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Investigation of the flow of gelatin gels at various temperatures
Investigation of the flow of gelatin gels
2599
14. V. A. SNEZHKO, L. N. SAMOILOVA, K. P. KHOMYAKOV, A. I. VALAKHANOVICH, R. V. ZARETSKAYA, A. D. VIRNIK, G. Ya. ROZENBERG and Z. A. ROGOVIN, Antibiotiki, 48, 1972 15. J. MESTER, J. Amer. Chem. Soc. 77: 5452, 1955 16. J. McCORMICK, J. Chem. Soc. C, 2121, 1966 17. R. D. GUTHRIE, Adv. in Carbohydr. Chem. 16: 105, 1961 18. R. G. KRYLOVA, S. N. RYADOVSKAYA and O. P. GOLOVA, Vysokomol. soyed. Ag: 993, 1967 (Translated in Polymer Sci. U.S.S.R. 9: 5, 1106, 1967) 19. N. Ya. KUZNETSOVA-LENSHINA, G. A. TIMOKHINA, V. Ye. ZHAVORONKOV and V. I. IVANOV, Izv. A N Kirg. SSR, No. 3, 59, 1968 20. K. P. KHOMYAKOV, A. D. VIRNIK, Z. A. ROGOVIN and S. N. USKAKOV, Vysokomol. soyed. 7 : 1 0 3 5 1965 (Translated in Polymer Sci. U.S.S.R. 7: 6, 1145, 1965) 21. K. P. KHOMYAKOV, A. D. VIRNIK and Z. A. ROGOVIN, K i m i y a prirodn, soyed. 3: 213, 1966 22. A. D. VIRNIK, O. P. LALETINA, M. A. PENENZHIK, K. P. KHOMYAKOV, Z. A. ROGOVlN and G. Ya. ROZENBERG, Vysokomol. soyed. A10: 362, 1968 (Translated in P o l y m e r Sci. U.S.S.R. 10: 2, 423, 1968) 23. P. N. KASHKIN, A. I. BEZBORODOV and N. P. YELINOV, Antibiotiki (Antibiotics). p. 55, "Meditstina", 1970
INVESTIGATION OF THE FLOW OF GELATIN GELS AT VARIOUS TEMPERATURES* YE. YE. BRAUDO, I. G. 1)LASHCHINA, ]~. S. KUZ'MIi~A and V. B. TOLSTOGUZOV Institute for Elemento-Organic Compounds, U.S.S.R. Academy of Sciences (Received 28 March 1973) The flow of 5 ~o gelatin gels in the linear visco-elastic region has been investigated in the t e m p e r a t u r e range 12-24°C. I t has been established t h a t the a b i l i t y of gelatin gels to undergo irreversible deformation arises as the temperature is raised over a narrow t e m p e r a t u r e interval. The temperature dependence of the greatest Newtonian viscosity of the gelatin gels is described b y an Arrhenius equation. The form of the relaxation curve for the reversible deformation of gelatin gels cor)~esponds to the properties of systems located in the region where the transition f r o n f t h e glassy to the highly elastic condition begins. DESPITE t h e f a c t t h a t t h e flow o f g e l a t i n gels h a s b e e n u s e d a s t h e s u b j e c t f o r a n u m b e r o f i n v e s t i g a t i o n s [1-6], t h e r e a r e a l m o s t n o d a t a a b o u t t h e c o u r s e o f this process at various temperatures. It can only be recorded that, according * Vysokomol. soyed, h i 6 : No. 10, 2240-2247, 1974.
2600
YE. YE. BRAUDO et al.
t o t h e d a t a i n [5], t h e p l a s t i c i t y o f t h e g e l s i n c r e a s e s s h a r p l y o v e r a n a r r o w perature We range
tem-
interval close to the melting point. have
studied
12-24°C.
molecular
the flow of 5%
Since the
characteristics
mechanical of the
gelatin gels in shear
in the temperature
properties
gels depend
preparation
of gelatin
[7, 8], t h e
on the
flow of gels prepared
from two different specimens of gelatin was studied. EXPERIMENTAL T w o specimens of alkaline p h o t o g r a p h i c gelatin, w h i c h we shall d e n o t e b y GI and G I I , were selected for t h e investigation. T h e gelatins were purified b y L o b ' s m e t h o d of dialysis, traces of d i b u t y l t i n o x i d e were a d d e d as a n a n t i s e p t i c a n d t h e gelatins were stored as gels in an exsiccator o v e r water. The G I and G I I gels had [7]* = 59=t= 1 a n d 57 =t=1 m l / g a n d M w t × X 1 0 - a = 2 1 0 and 190 respectively. T h e i n v e s t i g a t i o n s of flow were m a d e b y t h e m e t h o d described in [4], the essentials of w h i c h consist in t h e o b s e r v a t i o n of d e f o r m a t i o n in p u r e shear of a gel s p e c i m e n placed b e t w e e n two g r o o v e d flat parallel plates, b y o b s e r v i n g t h e m o v e m e n t of the u p p e r plate to w h i c h a l o a d is a t t a c h e d , hanging o v e r a p u l l e y (Tolstoi a p p a r a t u s [9]). The end effect error, c a l c u l a t e d as in [10], does n o t exceed 3.2~o for the g i v e n s p e c i m e n dimensions a n d was n o t t a k e n into a c c o u n t in the calculations. The loads corresponding to t h e s t a r t of r o t a t i o n of t h e pulleys in t h e double a p p a r a t u s used b y us were 0 . 1 9 i 0 . 0 3 and 0 . 2 6 ± 0 . 0 3 g (1-5°/o of t h e load in t h e e x p e r i m e n t ) . These d a t a were t a k e n into a c c o u n t in t h e calculation of stresses. The m o v e m e n t of t h e u p p e r plate was m e a s u r e d w i t h an M I R microscope with a M O V - I - 1 5 K h (scale division, 1.3 pm). The s p e c i m e n thickness was m e a s u r e d w i t h a horizontal microscope h a v i n g an ocular m i c r o m e t e r ; t h e p a r a l l e l a r i t y of t h e u p p e r and lower surfaces of the s p e c i m e n was m o n i t o r e d a t t h e s a m e time. i n order to preven~ d r y i n g o u t of t h e specimen, w a t e r was flooded into the channel in t h e w o r k i n g c h a m b e r of the a p p a r a t u s ; t h e t e m p e r a t u r e in t h e c h a m b e r s was held c o n s t a n t w i t h an a c c u r a c y of :]:0.1°C b y m e a n s of an u l t r a t h e r m o s t a t . Certain changes in t h e m e t h o d of p r e p a r i n g these specimens were i n t r o d u c e d as c o m p a r e d w i t h [4]: t h e gel s p e c i m e n to be t e s t e d was m e l t e d a n d held at 40°C for 30 rain, after w h i c h t h e m e l t was cast i n t o p e r s p e x mould, in which inserts w i t h the w o r k i n g plates were located. T h e m o u l d s w i t h t h e m e l t were placed in t h e exsiccator w i t h w a t e r and held in t h e m a t r o o m t e m p e r a t u r e for 2 hr. T h e n t h e plates t o g e t h e r w i t h the gelled s p e c i m e n were carefully r e m o v e d f r o m t h e mould, placed once m o r e in the exsiccator w i t h w a t e r a n d t h e r m o s t a t i cally controlled u n d e r the conditions selected. D u r i n g s t r u c t u r e f6rmation, t h e u p p e r p l a t e could m o v e freely r e l a t i v e to ffhe lower plate, and i n t e r n a l stresses, which could serve as a source of errors, did n o t d e v e l o p in t h e specimen. A p e r t u r e s (2 m m in d i a m e t e r ) were m a d e in t h e walls of t h e m o u l d to allow the outflow of air, a n d these were c o v e r e d w i t h a p l a t e before t h e m e l t was cast. The insert was l u b r i c a t e d with silicone grease on b o t h sides. One of t h e walls of t h e insert was n o t secured to the b o t t o m a n d could be freely r o t a t e d a b o u t an u p p e r crossbar. A f t e r r e m o v a l of the insert f r o m t h e mould, this wall was tilted and t h e insert carefully s e p a r a t e d w i t h o u t d a m a g i n g t h e lateral surfaces of the specimen. Before d e t e r m i n i n g t h e flow, the specimens were subjected to s t r u c t u r e f o r m a t i o n at 10~=1.5°C for 7 days. The r a t e of the s t r u c t u r e f o r m a t i o n processes, w h i c h d e t e r m i n e t h e s t r e n g t h [11] a n d h e a t of m e l t i n g [12] of gelatin gels, are k n o w n to become v e r y small in 5-7 days. Before t h e s t a r t of e x p e r i m e n t s , t h e specimens were held for 3 hr at the test t e m perature. * I n 2 M K S C N at 25°C. t D e t e r m i n e d b y l i g h t - s c a t t e r i n g in 0-15 M NaC1 at 35°C.
