Langmuir 1995,11, 750-757
750
Rheological Behavior during Thermoreversible Gelation of Aqueous Mixtures of Ethyl(hydroxyethy1)cellulose and Surfactants B. Nystrom," H. Walderhaug, and F. K. Hansen Department of Chemistry, The University of Oslo, P.O. Box 1033, Blindern, N-0315 Oslo, Norway
B. Lindman Physical Chemistry 1, Chemical Center, Lund University, P.O. Box 124, S-221 00 Lund, Sweden Received August 29, 1994. I n Final Form: November 24, 1994@ The evolution of linear viscoelasticity during the thermoreversible gelation of the aqueous systems ethyl(hydroxyethy1)cellulose (EHEC)/cetyltria"onium bromide (CTAB),and EHEC/sodium dodecyl sulfate (SDS) was measured by oscillatory shear. The experiments were carried out at constant surfactant concentrationbut at different EHEC concentrations. The gel point, determined by the observation of a frequency independent loss tangent, was found to be shifted toward lower temperatures with increasing EHEC concentrationfor both systems. At the gel point, a power law frequency dependence of the dynamic was constantly observed with n' = n" = n. The storage modulus ( G wn') and loss modulus ( G an") viscoelastic exponent n was observed to decrease slightly(0.43to 0.38)with increasingEHEC concentration for the EHEC/CTAB system, while for the EHEC/SDS system a pronounced increase (0.24-0.41)was detected. The implications of these observations with respect to the structure of the critical gels are discussed qualitatively in the framework of the fractal model of Muthukumar. The critical gel strength parameter S was found, for both systems, to increase with EHEC concentration, but especially at low polymer concentration a significant difference in the value of S of the systems was revealed.
-
Introduction In recent years significant a d ~ a n c e s l -have ~ been achieved in developing an understanding of the underlying physics controlling the gelation process in especially chemically gelling systems. These gels are characterized by covalently cross-linked networks. Physical gelation is a phenomenon that is much less understood than chemical gelation, principally due to the transient nature of the physical network junctions, which makes it difficult to study physical gels near their gel point. Physical gels are built up by thermoreversibly cross-linked networks in which the junctions are formed by secondary forces capable of forming bonds typically weak enough to be broken by thermal fluctuations. The principle differences between chemical and physical gels lie in the lifetime and the functionality of the network functions. Chemical bonds are considered to be permanent while the physical junctions have finite lifetime and in general the functionality of the chemical junctions is much lower than that of physical junctions. In the present work the temperature induced gelation of aqueous solutions of ethyl(hydroxyethy1)cellulose (EHEC) in the presence of two different surfactants, namely the anionic sodium dodecyl sulfate (SDS)and the cationic cetyltrimethylammonium bromide (CTAB), is studied with the aid of oscillatory shear measurements over an extended temperature range. Some preliminary rheological experiments on EHEC/surfactant systems Abstract published in Advance A C S Abstracts, February 1, 1995. (1)De Gennes, P.-G. Scaling Concepts in Polymer Physics; Cornel1 University Press: Ithaca, NY, 1979. (2) Winter, H. H. In Encyclopedia ofPolymerScience and Engineering, Supplement Vol.; 1989; p 343. (3) Martin, J. E.; Adolf, D. Annu. Reu. Phys. Chem. 1991,42,311. @
-
have already been r e p ~ r t e d ?but ~ a systematic rheological study is lacking. Our general knowledge of these systems is fairly good, due to extensive investigations by various experimental technique^.^-^ These studies have established that an aqueous solution of EHEC in the presence of an ionic surfactant forms a physically cross-linked network in the semidilute concentration regime at temperatures around 30-40 "C. The position of the gel point temperature is governed by polymer factors such as substituent, degree, and heterogeneity of substitution, whereas the degree of polymerization seems to be less crucial. We may note that similar observations have been reportedg from a study on thermally reversible gelation of aqueous solutions of methyl and hydroxypropyl methyl cellulosein the absence of surfactant. However, at present our knowledge of the underlying gelation mechanism of aqueous EHEC solutions in the presence of an ionic surfactant is rather limited. In order to gain a deeper understanding of the gelling process of EHEUsurfactant systems, we have in the present work carried out oscillatory