Soft Glass Rheology in Liquid Crystalline Gels Formed by a

Dec 22, 2009 - The plateau modulus of G′ is described by a power−law with an exponent again common to soft materials, such as foams, slurries, etc...
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J. Phys. Chem. B 2010, 114, 697–704

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Soft Glass Rheology in Liquid Crystalline Gels Formed by a Monodisperse Dipeptide Geetha G. Nair, S. Krishna Prasad,* R. Bhargavi, V. Jayalakshmi, G. Shanker,† and C. V. Yelamaggad Centre for Liquid Crystal Research, Jalahalli, Bangalore 560 013, India ReceiVed: July 27, 2009; ReVised Manuscript ReceiVed: NoVember 30, 2009

Thermal and extensive rheological characterization of a nematic liquid crystal gelated with a novel monodisperse dipeptide, also a liquid crystal, has been carried out. For certain concentrations, the calorimetric scans display a two-peak profile across the chiral nematic-isotropic (N*-I) transition, a feature reminiscent of the randomdilution to random-field crossover observed in liquid crystal gels formed with aerosil particles. All samples show shear thinning behavior without a Newtonian plateau region at lower shear rates. Small deformation oscillatory data at lower frequencies exhibit a frequency dependence of the storage (G′) and loss (G′′) moduli that can be described by a weak power-law, characteristic of soft glassy rheological systems. At higher frequencies, while lower concentration composites have a strong frequency dependence with a trend for possible crossover from viscoelastic solid to viscoelastic liquid behavior, the higher-concentration gels show frequencyindependent rheograms of entirely elastic nature G′ > G′′. The plateau modulus of G′ is described by a power-law with an exponent again common to soft materials, such as foams, slurries, etc. Other features which are a hallmark of such materials observed in the present study are: (i) above a critical strain, a strain softening of the moduli with a peak in the loss modulus, (ii) power-law variation of the storage modulus in the nonlinear viscoelastic regime, and (iii) absence of Cox-Merz superposition for the complex viscosity. An attractive feature of these gels is the fast recovery upon removal of large strain and qualitatively different temporal behavior of the recovery between the low and high concentration composites, with the latter indicating the presence of two characteristic time scales. 1. Introduction Low molecular weight materials possessing the ability to gelate organic solvents, especially via physical interactions such as hydrogen bonds, have been receiving considerable attention in recent times.1-10 The gelation is caused by the fiber network formed by the hydrogen bonding of the gelating molecules, a process which is thermoreversible and therefore attractive. If a material exhibiting liquid crystalline properties is employed as the solvent, the resulting composites add a further dimension to such organogels since these gels retain the anisotropic properties of the liquid crystal (LC), exhibit thermoreversibility, and are mechanically more rigid. These physical gels comprising host LC materials and organic gelators that form fibrous aggregates are being investigated as a new class of dynamically functional materials.2 They are macroscopically soft solids and display improved electro-optical, photodriven, and electronic properties. Further, chiral gelator molecules are known in which the molecular chirality manifests as nanoscale helicity in the gel fibers formed.11 Recently,12 we have reported an attractive combination of a nematic LC and a novel chiral organogelator which itself is liquid crystalline having a helical structure. This gelator, a monodisperse homomeric dipeptide, recently synthesized and characterized by us,13 possesses built-in mechanisms for self-assembly, exhibiting the less frequently found helical columnar phase with an oblique two-dimensional lattice. The gels formed by a very small concentration of this dipeptide with a commercially available nematic liquid crystal (NLC) were * Corresponding author. E-mail: [email protected]. † Present address: Institute of Chemistry, Organic Chemistry, MartinLuther-University Halle-Wittenberg, Kurt-Mothes-Str. 2, D-06120 Halle/ Saale, Germany.

