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Rheological Properties and Structural Correlations in Molecular Organogels P. Terech,* D. Pasquier, V. Bordas, and C. Rossat Laboratoire Physico-Chimie Mole´ culaire, UMR 5819 CEA-CNRS-Universite´ J. Fourier, De´ partement de Recherche Fondamentale sur la Matie` re Condense´ e, C.E.A.-Grenoble 17, rue des Martyrs, 38054 Grenoble Cedex 09, France Received November 29, 1999. In Final Form: February 12, 2000 Organogels of 12-hydroxystearic acid (HSA) have been investigated to emphasize solvent-dependent relationships between rheological properties and nanostructures in this class of physical gels. Different length scales are considered: macroscopic with optical opacity, rheology, phase diagram data; nanoscopic with small-angle neutron scattering experiments and molecular with 1H NMR data. HSA networks are shown to be rigid fibrillar networks with rigid junction zones and behave as elastoplastic materials. Shear elasticities, yield stresses, and deformation behaviors appear connected to the crystallinity of networks through the cross-sectional shapes of fibers. Kinetics of molecular aggregation and flowing properties are also used to compare three classes of HSA gels (toluene, dodecane, nitrobenzene). The melting transitions as well as the concentration dependence of yield stresses exhibit remarkable behaviors analyzed in a context of molecular nanomaterials.
1. Introduction Thermally reversible gels made up of molecular agents (gelators) are fascinating materials by their multifaceted properties. Low-mass gelators1 can form soft solids in a very large variety of organic liquids, from apolar hydrocarbons to short chain alcohols, at concentrations e1 wt %. Certain gelators are even able to gelify both organic and aqueous solutions!2,3 The solution to gel phase transition is usually reversibly induced by lowering the temperature of the binary solutions. The typical consistency of the self-supporting gels is due to a network of entangled rodlike species. These supramolecular assemblies are spontaneously formed through autoassociation of gelators in the gel domain of the phase diagram. The effect on consistency is spectacular since an increase of viscosity by a factor 1010 is a common feature of these systems immobilizing up to 105 liquid molecules per gelator through interfacial nanoscopic forces! A determinant clue for gelification lies in the nature of gelator-gelator and gelator-organic liquid interactions which further determines the gel structure. Concerning gelator-gelator interactions, the most common mechanism involves hydrogen bonds in the growth of fibers. With gelatorliquid interactions, the melting temperature varies frequently as a function of the type of liquid and this effect can be used in molecular recognition properties.4,6 Structural studies revealed also solvent-dependent morphologies of the fibers and junction zones.5,7 The understanding of gelator-liquid relationships is a difficult task and requires both an accurate evaluation of * To whom correspondence should be addressed. (1) Terech, P.; Weiss, R. G. Chem. Rev. 1997, 97, 3133. (2) Lu, L.; Weiss, R. G. Langmuir 1995, 11, 3630. (3) Oda, R.; Huc, I.; Candau, S. J. Angew. Chem., Int. Ed. Engl. 1998, 37, 2689. (4) Murata, K.; Aoki, M.; Susuki, T.; Harada, T.; Kawabata, H.; Komori, T.; Ohseto, F.; Ueda, K.; Shinkai, S. J. Am. Chem. Soc. 1994, 116, 6664. (5) Geiger, C.; Stanescu, M.; Chen, L.; Whitten, D. G. Langmuir 1999, 15, 2241. (6) James, T. D.; Kawabata, H.; Ludwig, R.; Murata, K.; Shinkai, S. Tetrahedron 1995, 512, 555. (7) Terech, P.; Rodriguez, V.; Barnes, J. D.; McKenna, G. B. Langmuir 1994, 10, 3406.
Chart 1. 12-Hydroxystearic Acid Organogelator (HSA)a
a
Carbon C12, bearing the hydroxyl group, is asymmetric.
the structural, thermal, and mechanical differences between organogels in various liquids together with an analysis of the molecular structure of fibers and junction zones. Eventually, a model for the wetting phenomenon at nanoscales in fibrillar networks is desirable to support a sound description of gelification. We focus on organogels made up of 12-hydroxystearic acid (HSA) (Chart 1) to address the issue of the influence of the liquid upon mechanical properties. Attempts to draw basic correlations with nanostructural features are presented. HSA organogels are well-documented systems since the pioneering work of Vold.8 The studies were mainly motivated by the tribological properties of gels of the related soaps (lithium, sodium, calcium) used as industrial lubricating greases.9-14 On a fundamental point of view, HSA organogels constitute a good illustration of thermoreversible molecular networks.15-17 Modern scattering techniques using intense radiation sources (neutron, synchrotron) have revealed accurate topologies of the networks.7 To summarize, HSA fibers in hydrocarbon gels involve H-bonds forming zigzag sequences along the fiber axis (8) Marton, L.; McBain; Vold, R. D. J. Am. Chem. Soc. 1941, 63, 1990. (9) Vold, M. J.; Vold, R. D. J. Colloid Sci. 1950, 62, 1. (10) Hotten, B. W.; Birdsall, D. H. J. Colloid Sci. 1952, 7, 284. (11) Cox, D. B. J. Phys. Chem. 1958, 62, 1254. (12) Langman, C. A. J.; Vold, M. J.; Vold, R. D. NLGI Spokesman 1967, August, 152. (13) Suggitt, R. M. NLGI Spokesman 1960, December, 367. (14) Vinogradov, G. V.; Sinitsyn, V. V. J. Inst. Petrol. 1961, 47, 357. (15) Tachibana, T.; Kamabara, H. J. Colloid Interface Sci. 1968, 28, 173. (16) Tachibana, T.; Mori, T.; Hori, K. Bull. Chem. Soc. Jpn 1980, 53, 1714. (17) Tachibana, T.; Mori, T.; Hori, K. Bull. Chem. Soc. Jpn 1981, 54, 73.