shear measurements at temperatures below and above the gel point on different EHEC concentrations in the semidilute range in the presence of SDS or CTAB. The experiments have been performed at constant surfactant concentration (4 mm), and the results will reveal differences in behavior between the EHEC/CTAB and EHEC/SDS systems. (4) Carlsson, A.;Karlstrom, G.; Lindman, B. Colloids Surf. 1990,47, 147. (5)Lindman, B.;Carlsson, A,; Gerdes, S.; Karlstrom, G.; Piculell, L.; Thalberg, K.; Zhang, K. In Food Colloids and Polymers: Stability and Mechanical Properties; Walstra, P., Dickinson, E., Eds.; The Royal Society of Chemistry: London, 1993; pp 113-125. (6) Carlsson, A. Ph.D. Dissertation, Lund University, 1989. (7) Lindman, B.;Carlsson, A.; Karlstrom, G.; Malmsten, M. Adu. Colloid Interface Sci. 1990,32,183. (8)Nystrom, B.; Roots, J.;Carlsson, A,; Lindman, B. Polymer 1992, 33,2875. (9) Sarkar, N.J. Appl. Polym. Sci. 1979,24,1073.
0743-7463/95/2411-0750$09.00/00 1995 American Chemical Society
Gelation of EHEC and Surfactants
Langmuir, Vol. 11, No. 3, 1995 751
Basic Considerations Measurements of the oscillatory shear moduli are frequently used to monitor continuously the viscoelastic properties of cross-linking systems from the sol through the transition to the gel state. In the framework of the generalized rheological model of Chambon and Winterlo-lz the gel point (GP) for chemically cross-linked systems is described by thegel equation, which is a linear viscoelastic constitutive equation for the stress
~ ( t=)SJ'
cc
(t - t')-"p(t') dt'
--
(2)
where r(l - n ) is the Legendre gamma function. The phase angle ( 6 )between stress and strain is independent of frequency (w) but proportional to the relaxation exponent
6 = n d 2 or t a n 6 = G / G = t a n ( n d 2 )
(3)
These results suggest that GP is characterized by the following scaling relation
G(w)
-
-
G ( o ) on
+
n = df/(d, 2)
(1)
where CJ is the shear stress p(t), < t' < t , is the rate of deformation of the sample at GP, t is the present time, S is the gel strength parameter, depending on the crosslinking density and the molecular chain flexibility, and n is the relaxation exponent. The material parameters S (Pa sn)and n are characteristic parameters for each gel and n must be greater than 0 and less than 1. This equation (only valid at GP) has been found to predict all known rheological properties of critical gels of both chemical and physical origin.z It should be noted that the gel equation is restricted to small strains only. It was shown that the shear relaxation modulus G(t)is characterized by a power-law in time at GP: a t ) = St-". This situation, when an incipient gel forms, represents an intermediate state between a liquid and a solid. The same scaling behavior is also apparent in dynamic mechanical experiments where the storage modulus, G , and the loss modulus, G , at GP are given by13
G = G / t a n 6 = S oT(1- n ) cos 6
-
structure of the network at GP is represented by a fractal dimension df, which is defined by Rdf M, where R is the radius of gyration and M the mass of a molecular cluster. By consideringRouse dynamics (hydrodynamicinteraction is ignored) and taking into account the effect of screening of both excluded-volume and hydrodynamicinteractions, but ignoring entanglement effects, the following expresfor a monodisperse polymer sion for n has been derived21,zz system
(4)
A number of theoretical models have been advanced to predict the numerical value ofn. Simple electrical analogy and effective medium theory predict n = 0.5, as for regular and nonfractal RC (resistor-capacitor) line response.14 On the other hand, based upon a suggested1J5isomorphism between the complex modulus and the electrical conductivity of a percolation network with randomly distributed resistors and capacitors, a value of n = 0.72 has been predicted. Computer simulations,16performed in three dimensions, based on this analogy yielded a value of n = 0.7. On the basis of concepts such as dynamic scaling,fractal analysis, and percolation of clusters, a considerable to the detertheoretical i n t e r e ~ t ~has * ~been ~ - ~devoted ~ mination of the exponent n. Let us assume that the Chambon, F.; Winter, H. H. Polym. Bull. 1985,13,499. Winter, H. H.; Chambon, F. J . Rheol. 1986,30,367. Chambon, F.; Winter, H. H. J . Rheol. 1987,31,683. Izuka, A,; Winter, H.; Hashimoto. T. Macromolecules 1992.25, 2422. (14) Kirkpatrick, S. Rev. Mod. Phys. 1973,45,574. (15)Alexander, S. J . Phys. (Paris) 1984,45,1939. (16) Clerc, J . P.; Giraud, G.; Laugier, J. M.; Luck, J . M. Adu. Phys. 1990,39,191. (17) Durand, D.; Delsanti, M.; Adam, M.; Luck, J. M. Europhys. Lett. 1987,3,297.