,
Investigation of the flow of gelatin gels
2601
The optical density of the gelatin gels was measured at a wavelength of 589 n m m a thermostatically controlled cell 0-05 dm thick, with a polarimeter made b y the firm " J u a n Roussel" (France). The relative error in the measurements was J 0.3o/O. Because of the high sensitivity of the apparatus, the gelatin concentration in the specimens was reduced t¥om 5 to 3%. According to [I3], the specific optical rotation of gelatin gels does not (to a tirst approximation) depend on concentration. The specimens were subjected to structure formation in a cell under the same temperature and time conditions as for the investigation of flow. The temperature in the cell was monitored by means of a thermocouple. ~-V[easurements of the optical rotation were made under dynamic and static conditions. I n tile first case, the optical rotation was determined during a single experiment over the temperature range 9-26°C, by making measurements every 1-2°C and holding the specimens, before the recording of the parameters, for 2 hr aV each temperature of measurement. In the second case, an equilibrium value of optical rotation for a single temperature was measured in each experiment, and for this purpose, the specimen was thermostatically controlled for 6-8 hr. Those values of optical rotation were considered to be equilibrium values which remained unchanged after the temperature of the system had been raised or low(~red, and returned to its initial condition. Tile optical density of 3O/o gelatin gels was measured with a "Spekol" photometer ((Aerman Democratic I~epublic) at a wavelength of 436 nm, in a thermostatically controlled cell of thickness 1 cm. The conditions of preparing the specimens and carrying out the measurements was the same as for the polarimetric investigations. RESULTS AND DISCUSSION
The separation of the reversible and the irreversible deformation was made in the following way. The gel specimen was loaded for tile selected time interval, after which the load was removed and the equilibrium residual deformation was determined for the elastic after effect. A curve for the change, with time, of the reversible deformation was then constructed by subtracting its irreversible component from the total deformation. To achieve the equilibrium residual strain in the presence of the elastic after-effect, the specimen was held for 3 hr at tile test temperature, for 15 hr at room temperature and, finally, for 3--5 hr at 24°C until the equilibrium value of strain had been established. Separation of the reversible and irreversible deformation by the method adopted is possible only under conditions such that tile measurements lie within the region of linear viscoelasticity. I t is also assumed that the irreversible deformation develops linearly with tim(;, t h a t is, in conformity with Newton's law of flow. The validity of both assumptions was checked experimentally. F i g u r e 1 s h o w s t h e flow c u r v e for G I gel a t 20°C, o b t a i n e d f r o m e x p e r i m e n t s m a d e a t t w o d i f f e r e n t stresses. I t m a y be s e e n t h a t t h e c o m p l i a n c e does n o t d e p e n d o n stress. T h i s is also v a l i d for t h e o t h e r flow d a t a ( d e f o r m a t i o n u p t o 7.5%). I n v i e w of t h e f a c t t h a t g e l a t i n gels a r e n o n - e q u i l i b r i u m s y s t e m s , i t w~s n e c e s s a r y to satisfy oneself t h a t no m a r k e d changes in specimen properties o c c u r r e d u n d e r t h e effect of t e m p e r a t u r e d u r i n g tests. T o do t h i s , gel s p e c i m e n s p r e p a r e d b y the usual m e t h o d were repeatedly subjected to short-time loading a t 20°C for 6 hr. N o c h a n g e s i n t h e a l m o s t i n s t a n t a n e o u s d e f o r m a t i o n w a s t h u s o b s e r v e d a n d its r e v e r s i b i l i t y w a s r e t a i n e d . I n o r d e r t o v e r i f y t h e a p p l i c a b i l i t y of N e w t o n ' s l a w o f flow, t h e e q u i l i b r i u m
2602
YE. YE. BRAUDO
etal.
residual d e f o r m a t i o n was d e t e r m i n e d in t h e p r e s e n c e of t h e elastic after-effect, using gels t h a t h a d b e e n s u b j e c t e d to loading a t 24°C for v a r i o u s t i m e intervals. I t m a y be seen f r o m Fig. 2 t h a t t h e d e p e n d e n c e of t h e irreversible c o m p o n e n t of compliance, Iirr0v, on stress T m a y be e x p r e s s e d b y the e q u a t i o n Iirrev----V/t/, where ~ is t h e g r e a t e s t N e w t o n i a n v i s c o s i t y of t h e system.
1.8 -
I'~
l J
~
0.8
Z/rro~107m~/'v
0"5
y
-
0.2
03~
: I
O
Eg FIG. 1
log
I
150 Tz'me , rain
glI
~
200
if
0.1
l
3
Time,
_
hr
5
FIG. 2
FIG. 1. Flow curves for 5~/o gels of gelatins GI, at: •--24; 2--22; 3--20; 4--16; 5--14; 6--13.4°C. The solid points on curve 3 are for a stress of 64 ~T/m2, maximum strain 3.7~o; the open points for a stress of 129 N/m 2, 7"5~o. FIG. 2. Dependence of the irreversible component of the compliance of 5~/o gelatin gels on tb.e time of stressing at 24°C.
Temperaturedependenceof thereversibleand irreversibledeformationof gelatin gels. E l a s t i c after-effect flow curves were r e c o r d e d for 5~/o gelatin gels in t h e r a n g e 12-24°C. F o r t h e G I specimen, t h e c u r v e s were r e c o r d e d e v e r y 2°C, a n d for t h e G I I s p e c i m e n , e v e r y 1°C. T h e flow curves for t h e t w o specimens h a v e similar c h a r a c t e r i s t i c s a n d t h e d a t a for t h e G I s p e c i m e n only are s h o w n in Fig. 1. A l t h o u g h t h e t r e n d of t h e flow processes in t h e F i g u r e m a y be d e s c r i b e d b y s m o o t h curves, these processes occur, in fact, in a step wise m a n n e r , as s h o w n
Investigation of the flow of gelatin gels
2603
in [4]. I t m a y be assumed t h a t the step wise course of the flow processes is connected with the rearrangement of coarse supermolecular structural formations i n t h e g l e a t i n gels. I n t h e t e m p e r a t u r e r e g i o n 12-16°C, t h e d e f o r m a t i o n o f t h e g e l s is c o m p l e t e l y r e v e r s i b l e ; a t 19-24°C, a n e q u i l i b r i u m r e s i d u a l d e f o r m a t i o n i n t h e p r e s e n c e o f a n e l a s t i c a f t e r - e f f e c t is o b s e r v e d . T h e c a p a c i t y f o r g e l a t i n
3/4O ]- %
-d[,z]~
dt
G,w "Z~N/,'ne 30 (7
260
8
2 0
r
1
I
12
/6
Fa
12
I
20
28 T,°C
2 , y, oc
FIG. 3
FIG. 4
FIG. 3. Dependence of the shear modulus corresponding to the reversible strain of 5 ~o gels of a, GI and b, G I I on t e m p e r a t u r e for the following times of stressing: 1--0; 2--30; 3--60; 4--180 rain. FIo. 4. Dependence of the specific optical rotation of 3~o gelatin gels on temperature: 1, 2 - - d a t a from d y n a m i c measurements; 3 - - d a t a from static measurements; 4, 5--differential curves (from dynamic measurements): 1 and 4 are for gelatin GI gels, and 2, 3 and 5 for gelatin G I I gels.
