Langmuir 1995,11, 1500-1506
1500
Rheological Study of a Bicopper TetracarboxylatelDecalin Jelly Christoph Dammer,tst Pascale Maldivi,$ Pierre Terech," and Jean-Michel Guenet"37 Laboratoire d'Ultrasons et de Dynamique des Fluides Complexes, Universitk Louis Pasteur, CNRS URA 851, 4, rue Blaise Pascal, F-67070 Strasbourg Cedex, France, Dkpartement de Recherche Fondamentale sur la MatiBre Condende, SESAM-PCM, F-38054 Grenoble Cedex 9, France, and Dgpartement de Recherche Fondamentale sur la Matit%-eCondenske, CNRS URA 1194, SESAM-CC, F-38054 Grenoble Cedex 9, France Received November 22, 1994. I n Final Form: January 30, 1995@ The rheological properties of jellies of a binuclear copper(I1)-tetracarboxylate complex in decalin have been investigated as a function oftemperatureand concentration. The results are analyzed in the framework of living polymers. It is shown that the theory of living polymers can describe the system under certain conditions, that is below a given transition temperature Tt,,,,. Above Ttransthe theory of living polymers does not apply any longer. Below Tt,,,, it is suggested that a low degree of physical gelation takes place. The system is better described as thermoreversible (physical) "living" gel, where physical junctions are liable t o play the role of entanglements. The reasons why the theory worked out for "living"polymers can be used below Tt,,,, is discussed.
Introduction The present article reports on rheological investigations carried out on the solutions of a binuclear copper complex as CuzS8, Figure 1)in a n apolar ( C U ~ ( O ~ C ~designated H~& organic solvent, namely a mixture ofcis- and trans-decalin. The complex molecules assemble reversibly by piling up and subsequently form a viscoelastic, jelly-like solution as reported by Terech et al. for the system CuzS81 cyclohexane.1,2 The rheological behavior of these samples has been described in the framework of "living" polymers for which a comprehensive theory has been developed by Cates and c o - ~ o r k e r s . ~So - ~far, the field of living polymers has been mainly occupied by aqueous wormlike The CuzS8 complex is of special interest as organic solvents are used instead of water, which allows one to overcome the problems arising from this peculiar medium. As a matter of fact, most investigations concerning aqueous wormlike micelles have been performed under addition of salts so as to compensate for polar effects ofwater. As the rheological properties depend upon salt concentration, additional complications are introduced in the analysis of the results (see ref 7). Neutron scattering experiments have revealed that the CuzS8 molecules in cyclohexane stack up to form threads where the cross-section contains primarily one complex mo1ecule.l If one ignores the effect of the interaction between the aliphatic side chains and the solvent, on the one hand, as well as interactions between side chains of
* To whom correspondence should be addressed. Universite Louis Pasteur, CNRS UFL4 851.
* Present address: Dept.Materiauxet ProcBdBs,Physico-chimie
des PolymBres, Universite de Mons-Hainaut, Place du Parc, 20 B-7000 Mons, Belgium.
SESAM-PCMCNRS URA 1194. SESAM-CC. Abstract published in Advance A C S Abstracts, May 1, 1995. (1)Terech, P.;Schaffhauser, V.; Maldivi, P.; Guenet,J. M. Langmuir 5 "
@
1992,8,2104. (2) Terech, P.; Schaffhauser, V.; Maldivi, P.; Guenet, J. M. Europhys. Lett. 1992,17, 515. (3) Cates, M. E. Macromolecules 1987,20,2289. (4)Cates, M. E. J . Phys. (Paris) 1988,49,1593. (5) For a review see for instance Cates, M. E.; Candau, S. J. J . Phys. Condens. Mutter 1990,2,6869. (6)Lobl, M.; Thurn, H.; Hoffmann, H. Ber. Bunsenges. Phys. Chem. 1984,88,1102-1106.Hoffmann, H.; Lobl, M.; Rehage, H.; Wunderlich, J. Tenside Deterg. 1985,22,290. (7) Porte, G.; Appell, J.; Poggi, Y . J.Phys. Chem. 1980,84,3105.
