatin Symposium before the Division of Leather Chemistry at the 66th Meeting of the American Chemical Society, Milwaukee, Wis., September 10 to 14, 1923. 2 Communication No. 197 from the Research Laboratory of the Eastman Kodak Company. * J. Am. Chem. SOC.,48,539 (1921); 44, 1857 (1922). 4
THISJOURNAL, 16, 571 (1923).
DIMENSIONS OF TESTPIECES I n the paper referred to, it was shown that the apparent jelly strength, determined with plunger type of instruments, is a function of the actual size of test piece, or rather its ratio to the size of plunger, being independent for a sufficiently large value of the ratio. The empirical jelly strength value thus determined is related to the modulus of stretch or compression (Young's modulus) by a function not readily determinable, but a t the limit mentioned should be simply proportional thereto-that is, jelly strength P = c X E , where P is a value in arbitrary units and c is a constant. We should expect the effect of the dimensions of the test Diece to be shown, to some extent a t least. in the determination of the modulus of stretch, by the extension of test pieces of given size. Experiments were w run on rectangular blocks of jelly, a t three different lengths, but with the other dimensions the same. No grips were used, the test pieces being held a t top and bottom by adhesion to blocks of wood. They were stretched by static loading, and the load-elongation curves plotted (Fig. l), first for the actual (uncorrected) load, and second for the load per actual cross section (corrected). The graphs in the first place are straight lines, in the second they commence as straight lines and then become concave to the elongation axis. It is the slope of the curves of the second type (corrected for altered cross section) that FIG. APPARATUS *OR MEASURINGDILAT1oN STRETCH gives the modulus of stretch: (stretched piece) El = dP L d x' dP Lo Uncorrected (unstretched piece) E2 = Corrected
s
.
The modulus of stretch used by Leick6 was obtained by the formula E = -PIG - - P L
JIL Q
: +J]
-i. e., the infinitesimal value of the ratio of transverse to longitudinal strains. Assuming that p = 0.5 (see later), 1
this gives N = E / 3 or E = 3 N . Hence, if one of the elastic constants is known, the other can be ascertained directly, provided the volume of the material is unchanged during compression or extension.
Q
=0 2 (1
Q = cross section D.B = D 2 = (side)2 P = load in grams
L
1
E
&)2
= length
in cm.
= elongation in cm. = elastic modulus
Hence, since
E1 = dP z . L3 6
= $ , w h e n - dL
Ann.Phys. Chem.. [ 4 ] 14, la9 (1904).
1
L =Iz1
Leick’s modulus is Young’s modulus, the modulus of stretch for 100 per cent elongation.
1.4-
8
s
Vol. 16, N o . 6
INDUSTRIAL A N D ENGINEERING CHEMISTRY
594
I
k
Load Grains
L Stretch Cm.
0 100 300 500
0.075 0.25 0.50
0
TEST PIECE L E N G T H
I
I
I
2INCH
INCH %INCH
FIG.3
The relations of this expression to the dimensions of the test piece are shown in the table.
0.10
1000
....
20 Per cent
E1
El
2580 2060 1800 1955
5460 5210 5030
Concentration Per cent
..
4 5 7 8 10
OF
PLUNGER
AND
0
SMITH
JGLLY
360 TESTERS
I
0 0 0
-0.10 0 0
0.20 0.40 0.60 0.80
0 0 0
..
dV
o:io
o
0.2 0.55 0.90 1.30
OF
0 0 0
+0.10
TORSION TESTER AND PLUNGER TESTE%
Torsion Machine
Plunger Tester Load
Twist =
De$ection =
Ratio
18 25 37 40 45
45 40 47 40
Commercial Gelatin
0.4 0.6 0.8 1.1
..
1:s
Ash-free Gelatin 1.6 0:6
27
8
1.0 1.6
60
7
The constancy of volume of a material under stress corresponds to a value of Poisson’s ratio = 0.5. Maurer and BjerkQn both found the volume of gelatin jelly sensibly constant, but it appeared desirable to confirm this for the material used here. The arrangement used is shown diagrammatically in Fig. 2. The elongation of the jelly under a given load was measured on one scale, while any change in volume of the jelly was indicated by the rise or fall of liquid (kerosene) in the capillary of the dilatometer in which the jelly was enclosed. The results are given in Table 11. They show no appreciable change of volume of the jelly, and hencelconfirm the results of previous observers.
