SWELLING B X D HYDRATION OF GELATIXI RT JOHN H. KORTHROP AND M. KUSITZ
The swelling of gelatin when placed in aqueous solutions may be readily separated into three types: I . Swelling in acid or alkali. 2. Swelling on addition of small amounts of water to dry gelatin. 3 . Swelling of dilute gels of isoelectric gelatin in water or in salt solutions. The swelling in acid or in alkali and the effect of neutral salts on this swelling have been shown by the work of Procter and Wilson,* and I.oeb3 to be due to the osmotic pressure of the ions of the electrolyte, in accordance with the Donnan equilibrium. The initial swelling of dry isoelectric gelatin in water-which evidently is not connected with the Donnan equilibrium-has been carefully studied by K a t q 4 who was able to show that the heat effects, volume, pressure, and vapor changes were strictly analogous to those observed in the formation of concentrated solutions of many substances, and that the system as a whole behaved as an ideal concentrated solution. When sufficient water has been added, however, to reduce the gelatin concentration to less than j o per cent, the heat effects become very small and yet the gelatin may swell, under favorable conditions, until the concentration of gelatin is j per cent or less. The third type of swelling has peculiarities which cannot be reconciled with the idea of solution or of hydrate formation and it will be considered here as a distinct type. It is this type of swelling which is discussed in the present paper. The behavior of gelatin when placed in water has been described by anumber of investigators. The more striking peculiarities may be briefly described as follows. I n general the swelling increases with the temperature and with the concentration of gelatin. At a concentration of about I O per cent a t j”C no change in volume occurs, while below I O per cent the gelatin loses water instead of swelling. A block of gelatin which was brought to a definite concentration by allowing water to evaporate from a dilute gel swells much more than a similar block made by allowing a sol of the same concentration to set. Thin films of gelatin swell to a value which increases only slowly with time while large blocks do not give any indication of a maximum value but continue to swell until dissolved. At higher temperatures there is still less indication of an equilibrium value. If a block of gelatin is allowed to remain in water until i t has stopped swelling and then is raised to a higher temperature in air for a short time under such conditions that there is no change in volume, it will swell rapidly when replaced in water a t the first temperature. The work reported in this paper is a summary of a series of papers on swelling and hydration of gelatin published in J. Gen. Physiol., 1ga61g30. * J. Chem. SOC., 109, 307 (1916). *“Proteins and the Theory of Colloidal Behavior,” and Ed (1924). Kolloidchem. Beihefte, 9, I (1917-18).
’
SWELLING AND HYDRATION OF GELATIN
163
Previous Theories of Swelling A number of theories have been proposed to account for thesepeculiarities.5 Hardy assumed that a gel was a solid in contact with its saturated solution. Kat2 assumed that the gel is a solid solution of water and gelatin, and that 220
a 200
;
180
2 2 8
2 f 0
160
140
120 100
80 60
40 20 2
‘0
4
6
8
10
12
14
16
16
20
Gm.of gelatin per lCOgrn.&O
FIQ I Concentration and swelling or osmotic pressure of gelatin at different temperatures
220 200
g
180 160
g 140 2
g
120
100
y 80
L
8
60
40 2.0 ‘0
5
10
15
20
25
30
55 37 40
45
50
Temperature ‘C.
FIG.2 Osmotic or swelling pressure of vanous concentrations of gelatin at different temperatures
the gel is therefore one phase. (The writers agree with this idea for very concentrated gelatin-water systems.) Lloyd suggests that gelatin is made of two components, isoelectric gelatin which is insoluble, and gelatin salts which 6 Cf. Weber: Bogue’s “Theor and Application of Colloidal Behavior,” 1, 3 7 (192 ) . Bradford: Alexander’s “Colloid &emistry,” 1, 751; Lloyd: 767 (1925); FreundGch: “F!a: pillarchemie” (1923).