0743-7463/95/2411-1500$09.00/0
8-Q
cu
0
'"
Q
Figure 1. CuzS8 molecule as described in ref 8.
different main chains, on the other hand, then the CuzS8 in organic solvent systems could be regarded as a n ideal living polymer. Here we report on a study extended to the effect of temperature. We shall show that this system is in fact not ideally a living polymer despite that it obeys Cates' theory at low temperatures.
Experimental Section A CuzS8 sampleprepared as described in ref 8 was used (Figure 1). The solvent was agold label decalin (mixtureof cis and trans) purchased from Aldrich. In order to obtaina stable sample which
showed no time dependence,the solutionswere prepared at nearly 130 "C. After cooling to room-temperature, the sample formed a gel-like substance of dark-blue/greencolor. All rheological experiments were performed on a CarriMed CSLlOO rheometer, modified in such a way as to avoid both solvent evaporation and condensation of water. For the high concentration samplesa cone and plate geometry was used (angle 4", diameter 4 cm, gap 105pm). The low concentration samples were investigated with a couette geometry (inner radius 1.38 cm, outer radius 1.5 cm, cylinder height 3.2 cm). In the overlappingregimeboth geometrieswere used and gave the same results. Experimental scatter was about 5%,represented by the symbols size in the figures. A frequency range spanning from f =4 x Hz to f = 4 x lo1 Hz was investigated. Samples with concentrationsfrom C = 0.1 wt % t o C = 10 wt % (4 = 0.07 vol % to 4 = 7.1 vol 96) were studied between 6 = 0 "C up to 6 = 70 "C. The volume fractions 4 were calculated from the concentrationsC by assuming that the partial molar volumes were independent of the concentrations(idealsolution). ( 8 ) Maldivi, P. Thesis, Grenoble, France, 1989.
0 1995 American Chemical Society
Langmuir, Vol. 11, No. 5, 1995 1501
Study of Cuz(OzCa15)4in a n Organic Solvent Theoretical Framework So far the dynamic behavior of the Cu2S8 system has been analyzed by means of Cates’ theory. It seems therefore necessary to give a short account of its main prediction^.^,^ This theory is essentially based upon two mechanisms for stress relaxation: chain reptation and a competing breakinglre-formation mechanism. Regardless of the relaxation times of the two mechanisms, breaking and re-formation dynamics yield a length distribution function given by:
with a mean lengthz depending on concentration and on temperature as follows:
in which Escisis the scission energy of the chains and 4 is their volume fraction. The exponent 112 given here holds for the Flory-Huggins regime (mean-field) and must be replaced by 315 when excluded volume effects come into ~ l a y . Concerning ~,~ the balance between the two relaxation times Zb (for scission) and tr(for reptation), two limits are of particular interest. If t b tr,the stress decay a(t) is that of a pure reptation with a distribution of molecular weight as cited above (eq 1)
-
a(t) exp[-const($)”‘]
(4)
This spectrum is very broad, spreading over more than 1 decade. In the limiting case t b Normally, due to micellar-type growth, the entangled regime is attained shortly after the overlap concentration, which means that #*, the overlap concentration, and the entanglement concentration, are virtually the same.5 Also, the above exponents may vary if other effects than statistical scission and recombination are taken into a c c ~ u n t . ~For J ~the present purpose the aforementioned exponents are relevant. The scission energy is assumed to be independent of concentration which is not necessarily valid if solvent effects must be considered, i.e., if chaidsolvent interactions as occurring in some polymerholvent couples cannot be overlooked.l1 A second relaxation process has often been experimentally observed for wormlike micelles at higher frequencies. This process was investigated theoretically by Cates and Granek12who assigned it to local Rouse modes of the chain in its reptation tube. The fundamental result is the following relation Gmi[IG0