(5)
where df is the fractal dimension. If corrections due to polydispersity effectsof the clusters forming the incipient gel are taken into account and Rouse dynamics prevails, the following relationship is obtained17J8
n = df(z - l)/(df
+ 2)
(6)
where z is the scaling exponent describing the clustersize distribution function near GP. This polydispersity exponent is related to the fractal dimension (t= 1 d/df), where d (d = 3) is the space dimension. By use of percolation statistics (df = 2.5 and t 2.21, n assumes a value of V 3 . The dynamic scaling theory of Martin et al.,18 which is based on the percolation theory and on the idea of cluster-size-dependent viscosity, predicts a value of n = 1in the Zimm limit (hydrodynamicinteraction is taken into account). Several experimental studies have been undertaken to test the validity of the theoretical predictions. A number of investigations on various gelling systems, such as p~lyurethanesl~ ( n = 0.69 f 0.041,epoxy resinsla ( n = 0.70 f 0.051, polyesterslg (n = 0.69 f 0.021, tetraethoxysilanez3(n = 0.72 f 0.02), silyl terminated poly(oxypr0pylene)z4sz5 ( n = 0.66 f 0.021, and the physical gels of gelatinz6(n = 0.69 f 0.02) and of calcium p e ~ t a t e( n~=~ 0.71 f 0.02), seem all to support the percolation model. However, the data do not allow distinguishing between the dynamic scaling percolation prediction in the Rouse limit (n = 0.67) and the value ( n = 0.72) obtained from the electrical analogy. Studies on stoichiometrically balanced gelling systems of poly(dimethylsiloxane)loJ1 polyurethane,z8 and poly(ethy1ene oxide) with hydroxyl functions at both chain ends,z9have shown that n = 0.5 at GP. In order to accommodate this value in the theoretical description, Hess et al.30 suggested that swelling due to remaining unreacted chains and smaller clusters in the reaction bath may change the percolation value (2.5) of df to df = 2. By using eq 5, we thus arrive at n = 0.5.
+
(18)Martin, J. E.; Adolf, D.; Wilcoxon, J . P. Phys. Rev. Lett. 1988, 61,2620; Phys. Reu. A 1989,39,1325. (19)Rubinstein, M.; Colbs, R. H.; Gillmor, J. R. Am. Chem. Soc., Polym. Prepr. 1989,30,81. (20) Stauffer, D. Introduction to Percolation Theory; Taylor and Francis: London, 1985. (21) Muthukumar. J. J. Chem. Phvs. 1985. , 83. - - ,3161. (22) Cates, M. E. j.Phys (Paris) 1985,46, 1059. (23) Hodgson, D. F.; Amis, E. J. Macromolecules 1990,23,2512. (24) Koike, A.; Nemoto, N.; Takahashi, M.; Osaki, K. Polymer, 1994, 35,3005. (25) Takahashi, M.;Yokoyama, K ; Masuda, T.; Takigawa, T. J . Chem. Phys. 1994,101,798. (26) Hsu, S.; Jamieson, A. M. Polymer 1993,34,2602. (27)Axelos, M. A. V.; Kolb, M. Phys. Reu. Lett. 1990,64, 1457; Makromol. Chem., Macromol. Symp. 1992,45, 23. (28) Chambon, F.; Petrovic, Z. S.; MacKnight, W. J.; Winter, H. H. Macromolecules 1986,19,2146. (29)Muller, R.; GBrad, E.; Dugand, P.; Rempp, P.; Gnanou, Y. Macromolecules 1991,24,1321. (30) Hess, W.; Vilgis, T. A.; Winter, H. H. Macromolecules 1988,21, 2536. ~~~~~~~~~~~
~
I-
~~~~
~~~~
752 Langmuir, Vol. 11, No. 3, 1995
Nystrom et al.