10.1021/la991545d CCC: $19.00 © 2000 American Chemical Society Published on Web 04/21/2000
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Figure 1. Optical photographs of HSA/hydrocarbon gels. Test tubes (1 cm diameter) are turned upside down to illustrate the self-supporting property. Clear differences in turbidity differentiate the systems. From left to right: toluene, dodecane, and nitrobenzene at C ) 1 wt %.
and “head to head” contacts within the orthogonal plane between carboxylic acid groups. Fibers are rigid and very long (up to micrometers), and their cross-sectional shapes are dependent upon the liquid type. They are interconnected in crystalline monoclinic microdomains. The present work differentiates the rheology of HSA organogels, for three selected liquids (toluene, dodecane, nitrobenzene) for which clear optical differences are observed. Finally, data are related to salient structural features of the networks, as observed with small-angle neutron scattering experiments on swollen gels.7 Results reveal a variety of different thermodynamic, kinetic, mechanical, and structural properties, dependent upon the liquid type which can be partly correlated. 2. Experimental Section The racemic DL-HSA (F ) 81 °C) and liquids (toluene, dodecane, nitrobenzene, hexafluorobenzene) were obtained from Aldrich (99% purity). Gels were formed by dissolving the gelator in heated liquids followed with a decrease of temperature in the 0.1-10 wt % concentration range. The optically active D-HSA derivative (ca. 98% purity) was obtained from chromatographic purification18 of the technical product. Xerogels were formed by slow evaporation of the liquid from gels at room temperature. Rheological measurements used a Haake RS100 stress rheometer with a plate-plate geometry (20 mm diameter) with serrated surfaces to prevent slidings due to the liquid film expelled by certain dilute samples or at the melting transition.19 The value of the gap (0.4 or 0.6 mm) did not affect the determination of the elastic shear modulus values which indicated that no significant slip at the walls of the plates occurred during the measurements.20 Despite the nonhomogeneity of the stress within the gap, the plate-plate geometry was chosen as giving the most reproducible results. Oscillatory experiments were performed in a 0.001-61 Hz frequency range. A glass cap limited solvent evaporation (mainly with toluene), and temperature was regulated with an accuracy of ca. 0.1 °C. The heated HSA solution was introduced between the two plates regulated at 20 °C before the gap was adjusted to its nominal value. The liquid sandwich thickened very rapidly in the measuring position. The oscillatory experiments were done at constant stress in the linear regime of (18) Mansot, J. L.; Terech, P.; Martin, J. M. Colloids Surf. 1989, 39, 321. (19) Terech, P.; Rossat, C.; Volino, F. J. Colloid Interface Sci., in press. (20) Yoshimura, A. S.; Prud’homme, R. K.; Princen, H. M.; Kiss, A. D. J. Rheol. 1987, 31, 699.
Figure 2. Kinetic variation of the optical opacity, measured at λ ) 550 nm (optical path ) 1 mm), during the aggregation reaction of HSA/hydrocarbon systems. The equilibrated systems are organogels at an identical volume fraction φ ) 1.77%. (A) 1, toluene; 2, dodecane; 3, nitrobenzene; 4, hexafluorobenzene. (B) Details of the above kinetic curves: toluene (1) and dodecane (2). deformations (i.e., σ could be varied up to ca. 20 Pa for a gel at 0.5 wt % in dodecane and ca. 2000 Pa for a gel at 10 wt %). The apparent yield stresses were measured for comparisons between the three types of gels. A stress ramp (∆σ/∆t ) 0.9 Pa s-1) was applied until the deformation γ diverged, and a flow occurred which marked the end of the experiment. The speed of the stress ramp (∆σ/∆t) was not affecting the yield value but only the shape of the γ divergence. Opacity measurements were carried out at 20 °C with a PerkinElmer Lambda 9000 spectrometer in 1 mm optical cells. Small-angle neutron scattering (SANS) experiments were done at the ILL (Grenoble, France). The momentum transfer Q (Å-1) was defined as Q ) (4π/λ) sin θ, where θ was half the scattering angle. A complete scattering study was published elsewhere.7 T vs C phase diagrams, representing the gel to solution phase transition, were obtained both with the “falling ball” method and a rheology protocol. The first technique used a steel ball immersed in the gel while the temperature was measured with a thin copper-constantan thermocouple. At melting, the ball was released and dropped at the bottom of the tube. Since a previous study has shown that this method is not the most accurate,19 a more reliable approach was used with rheology. Gels were submitted to a slow-temperature ramp (dT/dt ≈ +0.007 °C s-1) and to a constant stress of 0.3 Pa oscillating at a frequency of 1 Hz. These conditions were the least possible disturbing to the slowly disaggregating fragile network near the melting transition. The analysis of the methodology for probing phase transitions in molecular gels has also shown that 1H NMR spectroscopy might bring valuable thermodynamic and kinetical information related to molecular aggregation.19 Kinetics information was obtained with NMR resonance of HSA protons (Bruker CXP spectrometer operating at 90 MHz) in gels of deuterated liquids (octane-d, toluene-d, nitrobenzened) into 4 mm diameter glass tubes. Upon a decrease of temperature, solidlike aggregates were formed with no fast tumbling motions. The free induction decay (FID) signal associated to this fraction of bounded HSA molecules disappeared from the FT NMR window (in reciprocal frequency space, this signal
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Figure 3. Oscillatory rheometry (ν ) 1 Hz, σ ) 20 Pa) probing the kinetics of HSA/nitrobenzene gelification reaction. A solution (C ) 0.5 wt %) is put at T ) 19.9 °C, and the variations of G′ and G′′ are recorded as the system equilibrates to a gel state.
Figure 4. Typical dynamical rheological behavior of a HSA/ hydrocarbon gel (dodecane, C ) 4 wt %): (b), G′; (O), G′′; (2), η*. Full line over G′′ results from application of expression 1 to G′ data. The straight line over G′ follows a (1.15 × 105)ν0.06 profile. A guide line for a slope -1 is also shown. would be a broad line). The results were that the 1H NMR amplitude was strikingly decreasing with time during the aggregation kinetics. Analysis of the profiles provided the kinetic constants while their variations with temperature gave an enthalpy Eagg associated with the aggregation.
Figure 5. Linear viscoelastic domains for HSA organogels at an identical volume fraction φ ) 0.88% and measured at a frequency ν ) 1 Hz: 1, toluene; 2, dodecane; 3, nitrobenzene.