I 64
JOHN H. NORTHROP AND M. KUNITZ
are soluble. Swelling is due to the osmotic pressure of the soluble gelatin salts. A number of other workers have outlined more or less similar theories. It would evidently be a great help in attempting to determine the nature of gels if the number of phases present could be determined. This could be done directly by an analytical phase rule study except for the fact that the (assumed) liquid phase is held in the meshes of the solid and cannot be separated from it, so that the concentration of gelatin in the liquid phase cannot be determined. Since the osmotic pressure is proportional to the concentration, the concentration could be determined indirectly by means of the osmotic pressure; and osmotic pressure-temperature or osmotic pressureconcentration curves could be used in the phase rule diagram. The osmotic or swelling pressure of gels, however, cannot be determined in the same way as the osmotic pressure of liquids owing to the mechanical resistance of the gel. It was found possible to obtain values for the swelling pressure of dilute gels by placing the gel outside a rigid membrane and measuring the pressure required to prevent the entrance of water. The swelling or osmotic pressure curves for different concentrations of gelatin a t different temperatures were measured in this way.6 The results of these measurements are shown in Figs. I and 2.' The osmotic pressure increases with both temperature and concentration but there are no breaks in the curves a t the point where the system becomes solid. If the phase rule be applied to these results it follows that no new phase appears when gelatin-water systems change from liquid to solid either by lowering the temperature or increasing the concentration of gelatin. The number of phases present in the system gelatin-water is therefore the same in either the liquid or solid form. It also follows that there is always present one more component than there are phases, since the system still has one degree of freedom, although the temperature and pressure are fixed. Therefore, if the phase rule is applied in its usual form, it must be assumed either ( I ) that there are two components, water and gelatin, and that the solid and liquid forms are the same phase, or ( 2 ) that there are three (or more) components and two (or more) phases. If n phases are assumed there must be n f I components. The first possibility would agRe with the idea that the system is a solution which may be either liquid or solid depending on the composition. It is not possible to amume that it consists of a solid phase of one component in equilibrium with its saturated solution since in the presence of the solid the system would be fixed if the temperature and pressure were fixed. It is probable that the concentrated gels studied by Kat2 are solid solutions of water and gelatin, as Kats concluded. It is very difficult, however, to account for the properties of the more dilute gelatin sols or gels on this basis owing to the peculiar hysteresis effects noticed in swelling experiments and the changes in viscosity with time, temperature and pH. The hysteresis
' Northrop and Kunits: J. Gen. Physiol., 10, I 6 1 (1927). 1 Since gels below I O per cent lose water the swelling-pressure curve must crow the Concentration axia a t about I O per cent gelatin content and then becomes negative. This could not be determined in the form of apparatus used since negative presaurea would not be recorded.
SWELLING AND HYDRATION OF GELATIN
165
effects, on the other hand, are exactly what would be expected of an elastic solid (or of a suspension). The facts that the swelling of gels a t low temperatures reaches an equilibrium value and that gels of less than I O per cent concentration lose water instead of imbibing water, also contradict the assumption of a solution. I n general therefore the assumption that dilute gelatinwater systems consist of two phases seems in much better agreement with the facts. It follows then from the pressure measurements summarized above that the system must consist of (at least) three components and since water is certainly one, gelatin must contain the other two. It was assumed therefore as a working hypothesis that the system gelatin-water, whether in the sol or gel state (at a concentration of less than 40 per cent gelatin) consists of (at least) two phases, one solid and one liquid, and (at least) three components, water, “soluble” gelatin, and “insoluble” gelatin. There are two possible systems which agree with the osmotic pressure measurements: I . The solid phase is a solid solution of “soluble” and “insoluble” fractions of gelatin and water. The liquid phase is an aqueous solution of the “soluble” and “insoluble” fractions of gelatin. 