IJL
(14)
in which Gmi,,”is the dip that can be observed for G”versus o or G versus G , 1, is the entanglement length (mean contour length of the chain between entanglements). Starting from eq 2 Cates and Granek came up with
42.3(excludedvolume) ( 5 )
zero-shear viscosity 43.5(mean-field) 43.7(excludedvolume) (6)
plateau modulus Go &(mean-field)
-
Go kBT[-3
plateau modulus
A further outcome of Cates’ theory is the temperaturedependence of the plateau modulus, Go, and the zeroshear viscosity, 70
Results and Discussion Figure 2a shows some typical curves of G and G versus angular frequency o in a logarithmic representation for the range of concentrations investigated and Figure 2b the same results represented by means of Cole-Cole plots. The curves show data obtained a t T = 293 K. One easily recognizes two relaxation processes. The process a t low frequencies is the terminal relaxation, characterized by variations of G o2 and G“ o. No plateau in G is observed a t low frequency which indicates the absence of permanent cross-linked network. Conseversely,a plateau modulus a t high frequency can be seen which indicates
-
-
(9)Doi, M.; Edwards, S. F. The Theory ofpolymerdynumics; Oxford: Clarendon, 1986. (10)Porte, G.; Gomati, R.; El Haimati, 0.;Marignan, J. J. Phys. Chen. 1986,90,5746. Cates, M. E.; Drye, T. J.J.Chem. Phys. 1991, 96,1367. (11)Klein, M.; Menelle, A,;Mathis, A,;Guenet, J. M.MucromoZecules 1990,23,4591. (12) Granek, R.; Cates, M. E. J. Chem. Phys. 1992,96,4758.
Dammer et al.
1502 Langmuir, Vol. 11, No. 5, 1995 le+3
340 330 320 Y 310
le+2 le+l
-:
300
!I
290
le+O le-1
1
l e - 2 le-1 le+O l e + l le+2 l e + 3
1 e+4
I
le-2 le-2 le-1 le+O l e + l le+2 le+3
'e+6g 171
280 270 260 1250 -4 0
I
le+5
u
le+O le+l le-2 le-1 le+O l e + l le+2 le+3
2e+l
Oe+O
4e+l
6e+l
le-2 le-1 le+O l e + l l
le+2
Oe+O
2e+2
e
w
3e+2
I
I
Oe+O
Figure 2. (a, top) Double logarithmic representation of the complex modulus G*(w) for different concentrations. (b, bottom) Cole-Cole representation of the same data ( Gvs G I . 1 e+4
6
8
1
0
This figure highlights two regimes: a t low temperature, the plateau modulii Go are virtually independent of temperature; at high temperature Go decreases with increasing T. The transition between both regimes occurs a t a relatively well defined temperature Tt,,,, . The evolution of T,,,,, with complex concentration is represented by the dotted line in the same figure. It is necessary to keep in mind that changing the temperature T of the system is to strongly modify the length of the polymeric chains following relation 2. Accordingly, the modulus behavior versus T could be simply regarded as a transition of the system from the fully entangled state to the nonentangled state. As known for classical polymers, the modulus does not depend on the chain length, E, any more when this length is above the entanglement length 1,. Conversely, for = I , the value of the plateau modulus should drop very rapidly. The variation of the temperature a t which this effect should take place with concentration can be straightforwardly deduced by assuming that the mean end-to-end distance which is proportional to E"(v = 0.5 meanfield, v = 0.588 excluded volume) is equal to the mesh size 6. As the variation of 6 with volume fraction is known (6 q@ for mean-field and 6 @0.77 for excluded volume), this yields for the transition temperature T , from an entangled to a nonentangled state in the case of a thermally-activated process:
-
1 e+3 m
4
4 I %vol Figure 4. Transition temperature as deduced from Figure 3 as a function of volume fraction. The solid line represents a fit by means of eq 18.
b * * b
Oe+O
2
le+2
n
-
z
0 le+l
++
f
Escis = -1.5 Log 4 + const 2kBTe
.