0
0
5 6
10
READING ON SMITH TESTER 330 340 350
0 0 0 0
Av.
CONSTANCY OF JELLYVOLUME AND POISSON’S RATIO
310 320 FIG.4-cOMPARISON
Stretch Cm. 0 0.3 1.1 2.0 ‘
dV
This shows that the fundamental relation E = 3 N can be assumed. Consequently, a simple proportional relation between the arbitrary (empirical) values of jelly strength given by a plunger type instrument and the values of the modulus of rigidity determined by a torsion instrument would be expected, provided both are operated under conditions insuring absence of systematic errors. While the calibration of the plunger type instrument on the torsion instrument has not been completed, so that unexceptional elastic moduli can be determined with the former, a preliminary comparison which shows substantial parallelism has been made.
These values show that the shorter pieces have an apparently higher elasticity-corresponding to the jelly strength measurements-the value becoming approximately constant for a length of 7.5 cm.
10
0 0 0 0
0.20 0.70
6
00
0
TABLE 111-COMPARISON
TABLE I 10 Per cent
L
Cm 2.54 5.08 7.62 10.16
0 0 0
0
0 100
300 500 700
1/2
-
Stretch Cm. 0 0.20 0.65 1.10
dV
20 Per cent Gelotin
f.0
0
-
TABLE 11-DILATION UNDER STRSTCH 10 Per cent Gelatin 2.54 Cm. L = 5.08 Cm. L 7.62 Cm.
..
’
46
.. 40
0.6
.. ..
43
,.
40 (33)
Av.
43
TABLE IV-10 P E R CENT N O . 6902 GELATIN -Theoretical Values--Actual Values2 . 5 C m . 1.25Cm. 5 Cm. 2.5Cm. 1.25Cm. 5 C m . (2 Inch) (1 Inch) (0.5 Inch) (2 Inch) (1 Inch) (0.5 Inch) 0.6 1.2 2.5 1.3 2.4 0.6 1.5 3.0 0.75 0.75 1.7 0.6 1.2 2.4 0.6 1.4 3:o -1.0 2.1 4.3 2.0 4.0 1.0 Values Reduced to Common Basis of 1
:t
Pn F I G 5-RELATION
OF JELLY
-
STRENGTH TO HYDROGEN-ION CONCENTRATION
June, 1924
INDUSTRIAL A N D ENGINEERING CHEMISTRY
595
DIMBNSIONS OF TEST PIECE AND TORSION INSTRUMENTDortionalitv of results was obtained. The chief obiection to the Smith “tester appears to be the imperfect reprohucibility The fact that test pieces held by adhesion a t the ends and the gradual of the rubber membrane. showed influence of the ends indicated that this effect was JELLY STRENQTH AND PH likely to be found with the torsion instrument. Therefore, molds of lesser and greater length than the standard (1 x The authors are not yet satisfied with the relation of 1inch) were made and the same jelly was used for comparison. jelly strength (elasticity) to hydrogen-ion concentrations. The results are shown in Table IV. It is to be noticed that there is still some end effect at 1 inch They consider that any critical values (maxima, etc.) are more likely to be smoothed out at high than a t low concen(2.5 cm.), but that it is very small. (Fig. 3) trations. A recent series using the plunger - t -w- e instrument C O M P A R I ~ O N O F PLUNGER TESTER AND S ~ ~ I TJELLY H TESTER on a 2 per cent ash-free gelatin jell;. gave results shown in Fig. 5. According to this, both of Wilson’s points of miniThe fjmith jelly strength tester and modifications6 are mum swelling show maxima of jelly strength-although a t widely used in gelatin and glue control. Its operation has pH 4.7 to 4.8 a minimum of viscosity is found.’ The authors been compared on the same jelly with the plunger type in- have been able to check repeatedly a maximum a t p H 7 to 9, strument, and, as will be seen from Fig. 4, satisfactory pro- but not with certainty a t gH 4 to 5. ’ THISJOURNAL, 16, 71 (1923). 0 THISJOURNAI,, ia, 355 (1920).