gels to undergo irreversible deformation arises over a narrow t em perat ure interval a t 17-18°C. T h e v a l u e s o f t h e g r e a t e s t N e w t o n i a n v i s c o s i t i e s o f 5~o g e l a t i n gels at various temperatures are shown below Temperature, °C .< 16 t? × l0 -s (N .see/mS): GI oo GII oo
18
19
20
21
22
23
24
4.9* 3"0*
-1 "6
2.3 1 "2
-0"8
0.8 0'5
-0"3
0.4 0-2
Figure 3 shows the t em pe r at ur e dependence of the shear moduli corresponding to the almost instantaneous deformation and to the reversible deformation a f t e r flow f o r 30, 60 a n d 180 m i n . T w o r e g i o n s o f a p p r o x i m a t e l y l i n e a r change in modulus with temperature, * Results with poor reproducibility.
corresponding to the temperature intervals
2604
YE. YE. BI~AUDO et al.
in which reversible deformation of the gels either is or is not observed, are found on all the curves (in the case of the GII gels, the data for 19 and 20°C deviate from the general relationship). The linear branches intersect at temperatures of 18°C for GI and 17°C for GII. The breaks are especially clearly marked on the curves for the temperature dependence of the moduli corresponding to deformation at comparatively long times of action of the load. It is possible that the absence of any breaks in similar figures presented in [14] may be explained by the fact, that, in this work, the shear modulus was determined at very short times of action of the load (3 × 10-3-4 × l0 -4 see). Since the reversible and irreversible deformation m a y be considered as independent in the region of linear viscoelasticity, the data presented are evidence that the creation of a capacity for irreversible deformation is only one of the manifestations of a structural transition in the gelatin gels. This transition is also reflected in the temperature dependence of the shear moduli corresponding to reversible deformation. For the systems studied, the transition temperature is 16-18°C. It is not surprising that marked scatter in the results is observed in the ease of flow measurements at these temperatures. Since a necessary condition for the existence of gels is the helical conformation of the gelatin macromolecules, it was natural to suppose that the temperature transition under consideration should be connected with a change in the average degree of helix formation of the macromoleeules. In order to verify this supposition, the temperature dependence of the optical rotation of the gelatin gels was investigated upon heating. The results of the experiments are shown in Fig. 4. I t m a y be seen that, as the temperature is increased, a gradual decrease occurs in the optical rotation, the rate of decrease of rotation having its greatest value (in the temperature interval studied) at 20°C for the GI gels and at 23°C for the G I I gels. The equilibrium values of specific rotation lie somewhat below the values obtained from measurements under dynamic conditions b u t both curves have similar characteristics. Attention should be given to the differences in the course of the curves for the temperature dependence of optical rotation below 16°C. In the case of GI, the value of [~]D changes comparatively little as the temperature is raised from 12 to 16°C. An abrupt decrease in rotation is observed for GII gel over the entire temperature interval investigated, in agreement with the data given in [13-15, 16]. The relative constancy of the optical rotation of gelatin gels at temperatures below 15°C has been demonstrated in [17]. The opinion has been expressed [7, 13] that this result m a y be explained b y experimental errors. It m a y be seen from Fig. 4 that, for different gelatin specimens under identical conditions of preparing the specimens and carrying out the measurements, the two types of relationship may be observed. It follows from the data presented that a sharp decrease occurs at 15-22°C in the degree of helix formation in the gelatin macromolecules, which is accompanied (at a certain temperature) b y the creation of the ability of the gels to undergo
2605
Investigation of the flow of gelatin gels
irreversible deformation and by a change in the trend of the temperature dependence of the shear modulus corresponding to reversible deformation. There is, however, no basis for stating (as was done previously [18] on the basis of the dat~ for GI alone) t h a t this change in the mechanical properties of the gels is caused by the onset of intensive helix unwinding of the gelatin macromolecules.
D5-83 g'8 ln~
C7
08
1920~18 ~
gII
04
17 I 3.38 3.#0 3.40 103i'T
I
r
I
1
FIG. 5 FIO. 6 FIG. 5. Temperature dependence of the optical density of a 3°/o GI gel. Flo. 6. Temperature dependence of the greatest Newtonian viscosity of 5% gelatin GI gels. We postulate t h a t the initial stages of the helix-unwinding process occur preferentially in the surface sections of fibrillar associates of gelatin macromolecules where the helical structures are stabilized to a lesser extent by intermolecular interactions. As a result of helix unwinding, the interaction between the elements of the gel network is weakened and the ability arises for the fibrils to slide rela+,ive to one another, which also leads to the irreversible deformation of the gels. Figure 5 shows the change in the optical density of the GI gel with change in temperature. Attention should be given to the likeness in shape of the curves for the temperature dependence of optical rotation (Fig. 4) and optical density (Fig. 5) recorded under the same conditions. The decrease in optical density is evidently connected with a reduction in the dimensions of the scattering elements in the gel. The small increase in optical density at relatively low temperatures (12-14°C) may be explained by the rise in mobility of the scattering elements, which is caused, in its turn, by a weakening of the interactions between associates of gelatin macromolecules. It may be seen from Fig. 3 that, above the transition temperature, the values of are less than at lower temperatures. Extrapolation of the curves to a zero value of shear modulus gives the melting point as 25.,526.0°C for GI gels and 26.4-27.8°C for GII gels. In fact, the melting poiat of a 5% GI gel is 29'7°C, and e. GII gel, 30-9°C. It is consequently necessary to expect a f u r t h e r reduction in the rate at which the shear modulus falls as the melting point is approached (see also [7]). The temperature dependence of the shear modulus has
(dG,.ev/dt)
YE. YE. BRAu~o et al.
2606
been shown in [19] to have similar characteristics in the case of a acrylonitrilevinylacetate copolymer gel in dimethylacetamide. I t m a y be seen from Fig. 6 that, over the temperature interval investigated, the temperature dependence of viscosity is described by a Arrhenius equation. The values of the experimental activation energies for the viscous flow of the gels, (E,~c)g~l, calculated by the method of least squares, are 7 6 i 4 for GI and 74=k2 kcal/mole for GII respectively. The fact that these values for the two gelatin samples differing in viscosity by a factor of 2 agree, m a y point to the functional importance of the parameter (Evis¢)g~l. This quantity has been identified with the heat of formation of the network nodes of the gelatin gel [20].
Concerning the characteristics of the reversible deformation of gelatin gels. Figure 7 shows relaxation curves for the reversible deformation of GI gels, represented in double logarithmic coordinates (the curves for GII gels have similar
l~ liter*3 O'g
0
-- f,O
Q
/,0
2.~7
lo~z"
FIG. 7. Relaxation curves for the reversible strain of 5% GI gels at: 1--24; 2--22; 3--20;
4-- 16; 5-- 14; 6-- 13.4°C. characteristics). Attention should be paid to the fact that the form of these curves does not agree with widely held concepts about the rubber like character of the deformability of gelatin gels in the usual times of observation, including dynamic test conditions [21]. The curves shown correspond in shape to the properties of systems located in the region where the transition from the glassy to the highly elastic condition is beginning [21]. At the same time, the order of magnitude of the shear moduli of the gelatin gels agree with the properties of dilute rubber like systems [22].
Investigation of the flow of gelatin gels
2607
Figure 8 shows how the almost instantaneous deformation, represented as a fraction of the total deformation in 180 min loading, varies with temperature. This quantity decreases to some extent as the temperature is raised, a fact t h a t reflects the "glassy" character of the flow curves. A similar result is shown in reference [2]. Relaxation curves, having a shape characteristic of the region of the transition from the glassy to the highly elastic condition, have also been observed previously in studies of the stress relaxation in 5-50~o gelatin gels [23-26] and also in polyvinyl-alcohol gels [27]. According to the data in [13], the tangent of the mechanical loss angle of gelatin gels increases as the temperature is raised, a fact which is also characteristic of the initial region of transition from the glassy to the highly elastic condition. These facts have, however, not been subjected to discussion.