The above picture is further complicated by the fact that there are other observations of n in the literature which cannot be described by the theoretical models discussed above. We may first note that values of n in the range 0.5 < n < 1 have been reported12 at GP for a stoichiometrically imbalanced poly(dimethylsi1oxane)gel with cross-linker deficiency. Lin et al.31 investigated crystallization induced gelation in the thermoplastic elastomer polypropylene and observed an exponent n = 0.13. Sillescu and c o - w o r k e r ~investigated ~~ micronetworks of polystyrene at GP and found that n increases from 0.2 to 0.5 as the number ofmonomersbetween crosslinks decreases. Scanlan and WinteS3studied end-linked poly(dimethylsi1oxane) at GP, values of n between 0.19 and 0.92, depending on stoichiometry, concentration, and polymer molecular weight, were reported. For the thermoreversible gelling system gelatin the values ofthe power law exponent in the incipient gelation zone is generally found to be located in the range 0.6 to 0.8,26,34J5 but values as low as 0.2-0.3 have been observed35under certain experimental conditions. These results indicate that the situation close to GP is complex, and these findings accentuate the need for a theoretical model that is capable of rationalizing values of n in the whole physically accessible range (0 < n < 1). A n attempt in this direction has recently been p r e ~ e n t e d .In ~ ~the theoretical model ofMuthukumar it is assumed that variations in the strand length between cross-linking points of the incipient gel network may give rise to changes of the excluded volume interactions. The surmise is that increasing strand length will enhance the excluded volume effect. In the case that the excluded volume effect is fully screened, the following expression emerges for a polydisperse system
n=
+
d(d 2 - 2df) 2(d 2 - d f )
+
+
w = l .o s-1 --tt w=2.0 s-1
-A-
-m-
h EHEC(1 wt%)/SDS
I
T
0 30
32
24
38
36
40
42
44
46
Temperature ("C)
24
26
i28
3'0
i2
3'4
i6
3'8
40
42
Temperature (OC)
uw=o.l5s~' 2-
-
(8)
In this case n changes from 1to 3/5 as df varies from 1to 3.
w=0.2 s-1 w=0.5 svl $=37 QC I A w=1.0 s-1 -v- w=2.0 s-l -0-
(7)
All values of the scaling exponent for 0 < n < 1are possible for a fractal in the physically realizable domain 1Idf I 3. In the case of unscreened excluded volume interactions the following relationship applies
n = d/(d, 2)
U w=0.5 s-'
EHEC(4 W%)/CTAB
+ 2J
Experimental Section Materials and Solution Preparation. The EHEC sample, designated Bermocoll DVT 89017, was manufactured by Berol Nobel (Stenungsund, Sweden) and utilized in all measurements reported here. The degree of substitution of ethyl groups DSethyl = 1.9 per anhydroglucose unit, and molar substitution of ethylene oxide groups MSEO= 1.3 per anhydroglucose unit. The number average molecular weight M , of this polydisperse sample (MW/ 2) is ca. 100 000. The surfactants CTAB and SDS were M, both obtained from Fluka and were used as received. Dilute EHEC solutions were dialyzed against pure water for at least 1week to remove salt (impurity from the manufacturer) and were thereafter freeze-dried. As dialyzing membrane, regenerated cellulose with a molecular weight cutoff of 8000 (Spectrum Medical Industries) was used. After freeze-drying, (31)Lin, Y. G . ; Mallin, D. T.; Chien, J. C. W.; Winter, H. H. Macromolecules 1991,24,850. (32)Antonietti, M.;Folsch, K. J.; Sillescu, H.; Pakula, T. Mucromolecules 1989,22,2812. (33) Scanlan, J. C.; Winter, H. H. Macromolecules 1991,24,47. (34)Hodgson, D.F.;Yu, Q.;h i s , E. J. Insynthesis,Characterization, and Theory ofPolymeric Networks, and Gels;Aharoni, S. M., Ed.; Plenum Press: New York, 1992. (35) Michon, C.; Cuvelier, G.;Launay, B. Rheol. Acta. 19f)3,32,94. (36)Muthukumar, M. Macromolecules 1989,22,4656.