Figure 1. Molecular structure of GSC98. The material exhibits an oblique columnar (Colob) mesophase upon melting.13

found to exhibit fast electro-optic switching and are mechanically robust. Here we report the detailed rheological characterization of this system, displaying soft glassy characteristics. 2. Experimental Section The NLC used for this study is the well-known, commercially available eutectic mixture E7 (from Merck), exhibiting the nematic phase over a wide temperature range through room temperature. The gelating material employed is a monodisperse homomeric dipeptide (referred to as GSC98 here);13 it is an enantiomer in which the first and second residues are derived from D-alanine. Being a chiral molecule, it also exhibits a macroscopic helical structure;13 in fact, alanine is known to have a high propensity for helix formation.14 The molecular structure as well as the transition temperatures of this material is shown in Figure 1. Structurally, GSC98 can be regarded as an intermediate between polycatenars and taper-shaped amphiphiles as it possesses two lipophilic (half-disk shaped) segments interlinked through a peptide unit. This compound is mesogenic

10.1021/jp9071394  2010 American Chemical Society Published on Web 12/22/2009

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Figure 2. Optical microscopy texture exhibiting the fingerprint pattern characteristic of the chiral nematic phase.

exhibiting a columnar phase, and the mesogenicity helps in preparing mixtures with better homogeneity. It is found that even at concentrations as low as 0.2% (by weight) GSC98 forms gels in E7. In the present study, we have prepared nine different gels of concentrations X ) 0.2, 0.4, 0.6, 0.8,1, 2, 4, 6, and 10 where X represents the concentration of GSC98 by weight % in E7. The procedure followed for preparing these gels is given below. In small quantities, GSC98 is completely solvable in E7. The required quantities of E7 and GSC98 were weighed in a glass vial. The mixture was heated to 100 °C (which is well above the isotropic temperature of E7 and the melting temperature of GSC98) and stirred constantly for homogeneous mixing. The homogeneity itself was checked by observing the transition temperature from the nematic to the isotropic phase under a polarizing microscope (Leica DMRXP) equipped with a temperature-controlled hot stage (Mettler FP82HT). After mixing at 100 °C, the sample in the vial was quenched to room temperature and kept in a refrigerator for 2 days to achieve gelation. GSC98, being a chiral material, induces a chiral nematic (N*) or cholesteric phase when mixed with E7, a feature that is evident from microscopy observations on mixtures with concentrations higher than X ) 2. The fingerprint optical microscopy texture characteristic of the chiral nematic phase obtained for X ) 4 is shown in Figure 2. Differential scanning calorimetric (Perkin-Elmer, Diamond DSC) measurements were carried out on some of the gels for which the freshly prepared mixtures were weighed in the DSC aluminum cups and gelated in situ by keeping the sealed cups under refrigeration. The rheological measurements were carried out using a controlled stress rheometer (ARG2, TA Instruments) provided with a magnetic thrust bearing for ultralow, nanotorque control. A parallel plate geometry was preferred over the cone-plate configuration owing to the fact that the geometry gap is quite narrow in the latter case. The narrow gap could perhaps influence the as-formed gel structure. The parallel plate geometry employed had a diameter of 8 mm and a gap of 800 µm between the plates. The temperature of the sample was kept constant at 25 °C using a built-in Peltier temperature controller. It is possible to perform controlled stress, direct strain, and controlled rate measurements with this apparatus. 3. Results and Discussion 3.1. Structure of the Gelator. Recently,13 we demonstrated with the widespread theme of residue patterning and stereochemical restraints of self-complementing proteinogenic amino acids15 that a new and rich class of homomeric oligopetides exhibiting two-dimensional fluid aggregates with hierarchical ordering can be obtained. X-ray measurements showed several sharp and intense reflections in the low-angle region and a

Figure 3. (a) Free-flowing pure NLC (E7) sample. (b) X ) 0.8 composite showing the immobilization of the formed gel. (c) Schematic diagram of the gel structure with the red band representing the helical structure of the gelating peptide, and the blue ellipses stand for the nematic liquid crystal molecules. Although the presence of the peptide imparts chirality to the nematic phase of E7, for simplicity, the helical structure of the resulting chiral nematic phase is not shown. (d) SEM image obtained for the gel.