15
2O
2O77°0
FIG. 8. Temperature dependence of IolIrev for 5~, GI gels. At the same time, in reference [28] devoted to the investigation of stress relaxation in 1-2~o gelatin gels, curves are shown whose shape corresponds to the transition to a developed highly elastic condition. According to [3], the flow of 1 ~o gelatin gels m a y be described on the basis of the retardation time distribution obtained b y Kirkwood [29] based on the kinetic theory of high elasticity. At the present time it is, in fact, difficult to establish, because of the inadequacy of the data, whether the relaxation processes occurring in relatively dilute 1 - 2 ~ ) gelatin gels do differ in character from those in concentrated (5-50~o) gels, or whether the known differences are caused b y experimental errors. It is clear that the question of the nature of the deformatio~l in gelatin gels cannot be solved simply by comparing t h e m with other polymeric systems. There are a number of cogent arguments in favour of concepts concerning the entropy nature of the elasticity of these gels [3, 12, 22, 30]. A number of features of the mechanical properties of gelatin gels can, however, be explained on the basis of concepts concerning the energy nature of the elasticity. A system of unordered fibrils has thus been considered as a model for gelatin gels, the space between the fibrils being filled with a liquid and the deformation of such a system being determined by the bending and stretching of the fibrils * [2]. The theoretically obtained relationship between the Young's modulus and the volume fraction of gelatin agrees well with the experimental data for gels [6, 32] although it does not predict the sharp increase in modulus in the transition to xero-gels. • Ideas that the bendEng of elements of their three dimensional framework lies at the basis of the reversible deformation of gels have also been developed in [31].
2608
YE. YE. BRAUDO et al.
On the whole none of the existing theories of the elasticity of gelatin gels enables the entire set of existing experimental data to be interpreted. Taking into account the fact that the network of gelatin gels is constructed of fibrillar associates of macromolecules [33, 34], one may suggest that large deformations of gels are caused in part b y the bending of these fibrils. This type of deformation has predominantly energy characteristics. Simultaneously, the change in the conformation of the bent sections of the gelatin macromolecules, rendered non-helical, should lead to the formation of a predominantly entropy component of elasticity. As experiment shows, the latter makes the major contribution to the heat effect in deformation [12, 22]. Free volume is also required for the change in conformation of the bent macromolecular sections and for the bending of the fibrils. In both cases, therefore, an increase in the polymer concentration in the gel or a reduction in temperature should finally lead to glass formation. However, the actual values of concentration or temperature at which glass formation occurs m a y be different for different types of deformation. Such a two stage trend in the process of glass formation is observed in the case of highly concentrated gelatin gels [22]. The authors wish to express their thanks to L. V. Ivanova for help in carrying out the experiments and to G. L. Slonimskii and A. I. Mzhel'skii for discussion of the results and valuable advice. Translated by G. F. MODLE~ REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
12. 13. 14. 15. 16. 17.
E. K I N K E L and E. SAUER, Z. angew. Chem. 38: 413, 1925 H. J. POOLE, Trans. F a r a d a y Soc. 21: 114, 1925 L. J. HASTWELL and R. ROSCOE, Brit. J. Appl. P h y s . 7: 441, 1956 L. V. IVANOVA-CItUM_AKOVA, P. A. R E B I N D E R and G. A. KRUS, Kolloidn. zh. 18: 682, 1956 V. A. PCHEL1N and N. A. SOLOMCHENKO, Kolloidn. zh. 22: 6, 1960 W. UENO and J. 0NO, Chem. Abstrs. 63: 14298, 1965 J. D. FERRY, Advances Protein Chem. 4: l, 1948 A. G. W A R D and P. R. SAUNDERS, in: Rheology, p. 8, vol. 2, ed. by F. R. Eirich, New York, 1958 D. M. TOLSTO1, Kolloidn. zh. 16: 133, 1948 W. T. READ and M. HILL, J. Appl. Mech. 17: 349, 1950 V. N. IZMAILOVA, V. A. PCHELIN and SAMIR ABU ALI, Dokl. AN SSSR 164: 131, 1965; V. N. IZMAILOVA, SAMIR ABU ALI and V. A. PCHELIN, V kn. Fiziko-khimieheskaya mekhanika dispersnykh struktur (In the book; Physico-ChemieM Mechanics of Disperse Structures). p. 77, ed. by P. A. Rebinder, Izd. " N a u k a " , 1966 Yu. K. GODOVSKII, I. I. MAL'TSEVA and G. L. SLONIMSKII, Vysokomol. soyed. A13: 2768, 1971 (Translated in Polymer Sci. U.S.S.R. 13: 12, 1971) J. D. F E R R Y and J. E. ELDRIDGE, J. Phys. Coll. Chem. 53: 184, 1949 J. D. FERRY, J. Amer. Chem. Soc. 70: 2244, 1948 E. O. K R A E M E R and J. R. FANSELOW, J. Phys. Chem. 29: 1169, 1925 (quoted from [71]) V. A. PCHELIN, V. N. IZMAILOVA and V. P. MF_~ZLOV, Vysokomol. soyed. 5: 1429, 1963 (Translated in P o l y m e r Sci. U.S.S.R. 5: 3, 526, 1964) C. R. SMITH, J. Amer. Chem. Soc. 41: 135, 1919
Diffusion of phosphoric acid into polyvinyl alcohol fihns
2609
18. V. B. TOLSTOGUZOV, Ye. Ye. BRAUDO et al., Vysokomol. soyed. B13: 16, 1971 (Not translated in Polymer Sci. U.S.S.R.) 19. D. It. PAUL, J. Appl. Polymer Sci. 11: 439, 1967 20. L. Z. ItOGOVINA, G. L. SLONIMSKII and L. L. AKSENOVA, Vysokomol. soyed. A13: 1451, 1971 (Translatcd in P o ly m e r Sci. U.S.S.R. 13: 7, 1631, 1971) 21. J. D. FEItItY, Vyazkouprugiye svoistva polimerov (Viscoelastic Properties of Polymers), ch. 2, p. 17, Izd. inostr, lit.. 1963 (Russian translation) 22. N. HIRAI, Bull. Inst. Chem. Res. K y o to Univ. 33: 21, 1955 23. M. MILLER, J. D. FERRY, E. W. SCHREMP and J. E. ELDRIDGE, J. Phys. Coll. Chem. 55: 1387, 1951 24. K. A R A K A W A , Bull. Chem. Soc. Japan, 35: 309, 1962 25. K. A R A K A W A and N. TAKENAKA, Nippon Kagaku Dsasshi 83: 1065, 1962 26. M. W A T A S E and K. A I t A K A W A , Ibid. 88: 317, 1967: 90: 658, 1969 27. K. A R A K A W A , Bull. Chem. Soc. J a p a n 31: 842, 1958; 32: 1248, 1959; 33: 1568, 1960; 34: 1549, 1961 28. S. Ya. VEILER, V. I. LIKHTMAN and P. A. ItEBINDER, Kolloidn. zh. l I : 8, 1949 29. J. KIRKWOOD, J. Chem. Phys. 14: 51, 1946 30. It. ROSCOE, In: Proceedings of 4 th International Congress on Rheology, part 3, p. 593, New York~ 1965 31. M. M. IOVLEVA and S. P. PAPKOV, Vysokomol. soyed. 8: 855, 1966 (Translated in Polymer Sci. U.S.S.R. 8: 5, 938, 1966) 32. A. LEICK, Ann. Phys. 14: 139, 1904 33. W. THEIMER, Z. Naturforsch. 15b: 346, 1960 34. G. L. SLON]2YlSKII, A. I. KITAIGORODSKII, V. M. BELAVTSEVA, V. B. TOLSTOGUZOV and I. I. MAL'TSEVA, Vysokomol. soycd. B10: 640, 1968 (Not translated in P o l y m er Sci. U.S.S.R.)
DIFFUSION OF PHOSPHORIC ACID INTO POLYVINYL ALCOHOL (PVALC) FILMS SWOLLEN IN WATER* A. L. IORDA~SKII, YE. I. MERKULOV, YU. V. MOISEYEV
and G. YE. ZAIKOV Chemical Physics Institute U.S.S.R. Academy of Sciences
(Received 6 April 1973) The diffusion and the electroconductance of the system polyvinyl alcohol (PVALC)-phosphoric acid (H3PO~) was studied to discover the mechanisms of diffusion of a slightly acid aqueous solution into hydrophilic polymers. TILe concentratio,J dependence of the diffusion of electrolyte is due to a change in the ratio of the concentrations of undissociated and dissociated acid, and to a deviation from ideal diffusion. The a c t i v i t y coefficient of HaPO 4 in the polymer' matrix was calculated from th~ diffusion measurements. * Vysokomol. soyed. A16: No. 10, 2248-2254, 1974.