Figure 6. Comparison of the elastic shear modulus G′ profiles versus frequency ν for three HSA/hydrocarbon systems (φ ) 0.88%): nitrobenzene (9), dodecane (O) and toluene (2) gels. G′ ∝ νR profiles are shown as straight lines.
3. Results Properties of three types of HSA organogels (toluene, dodecane, and nitrobenzene) are compared. These gels are assumed to be model systems for which clear structural and mechanical distinct behaviors can be expected (vide infra). The strategy was guided by their different visual aspects (Figure 1). Figure 2 shows the variation of optical opacity with the three organogels during the kinetics of aggregation. A very turbid gel in hexafluorobenzene is also shown, but due to the volatility of the liquid, rheology could not be used. Figure 3 shows the onset of viscoelasticity in a HSA/ dodecane solution cooled at 20 °C and its final equilibration. Figure 4 is a typical rheogram of a HSA organogel showing the elastic shear modulus G′′, the loss modulus G′′, and the complex viscosity η* versus the frequency of the oscillatory stress. Figure 5 shows the rheological behavior of HSA organogels submitted to increasing oscillatory shearing stresses σ. The G′ versus γ profiles define the mechanical threshold between the linear and nonlinear regimes of deformations. Figure 6 shows comparative plots of the variation of the storage modulus G′ versus frequency for the three types of HSA organogels at identical volume fraction.
Figure 7. Dependence of G′ upon HSA volume fraction φ in organogels: comparison between nitrobenzene (9), dodecane (O), and toluene (2) gels. Straight full lines correspond to power law relations (see Table 1).
Comparative plots of the variation of the elastic shear modulus G′ versus the volume fraction of gelator are shown in Figure 7 for the three types of HSA organogels. Adjustments to scaling laws are also drawn and parameters collected in Table 1. Deformation curves γ versus σ, used for the determination of the yield stress value σ*, are shown in Figure 8A for the three types of gels at identical volume fraction. Figure 8B shows the flowing behavior of the gels illustrated with σ versus γ˘ curves. The variation of the yield stress
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Figure 10. Temperature versus volume fraction phase diagrams for the three types of HSA organogels: 1, dodecane (b, O); 2, nitrobenzene (9, 0); 3, toluene (s, 4). Full symbols are for rheological determinations and open symbols correspond to the “falling ball” method. The horizontal dotted line represents the melting temperature of the pure HSA solid.
Figure 8. Deformation (A) and flow (B) curves for the three types of HSA organogels at φ ) 0.88%: nitrobenzene (9), dodecane (O), and toluene (2). Speed of the stress ramp dσ/dt ) 0.33 Pa s-1. From the divergence of the strain (A) or the onset of a steady flowing state (B), apparent yield stress values σ* can be estimated.
Figure 9. Variation of the yield stress σ* with the HSA volume fraction for the three types of organogels: nitrobenzene (9), dodecane (O), and toluene (2). The straight full line corresponds to the best agreement with a power law profile (σ* ∝ (6.38 × 104)φ1.5).
with HSA volume fraction for the three types of liquids is shown in Figure 9. Figure 10 shows the melting temperatures TGS (gel to the solution transition) as a function of HSA volume fraction for the three types of gels. The phase diagrams are obtained by the rheology and “falling ball” methods (see Experimental Section). SANS curves are shown in Figure 11 for the three types of organogels. Figure 11A presents the cross-sectional scattering curves QI versus Q while Figure 11B emphasizes the interfacial scattering as represented by Q4I versus Q plots.
Figure 11. Neutron scattering curves of the three “model” HSA organogels: 1 (2) benzene-d, C ) 0.014 477 g cm-3; 2 (b) cyclohexane-d, C ) 0.013 45 g cm-3; 3 (9) nitrobenzene-d, C ) 0.0115 g cm-3. (A) Concentration normalized cross-sectional intensity QI vs Q. The vertical arrow points at a Bragg peak at Q ≈ 0.14 Å-1. (B) Interfacial scattering Q4I intensities normalized by concentration, contrast, and scattering invariant vs Q. Dotted horizontal segments indicate the asymptotic largeangle limits. Full lines are indicative adjustments for the extreme situations: toluene, “cylindrical” fibers, s ) s′ ) 180 Å; nitrobenzene, ribbons, thickness, s ) 300 Å (s′ ≈ 1500 Å). Scale for nitrobenzene gel is the right ordinate axis.
4. Analysis and Discussion All HSA/hydrocarbon systems are self-supporting materials as demonstrated with Figure 1, which shows tubes placed upside down. A visual examination is sufficient to distinguish the three types of organogels. Benzene/HSA gels are transparent while dodecane and nitrobenzene gels are more turbid (a complete and white opacity is observed with hexafluorobenzene, not shown). This is an indication that polydisperse nanostructures in the systems
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Table 1. Comparison between the Three Types of HSA/Hydrocarbon Gels (Nitrobenzene, Dodecane, Toluene)a organic liquid
G′ (Pa) C ) 1 wt %
G′ (Pa) C ) 7 wt %
β G′ ) φβ
x SGM model
σ* (Pa) φ ) 0.89%
A∞
t1/2 (min)
nitrobenzene dodecane toluene
40 190 9 010 8 390
1 790 000 580 000 423 000
1.89 2.22 2.04
1.07 1.02 1.05
622 491 370
0.237 0.160 0.073
4.6 1.6 4.1
a Collected parameters are shear elasticity (at ν ) 1 Hz), exponent of related power law G′ ∝ φβ, clue parameter x of the SGM model, yield stress σ*, optical opacity at φ ) 1.77%, typical kinetic time for the variation of optical absorption during the aggregation reaction.