--
j le-1 --l270
2kBTe
290
310 TIK
330
350
.,
Figure 3. Dependence of the plateau modulus Go as a function of the temperature for different concentrations: 10 wt %; +, 5 wt %; A,3 wt %; 0 , 2 wt %; +, 1wt %. The dotted line shows the position of Tt,,,,.
the existence of a transient network. This type ofbehavior is expected for living p01ymers.l~ The results are further analyzed in Figure 3 which shows the dependence of the plateau modulii Go obtained from the high-frequency range as a function of temperature. (13) Shikata, T.; Hirata, H.; Kotaka, T. Langmuir 1988, 4, 354. Appell, J.; Porte, G.; Kathory, A,; Kern, F.; Candau, S.J. J.Phys. 11 1992, 2, 503.
-
-1.9 log 4
+ const
(mean-field)
(16)
(excluded volume)
(17)
To get rid of the constant term it suffices to choose a reference temperature Teref,which finally gives the following Schroder-Le Chktelier type relation:
with A = 1.5 (mean-field) or A = 1.9 (excluded volume). The variation of the transition temperature as deduced from the plateau modulus behavior (see Figure 4)can be reproduced by means of eq 18 by using Fef= 7.1 vol %, Pef= 327 K, and Escis= 48 kJ/mol (mean-field)or Escis= 39 kJ/mol (excluded volume). Two comments are worth making:
Study of C U Z ( O ~ C ~in H an I ~ Organic )~ Solvent
Langmuir, Vol. 11, No. 5, 1995 1503
1 e+4
1 e+4
1 e+3
1 e+3
1 e+2
c = 5%wt.
1 et2 1 e+l le-5 le-4 le-3 le-2 le-1 le+O l e + l le+2 le-5 le-4 le-3 le-2 le-1 le+O l e + l l e t 2
1 e+3
c = 2%wt.
1 e+3
1 e+2
1 e+2
............:...........................
le+l
1 e+l
..........
....................................................
i
i
.....
#
1 e+O 1 et0 1 le-5 le-4 le-3 le-2 le-1 le+O l e + l le+2 le-5 le-4 le-3 le-2 le-1 le[ W a m I H z I
Figure 5. Master curves for temperatures below Tt,,,,. (i) Compared to other systems, such as aqueous giant micelles, these activation energies are notably lower (for instance, Kern et al. report values of about 130 kJ/mol16). At first sight the energies derived by this method are consistent with lower values of E. (ii) As will be seen in what follows, the behavior of viscosity as a function of temperature is in conflict with a smooth disentanglement process. Also, activation energies derived from the evolution of zero-shear viscosity as a function of temperature are not self-consistent. A detailed discussion of the mechanisms involved in the transition will be postponed after a further analysis of the curves G and G vs w and the viscosity behavior as a function of temperature. Noteworthy is the similarity of the curves in Figure 3 with those encountered in thennoreversible gels.14 Below T,,,,, the superimposition principle of the curves of the relaxation modulus G*was used to find out whether master curves as described by William, Landel, and Ferry (WLF)15could be obtained. The result is shown in Figure 5. The master curves show nearly perfect superimposition for the relaxation processes a t low frequencies while noticeable discrepancies appear a t high frequencies. As shown in Figure 5 the superimposition principle works for the low frequency process a t all temperatures (14)Koltisko, K.; Keller, A.; Litt, M.; Baer, E.; Hiltner, A. Mucromolecules 1986,19,1207.Dammer, C . Master thesis, Ulm, Germany, 1991. (15)Ferry, J. D. Viscoelasticpropertiesofpolymers;Wiley: New York, 1980.
le+4
-
le+3
-
le+2
-
(3
l e 4 le-5 l e 4 le-3 le-2 l e - I le+O l e + l
w . a ( r )I HZ
Figure 6. Absence of master curve for c = 10 wt % and T = 303,313, and 323 K by using the same procedure as in Figure 4.
below TtranS for all concentrations except for the 10% concentration for which discrepancies already appear well below T,,,,,. The more rapid departure from superimposition observed for the 10%sample is shown in Figure 6. As can be seen, a flattening of the curves around the maximum in G" occurs. The higher the temperature the flatter the curve, reaching a behavior in the middle range frequencies where both G and G ou2.This type of
-
Dammer et al.
1504 Langmuir, Vol. 11, No. 5, 1995
1e+2
1
1e-I
1e+O
4 270 275 280 285 290 295 300 305
TIK
le+l
I %vol.