1
\I
+o=2.0
s-'
- 7
EHEC(4 wt%)/SDS
0 22
24
26
28
30
32
34
36
38
Temperature ("C)
Figure 1. Viscoelastic loss tangent as a function oftemperature for the systems and frequencies indicated. the polymer was redissolved in water. Samples were prepared by weighing the components and the solutions were homogenized by stirring at room temperature for several days. OscillatoryExperiments. Oscillatory shear measurements were performed in a Bohlin VOR rheometer system with a coneand-plate geometry, with a cone angle of 5" and a diameter of 30 mm, at a maximum strain amplitude of 10%. The level of strain was checked in order to ensure that all measurements were made within the linear viscoelastic regime. The experiments were carried out in the temperature range 25-45 "C on semidilute EHEC/CTAB and EHEC/SDS systems at three EHEC concentrations (1,2,and 4 wt %) and in the presence of a constant surfactant concentration of 4.0 mm, well above the critical concentration for formation of polymer bound micelles. A layer
Langmuir, Vol. 11, No. 3, 1995 753
Gelation of EHEC and Surfactants
menced. In these experiments no disturbing hysteresis effects
0
EHEC(1 wt%)/CTAB
0 31%
A x
2-
33OC 35OC
Results and Discussion
I
t o
'
s 2 1 F
I
4
2
0 8
6 I I 0 3loC A 33~c.
1
EHEC(1 wt%)/SDS
x 35%0 3PC 4OoC,
1-
"
were observed.
.
9
0
4
2
6
Frequency (s-') EHEC(2 wtO/)/CTAB
~
3
1
0
+34oc -D- 35OC
1
0
2
4
I
I
I
a
i
I
EHEC(2 wl%)/SDS
i
2
Frequency (s")
EHEC(4 wt%)/SDS
0
2
4
Frequency (d)
Figure 2. Frequency dependence of the loss tangent for the systems and temperatures indicated. of silicone oil was added to the sample to avoid evaporation of solvent. The temperature in the measuring cell of the rheometer was maintained with the aid of a computer-controlled water bath. Temperature calibration of the sample chamber over the whole temperature range was carried out with an external temperature probe because the bath temperature and the temperature of the sample chamber were slightly different. However, at a preset temperature, the temperature variation of the sample chamber was small ( f O . l "C) over the investigated region. At a given temperature a frequency sweep extending from about 0.01 to 3 Hz was conducted. At each temperature the sample was allowed to equilibrate for about 2 h before measurements were com-
~
The gel point (t,) of a thermoreversible gelling system may be determined by observation of a frequencyindependent value of tan 6obtained from a multifrequency plot of tan 6 versus temperature. This type of plot is depicted in Figure 1 for the different EHEChrfactant systems at constant surfactant concentration. All systems exhibit a similar pattern of behavior, namely a steady decrease in tan 6 with increasing temperature, with the decrease being most significant for the lowest measurement frequency. The intersection of the curves, representing different frequencies, is indicative of GP. It is not obvious from the curves displayed in Figure 1 that the incipient gel temperature is well characterized for all concentrations. However, it turns out that GP for the different concentrations could be determined well by a thorough analysis of the tan 6 data. From this analysis the gel temperature was identified a t the particular temperature where the loss tangent first became frequency independent. It is interesting that a t the lowest polymer concentration (1 wt %) GP is located a t the same temperature (37 "C)for both EHEC/surfactant systems, whereas as the EHEC concentration increases GP is gradually shifted toward lower temperatures, and the GP temperature (t,) is lower for the EHECISDS system than for the corresponding EHECKTAB system. This trend seems to be enhanced with increasing EHEC concentration. In