diffract light at characteristic distances comparable to the visible wavelength range (400-800 nm). It is assumed that the optical aspect is related to the crystallinity of the gels. The crystalline diffracting units in the networks are fibers and junction zones whose sizes and volume proportions contribute to scatter light. HSA gels can then be classified into the sequence of crystallinity, toluene , dodecane, nitrobenzene consistent with a previous diffraction/scattering study (more crystalline networks were in hexafluorobenzene).7 Measurements of the optical opacity (λ ) 550 nm) as a function of time, obtained with heated gelling HSA solutions suddenly put at room temperature, provide a sequence toluene < dodecane < nitrobenzene < hexafluorobenzene (Figure 2A) identical to that obtained from the visual aspects. All curves show a sudden increase of opacity while the jump for toluene gel can hardly be seen, as expected for almost transparent gels (details are shown in enlargements of Figure 2B). With all systems, the kinetics of growth of the HSA aggregates is relatively fast and t1/2 ranges from approximately 0.8 to 4.6 min in the sequence hexafluorobenzene < dodecane < toluene < nitrobenzene (Table 1). The detailed profile also shows a slight decrease of opacity after the “gelification jump”, except with nitrobenzene gels which show a continuous increase and a much slower variation. This behavior reveals two features of the networks. First, it indicates the specificity of HSA aggregation in a polar liquid such as nitrobenzene. Second, it points at the existence of a second mechanism of aggregation. After the main step of network formation, its minor contraction could cause the slight opacity decrease. The contraction would proceed through fiber sticking into bundles, and the modification of correlation lengths of the resulting larger aggregates would account for the opacity decrease. This process would also be responsible for the limited liquid expulsion observed with certain dilute gels (C < 0.5 wt %). The observation is common with many other gelators and could be a more general feature of rigid fibrillar networks in molecular gels. Figure 3 shows the time evolution of the flowing properties of a heated HSA/nitrobenzene solution and reveals the sharp onset of shear elasticity when the temperature is lowered at 20 °C. Within approximately 1500 s, the system reaches a stabilized G′ value with a characteristic time t1/2 ≈ 200 s. The outbreak of viscoelasticity is concomitant with the opacity jump in gelling systems (Figures 2) and supports the above discussion in terms of aggregation of crystalline species. The shear elasticity (G′ ) 6374 Pa) is much larger than the corresponding heat dissipation (G′′ ) 555 Pa) and shows that the system has equilibrated into a gel state. With this class of low-mass gelators, it is accepted that only a nonsoluble fraction of molecules participates to the aggregation reaction. Gels are considered as supersaturation gels at equilibration temperature T.21 The super(21) Hermans, P. H. Colloid Science, Reversible Systems; Elsevier: Amsterdam, 1969; Vol. II.
Figure 12. Exponential variation of the kinetic constants associated to the HSA molecular aggregation reaction as a function of the reciprocal temperature. From these 1H NMR data, enthalpies Eagg are deduced. octane-d (O), nitrobenzene-d (9), and toluene-d (2) HSA organogels (φ ) 0.03).
saturation degree, defined as σT ) ∆C/CTsol (with CTsol being the gelator solubility at T, C0 the initial concentration, and ∆C ) C0 - CTsol) is a driving parameter for fiber formation. The low solubility of gelators in hydrocarbons (i.e., ca. 20 at C ) 10 wt %). As a consequence, the unidirectional crystallization and junction formations proceed with important velocities as shown with sigmoids of Figures 2 and 3. Kinetics observations made at a macroscopic scale (optical, rheological measurements) may differ from that at a molecular scale. For instance, the thermal dependence of the kinetic constants characterizing the time variation of the amplitude of 1H NMR signal (HSA methylene groups) during the gelification in a deuterated liquid is exponential and provides a different sequence of enthalpies Eagg (Figure 12). Table 2 collects the Eagg values, expressed with reference to the situation in toluene gels, and a sequence nitrobenzene < octane < toluene is observed. A correlation with the mechanism of formation of molecular arrangements within the crystalline nanoaggregates of HSA networks is expected (vide infra). The rheogram of Figure 4, representative of all HSA/ hydrocarbon gels, presents slightly sloped G′ and G′′ variations as a function of the frequency (G′ ∝ ν0.06) of the imposed stress. Over the whole range of frequencies, the HSA gel network exhibits lifetimes long enough (>10 000 s) to consider the systems as gels. The profiles and amplitude of the shear elasticity (ca. 12 times higher than the viscous loss) are typical of viscoelastic soft solids. The validity of dynamical measurements can be checked with the Kronig-Kramers relation.22
G′′(ω) )
π dG′(ω) 2 d ln(ω)
(1)
Figure 4 shows the correct agreement between experimental and calculated G′′ values confirming that experi-
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Table 2. Comparison between the Three Types of HSA/Hydrocarbon Gels (Nitrobenzene, Dodecane, Toluene)a organic liquid
Tm (°C) at φ ) 1%
Eagg ratios (NMR)
G′ ratios
low-Q limit ratios
high-Q limit ratios
section (Å)
nitrobenzene dodecane toluene
36.9 60.5 26.0
2.5 1.5 1
4.5 1.2 1
2.9 1.2 1
350 1.43 1
ribbon (s ≈ 300) rectangular square (200 × 200)
a Collected parameters are melting temperature of gels at φ ) 1%, enthalpies E agg for the molecular aggregation reaction (NMR data), shear elasticity ratio by reference to the toluene situation, SANS low-Q limit (ratio) in QI vs Q plots, high-Q limit (ratio) in Q4I vs Q plots normalized by the scattering invariant (see text), basic cross-sectional topological features (SANS data).7 For SANS experiments, dodecane has been replaced by cyclohexane-d and by octane-d in NMR experiments.