2599
14. V. A. SNEZHKO, L. N. SAMOILOVA, K. P. KHOMYAKOV, A. I. VALAKHANOVICH, R. V. ZARETSKAYA, A. D. VIRNIK, G. Ya. ROZENBERG and Z. A. ROGOVIN, Antibiotiki, 48, 1972 15. J. MESTER, J. Amer. Chem. Soc. 77: 5452, 1955 16. J. McCORMICK, J. Chem. Soc. C, 2121, 1966 17. R. D. GUTHRIE, Adv. in Carbohydr. Chem. 16: 105, 1961 18. R. G. KRYLOVA, S. N. RYADOVSKAYA and O. P. GOLOVA, Vysokomol. soyed. Ag: 993, 1967 (Translated in Polymer Sci. U.S.S.R. 9: 5, 1106, 1967) 19. N. Ya. KUZNETSOVA-LENSHINA, G. A. TIMOKHINA, V. Ye. ZHAVORONKOV and V. I. IVANOV, Izv. A N Kirg. SSR, No. 3, 59, 1968 20. K. P. KHOMYAKOV, A. D. VIRNIK, Z. A. ROGOVIN and S. N. USKAKOV, Vysokomol. soyed. 7 : 1 0 3 5 1965 (Translated in Polymer Sci. U.S.S.R. 7: 6, 1145, 1965) 21. K. P. KHOMYAKOV, A. D. VIRNIK and Z. A. ROGOVIN, K i m i y a prirodn, soyed. 3: 213, 1966 22. A. D. VIRNIK, O. P. LALETINA, M. A. PENENZHIK, K. P. KHOMYAKOV, Z. A. ROGOVlN and G. Ya. ROZENBERG, Vysokomol. soyed. A10: 362, 1968 (Translated in P o l y m e r Sci. U.S.S.R. 10: 2, 423, 1968) 23. P. N. KASHKIN, A. I. BEZBORODOV and N. P. YELINOV, Antibiotiki (Antibiotics). p. 55, "Meditstina", 1970
INVESTIGATION OF THE FLOW OF GELATIN GELS AT VARIOUS TEMPERATURES* YE. YE. BRAUDO, I. G. 1)LASHCHINA, ]~. S. KUZ'MIi~A and V. B. TOLSTOGUZOV Institute for Elemento-Organic Compounds, U.S.S.R. Academy of Sciences (Received 28 March 1973) The flow of 5 ~o gelatin gels in the linear visco-elastic region has been investigated in the t e m p e r a t u r e range 12-24°C. I t has been established t h a t the a b i l i t y of gelatin gels to undergo irreversible deformation arises as the temperature is raised over a narrow t e m p e r a t u r e interval. The temperature dependence of the greatest Newtonian viscosity of the gelatin gels is described b y an Arrhenius equation. The form of the relaxation curve for the reversible deformation of gelatin gels cor)~esponds to the properties of systems located in the region where the transition f r o n f t h e glassy to the highly elastic condition begins. DESPITE t h e f a c t t h a t t h e flow o f g e l a t i n gels h a s b e e n u s e d a s t h e s u b j e c t f o r a n u m b e r o f i n v e s t i g a t i o n s [1-6], t h e r e a r e a l m o s t n o d a t a a b o u t t h e c o u r s e o f this process at various temperatures. It can only be recorded that, according * Vysokomol. soyed, h i 6 : No. 10, 2240-2247, 1974.
2600
YE. YE. BRAUDO et al.
t o t h e d a t a i n [5], t h e p l a s t i c i t y o f t h e g e l s i n c r e a s e s s h a r p l y o v e r a n a r r o w perature We range
tem-
interval close to the melting point. have
studied
12-24°C.
molecular
the flow of 5%
Since the
characteristics
mechanical of the
gelatin gels in shear
in the temperature
properties
gels depend
preparation
of gelatin
[7, 8], t h e
on the
flow of gels prepared
from two different specimens of gelatin was studied. EXPERIMENTAL T w o specimens of alkaline p h o t o g r a p h i c gelatin, w h i c h we shall d e n o t e b y GI and G I I , were selected for t h e investigation. T h e gelatins were purified b y L o b ' s m e t h o d of dialysis, traces of d i b u t y l t i n o x i d e were a d d e d as a n a n t i s e p t i c a n d t h e gelatins were stored as gels in an exsiccator o v e r water. The G I and G I I gels had [7]* = 59=t= 1 a n d 57 =t=1 m l / g a n d M w t × X 1 0 - a = 2 1 0 and 190 respectively. T h e i n v e s t i g a t i o n s of flow were m a d e b y t h e m e t h o d described in [4], the essentials of w h i c h consist in t h e o b s e r v a t i o n of d e f o r m a t i o n in p u r e shear of a gel s p e c i m e n placed b e t w e e n two g r o o v e d flat parallel plates, b y o b s e r v i n g t h e m o v e m e n t of the u p p e r plate to w h i c h a l o a d is a t t a c h e d , hanging o v e r a p u l l e y (Tolstoi a p p a r a t u s [9]). The end effect error, c a l c u l a t e d as in [10], does n o t exceed 3.2~o for the g i v e n s p e c i m e n dimensions a n d was n o t t a k e n into a c c o u n t in the calculations. The loads corresponding to t h e s t a r t of r o t a t i o n of t h e pulleys in t h e double a p p a r a t u s used b y us were 0 . 1 9 i 0 . 0 3 and 0 . 2 6 ± 0 . 0 3 g (1-5°/o of t h e load in t h e e x p e r i m e n t ) . These d a t a were t a k e n into a c c o u n t in t h e calculation of stresses. The m o v e m e n t of t h e u p p e r plate was m e a s u r e d w i t h an M I R microscope with a M O V - I - 1 5 K h (scale division, 1.3 pm). The s p e c i m e n thickness was m e a s u r e d w i t h a horizontal microscope h a v i n g an ocular m i c r o m e t e r ; t h e p a r a l l e l a r i t y of t h e u p p e r and lower surfaces of the s p e c i m e n was m o n i t o r e d a t t h e s a m e time. i n order to preven~ d r y i n g o u t of t h e specimen, w a t e r was flooded into the channel in t h e w o r k i n g c h a m b e r of the a p p a r a t u s ; t h e t e m p e r a t u r e in t h e c h a m b e r s was held c o n s t a n t w i t h an a c c u r a c y of :]:0.1°C b y m e a n s of an u l t r a t h e r m o s t a t . Certain changes in t h e m e t h o d of p r e p a r i n g these specimens were i n t r o d u c e d as c o m p a r e d w i t h [4]: t h e gel s p e c i m e n to be t e s t e d was m e l t e d a n d held at 40°C for 30 rain, after w h i c h t h e m e l t was cast i n t o p e r s p e x mould, in which inserts w i t h the w o r k i n g plates were located. T h e m o u l d s w i t h t h e m e l t were placed in t h e exsiccator w i t h w a t e r and held in t h e m a t r o o m t e m p e r a t u r e for 2 hr. T h e n t h e plates t o g e t h e r w i t h the gelled s p e c i m e n were carefully r e m o v e d f r o m t h e mould, placed once m o r e in the exsiccator w i t h w a t e r a n d t h e r m o s t a t i cally controlled u n d e r the conditions selected. D u r i n g s t r u c t u r e f6rmation, t h e u p p e r p l a t e could m o v e freely r e l a t i v e to ffhe lower plate, and i n t e r n a l stresses, which could serve as a source of errors, did n o t d e v e l o p in t h e specimen. A p e r t u r e s (2 m m in d i a m e t e r ) were m a d e in t h e walls of t h e m o u l d to allow the outflow of air, a n d these were c o v e r e d w i t h a p l a t e before t h e m e l t was cast. The insert was l u b r i c a t e d with silicone grease on b o t h sides. One of t h e walls of t h e insert was n o t secured to the b o t t o m a n d could be freely r o t a t e d a b o u t an u p p e r crossbar. A f t e r r e m o v a l of the insert f r o m t h e mould, this wall was tilted and t h e insert carefully s e p a r a t e d w i t h o u t d a m a g i n g t h e lateral surfaces of the specimen. Before d e t e r m i n i n g t h e flow, the specimens were subjected to s t r u c t u r e f o r m a t i o n at 10~=1.5°C for 7 days. The r a t e of the s t r u c t u r e f o r m a t i o n processes, w h i c h d e t e r m i n e t h e s t r e n g t h [11] a n d h e a t of m e l t i n g [12] of gelatin gels, are k n o w n to become v e r y small in 5-7 days. Before t h e s t a r t of e x p e r i m e n t s , t h e specimens were held for 3 hr at the test t e m perature. * I n 2 M K S C N at 25°C. t D e t e r m i n e d b y l i g h t - s c a t t e r i n g in 0-15 M NaC1 at 35°C.