2 . The solid phase is the “insoluble” fraction alone and the liquid phase is a solution of the “soluble” and “insoluble” fractions. In either case the solid phase exists in the sol state as finely divided particles-&. micellae. The facts observed in connection with the viscosity of sols and syneresis of gels, however, necessitate the assumption of structure in the particles (micellae) of solid present, since, in order to account for these results it is necessary to assume that the micellae contain liquid phase and that the concentration of gelatin in this “internal” liquid phase is higher than that in the bulk of the liquid phase surrounding the micellae, with the result that the micellae take up water, or swell. I t is difficult to derive this condition from the assumption that the solid phase is a solid solution and it is therefore necessary to conclude that the micellae form a separate system, consisting of an elastic membrane of insoluble gelatin, in equilibrium with the “external” liquid phase and containing an internal liquid phase which is a solution of one or more partly “soluble” components. The walls of the micellae are impermeable to these components. In the sol state therefore gelatin consists of a suspension of micellae in a solution of the “soluble” and “insoluble” components. These micellae are in equilibrium with the surrounding solution, the difference between the osmotic pressure inside and outside of the micellae being balanced by the elastic resistance of the walls. They are therefore capable of swelling or contracting as Loeb assumed. As the total concentration of the sol increases the osmotic pressure of the external liquid-phase increases, while that of the internal liquid remains the same so that the micellae swell less in concentrated sols. This accounts for the effect of concentration on the viscosity and also, as will be shown later, for syneresis of dilute gels. As the sol is cooled or as more gelatin is added, the amount of the “insoluble’’ fraction present as solid increases, and the micellae increase in size and possibly in number. When they occupy a large enough proportion of the
166
JOHN H. NORTHROP AND M. KUNITZ
total volume the “insoluble” fraction becomes connected to form an elastic network and the sol becomes a gel. The liquid phase surrounding the micellae still contains the “soluble” component in solution and therefore has an osmotic pressure. When a block of gel is placed in water this osmotic pressure causes water to enter and the block swells. As swelling continues the osmotic pressure becomes less owing to dilution, and a t the same time an elastic stress appears in the block owing to the stretching of the elastic network. When this elastic stress is equal to the osmotic pressure the system is in equilibrium and swelling stops. Under certain conditions the osmotic pressure of the solution in the micellae is decreased on cooling so that water is forced out of them by the elastic contraction of the walls of the micellae. Under these conditions the block as a whole may lose water. Any conditions therefore such as higher temperature or strong salt solutions which increase the solubility of gelatin will increase the swelling. The elastic stress of the block shows fatigue as do all elastic bodies and this fatigue accounts for the hysteresis effects and for the difference in the swelling of large and small blocks. The picture of gel formation and the mechanism of swelling outlined above is similar to that proposed by Duclaux* for the swelling of rubber and published during the course of the present work; a somewhat similar mechanism had also been proposed previously by Lloyd. This mechanism has been found adequate to account qualitatively for all the properties of gelatin of which the writers are aware and quantitatively for a large number. It has predicted several properties which had not been suspected. Application of the Hypotheses to the Properties of Gelatin
Hydratzon of Isoelectric Gelatin a s determined from Osmotzc Pressure a n d T’zscosily i M e a s ~ r e m e n t s . ~ Figures 3 and 4 give the curves for osmotic pressure and viscosity of sols of various concentrations of isoelectric gelatin at 3 j”C. On the same figures are drawn, for comparison, curves for osmotic pressure and viscosity of electrolyte-free isoelectric egg albumin measured at zo°C. The osmotic pressure-curve for egg albumin is a straight line, while in the case of gelatin the curve rises rapidly with increase in concentration of gelatin. The same difference is shown by the viscosity curves. The viscosity of gelatin even in low concentrations is much higher a t 3 j T than the viscosity of egg albumin at the corresponding concentrations and increases enormously with increase in concentration. This difference in the behavior of egg albumin and gelatin with respect both to osmotic pressure and viscosity is explainable by the difference in their degrees of hydration.1° Egg albumin is hydrated very little, while gelatin is highly hydrated even at 3 j”C. The high degree of hydration BBdl., 33, 36 (1923). ”unitz: J. Gen. Physiol., 10, 811 (1927). ’OKunitz: J. Gen. Physiol., 9,71j (1926).
SWELLING AND HYDRATION OF GELATIN
167
of gelatin is due to the swelling of the micellae which, in turn, is caused by the difference in the concentrations of gelatin in the internal and external liquid phases. It is possible to determine approximately the degree of hydration of gelatin independently from both osmotic pressure and viscosity measurements. Osmotic Pressure and Hydration of Gelatin.-The osmotic pressure of a dilute molal solution of a hydrated substance may be expressed'O as
I , ! ! ' ! ! !