ments were done in the linear regime of deformations (see also Figure 5). The extension of the linear regime is compared in Figure 5 for the three types of gels at a low and identical concentration (φ ) 0.88%). It shows that the linear domain, defined as the region where the dynamic moduli are independent of the strain amplitude (in the frequency range), is restricted to small levels of strain (γ < 0.01 at C ) 1 wt %). No significant variation with the concentration was observed (not shown). Figure 5 gives a sequence of elasticity, toluene < dodecane < nitrobenzene (at ν ) 1 Hz), and linear domains which are about comparable (that of nitrobenzene is only slightly narrower). At this stage, nitrobenzene gels appear singular with their degree of opacity, kinetics and mechanism of aggregation, elasticity, and sensitivity to mechanical ruptures. The complex viscosity η* (Figure 4) does not show any Newtonian plateau in the experimental frequency range but does show a decay with a slope -1 in a double logarithmic plot. This is confirmed with simultaneous plots (not shown) of the steady and complex shear viscosities as a function of the shear rate γ˘ and angular frequency or effective shear rate γω. In such a representation, the two profiles are not superimposed and exhibit a -1 slope typical of a shear thinning behavior. Identical observations are made with two oscillatory experiments at two strain levels (γ ) 0.001 and γ ) 0.005, not shown). The nonobservation of a Newtonian plateau prevents the Carreau expression23 from being used for describing the shear rate dependence of the viscosity. All these features suggest that the Cox-Merz rule (expression 2a)24 is not obeyed and characterize systems with a limited linear viscoelastic domain and a yield stress value separating elastoplastic and viscous behaviors. For such systems, Doraiswamy’s expressions (2b) have been proposed as an extension of the Cox-Merz rule:
η*(γω) ) η(γ˘ ) τ ) Gγ˜ for τ)
(τ*γ˘ + Kγ˘ ) γ˘ n-1
(2a)
γ˜ < γc for γ˜ ) γc
(2b)
γ˜ is a recoverable strain tensor and σ* ) Gγc. In the Doraiswamy model,25 the system is assumed to exhibit completely recoverable elastic deformations below the yield stress and viscous shear thinning. Figure 4 has shown that the complex viscosity tends to infinite values at small frequencies confirming also the existence of a yield stress. Different methods can be used to extract the (22) Tschoegl, N. W. The phenomenological theory of linear viscoelastic behavior; Springer-Verlag: Berlin, 1989. (23) Carreau, P. J.; DeKee, D.; Daroux, M. Can. J. Chem. Eng. 1979, 57, 135. (24) Cox, W. P.; Merz, E. H. J. Polym. Sci. 1958, 28, 619. (25) Doraiswamy, D.; Mujumdar, A. M.; Tsao, I.; Beris, A. N.; Danforth, S. C.; Metzner, A. B. J. Rheol. 1991, 35, 647.
yield stress26 but only that detailed in the Experimental Section will be considered. Yield stress values of HSA gels are estimated using γ versus τ curves (Figure 8A) as the point at which significant flow appears (Figure 8B). A comparison made at identical concentration (φ ) 0.885%) gives a sequence toluene < dodecane < nitrobenzene, again identical with that from other indicators (e.g., turbidity, kinetics of aggregation, elasticity). Figure 9 shows the τ* versus φ profiles of the three types of gels and the good agreement found with a power law τ* ≈ (6.38 × 104)φ3/2. The evaluation assumes that the mechanism of rupture of fibers is similar for the three gels. The critical deformation γc, at rupture would thus differentiate the three types of gels according to the way that a fiber, of given shape and interfacial polarity, interferes with a neighboring one. Very few theoretical formulations of the yield stress variation with the concentration of hardener are available. For instance, expression 3 which involves a nonfluctuating semidilute fractal concept was used with silica-silicone gels.27
σ* ∝ (φ)4/(3-D)
(3)
With fibers, the fractal dimension D is unity and, consequently, a φ2 variation of σ* vs φ is expected. In such a formalism, the experimental scaling exponent (3/2) would lead to a fractal dimension of 1/3. Scattering curves did not show up the corresponding typical variation I(Q) ∼ Q-D expected for a fractal structure of dimension D.28 Actually, SANS curves (Figure 11A) show that only the form factor of HSA aggregates (dI/dQ ) -1)29 is observed within the Q window. In the concentration range 0.5-3 wt %, the interference scattering features between aggregates are rejected in the innermost low-Q part. The hypothetical self-similarity relation would not involve such a low exponent (1/3) since extra scattering for concentrated gels is expected to be either in a form I ≈ Q-2 attributable to lamellar-like bundles or I ≈ Q-4 for even larger heterogeneities. The increase of yield stress with the solid concentration is also very rapid in other very different systems. For instance, an exponential variation was measured with mud suspensions.30 With HSA gels, the power law variation is slower and related to the increase of interactions between fibers. The contribution to shear elasticity and yield stress from either fibers or junction zones is difficult to be discerned, and only global trends can be briefly considered. Assuming a statistical and isotropic distribution of fibers (diameter D) so as to subdivide the (26) Hoffmann, H.; Thunig, C.; Schmiedel, P.; Munkert, U. Faraday Discuss. 1995, 101, 319. (27) Piau, J. M.; Dorget, M.; Palierne, J. F.; Pouchelon, A. J. Rheol. 1999, 43, 305. (28) Teixeira, J. J. Appl. Crystallogr. 1988, 21, 781. (29) Glatter, O.; Kratky, O. Small-Angle X-ray Scattering; Academic Press: London, 1982. (30) Coussot, P.; Piau, J. M. Rheol. Acta 1994, 33, 175.
Molecular Organogels
Figure 13. Thixotropic loop followed by a recovery step with a HSA/nitrobenzene gel (C ) 1.9 wt %) characterizing the elastoplastic behavior. Strain versus stress profile (A) and strain versus time profile (B). The corresponding stress sequence is the full segmental line in B.