,
Investigation of the flow of gelatin gels
2601
The optical density of the gelatin gels was measured at a wavelength of 589 n m m a thermostatically controlled cell 0-05 dm thick, with a polarimeter made b y the firm " J u a n Roussel" (France). The relative error in the measurements was J 0.3o/O. Because of the high sensitivity of the apparatus, the gelatin concentration in the specimens was reduced t¥om 5 to 3%. According to [I3], the specific optical rotation of gelatin gels does not (to a tirst approximation) depend on concentration. The specimens were subjected to structure formation in a cell under the same temperature and time conditions as for the investigation of flow. The temperature in the cell was monitored by means of a thermocouple. ~-V[easurements of the optical rotation were made under dynamic and static conditions. I n tile first case, the optical rotation was determined during a single experiment over the temperature range 9-26°C, by making measurements every 1-2°C and holding the specimens, before the recording of the parameters, for 2 hr aV each temperature of measurement. In the second case, an equilibrium value of optical rotation for a single temperature was measured in each experiment, and for this purpose, the specimen was thermostatically controlled for 6-8 hr. Those values of optical rotation were considered to be equilibrium values which remained unchanged after the temperature of the system had been raised or low(~red, and returned to its initial condition. Tile optical density of 3O/o gelatin gels was measured with a "Spekol" photometer ((Aerman Democratic I~epublic) at a wavelength of 436 nm, in a thermostatically controlled cell of thickness 1 cm. The conditions of preparing the specimens and carrying out the measurements was the same as for the polarimetric investigations. RESULTS AND DISCUSSION
The separation of the reversible and the irreversible deformation was made in the following way. The gel specimen was loaded for tile selected time interval, after which the load was removed and the equilibrium residual deformation was determined for the elastic after effect. A curve for the change, with time, of the reversible deformation was then constructed by subtracting its irreversible component from the total deformation. To achieve the equilibrium residual strain in the presence of the elastic after-effect, the specimen was held for 3 hr at tile test temperature, for 15 hr at room temperature and, finally, for 3--5 hr at 24°C until the equilibrium value of strain had been established. Separation of the reversible and irreversible deformation by the method adopted is possible only under conditions such that tile measurements lie within the region of linear viscoelasticity. I t is also assumed that the irreversible deformation develops linearly with tim(;, t h a t is, in conformity with Newton's law of flow. The validity of both assumptions was checked experimentally. F i g u r e 1 s h o w s t h e flow c u r v e for G I gel a t 20°C, o b t a i n e d f r o m e x p e r i m e n t s m a d e a t t w o d i f f e r e n t stresses. I t m a y be s e e n t h a t t h e c o m p l i a n c e does n o t d e p e n d o n stress. T h i s is also v a l i d for t h e o t h e r flow d a t a ( d e f o r m a t i o n u p t o 7.5%). I n v i e w of t h e f a c t t h a t g e l a t i n gels a r e n o n - e q u i l i b r i u m s y s t e m s , i t w~s n e c e s s a r y to satisfy oneself t h a t no m a r k e d changes in specimen properties o c c u r r e d u n d e r t h e effect of t e m p e r a t u r e d u r i n g tests. T o do t h i s , gel s p e c i m e n s p r e p a r e d b y the usual m e t h o d were repeatedly subjected to short-time loading a t 20°C for 6 hr. N o c h a n g e s i n t h e a l m o s t i n s t a n t a n e o u s d e f o r m a t i o n w a s t h u s o b s e r v e d a n d its r e v e r s i b i l i t y w a s r e t a i n e d . I n o r d e r t o v e r i f y t h e a p p l i c a b i l i t y of N e w t o n ' s l a w o f flow, t h e e q u i l i b r i u m
2602
YE. YE. BRAUDO
etal.
residual d e f o r m a t i o n was d e t e r m i n e d in t h e p r e s e n c e of t h e elastic after-effect, using gels t h a t h a d b e e n s u b j e c t e d to loading a t 24°C for v a r i o u s t i m e intervals. I t m a y be seen f r o m Fig. 2 t h a t t h e d e p e n d e n c e of t h e irreversible c o m p o n e n t of compliance, Iirr0v, on stress T m a y be e x p r e s s e d b y the e q u a t i o n Iirrev----V/t/, where ~ is t h e g r e a t e s t N e w t o n i a n v i s c o s i t y of t h e system.
1.8 -
I'~
l J
~
0.8
Z/rro~107m~/'v
0"5
y
-
0.2
03~
: I
O
Eg FIG. 1
log
I
150 Tz'me , rain
glI
~
200
if
0.1
l
3
Time,
_
hr
5
FIG. 2
FIG. 1. Flow curves for 5~/o gels of gelatins GI, at: •--24; 2--22; 3--20; 4--16; 5--14; 6--13.4°C. The solid points on curve 3 are for a stress of 64 ~T/m2, maximum strain 3.7~o; the open points for a stress of 129 N/m 2, 7"5~o. FIG. 2. Dependence of the irreversible component of the compliance of 5~/o gelatin gels on tb.e time of stressing at 24°C.
Temperaturedependenceof thereversibleand irreversibledeformationof gelatin gels. E l a s t i c after-effect flow curves were r e c o r d e d for 5~/o gelatin gels in t h e r a n g e 12-24°C. F o r t h e G I specimen, t h e c u r v e s were r e c o r d e d e v e r y 2°C, a n d for t h e G I I s p e c i m e n , e v e r y 1°C. T h e flow curves for t h e t w o specimens h a v e similar c h a r a c t e r i s t i c s a n d t h e d a t a for t h e G I s p e c i m e n only are s h o w n in Fig. 1. A l t h o u g h t h e t r e n d of t h e flow processes in t h e F i g u r e m a y be d e s c r i b e d b y s m o o t h curves, these processes occur, in fact, in a step wise m a n n e r , as s h o w n
Investigation of the flow of gelatin gels
2603
in [4]. I t m a y be assumed t h a t the step wise course of the flow processes is connected with the rearrangement of coarse supermolecular structural formations i n t h e g l e a t i n gels. I n t h e t e m p e r a t u r e r e g i o n 12-16°C, t h e d e f o r m a t i o n o f t h e g e l s is c o m p l e t e l y r e v e r s i b l e ; a t 19-24°C, a n e q u i l i b r i u m r e s i d u a l d e f o r m a t i o n i n t h e p r e s e n c e o f a n e l a s t i c a f t e r - e f f e c t is o b s e r v e d . T h e c a p a c i t y f o r g e l a t i n
3/4O ]- %
-d[,z]~
dt
G,w "Z~N/,'ne 30 (7
260
8
2 0
r
1
I
12
/6
Fa
12
I
20
28 T,°C
2 , y, oc
FIG. 3
FIG. 4
FIG. 3. Dependence of the shear modulus corresponding to the reversible strain of 5 ~o gels of a, GI and b, G I I on t e m p e r a t u r e for the following times of stressing: 1--0; 2--30; 3--60; 4--180 rain. FIo. 4. Dependence of the specific optical rotation of 3~o gelatin gels on temperature: 1, 2 - - d a t a from d y n a m i c measurements; 3 - - d a t a from static measurements; 4, 5--differential curves (from dynamic measurements): 1 and 4 are for gelatin GI gels, and 2, 3 and 5 for gelatin G I I gels.