Figure 8. Variation of the relaxation time t~ with complex volume fraction.
Figure 7. Shift factors a(T) of the master curves (Figure 5): ., 10 W t %; e, 5 Wt %; A, 3 W t %; 0 , 2 Wt %; +, 1 W t %.
behavior is observed in a special case for classical polymers: when the ratio of the chains length to the persistence length becomes small enough, the length of the plateau in G decreases and the curves tend to flatten. This analogy is relevant, since rising the temperature of our system decreases strongly the length of the chains without altering significantlythe persistence length. This phenomenon can occur a t high concentration because the mesh size is comparable to the persistence length. Above T,,,,, no superimposition of the curves can be achieved whatever the sample concentration is. Figure 7 shows the shift factors a(T)ofthe master curves of Figure 4. As the transition temperatures T,,,,, depend on the concentration of the samples, we chose the same reference temperature Treffor all samples for the WLF shifts (Tref= 273 K). This temperature is below T,,,,, for all the investigated samples, which makes possible a direct comparison of the shift factors a(T). Figure 7 shows that the shift factors do not depend on the samples’ concentration. Although a satisfactory agreement is obtained for the time-temperature equivalence a t low frequencies, superimposition cannot be achieved a t high frequencies whatever the concentration or the temperature are. The impossibility of superposing starts just after the minimum of G , whose value Gmin”is independent of temperature. The theory of “living” polymers12provides a relation between the minimum in the imaginary part of G and the length of the chains (eq 14) if rouse modes govern the relaxation process a t high frequencies. Experimentally it is found that this minimum does not depend upon temperature, so that no relation between the minimum and the mean chain length (at constant Go and 1,) can be established. This suggests that rouse modes are not appropriate for describing the relaxation process a t high frequencies. It is of interest to determine the variation of the terminal relaxation time t~ as a function of volume fraction. This time can be determined from the value of angular frequency COR corresponding to the maximum of G by using ZR = ~ / w R . Data plotted in Figure 8 show that ZR varies like SR @1.6*o.1 which indicates that the relaxation process is mainly controlled by reversible scissionrecombination. We now analyze the behavior of the zero shear viscosity T O derived from the low-frequencydomain ofthe imaginary part of G* (TO = G l w ) . Figure 9 shows the dependency of the viscosity 7 0 in a semilogarithmic representation over the reciprocal ofthe temperature. Usually these types of curves can be fitted by means of a straight line. From
-
I le-2 I ++
2.8
3.0
3.2
3.4
3.6
3.8
T I IO-~K-I
Figure 9. Dependence of the zero shear viscosity TO on the temperature: . , 10 wt %; e, 5 wt %; A, 3 w t %; 0 , 2 wt %; +, 1 wt %. The dotted line indicates the position of Ttrans.
the slope the activation energy of the relaxation process can be determined (eq 12). Presently, any attempt to fit the data by a straight line over the whole temperature range, as expected for a living polymer, is irrelevant. Interestingly, however, the viscosities are seen to follow the expected Arrhenian behavior for temperatures below the transition temperature Tkms(in the right part of Figure 9 with T,,,,, represented by a dotted line), which leads to a mean activation energy ER = 77 f5 kJ/mol. As the shift factors a(T) in Figure 7 are independent of complex concentration, all the fits below Tt,,,, must give parallel lines (in Figure 9). The activation energy therefore has to be the same for all the concentrations investigated. As shown in eqs 12 and 13 this activation energy contains two terms Eb and Escis.Using the value of Escis derived above, we obtain Eb = 78 kJlmol (mean-field)and 93 kJ/mol (excluded volume). The discrepancy between Eb and Escisseems unusually high. Indeed, Kern et a1.16 have reported that Eb Escisfor giant micelles. As mentioned above there might be an apparent inconsistency between the different activation energies which might be an indication that the phenomenon taking place when increasing the temperature differs from a simple disentanglement process. The most relevant argument against such a process is, however, the steep decrease of the zero-shear viscosity above Ttrans.As is apparent from eq 2, the reciprocal temperature 11T is equivalent to the logarithm of molecular weight log(M). For a smooth transition from nonentangled to entangled state the slope in the entangled (16)Kern, F.; Zana, R.; Candau, S. J. Langmuir 1991, 7, 1344,and references therein.