volume into cubic cells of size ξ, a relation ξ > D(3π/4φ)1/2 is expected (the inequality takes into account contributions from heterogeneities and nonrandom distributions of fibers which both affect the statistical average 〈ξ〉). Simple relations, such G ∝ kT/ξ3 and σ* ) γcGo, can be used to get σ* ∝ φ3/2kTγc/D3. This oversimplified description implies thermodynamic considerations which make the network more entropic than energetic. Nevertheless, the above agreement brings back to the structural origin of the yield stress and more specifically to the role of the junction zones. The deformation and recovery behaviors of HSA gels can be illustrated with Figures 13 and 14 for a system submitted to a specific sequence made up of a thixotropic loop followed by a relaxation step. An ascending stress ramp (dσ/dt ≈ 1 Pa s-1) was followed by a descending stress ramp at the same speed, and then the relaxation behavior was measured (at σ ) 0 Pa). Specificities of the elastoplastic character of HSA gels are revealed with both the area of the thixotropic loop and the lack of complete reversibility of the deformation on the time scale of the experiments. Figure 14 show that the area of the thixotropic loop depends strongly upon the ratio of the maximum stress which is applied over the yield value σ*. Actually, Figure 14B illustrates the exponential divergence of the area when σ/σ* approaches unity. These features demonstrate that such rigid networks are elastically deformed only within restricted stress conditions. Before the flow occurrence at σ* (in Figure 13A, σ/σ* ≈ 0.84), an irreversible creeping process takes place with its own characteristic thixotropic time. The associated topological modifications in the network which control the flowing properties, appear to be shear-sensitive well before σ*. Figure 14B shows that the characteristic time for recovery is much longer than the thixotropic time constant chosen for the decreasing stress step (second step
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Figure 14. Variation of the area A of the thixotropic loops obtained at different σ/σ* ratios with a HSA/dodecane gel at C ) 3 wt %. Arrows indicate the ascending and descending parts of the stress ramp. (A) Strain versus stress profiles at different imposed stress values σimp. (1) σimp ) 2567 Pa, A ) -0.79, σ* ) 2610 Pa; (2) σimp ) 1532 Pa, A ) -0.58, σ* ) 1600 Pa; (3) σimp ) 2360 Pa, A ) -0.26, σ* ) 2725 Pa; (4) σimp ) 1842 Pa, A ) -0.06, σ* ) 2770 Pa. (B) Thixotropic loop area A versus σ/σ*. The variation can be modeled as an exponential variation A ) 0.000127 exp(9.26σ/σ*).
in protocol of Figure 13B). The third step, i.e., a relaxation process, exhibits hyperbolic strain recovery kinetics with a much weaker time constant (ca. 0.02 s-1). Without going into details of the determination of σ*, its real existence, or its more complex constitution (possibly involving dynamic and static components),31 a similarity is observed between salient rheological behaviors (G′ vs G′′, σ*, etc.) and behaviors of very different systems. Thus, if expressions 2b are used with HSA, a theoretical yield stress value can be obtained with an acceptable agreement as shown in Figure 15. The theoretical value (680 Pa) is not so different from the measured one (510 Pa), and the exponent n (ca. 0.3) is similar to that found with mud suspensions, for instance.30 These common observations (gels, muds, slurries, etc.) require a more global consideration. Recently,32 a rheological constitutive equation has been proposed for soft glassy materials to which HSA organogels may refer. Slow relaxation modes out of the experimental window associated with properties such as structural disorder and metastability would be common properties of this class of materials. The soft glassy rheological (SGR) model is phenomenological and proposes that large energy barriers have to be crossed to induce rearrangements of trapped constitutive elements (fibers for physical gels). Expressions 4 describe the rheological (31) Cheng, D. C.-H. Rheol. Acta 1986, 25, 542. (32) Sollich, P. Phys. Rev. E 1998, 58, 738. (33) Mas, R.; Magnin, A. Rheol. Acta 1997, 36, 49.
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G′′ and the loss tangent tan(δ), which expresses the ratio of dissipated and stored powers (δ being the phase lag between strain and stress). If a comparison is made at different concentrations, the sequence can be marginally altered between dodecane and toluene but nitrobenzene gels remain the more solidlike materials. Figure 7 shows that scaling laws can be established for the variations of G′ with volume fraction for each type of HSA gel. The exponents (Table 1) are in the sequence dodecane > toluene > nitrobenzene, and the average values are 2.05 for G′ and 2.14 for G′′. The analysis of the elasticity requires considering the appropriate thermodynamical context describing the free energy of such networks. With entropic networks, involving fixed cross-links,35 expression 5 can be used. Figure 15. Flowing properties of a HSA/dodecane gel (C ) 1.0 wt %). Full line corresponds to the agreement of Doraiswamy’s model (expression 2b) to the data with σ* ) 680 Pa and n ) 0.294.
properties ruled out with a parameter x such that a glass transition occurs at x f 1.
G′ ≈ ωx-1 G′′/G′ ≈ x - 1
(4)
With HSA/nitrobenzene gels, the profile G′ ∝ ν0.06 (Figure 4) gives x ≈ 1.06 while G′′/G′ ≈ 555/6374 provides x ≈ 1.09. A sequence for x values, dodecane < toluene < nitrobenzene, is observed which, according to the SGR model, suggests that dodecane gels are the closest to the glassy state and that the Cox-Merz rule cannot be valid for any HSA gel (as observed). To some extent, a comparison can be drawn with lithium lubricating greases despite a different chemical composition (C ≈ 8 wt % in heavy oils loaded with various additives).33 Nevertheless, it has been shown14,15 that a comparable fibrillar network was also responsible for gellike properties in lithium greases. A superposition of steady and complex shear viscosities is obtained when the elastic and plastic components are low with respect to the viscous stresses. With these conditions, high strains prevent any restructuring of the fibrillar networks under shear within the range of the thixotropic times. Out of these conditions, nonlinearity effects linked to microstructural modifications are apparent as shown in Figures 13 and 14. To account for the thixotropic behavior, certain theories describing the shear thinning and structural recovery phenomena consider a time-dependent yield stress concept.31,34 The yield stress measures then the internal strength of the aggregated structure and results from the balance of structural breakdown and recovery of rheologically active units. These developments are beyond the scope of the present study but probably constitute promising tracks for the understanding of flowing properties in HSA elastoplastic gels. In such a context, structural correlations at rest and during flow are much needed: as a first step, structural correlations at rest will be provided in the following with SANS experiments. Coming back to the linear regime of deformations, Figure 6 compares G′ and G′′ profiles as a function of frequency ν of the oscillatory stress (at constant amplitude) for the three types of gels at a same concentration (φ ) 0.886%). It distinguishes the behavior of nitrobenzene gel from the others (dodecane or toluene). A similar sequence is naturally observed (not shown) with the loss modulus (34) Toorman, E. A. Rheol. Acta 1997, 36, 56.