this context we may note that in a previous studyg on thermally reversible gelation of aqueous solutions of hydroxypropyl methyl cellulose in the absence of surfactant, it was also observed that the incipient gelation temperature decreased with increasing concentration. The difference in behavior between the systems a t higher polymer concentration suggests that the physical cross-linking efficiency during the gel formation process is more strongly temperature dependent for the EHEC/ SDS system than for the EHECKTAB system. The depression of GP of the EHEChurfactant systems with increasing EHEC concentration as well as the difference in the value oft, between the systems can probably be traced to the intricate interplay between surfactant induced associations and enhanced polymer chain associations generated as phase separation is approached a t elevated temperatures. The phase behavior of aqueous solutions of EHEC in the presence of SDS has recently been disc~ssed,~' and it was concluded that there is a strong attraction between the polymer and the ionic surfactant. It should be noted that for these systems phase separations occur not too far above GP and that the difference between the GP temperature and phase separation shrinks with increasing polymer concentration. For the systems of the highest EHEC concentration a harbinger of macroscopic phase separation is observed already a few degrees above GP in the form of incipient turbidity. There are results3s that suggest that the general thermodynamic conditions are different for the EHEC/CTAB system and the EHEUSDS system at a given temperature. In this context we may note a recent theoretical work,39 where the intricate interplay between macroscopic phase separation and gelation was studied for thermoreversible gelling systems. The influence of factors such as polymer (37) Zhang, K.; Karlstrom, G.; Lindman, B. Prog. Colloid Polym. Sci. 1992,88,1. (38)Karlstrom, G.;Carlsson, A,; Lindman, B. J . Phys. Chem. 1990, 94,5005. (39)Tanaka, F.;Stockmayer, W. H. Macromolecules 1994,27,3943.
Nystrom et al.
754 Langmuir, Vol. 11, No. 3, 1995
2,5{
SOCi
EHEC(1 wt%)/CTAB
2 0-
-0,5i * -1.O!
l
-2
.
,
0
.
0 ,
2
.
l
4
l
,
6
l
l
8
.
,
10
.
l
12
l
,
14
.
,
16
!
,
18
,
20
,
.
o . o . l . , . , . , . l
~
0
-2
22
2
4
3.0,.
-1
EHEC(2 wt%)/CTAB
34%
.
-I
40%
970,-
25-
,
,
.
,
.
(
1
10
8
B + log w
B + log 0 (s-')
3,0
.
6
1
1
1
12
1
,
14
1
16
18
($1)
,
,
I
,
,
,
EHEC(2 wt%)/SOS
2 520-
t,=359c h
.
m
4
15-
b
b- 1 0 m
. 33 34
05-
.
00-0.5 0
10
5
15
20
6 + log o (s-')
6 + log w (s-')
4,0
30-
4
EHEC(4 wt%)/SOS
1
34OC
370c
i
25e
m
.
b
-
m
.
e 20b-1 5 -
3 100537
I
,
+19
o , o ~ , . l . , . l . , , , , , , , , , . , . , , l -2
0
2
4
6
8
10
B + log 0
12
14
16
18
20
(d)
-4
-2
0
2
4
6
8
10
12
14
16
18
20
22
6 + log o (s-')
Figure 3. Frequency dependences of the storage modulus G (open symbols and stars) and the loss modulus G (solid symbols and crosses) at different stages of the gel forming process for the systems indicated. The curves have been shifted horizontally by a factor B of the value listed in the insert.
molecular weight, functionality, and the multiplicity of the network junctions were considered. Figure 2 shows plots of the loss tangent as a function of frequency a t various temperatures for the different EHEC/surfactant systems. As expected, tan 6 a t GP is found to be practically independent of frequency for all systems. Below the gelation temperature, tan 6 decreases as the frequency increases, as is typical for a viscoelastic liquid. At temperatures above GP, tan 6 increases smoothly with frequency (this trend seems to be more pronounced at higher polymer concentration), indicating that the system has transformed versus the viscoelastic solid state.