gels to undergo irreversible deformation arises over a narrow t em perat ure interval a t 17-18°C. T h e v a l u e s o f t h e g r e a t e s t N e w t o n i a n v i s c o s i t i e s o f 5~o g e l a t i n gels at various temperatures are shown below Temperature, °C .< 16 t? × l0 -s (N .see/mS): GI oo GII oo
18
19
20
21
22
23
24
4.9* 3"0*
-1 "6
2.3 1 "2
-0"8
0.8 0'5
-0"3
0.4 0-2
Figure 3 shows the t em pe r at ur e dependence of the shear moduli corresponding to the almost instantaneous deformation and to the reversible deformation a f t e r flow f o r 30, 60 a n d 180 m i n . T w o r e g i o n s o f a p p r o x i m a t e l y l i n e a r change in modulus with temperature, * Results with poor reproducibility.
corresponding to the temperature intervals
2604
YE. YE. BI~AUDO et al.
in which reversible deformation of the gels either is or is not observed, are found on all the curves (in the case of the GII gels, the data for 19 and 20°C deviate from the general relationship). The linear branches intersect at temperatures of 18°C for GI and 17°C for GII. The breaks are especially clearly marked on the curves for the temperature dependence of the moduli corresponding to deformation at comparatively long times of action of the load. It is possible that the absence of any breaks in similar figures presented in [14] may be explained by the fact, that, in this work, the shear modulus was determined at very short times of action of the load (3 × 10-3-4 × l0 -4 see). Since the reversible and irreversible deformation m a y be considered as independent in the region of linear viscoelasticity, the data presented are evidence that the creation of a capacity for irreversible deformation is only one of the manifestations of a structural transition in the gelatin gels. This transition is also reflected in the temperature dependence of the shear moduli corresponding to reversible deformation. For the systems studied, the transition temperature is 16-18°C. It is not surprising that marked scatter in the results is observed in the ease of flow measurements at these temperatures. Since a necessary condition for the existence of gels is the helical conformation of the gelatin macromolecules, it was natural to suppose that the temperature transition under consideration should be connected with a change in the average degree of helix formation of the macromoleeules. In order to verify this supposition, the temperature dependence of the optical rotation of the gelatin gels was investigated upon heating. The results of the experiments are shown in Fig. 4. I t m a y be seen that, as the temperature is increased, a gradual decrease occurs in the optical rotation, the rate of decrease of rotation having its greatest value (in the temperature interval studied) at 20°C for the GI gels and at 23°C for the G I I gels. The equilibrium values of specific rotation lie somewhat below the values obtained from measurements under dynamic conditions b u t both curves have similar characteristics. Attention should be given to the differences in the course of the curves for the temperature dependence of optical rotation below 16°C. In the case of GI, the value of [~]D changes comparatively little as the temperature is raised from 12 to 16°C. An abrupt decrease in rotation is observed for GII gel over the entire temperature interval investigated, in agreement with the data given in [13-15, 16]. The relative constancy of the optical rotation of gelatin gels at temperatures below 15°C has been demonstrated in [17]. The opinion has been expressed [7, 13] that this result m a y be explained b y experimental errors. It m a y be seen from Fig. 4 that, for different gelatin specimens under identical conditions of preparing the specimens and carrying out the measurements, the two types of relationship may be observed. It follows from the data presented that a sharp decrease occurs at 15-22°C in the degree of helix formation in the gelatin macromolecules, which is accompanied (at a certain temperature) b y the creation of the ability of the gels to undergo
2605
Investigation of the flow of gelatin gels
irreversible deformation and by a change in the trend of the temperature dependence of the shear modulus corresponding to reversible deformation. There is, however, no basis for stating (as was done previously [18] on the basis of the dat~ for GI alone) t h a t this change in the mechanical properties of the gels is caused by the onset of intensive helix unwinding of the gelatin macromolecules.
D5-83 g'8 ln~
C7
08
1920~18 ~
gII
04
17 I 3.38 3.#0 3.40 103i'T
I
r
I
1
FIG. 5 FIO. 6 FIG. 5. Temperature dependence of the optical density of a 3°/o GI gel. Flo. 6. Temperature dependence of the greatest Newtonian viscosity of 5% gelatin GI gels. We postulate t h a t the initial stages of the helix-unwinding process occur preferentially in the surface sections of fibrillar associates of gelatin macromolecules where the helical structures are stabilized to a lesser extent by intermolecular interactions. As a result of helix unwinding, the interaction between the elements of the gel network is weakened and the ability arises for the fibrils to slide rela+,ive to one another, which also leads to the irreversible deformation of the gels. Figure 5 shows the change in the optical density of the GI gel with change in temperature. Attention should be given to the likeness in shape of the curves for the temperature dependence of optical rotation (Fig. 4) and optical density (Fig. 5) recorded under the same conditions. The decrease in optical density is evidently connected with a reduction in the dimensions of the scattering elements in the gel. The small increase in optical density at relatively low temperatures (12-14°C) may be explained by the rise in mobility of the scattering elements, which is caused, in its turn, by a weakening of the interactions between associates of gelatin macromolecules. It may be seen from Fig. 3 that, above the transition temperature, the values of are less than at lower temperatures. Extrapolation of the curves to a zero value of shear modulus gives the melting point as 25.,526.0°C for GI gels and 26.4-27.8°C for GII gels. In fact, the melting poiat of a 5% GI gel is 29'7°C, and e. GII gel, 30-9°C. It is consequently necessary to expect a f u r t h e r reduction in the rate at which the shear modulus falls as the melting point is approached (see also [7]). The temperature dependence of the shear modulus has
(dG,.ev/dt)
YE. YE. BRAu~o et al.
2606
been shown in [19] to have similar characteristics in the case of a acrylonitrilevinylacetate copolymer gel in dimethylacetamide. I t m a y be seen from Fig. 6 that, over the temperature interval investigated, the temperature dependence of viscosity is described by a Arrhenius equation. The values of the experimental activation energies for the viscous flow of the gels, (E,~c)g~l, calculated by the method of least squares, are 7 6 i 4 for GI and 74=k2 kcal/mole for GII respectively. The fact that these values for the two gelatin samples differing in viscosity by a factor of 2 agree, m a y point to the functional importance of the parameter (Evis¢)g~l. This quantity has been identified with the heat of formation of the network nodes of the gelatin gel [20].
Concerning the characteristics of the reversible deformation of gelatin gels. Figure 7 shows relaxation curves for the reversible deformation of GI gels, represented in double logarithmic coordinates (the curves for GII gels have similar
l~ liter*3 O'g
0
-- f,O
Q
/,0
2.~7
lo~z"
FIG. 7. Relaxation curves for the reversible strain of 5% GI gels at: 1--24; 2--22; 3--20;
4-- 16; 5-- 14; 6-- 13.4°C. characteristics). Attention should be paid to the fact that the form of these curves does not agree with widely held concepts about the rubber like character of the deformability of gelatin gels in the usual times of observation, including dynamic test conditions [21]. The curves shown correspond in shape to the properties of systems located in the region where the transition from the glassy to the highly elastic condition is beginning [21]. At the same time, the order of magnitude of the shear moduli of the gelatin gels agree with the properties of dilute rubber like systems [22].
Investigation of the flow of gelatin gels
2607
Figure 8 shows how the almost instantaneous deformation, represented as a fraction of the total deformation in 180 min loading, varies with temperature. This quantity decreases to some extent as the temperature is raised, a fact t h a t reflects the "glassy" character of the flow curves. A similar result is shown in reference [2]. Relaxation curves, having a shape characteristic of the region of the transition from the glassy to the highly elastic condition, have also been observed previously in studies of the stress relaxation in 5-50~o gelatin gels [23-26] and also in polyvinyl-alcohol gels [27]. According to the data in [13], the tangent of the mechanical loss angle of gelatin gels increases as the temperature is raised, a fact which is also characteristic of the initial region of transition from the glassy to the highly elastic condition. These facts have, however, not been subjected to discussion.