G ) gκRT
(5)
κ is the moles of network strands per unit volume and g is a numerical factor. Such a framework entails two remarks. First, real networks are more complex due to the presence of dangling ends, sol fraction (no elastic contribution), length polydispersity, and network defects such as trapped, mobile, or slipping entanglements. Second, previous scattering and electron microscopy experiments have shown that HSA strands were rigid fibers connected into rigid 3-D networks. It is thus expected that the entropic contribution from the different fiber trajectories should be weak. A more realistic context is constituted of an idealized network made up of rigid elements (fibers) joined at crosslink points or junction zones. The elasticity of energetic networks combines the stiffness of the elements and their mobility at nodal points. In a network of rigid chains permanently (i.e., for short time modulus measurements) and rigidly (i.e., no freely articulation) cross-linked, the temperature-independent elastic modulus is given by expression 6.36
G′ ) BΦ2
(6)
B is related to the bending constant of fibers which, in turn, is dependent upon their cross-sectional size (B ) f(kEs)) with E being the rod material modulus, s the crosssectional dimension, and parameter k taking into account the cross-sectional shape and the persistence length). If the elements can change their angles in the permanent cross-links, an entropic contribution is gained and the scaling becomes G′ ≡ gkBTΦ3/2. Rheological measurements during the melting of networks19 show (vide infra) that G′ is slightly decreasing in a large range of temperatures before a much sharper decay preceding the melting transition. HSA micellar fibers are in thermal equilibrium, and their lengths can be described with an expression of the type 〈L〉 ∝ φR exp(Escis/kT). With neutral micelles, Escis is assimilated to the scission energy or end-cap energy. Fibers are fully entangled in gels, and the thermal effect consists, as a first step, of decreasing the cross sections of bundles of fibers (slight decrease of G′) before the point where the decrease of lengths affects the statistical mesh size (sharp decrease of G′). The observed G′(T) variations are more due to first-order equilibration reactions in rigid fibrillar micelles than to entropic variations associated to fluctuations of fiber trajectories. In addition, the average experimental value 2.05 of the exponent fits a description of HSA networks made up of rigid fibers connected into (35) Ferry, J. D. Viscoelastic Properties of Polymers; Wiley: New York, 1980. (36) Jones, J. L.; Marques, C. M. J. Phys. (Paris) 1990, 51, 1113.
Molecular Organogels
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fixed and permanent cross-links (on the time scale of the measurements). Following expression 6, it is expected that the sequence of elasticity (G′nitrobenzene > G′dodecane > G′toluene) of the three types of networks, at a given concentration, should reveal similar trends in bending rigidities B and cross-sectional shapes s. Table 1 collects rheological, optical, and kinetical parameters which are potentially connected to nanostructures. The small-angle neutron scattering technique (SANS) is appropriate to analyze the nanostructures, and consistently with a previous study,7 all HSA/hydrocarbon gels develop fibers at rest (Figure 11). The unidirectionality of the aggregates is characterized by a Q-1 intensity decay at low angles (a plateau in QI vs Q plots) as shown with expression 7.37 The Gaussian decay at Q > 0.02 Å-1 is typical of finite cross sections. At even larger angles, weak oscillations are due to interfacial features better visualized in a Q4I vs Q plot. Such a representation reveals the crosssectional shape, contrast homogeneity, and monodispersity.29,37
QI ) πLV∆F2(ss′)2
∫02π ×
[sinQAQAcoscosφ/2φ/2 sinQBQBsinsinφ/2φ/2] dφ (7) 2
∆F is the volumic neutron contrast of the fiber, L is the length of the fibers, ss′ is their rectangular cross-sectional areas with sides s and s′, and I is expressed in cm-1. Figure 11A shows that the scattering curves for toluene and cyclohexane gels exhibit the typical features for dispersed fibers. With nitrobenzene, the asymptotic low-Q behavior differs within the experimental Q window due to a different cross-sectional shape (vide infra). The levels of cross-sectional intensity (concentration normalized) vary significantly according to the type of gelified liquid. The comparison for dilute gels assumes that the signal is dominated by the form factor of fibers while the contribution from their interaction domains is rejected at very low angles. Fibers in benzene (or toluene) are known7 to exhibit square cross-sectional shapes (side s ≈ 200 Å) while in cyclohexane they are slightly rectangular and ribbon-like in nitrobenzene with a thickness ca. 300 Å (see caption, Table 2, and ref 7). The special cross-sectional shape of fibers in nitrobenzene accounts for an apparent Q-2 decay within the experimental Q window (Figure 11A). These structural parameters are deduced from adjustments of expression 7 to experimental curves with special attention paid both to regions of the Gaussian decay and subsequent oscillations at larger Q. From these regions, information about the radius of gyration and cross-sectional shape, respectively, is extracted. The extrapolated values (QI/ C)o at Q ) 0 are in the sequence nitrobenzene > cyclohexane > benzene which, according to expression 7, indicate the amount of aggregated HSA molecules per cross section. Table 2 gives the asymptotic low-Q limits (contrast and concentration normalized) as ratios with respect to the situation in toluene gels. Taking into account the neutron contrast of each system (((QI)o/C∆F2)1/2 ∝ s) and a minor correction for the HSA fraction remaining in solution, the sequence reveals the variation of crosssectional sizes. The Q4I vs Q representation of Figure 11B emphasizes also the distinct scattering behaviors of the three networks, and the different oscillations characterize the differences in cross-sectional shape and monodipersity. The upturn (37) Guinier, A.; Fournet, G. Small Angle Scattering of X-rays; Wiley: New York, 1955.