FIG 3 Osmotir pressure curves of isoelectric gelatin a t 35°C and of isoelectric egg albumin at 20°C
where I< = R T / M (M = mole weight of solute) c' = gm. of solute per cc of solution p = volume of C gm of the hydrated solute which means that the osmotic pressure is proportional to the concentration, expressed as moles per cc of free solvent. The value of p can be calculated from the osmotic pressure measurement i f I< is known. From the relation K = P c ( I - p) it follows that as C approaches zero, p = 0 and K = P/C Thus the value of K may be obtained by plotting P C against C. The intercept on the P/C
ordinate gives the value of K. Table I gives the values of p as calculated from the osmotic pressure measurements.
168
JOHN H. NORTHROP AND M . KUNITZ
TABLE I C
P
Gm/cc solution 0 .o
Mm Hg
0 .OI
3.5
0.02
7.5
0.03 0.04
I 2 .o
0.Oj
23 .o
0.06
29.40 37.50 47 . o
0.07
0.08
PIC
-
325 3 50 375 400 42 5 460 492 537
I 7 .o
588
q c X IO* Cc H 2 0 / G m gelatin 7.2
‘3.4 19.8 23 . 6 29.5 34.0 39.6 44.8
6.45 5.95
5.85 5.15 5.15 4.91 4.91 4.85
FIG.4 Viscosity concentration curves of isoelectric gelatin at 35°C and of isoelectric egg albumin a t zo°C.
The last column contains the values of the water of hydration per gram of gelatin as obtained from the values of ‘p, namely q = ‘p,’C - 0 . 7 5 where 0.75 equals the volume of
I
gram of dry gelatin.
SWELLING AND HYDRATION O F GELATIN
169
Viscosity and Hydration of Gelatin.-The viscosity of a number of colloidal solutions, as well as of various sugar solutions, may be represented approximately by the empirical formula10
where q = relative viscosity of solution and
a fraction of the total volume of the solution = cc of solute per cc of solution.
p = volume occupied by the solute expressed as
In the case of various sugar solutions and also in the case of sulfur suspensions, the volume of the solute as calculated from the viscosity values agrees with the actual volume of the substance in the dry state, as determined from specific gravity measurements. I n the case of hydrated or solvated substances cp represents the volume of the solvated solute. This was checkedI0 for various colloidal solutions. Thus in the case of solutions of caoutchouc in benzene the values of p as calculated from the viscosity measurements were found to fit remarkably well in the equation for osmotic pressure of the same solutions. Table I1 shows the values for cp and hence also for q as calculated from the viscosity measurements of gelatin by means of the same formula.
TABLE 11 C
Grn k c solution 0.01 0.02
0.03 0.04 0.05 0.06 0.07
0.08
9 at
35°C.
1.43 2.06 2.96 4 2 4
6 .oo 8.20
ro.8j 13.9
v x
IO*
7.75 ' 5 .os 21.80 27.90 33.40 38. IO 42.18 45.52
9
Cc H20/Grn gelatin
7 .oo 6.78 6.j2 6.30 5.93 5.60 5.28
4.94
The values for hydration of gelatin as obtained from the viscosity measurements are quite close to those obtained from the osmotic pressure measurement. Figure 5 shows that when the various concentration values have been corrected for the values of 'p as obtained from viscosity measurements the osmotic pressure values lie on a straight line. I t is to be noted that the value of water of hydration in cc per gm of gelatin becomes smaller as the concentration of gelatin increases. This agrees with the theory that the hydration of gelatin is due to the swelling of the micellae, owing to the difference between the osmotic pressure of the internal liquid phase and the osmotic pressure of the gelatin sol as a whole. The micellae swell until this difference in osmotic pressure becomes equal to the elastic resistance of the walls of the micellae.