In Figure 3, the frequency dependence curves of G and G a t different temperatures during the gel evolution is shown. The curves have been shifted horizontally by a factor B (see the inserts in Figure 3) to avoid overlap. The plots of G and G follow the same general pattern for all EHEC/surfactant systems. At temperatures below GP, G is smaller than G"at low frequencies and the frequency dependence curves indicate liquid-type behavior. At GP, G and G curves become parallel and the power law feature is observed (cf. Figures 5-7). At temperatures above GP, G increases rapidly and becomes larger than G". This behavior is characteristic of the solidlike state that evolves above GP.
Gelation o f EHEC and Surfactants
Langmuir, Vol. 11, No. 3, 1995 755
.
, -@-
n'
+",,
0
X W
EHEC(1 wt%)/CTAB
+
. . . ..., I
,
. . . , ,,.,
,
,
.,,
2.0
EHEC(1 Wh)lSOS n'=0.24M.01 n"=0.23*0.01 EHEC(1 wt%)/CTAB n'=0.43M0.01n"=0.42*0.02
0.8
0.6
2
0.4
0.2
X-X-XW-*X-*X)66d#(c-XX-X0.1
0.0 30
34
32
36
38
40
42
44
46
0.01
0.1
1
Frequency (s-') Figure 5. Plot of G and G versus frequency for the indicated
Temperature (OC)
systems at the gel point showing the power law behavior.
-0- "' -0- n" 0.8
-
0.6
-
P
B C
EHEC(2 Wt0h)lCTAB
. 0.4
-
0.2
-
_.-
,
-T&
t,.340C
'
!
'
1
2%
26
'
1
30
'
1
32
'
1
34
'
1
36
'
1
38
'
,
40
'
,
42
44
Temperature (OC)
-=.
1
1
0.0
i
22
.
I
24
.
l
'
26
,
.
28
l
'
30
I
.
32
1
.
34
I
.
36
,
I
38
Temperature (OC)
Figure 4. Changes of the apparent exponents n' for the storage and n" for the loss shear moduli during the course of gelation
for the systems indicated.
In the analysis above, the GP temperature was determined by the observation of a frequency independent loss tangent in a plot of tan 6 versus temperature (see Figure 1). An alternative procedure to establish GP has recently been suggested,4Oviz., plotting the "apparent" viscoelastic exponents n' and n" ( G an', G an") obtained from the frequency dependence of G and G" a t each temperature of measurement (see Figure 3) and observing a crossover where n' = n" = n. Approximate scaling laws are usually observed even at temperatures removed from the GP temperature, but this method is probably less accurate than that resorted to above. Figure 4 illustrates the temperature dependences of the apparent exponents n' and n" during the course of
-
-
gelation for each system. The general trend is the same for all systems. The values of both n' and n" decrease as the gel forms and strengthens. However, the value of n', representing the dynamic storage modulus, falls off more strongly with increasing temperature than that of n", representing the dynamic loss modulus. For all systems, the crossover points are located at the same temperature as inferred from the other method used to determine GP. A similar behavior has been o b ~ e r v e dduring ~ ~ , ~the ~ gel forming process of gelatin. In Figures 5-7 the dynamic storage and loss moduli, together with the data of the parameter 26/z, are plotted against frequency for all the studied EHEChurfactant systems at the gel point. At GP, G and G of each system exhibit a power law behavior over the considered frequency range, and G' > G , which is frequently observed4I for "weak gels". The lines (least-square fits of the data) representing the frequency dependences of G and G are practically parallel and the resulting values of n' and n" are, within experimental error, equal (see the inserts of Figures 5-7). The dashed lines represent the values of n at GP (see eq 3). Figure 8 shows the concentration dependences of the viscoelastic exponent and the critical gel strength parameter for the systems EHECXTAB and EHEC/SDS at GP. Let us first discuss the gel strength parameter S, which has been calculated from eq 2. This parameter is found to increase strongly with increasing polymer concentration for both systems. This tendency seems to be reasonable, because S depends on the mobility of chain segments of the system and this effect should be strongly dependent on the concentration of macromolecules composing the network and the cross-link density. Increased polymer concentration is expected to strengthen the network. The significantly higher value of Sfor the EHEC/ SDS system as compared with that of the EHECKTAB system at the lowest polymer concentration (1 wt %), indicates that the strongest interaction effect is obtained in the presence of the anionic s ~ r f a c t a n t .This ~ , ~ finding ~ is supported by a recent dynamic light scattering studf2 on the systems EHEC (1wt %)/CTAB(4 mmM) and EHEC (1wt %)/SDS (4 mm), where the slow relaxation time, associated with the chain disengagement relaxation, was observed to be much larger for the latter system in the vicinity of the gel point. The observation that the values of S of the systems progressively approach each other as (40)Hodgson, D. F.;Amis, E.J. J.Non-Cryst.Solids 1991,131 -133, 913. (41)Clark, A. H.; Ross-Murphy, S. B. Adu. Polym. Sci. 1987,83,57. (42) Nystrom, B.; Lindman, B. Macromolecules, in press.