Effect of Calcium Chloride on Acid-Sugar-Pectin Gels1 By Evelyn G. Halliday and Grace R. Bailey DEPARTMENT OF HOME ECONOMICS, UNIVERSITY OF CHICAGO, CHICAGO, ILL
T
The percentages of pectin, acid, and sugar used for a standard in Part to the salt content HE purpose of this jelly were each in turn lowered to the point where an acceptable of the respective solutions investigation Was to learn what effect, if jelly failed to form in a given time. To these nonjellying mixtures used. Perhaps the widest calcium chloride was then added, and in each case gelation occurred. divergence in the results of any, calcium chloride has on Above a certain maximum amount furfher additions of calcium any two workers is found the concentration of pectin, chloride had no appreciable effect on the stiffness of the jelly, but in Some research done in acid, and sugar required for this laboratory and some tended to cause syneresis. the gelation O f fruit jellies. The writers have considwork reported by Singh.6 erable evidence that certain Using the analyzed hot salts may increase the gelation efficiency of a mixture. Tarr2 water extract of Ben Davis and Baldwin apples as a found that jelly formed a t a slightly lower hydrogen-ion source of pectin and acid and calculating the composition concentration in an apple pomace pectin solution than it did of the jelly from the weight of juice and sugar taken and in a water solution of the same pectin concentration. This of the jelly obtained, it was found that the pectin content difference, it appears, can only be attributed to the favoring of satisfactory jellies ran anywhere from 0.424 to 0.7 per action of the salts present in the apple pomace extract. That cent. At the lower pectin value, 0.424 per cent, the acid such extracts contain an appreciable amount of salts can be calculated as malic was 0.165 per cent, the sugar 63 per cent. inferred from the ash content of apples, which Sherman* Singh, however, who used lemon pectin and citric acid, places a t about 0.2 per cent of the edible portion. More- reports that it was impossible to obtain a jelly a t any concenover, the apple pomace extract used for this investigation tration of sugar a t a pectin content below 0.9 per cent with contained 3.3 per cent of ash, of which 15.8 per cent was the acid kept constant at 1.5per cent. calcium. The fact that Singh’s jellies were made with citric acid Haynes4 observed that all the alkaline-earth hydroxides while those of the writers contained chiefly malic6 could and, to a lesser degree, the alkali hydroxide induced the gela- hardly account for his high pectin requirement, because, tion of pectin solutions without the aid of either sugar or acid, although Tarr estimates citric acid to be less efficient than and that the speed of gelatin was much accelerated by the malic, the larger amount of citric used by Singh, 1.5 per various salts of the respective hydroxides. Furthermore, cent as against the writers’ 0.165 per cent, ought to more Haynes found that calcium hydroxide and its salts were more than compensate for the lower efficiency of the citric acid. effective than any of the other alkaline earths. The fact A possible difference in the jellying value of the two pectins that the weaker alkali had the greater effect, and that this may be partly responsible for the difference in results. As effect was increased by salts which would depress the ion- Denton? has observed, the alcohol precipitation method iaation of the hydroxide and thus lower the concentration of estimating pectin cannot be relied upon to give products of the hydroxyl ion, make it appear that the positive rather of uniform jellying properties. than the negative ion is the reactive agent. It is highly probable, however, that the writers’ low pectin Since, then, certain positive ions seem to favor the gelation and acid requirement was a t least partly due to the favoring of pectin, it is probable that the apparent lack of agreement action of certain salts, more especially certain positive ions, among investigators regarding the relative concentrations which were present in their apple juices. of pectin, acid, and sugar required for gelation may be due The experimental work which follows was done for the * Received January 5, 1924. 6 THISJOURNAL, 14, 710 (1922). * Delaware Agr. Expt. Sta., Bull. 184 (1923). fl Bigelow and Dunbnr, Ibid., 9, 762 (1917); Franzen and Helwert, C. 4
Sherman, “Chemistry of Food and Nutrition.” Biochem J., 8, 553 (1914).
A , 17, 290A (1923). 1
THISJOURNAL, 16, 778 (1923).