JOHN H. NORTHROP AND Y. KUNITZ
170
The equilibrium state between the micellae and the total sol can be expressed as follows: Pi - Po = El q where Pi and Poare the osmotic pressures inside and outside of t,he micellae, El is a constant proportional to the bulk modulus of elasticity of the micellae and q is the amount of water held by the micellae (water of hydration) per gram of gelatin. At low concentrations of gelatin the outside osmotic pressure
120
m* r
!60
e
Y E
do x)
1
2
3 I 5 6 I
8
910ii1213i4151617l8
Concentration in gmpr100cc.H20 FIQ.5
Effect on the osmotic pressure-concentration curves of isoelectric gelatin of correcting the concentration of the gelatin for the water of hydration as calculated from viscosity measurements
is much smaller than the osmotic pressure inside of' the micellae, hence the micellae take up relatively large amounts of water. But as the total concentrat,ion of gelatin increases the opposing outside osmotic pressure increases and the micellae swell less with the result that q, i.e., the amount of hydration per gram of gelatin, gradually becomes less and less. Thus, although the micellae are at equilibrium with the outside solution, they are still under an elastic stress exerted by a pressure equal to E, q, the magnitude of which decreases with the increase in the total concentration of gelatin. It is assumed that this elastic stress in the micellae is the cause of syneresis of gels, as will be described later. Effect of Concentration of Gelatin on the pH-Viscosity Curves. I t is generally known that the addition of either acid or alkali to a freshly prepared gelatin sol raises its viscosity. I n the presence of acid the viscosity reaches a maximum at pH 3.0 and then drops again. The pH effect on the viscosity of gelatin has been explained by Loeb as due to the swelling of the micellae in the gelatin sol. I t is assumed that the micellae are of higher gelatin concentration than the total concentration of the gelatin in the out-
SWELLING AND HYDRATION O F GELATIN
171
side solution; hence there is a greater concentration of acid in the micellae than in the solution outside of the micellae. I t is this unequal distribution of the acid or alkali which causes the micellae to swell and hence brings about a rise in the viscosity of the gelatin sol. With increase in the total concentration of gelatin the difference in the concentrations of gelatin in the internal and
*
1'2 14 16 18 20 2 2 24 26 28 30 32 3 4 36 38 40 4 2 44 46 48 pH ofgelatin-HCL solutions of various a n c
FIG 6 Effect of concentration on the hydration of gelatin a t various pH
The hgdration values
were calculated from viscosity measurements a t 35°C h) means of the formula
7 = (1 - V I 4
external liquid phases and hence also the difference in the distribution of the ions of the acid or alkali is gradually diminished At the same time the total osmotic pressure of the gelatin solution which opposes the swelling of the micellae is continually increased. Hence the increase in viscosity a t pH 3 o over that of isoelectric gelatin should become less conspicuous with increase in the total concentration of the gelatin sol. That this is exactly what happens is shown in Table 111.
172
JOHN H. NORTHROP AND 31. KUNITZ
TABLE I11 Viscosity Measurement of Various Concentrations of Gelatin pH 4.7 and pH 3.0 a t 37OC Concentration in gm per 100 cc solution
Relative viscosity of gelatin pH 4.7 Additional viscosity = relative viscosity - I Relative viscosity of gelatin pH 3.0 Additional viscosity Ratio of additional viscosity, PH 3.0,’PH 4.7 Concentration in gm per 100 cc solution
Relative viscosity of gelatin pH 4.7 Additional viscosity = relative viscosity - I Relative viscosity of gelatin pH 3.0 Additional viscosity Ratio of additional viscosity, PH 3 d P H 4.7
I .0
0.5
16
1.43
0.16 I .84 0.84
0.43 2.39
0.95
1.75
3.44
1.39
2.44
4.54 3.54
5.24
3,23
2.57
2.02
5.0 5.28
ti.0
8.0
10.0
6.70
12.40
21.3
11.40
20.3
14.20
22.0
6.12
5.70 9.06 8.06
13.20
21.0
.43
1.42
I .