at Q ≈ 0.14 Å-1 corresponds to a (001) Bragg reflection in a monoclinic P21/a organization of DL-HSA domains (fibers and junction zones). The interfacial scattering intensities IQ4 can be normalized by the concentration, the volume contrast ∆F2, and the scattering invariant (INV ) ∫Q2I(Q)dQ ) 2π2∆F2V). The asymptotic limits are also different, slightly between benzene and cyclohexane and more strongly with nitrobenzene. The limits are proportional to the scattering surfaces following lim IQ4 ) 2πS∆F2.29 The ratio between the large-angle limit and the scattering invariant INV gives a simple relation lim IQ4/ INV ∝ 1/s (s being the thickness of a ribbon-like aggregate). Values of such normalized limits are collected in Table 2. The sequence nitrobenzene < cyclohexane < benzene is again observed which corresponds to the inverse sequence of S/V ratios or thicknesses. Aggregates are much larger in nitrobenzene than in cyclohexane or benzene. Within the SANS experimental window (such that ca. 2π/10s g Qmin), aggregates in nitrobenzene appear more ribbonlike than those in toluene which exhibit a cylindrical symmetry. The structural sequence (low-Q and high-Q limits in Table 2) are comparable to the shear elasticity sequence as well as to the NMR kinetic or absorbance or yield stress sequences. They are first simple and direct correlations between nanostructures and mechanical properties in HSA gels. Among the different molecular parameters which may affect the supramolecular structure, chirality is a recognized one. With aqueous systems, chirality can be essential both for the existence of helical superstructures38 and enantiomorphic relations15 and for gel formation. A known example of the importance of the formation of chiral junction zones for the flowing properties is found with gelatin aqueous solutions whose gelification is induced by the partial recovery of the native conformation of the chains in triple helices within the junction zones.39,40 With organogels, despite clear examples are known,41 the situation is much less crucial and racemates can produce either 3-D crystals and phase separation (with no gel) or ribbons (and gels).7 For instance, HSA organogels can be formed both with the optically active D-derivative or the racemic DL-compound. The contribution of solute chirality to mechanical properties of networks made up of a same gelator can thus be addressed by comparing HSA gels. With dodecane (C ) 2%), oscillatory and steady shear experiments (not shown) do not reveal any significant difference between the racemic and the optically active HSA gelators as long as the elastic shear moduli and the yield stresses are considered. Previous scattering and diffraction experiments7 have shown that racemic HSA organogels were only slightly more crystalline than the chiral ones. The present rheological measurements show that chirality is not determinant for the mechanical properties of HSA organogels. Architecture details at molecular scale within fibers (i.e., twists) and bundles of fibers do not affect the elastic response of energetic networks and are not a major mechanism for interconnection of fibers. To conclude the search for distinct properties in HSA organogels, thermal behaviors can be examined. Figure 10 presents T versus C phase diagrams measured with the falling ball and rheological methods. At any concen(38) Pfannemu¨ller, B.; Welte, W. Chem. Phys. Lipids 1985, 37, 227. (39) Djabourov, M. Contemp. Phys. 1988, 29, 273. (40) Djabourov, M.; Leblond, J.; Papon, P. J. Phys. (Paris) 1988, 49, 333. (41) Hanabusa, K.; Okui, K.; Karaki, K.; Koyama, T.; Shirai, H. J. Chem. Soc., Chem. Commun. 1992, 1371.
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tration, a sequence Tdodecane > Tnitrobenzene > Ttoluene is observed. The rheological curve stands above that with the falling ball method. A previous study19 comparing rheometry, NMR, and falling ball procedures has concluded that rheometry was more appropriate to determine the transition temperatures in molecular gels. Assuming4,42,43 that gel-to-solution transitions are dissolution processes of microcrystals, the solubility CTsol can be described by expression 8 for ideal solutions
ln CTsol ) -
(
)
∆Hm 1 1 R T Tm
(8)
where ∆Hm is the melting enthalpy and Tm the melting point. The profile ln(φ) versus 1/T (not shown) provides a value |∆H| ≈ 24.8 kcal mol-1 in toluene. Identical slopes (not shown) R ) ∂(ln φ)/∂(1/T) for the three organogels correspond to identical melting enthalpies and suggest that the mechanism of aggregation is identical. Only minor crystallographic variations with the solvent type (polytypism) are generated whose amplitude was estimated by crystallographic and calorimetric studies.7 The unusual location of dodecane gels in the melting sequence shows that their molecular structure is close to the most stable one forming 3-D crystals in nongelling liquids. Variations in molecular structures do not affect the bending constant of HSA fibers, which depends more strongly upon their cross-sectional sizes and shapes. The high degree of dispersion of solid HSA in nanofibers can also contribute to the temperature depressions. The assumption that regions of solid and liquid are large enough so that contributions from their surfaces is (42) Eldridge, J. E.; Ferry, J. D. J. Phys. Chem. 1954, 58, 992. (43) Amanokura, N.; Yoza, K.; Shinmori, H.; Shinkai, S.; Reinhoudt, D. N. J. Chem. Soc., Perkin Trans. 2 1998, 2585. (44) Buffat, P.; Borel, J.-P. Phys. Rev. A 1976, 13, 2287. (45) Couchman, P. R.; Jesser, W. A. Nature 1977, 269, 481. (46) Pawlow, P. Z. Phys. Chem. 1909, 65, 1. (47) Wautelet, M. Phys. Lett. A 1998, 246, 341.
negligible cannot be maintained at nanoscale, and the lowering of the melting point can be given by expression 9.44,45
∆T ≈
(
())
2Tbulk Fs γs - γl FsHLR Fl
2/3
(9)
Tbulk is the bulk melting temperature, Fs, γs and Fl, γl are the density and surface tension of the crystal and liquid, respectively, HL ) ∆STbulk is the latent heat of fusion proportional to the entropy of fusion, and R is the size of the particles. Parameters HL, R,46,47 and γs affect the melting temperature and can be variable parameters in HSA organogels. Dodecane gels are assumed to have the largest entropy change, associated to either melting or solubilization, and have a moderate temperature depression in comparison with toluene gels which exhibit a weaker entropy change. The size effect leads to a similar trend since nanodimensions in dodecane gels are larger than those in toluene gels. γs variations, for nanocrystallites of shape and crystallographic arrangement specific to aggregates grown in a given liquid, may account for variations in the sequence of liquids (between dodecane and nitrobenzene). As a conclusion, it has been demonstrated that HSA organogels display a variety of rheological, kinetical, and thermodynamical behaviors which depends on the type of liquid which is gelified. Shear elasticities, yield stresses, kinetics of aggregation, deformation, and melting behaviors are related to the cross-sectional sizes of fibers in such rigid networks. Scaling laws of the shear elasticity and yield stresses versus the concentration of gelator are identified. Acknowledgment. The authors are grateful to Dr. F. Volino for his help during the NMR experiments. Institut Lave Langevin (I.L.L., Grenoble, France) is acknowledged for providing access to the neutron facility. LA991545D