Study of Cu2(02Ca1& in an Organic Solvent
Langmuir, Vol. 11, No. 5, 1995 1505
Y
melting
I
-3.0
5
t
-3.5
'0
1
A H : 0.3Jlg peak: 57.9"C
-4.5
smooth disentanglement
"."
I
0
I I T or Log M
Figure Schematic remesentation of the variation o viscosity as a function of the reciprocal of temperature or the logarithm of the molecular weight when a melting process is involved (uppercurve)or when smooth disentanglement occurs (lower curve).
40
20
60
80
100
9 I"C Figure 12. DSC curves as observed for the Cu2S8 cis-trunsdecalin system (c = 5 wt %). The melting starts at about 30 "C (Ttr,,, = 34 "C from Go vs T )and is spread over 50 "C. Such a large "melting domain" is expected when dealing with twocomponent systems.
I
le+4
m I
(3
L
le+l
\ I
,
* - /
I
Figure 11. Schematic representation of a path in which different chains are linkgd by a physicaljunction thus increasing the apparent value of L.
regime should be much steeper than that in the nonentangled regime (see Figure lo), unlike what is experimentally observed. The dramatic decrease of the viscosity above T,,,, occurring in the present system is rather reminiscent of a melting process involving a first-order transition as opposed to a smooth disentanglement process (see Figure 10). Manifestly, the observed transition can be better understood as being due to partial aggregation of the chains as occurs in physical gels. The stacking of the complex molecules alone is a continuous, one-dimensional aggregation in the direction of the chains and, thus, cannot account for the observed behaviour. We therefore have to consider a three-dimensional aggregation between the chains as in thermoreversible (physical) gels giving a fringed-micellar structure (see Figure 11). That the threads formed by this complex are locally rigid2promotes such type of aggregation. It is worth emphasizing that, as far as the shapes of the curves G and G vs w are concerned, there is no fundamental difference between the CuS8/decalin jelly and some systems designated as thermoreversible gels. Some thermoreversible gels such as those produced from isotactic polystyrene or poly(methy1methacrylate) show considerable relaxation when submitted to a deformation.17 No zero-frequency modulus is actually observed. This behavior is accounted for by the disappearance of the physical junctions under stress that can re-form afterward to reach a new equilibrium. In other words, introducing physicaljunctions as those portrayed in Figure 11does not necessarily entail that, in the low-frequency (17)Guenet, J . M. Thermoreuersible Gelation of Polymers and Biopolymers; Academic Press: London, 1992.
le+O
+
f
X
le-1 1e-I
1e+O I$
le+l
I %vol.
Figure 13. Dependence of the plateau modulus Go on the concentration: U, 273 K, A, 283 K 293 K 0,303 K, +, 313 K, x 323 K. The solid line possesses a slope of 1.95.
*,
range, G > G . The curves G or G vs w presented here, for which G > G i n the low frequency range, are therefore still compatible with the presence of such physical junctions. So far indication of the possible involvement of a firstorder transition rests only upon the anomalous behavior of the zero-shear viscosity with temperature. Such a hypothesis can be tested by thermal analysis as a latent heat, AHm,is expected to be detected. DSC investigations do reveal the existence of such a transition in the same temperature range as determined by mechanical testing (Figure 12). The value of the latent heat, AHm = 0.3 Jlg, is quite low which suggests that the proportion of material involved in the physical junctions is small. A complete thermal analysis of the Cu&3 molecules in different solvents is in progress and will be reported in due course. Heretofore, we have discussed the dependence of the plateau modulus Go and viscosity 70 on temperature only. As detailed in the theoretical section, Cates' theory for "living" polymers predicts the variation of these variables with volume fraction. Figure 13 shows the dependence of the plateau moduli Go upon volume fraction in a double logarithmic scale. In the asymptotic range, for T < Tt,,,,, the points can be fitted by a straight line which yields a n exponent close to 1.95. This value is what is predicted by Cates' theory in the mean-field approximation.16 It is, however, worth
1506 Langmuir, Vol. 11, No. 5, 1995
Dammer et al.