4.28 7.12
1
1.16
2.83 5’78
4,78 I
I
.69
.03
The effect of the concentration of the gelatin on the hydration of gelatin at various pH is shown in Fig. 6. The hydration values were obtained from viscosity measurements at 3 5°C of various concentrations of gelatin freshly made up to various pH by means of HCl. The curves show that at a concentration of gelatin of about I O per cent the pH effect on the viscosity of the sol disappears entirely, which indicates that at this concentration, the concentrations of gelatin inside and outside of the micellae are equal so that the osmotic pressure in the micellae is completely balanced by the osmotic pressure of the total sol. Swelling and Syneresis of Isoelectric Gelatin” When gels containing various amounts of gelatin are placed in cold water or dilute buffer solution of the same pH as that of the isoelectric point of the gelatin the following results are obtained. Gels of a gelatin content of more than I O per cent swell while those of less than IO per cent lose water and shrink. A gel containing about I O gm of gelatin per roo cc of solution neither swells nor shrinks. This is shown in Fig. 7 . This striking difference in the behavior of gels of various gelatin content may be explained qualitatively and predicted quantitatively on the basis of the following assumptions: Swelling in gels of concentrations above I O per cent is caused by I. osmotic pressure of the “soluble” component of gelatin which exists in solution ”Kunitz: J. Gen. Physiol., 12, 289 (1928)
SWELLING AND HYDRATION O F GELATIN
I73
in the liquid phase of the gel a t a temperature even as low as o°C. The amount of the dissolved component gelatin in the liquid phase, and hence the swelling, increases both with the total concentration of gelatin in the gel and with temperature. Shrinking or syneresis in gels of a gelatin content of less than I O per 2. cent is caused by the elastic stress in the micellae of the gelatin sol before it was cooled and allowed to set. The elastic stress in the micellae is due to the osmotic pressure of the dissolved gelatin in the internal liquid phase in the
FIG.7 Percentage change in weight of gels of various concentrations of isoelectric gelatin when placed in M/rooo acetate buffer pH 4.7 at 5OC
micellae. But as the gelatin solution is cooled and allowed to set the dissolved gelatin in the micellae becomes insoluble and precipitates out. The force which kept the micellae stretched is thus diminished. This allows the elastic walls of the micellae to shrink and lose water. The shrinking of each individual micella brings about a contraction of the whole network with the result that water is expelled not only from the micellae but also from the spaces between the micellae and the whole block of gel loses weight. This process is most rapid when the gel is placed in contact with water, since the loss of water from a dry gel is slow owing to the resistance offered by the dry surface film. As stated before, the elastic stress in the micellae of a gelatin sol due to the inner osmotic pressure becomes less as the total concentration of the gelatin increases. Hence when the stress on the micellae is removed by the precipitation of inner liquid on cooling of the sol there is less contraction in the micellar network of concentcated gels than in the dilute ones. Thus while swelling increases with increase in concentration of gelatin in the gel, syneresis diminishes with the concentration. At a gelatin content of I O per cent the force that causes swelling apparently balances the opposite force that causes syneresis or shrinking of the gel, and the gel neither swells nor shrinks.
JOHN H. NORTHROP AND M. KUNITZ
Ii4
3. -4block of freshly set gel is under no elastic stress but becomes subjected to a tensile stress on swelling and to a compressive stress on shrinking, both forms of stresses being proportional to the amount of swelling or shrinking correspondingly. This is confirmed experimentally by double refraction measurements.12 A block of gelatin a t setting has no double refraction. A swollen block shows positive double refraction, corresponding to tension or stretching, while blocks which shrink show negative double refraction, corresponding to compression. It follows therefore that both forces, namely the osmotic pressure of the liquid phase and the elastic stress in the micellae both of which tend to change the volume of the block, act against the elastic resistance of the block of gel. The amount of either swelling or shrinking of a gel depends then on the three forces, and at equilibrium we have
where Po = osmotic pressure of liquid phase, P, = pressure due to the stress in the micellae, K = bulk modulus of elasticity of the gel, both for tension and compression, Yo = volume of gel a t setting, V, = volume of gel a t equilibrium. It is to be noted that Po - P, represents the total swelling pressure of the gel. The swelling pressures of gels of concentrations of higher than I O per cent have been measured directly a t IO’C and can be expressed approximately as the following function of Ire,where V, is taken in cc of HzO per gm of dry gelatin, namely
Po - P, When
V,
v. v.
I330
= - - 140 v e
then Po - P, = 0 < 9 . 5 ” P,>P, > 9 . ; ” P,