756 Langmuir, Vol. 11, No. 3, 1995
1
Nystrom et al.
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the EHEC concentration increases (see Figure 8) is not unexpected since at higher polymer concentration the polymer- polymer interactions will gradually play a more prominent role in the network forming process and the type of surfactant should not be crucial. The concentration dependence of the viscoelastic exponent reveals some interesting features. The value of the exponent of the system EHEC/SDS increases strongly (from 0.24 to 0.41) with increasing EHEC concentration, whereas n representing the system EHECICTAB decreases slightly (from 0.43to 0.38) with concentration. These values are located in a range which can be addressed in the framework of the Muthukumar which considers screened excluded volume interactions (see eq 7). On the basis of eq 7, the values of n for the EHEC/ CTAB system suggest adfof2.1 and then values observed for the EHEC/SDS system indicate that the fractal dimension decreases from 2.3 to 2.1 as the EHEC concentration increases from 1to 4 wt %. This trend in d f may suggest that the network of the critical gel for the EHECISDS system becomes more pen''^^,^^ as the polymer concentration increases. A tentative explanation of this unexpected tendency may be that the inclination of the EHEC/SDS system to form dense of strongly associating polymer chains is strengthened as the EHEC concentration increases a t GP. Such a process may give rise to a more open network. (43) Cabane, B. Lecture presented at the Eighth International Cellucon Conference "Cellucon '93" in Lund, Sweden.
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Concentration (wt%) Figure 8. Plot of the gel strength parameter S (calculated from eq 2) and the viscoelastic exponent n as a function of EHEC concentration for the indicated systems at their respective gel point temperature. Summary and Conclusions
The temperature-dependent growth of viscoelasticity has been described for the systems EHECKTAB and EHEC/SDS that undergo temperature induced sol-gel transitions. The gel points have been obtained from the observation of a frequency independent loss tangent and by the registration of the crossover of the apparent viscoelastic exponents of the power laws relating G and G to the frequency. The results from these two methods were consistent. The gel point temperature has been found to decrease with increasing EHEC concentration, and this trend is stronger for the EHEC/SDS system.
Langmuir, Vol. 11,No.3, 1995 757
Gelation of EHEC and Surfactants The frequency dependence of the loss tangent reveals for both EHEC/surfactant systems that this quantity falls off (liquid-like behavior) at temperatures below GP and increases with frequency (solid-like behavior) at temperatures above GP. This feature of the systems has also been endorsed by studying the frequency dependence of the dynamic moduli at various temperatures. At GP, the gel strength parameter S increases considerably with increasing EHEC concentration for both EHEC/surfactant systems, but the increase is more pronounced for the EHECETAB system. This difference in behavior probably reflects that these two surfactants generate a different interaction situation. Furthermore,
it is observed at GP that G parallels G over the considered frequency domain and the moduli can be described by power laws G G W” for all the investigated systems. It was observed that the value of n for the EHEC/CTAB system exhibits only a slight decrease (0.43-0.38) with increasing polymer concentration, while n increases strongly (0.24-0.41)for the EHECISDS system. These values of n can qualitatively be rationalized within the framework of the fractal “screening” model of Muthukumar. The trend observed for the EHEC/SDS system suggests that the critical gel network becomes more “open” as the EHEC concentration increases.
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LA9406766
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