15
2O
2O77°0
FIG. 8. Temperature dependence of IolIrev for 5~, GI gels. At the same time, in reference [28] devoted to the investigation of stress relaxation in 1-2~o gelatin gels, curves are shown whose shape corresponds to the transition to a developed highly elastic condition. According to [3], the flow of 1 ~o gelatin gels m a y be described on the basis of the retardation time distribution obtained b y Kirkwood [29] based on the kinetic theory of high elasticity. At the present time it is, in fact, difficult to establish, because of the inadequacy of the data, whether the relaxation processes occurring in relatively dilute 1 - 2 ~ ) gelatin gels do differ in character from those in concentrated (5-50~o) gels, or whether the known differences are caused b y experimental errors. It is clear that the question of the nature of the deformatio~l in gelatin gels cannot be solved simply by comparing t h e m with other polymeric systems. There are a number of cogent arguments in favour of concepts concerning the entropy nature of the elasticity of these gels [3, 12, 22, 30]. A number of features of the mechanical properties of gelatin gels can, however, be explained on the basis of concepts concerning the energy nature of the elasticity. A system of unordered fibrils has thus been considered as a model for gelatin gels, the space between the fibrils being filled with a liquid and the deformation of such a system being determined by the bending and stretching of the fibrils * [2]. The theoretically obtained relationship between the Young's modulus and the volume fraction of gelatin agrees well with the experimental data for gels [6, 32] although it does not predict the sharp increase in modulus in the transition to xero-gels. • Ideas that the bendEng of elements of their three dimensional framework lies at the basis of the reversible deformation of gels have also been developed in [31].
2608
YE. YE. BRAUDO et al.
On the whole none of the existing theories of the elasticity of gelatin gels enables the entire set of existing experimental data to be interpreted. Taking into account the fact that the network of gelatin gels is constructed of fibrillar associates of macromolecules [33, 34], one may suggest that large deformations of gels are caused in part b y the bending of these fibrils. This type of deformation has predominantly energy characteristics. Simultaneously, the change in the conformation of the bent sections of the gelatin macromolecules, rendered non-helical, should lead to the formation of a predominantly entropy component of elasticity. As experiment shows, the latter makes the major contribution to the heat effect in deformation [12, 22]. Free volume is also required for the change in conformation of the bent macromolecular sections and for the bending of the fibrils. In both cases, therefore, an increase in the polymer concentration in the gel or a reduction in temperature should finally lead to glass formation. However, the actual values of concentration or temperature at which glass formation occurs m a y be different for different types of deformation. Such a two stage trend in the process of glass formation is observed in the case of highly concentrated gelatin gels [22]. The authors wish to express their thanks to L. V. Ivanova for help in carrying out the experiments and to G. L. Slonimskii and A. I. Mzhel'skii for discussion of the results and valuable advice. Translated by G. F. MODLE~ REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
12. 13. 14. 15. 16. 17.
E. K I N K E L and E. SAUER, Z. angew. Chem. 38: 413, 1925 H. J. POOLE, Trans. F a r a d a y Soc. 21: 114, 1925 L. J. HASTWELL and R. ROSCOE, Brit. J. Appl. P h y s . 7: 441, 1956 L. V. IVANOVA-CItUM_AKOVA, P. A. R E B I N D E R and G. A. KRUS, Kolloidn. zh. 18: 682, 1956 V. A. PCHEL1N and N. A. SOLOMCHENKO, Kolloidn. zh. 22: 6, 1960 W. UENO and J. 0NO, Chem. Abstrs. 63: 14298, 1965 J. D. FERRY, Advances Protein Chem. 4: l, 1948 A. G. W A R D and P. R. SAUNDERS, in: Rheology, p. 8, vol. 2, ed. by F. R. Eirich, New York, 1958 D. M. TOLSTO1, Kolloidn. zh. 16: 133, 1948 W. T. READ and M. HILL, J. Appl. Mech. 17: 349, 1950 V. N. IZMAILOVA, V. A. PCHELIN and SAMIR ABU ALI, Dokl. AN SSSR 164: 131, 1965; V. N. IZMAILOVA, SAMIR ABU ALI and V. A. PCHELIN, V kn. Fiziko-khimieheskaya mekhanika dispersnykh struktur (In the book; Physico-ChemieM Mechanics of Disperse Structures). p. 77, ed. by P. A. Rebinder, Izd. " N a u k a " , 1966 Yu. K. GODOVSKII, I. I. MAL'TSEVA and G. L. SLONIMSKII, Vysokomol. soyed. A13: 2768, 1971 (Translated in Polymer Sci. U.S.S.R. 13: 12, 1971) J. D. F E R R Y and J. E. ELDRIDGE, J. Phys. Coll. Chem. 53: 184, 1949 J. D. FERRY, J. Amer. Chem. Soc. 70: 2244, 1948 E. O. K R A E M E R and J. R. FANSELOW, J. Phys. Chem. 29: 1169, 1925 (quoted from [71]) V. A. PCHELIN, V. N. IZMAILOVA and V. P. MF_~ZLOV, Vysokomol. soyed. 5: 1429, 1963 (Translated in P o l y m e r Sci. U.S.S.R. 5: 3, 526, 1964) C. R. SMITH, J. Amer. Chem. Soc. 41: 135, 1919
Diffusion of phosphoric acid into polyvinyl alcohol fihns
2609
18. V. B. TOLSTOGUZOV, Ye. Ye. BRAUDO et al., Vysokomol. soyed. B13: 16, 1971 (Not translated in Polymer Sci. U.S.S.R.) 19. D. It. PAUL, J. Appl. Polymer Sci. 11: 439, 1967 20. L. Z. ItOGOVINA, G. L. SLONIMSKII and L. L. AKSENOVA, Vysokomol. soyed. A13: 1451, 1971 (Translatcd in P o ly m e r Sci. U.S.S.R. 13: 7, 1631, 1971) 21. J. D. FEItItY, Vyazkouprugiye svoistva polimerov (Viscoelastic Properties of Polymers), ch. 2, p. 17, Izd. inostr, lit.. 1963 (Russian translation) 22. N. HIRAI, Bull. Inst. Chem. Res. K y o to Univ. 33: 21, 1955 23. M. MILLER, J. D. FERRY, E. W. SCHREMP and J. E. ELDRIDGE, J. Phys. Coll. Chem. 55: 1387, 1951 24. K. A R A K A W A , Bull. Chem. Soc. Japan, 35: 309, 1962 25. K. A R A K A W A and N. TAKENAKA, Nippon Kagaku Dsasshi 83: 1065, 1962 26. M. W A T A S E and K. A I t A K A W A , Ibid. 88: 317, 1967: 90: 658, 1969 27. K. A R A K A W A , Bull. Chem. Soc. J a p a n 31: 842, 1958; 32: 1248, 1959; 33: 1568, 1960; 34: 1549, 1961 28. S. Ya. VEILER, V. I. LIKHTMAN and P. A. ItEBINDER, Kolloidn. zh. l I : 8, 1949 29. J. KIRKWOOD, J. Chem. Phys. 14: 51, 1946 30. It. ROSCOE, In: Proceedings of 4 th International Congress on Rheology, part 3, p. 593, New York~ 1965 31. M. M. IOVLEVA and S. P. PAPKOV, Vysokomol. soyed. 8: 855, 1966 (Translated in Polymer Sci. U.S.S.R. 8: 5, 938, 1966) 32. A. LEICK, Ann. Phys. 14: 139, 1904 33. W. THEIMER, Z. Naturforsch. 15b: 346, 1960 34. G. L. SLON]2YlSKII, A. I. KITAIGORODSKII, V. M. BELAVTSEVA, V. B. TOLSTOGUZOV and I. I. MAL'TSEVA, Vysokomol. soycd. B10: 640, 1968 (Not translated in P o l y m er Sci. U.S.S.R.)
DIFFUSION OF PHOSPHORIC ACID INTO POLYVINYL ALCOHOL (PVALC) FILMS SWOLLEN IN WATER* A. L. IORDA~SKII, YE. I. MERKULOV, YU. V. MOISEYEV
and G. YE. ZAIKOV Chemical Physics Institute U.S.S.R. Academy of Sciences
(Received 6 April 1973) The diffusion and the electroconductance of the system polyvinyl alcohol (PVALC)-phosphoric acid (H3PO~) was studied to discover the mechanisms of diffusion of a slightly acid aqueous solution into hydrophilic polymers. TILe concentratio,J dependence of the diffusion of electrolyte is due to a change in the ratio of the concentrations of undissociated and dissociated acid, and to a deviation from ideal diffusion. The a c t i v i t y coefficient of HaPO 4 in the polymer' matrix was calculated from th~ diffusion measurements. * Vysokomol. soyed. A16: No. 10, 2248-2254, 1974.