efficiently the role of entanglements. Once above T,,,,,, the gradual disappearance of the physicaljunctions entails a very rapid shortening of the path sketched in Figure 11. Under these conditions the prerequisite of Cates’ theory, i.e., to be in the entangled state, is no longer fulfilled. The scheme put forward here implies that the threads of copper complex are shorter than expected, something in contrast to the activation energy derived experimentally. In fact, if melting processes are involved, then it is quite likely + that determining the activation energy of the scission le-1 x process is not possible from the present Cates’ theory. Finally, it is worth mentioning that the complex gives 8 jellies in trans-decalin but not in cis-decalin a t room le-3 I temperature. In a mixture, as the one used here, there le-I le+O le+l is probably a subtle balance that controls the piling up 4 I %vol. process of the complex molecules and, therefore, controls the value of L. This suggests that the solvent type plays Figure 14. Dependence of the zero shear viscosity 70 on the a decisive role in this process. concentration: W, 273 K, 283 K, A, 293 K 0 , 3 0 3 K +, 313 K, x, 323 K. Solid lines have a slope of 3.3. The dotted line Concluding Remarks highlights the position of T,,,,,. We have studied the rheological properties of a bicopper tetracarboxylate complex as a function of temperature keeping in mind that such a value can be found for many and concentration. The results have been examined in other systems, such as a network of disordered rods.ls the framework of the theory developed by Cates and coFigure 14 shows the dependence of the zero shear workers. The main outcome of this study is the observaviscosity T Oupon volume fraction in a double logarithmic tion of a transition whose temperature, T,,,,,, is concenscale. As the temperature dependence of the viscosity is tration dependent. The existence of this transition can the same for all concentrations, the fitted lines in Figure be accounted for by considering the occurrence of a low 12 must be parallel for T < Tt,,,,. Under these conditions degree of physical gelation. While above Tt,,,, the theory the correlated fits give a n exponent of 3.3 f 0.1. This of “living” polymers does not hold, good agreement is exponent indicates that Cates’theory is relevant to account obtained for T < T,,,,,. A molecular model involving a low for the present results. This exponent together with those degree of physical gelation is contemplated for expounding found for GOand t~ vs 4 also suggests that the system is both the existence of a transition temperature and the better described in the mean-field approximation. fairly good agreement with the theory of “living”polymers. Exponents predicted by Cates’ theory are therefore The physical links are thus believed to play a role similar found below T,,,,, but not above T,,,,,. One may wonder to that of entanglements and also to increase in some way why this theory holds for a system which, a t first sight, the value of L. It would be, however, interesting to find differs from the structure described by Cates in the theory‘s out theoretically whether this type of junctions can have formulation. In fact, provided the number of organized any influence on some rheological parameters. All these fringes be not too large, there is no fundamental difference effects are also dependent upon the solvent type which is, between the fringed-micellar structure and a totallyaccordingly, a new parameter to be taken into account in disordered solution. Yet, consideration of the path as future investigations. represented in Figure 11 makes it manageable to account for a sudden drop both in plateau modulus and viscosity. Acknowledgment. Christoph Dammer is indebted to This path consists of several “chains”joined together by the Gottlieb Daimler- und Karl Benz-Stiftung (Ladenburg, physical junctions. Below T,,,,,, i.e. below the melting of Germany) for a research grant. We are indebted to Drs. these junctions, a long chain can be obtained. If the S. Candau and F. Lequeux for helpful discussions and junction are not too large, there is virtually no difference criticisms of the manuscript. Odile Gavat is gratefully between two chains connected either end-to-end or sideacknowledged for the synthesis of a part of the material to-side. Furthermore, physical junctions can play very used in this study. le+7
I
1
*,
(18)Jones, J. L.; Marques, C. M. J. Phys. (Paris) 1990, 51, 1113.
LA9409283