diffuse, broad reflection in the wide-angle region. By checking for systematic absence, the pattern was indexed to a twodimensional columnar oblique lattice having four molecules per unit cell. Interestingly, an X-ray peak (at angles higher than that of the diffuse peak mentioned above) which is typical in systems possessing a finite, albeit short-range, interaction between the rigid cores of the neighboring molecules of the same column was not observed. This could perhaps be owing to the fact that alanine promotes weak hydrophobic interactions16 and therefore may not allow the cores of neighboring molecules within the same column to pack better than their alkyl chains. These features suggest that the structure has an extremely welldefined 2D lattice but hardly any positional order perpendicular to the lattice plane. CD measurements establish that in solution as well as in the mesophase the chirality of the molecule manifests itself as a helical superstructure. Pictorial evidence of the good gelation capability of GSC98, as realized for a representative E7-GSC98 composition, is shown in Figure 3 along with a schematic representation of the gel structure and the obtained SEM photograph. At temperatures above 60 °C, the composite flows like a fluid (just like the host pure NLC), but when cooled below this temperature, it gets immobilized establishing its gel nature, which is thermoreversible. 3.2. Thermal Behavior. Figure 4 shows the differential scanning calorimetric scans for representative concentrations, X ) 1, 2, 4, and 10. The scans for both X ) 1 and 10 composites are quite similar to those for the rest of the composites studied having a single peak but qualitatively different from those for the X ) 2 and 4 composites. The twin-peak profile seen for the latter two concentrations is quite reminiscent of the behavior seen in aerosil-liquid crystal composites,17,18 wherein the liquid crystal molecules are confined in a fragile network formed due to the hydrogen bonding between the silica particles of aerosil. [An important difference between the network formed in aerosil-LC and the present case of peptide-LC should be

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Figure 5. Partial temperature-concentration phase diagram, where X indicates the concentration (weight %) of the organogelator GSC98 in the host NLC, E7. The region labeled LC: RD-like is argued to be in the random-dilution regime (see text for details). Figure 4. Differential scanning calorimetric scans for concentrations ranging from X ) 1 to 10, in the vicinity of the chiral nematic to isotropic transition. To be noted is the double peak profile clearly seen for X ) 2 and X ) 4 composites. The transition temperature is taken to be the peak temperature and in the case of X ) 2 and 4 is determined by fitting the data to two Gaussian expressions (shown as solid line).

mentioned. The origin for both networks is the hydroxyl group present within the molecule for the peptide case and existing as a terminal group attached to SiO2 in the case of aerosil particles. Therefore, the interaction between the hydroxyl groups of neighboring peptide moelecules is augmented if the orientational order is nonzero; consequently, it will be weakened for small values of orientational order and certainly in the isotropic phase. Since the aerosil particles do not take part in the formation of the LC structure, the strength of hydrogen bonding between neighboring aersoil particles is not affected by the liquid crystalline order.] The notable feature is that it has been established that the gel is soft in this concentration range up to 10%, showing soft glass behavior generally seen for materials such as foams, emulsions, particulate suspensions, and slurries.19 High-resolution ac calorimetry20 as well as DSC measurements17,18 have shown that for certain concentrations these soft gels exhibit two closely spaced and sharp thermal features, which have been used21 to propose that the nematic order develops from the isotropic phase through a two-step process and that the double peak in the calorimetry data is due to a crossover from a randomdilution regime, where the silica gel couples to the scalar part of the nematic order parameter, to a low-T random-field regime, where the coupling induces distortions in the director field. Owing to the common feature that in the present case also the gel formation involves a network of hydrogen-bonded entities (GSC98 molecules), we borrow these ideas to interpret the DSC results. For the quantitative analysis, the data for X ) 2 and 4 were fit to a sum of two Gaussian expressions. Just as in the aerosil case, the DSC scans for X ) 2 and 4 composites show a double peak profile but with a major difference. Whereas in the aerosil system the temperature difference between the two peaks is always a fraction of a degree, in the present case the peaks are well separated, by as much as 3 °C! This perhaps suggests that even for small values of the nematic orientational order the network gains strength in aerosil systems but requires higher orientational order in the present case. However, as we shall see later, deeper in the mesophase the network strengths of the two systemssas can be quantified by the storage modulussare comparable. The transition enthalpy ∆H, calculated from the area under the peak, is smaller for the composites, suggesting that the transition becomes weaker in the presence of the quenched disorder. For the X ) 2 composite, which shows

Figure 6. Shear rate (γ˙ ) dependence of bulk viscosity η for different concentrations of the composite. Shear thinning and the absence of low shear-rate Newtonian plateau is clearly observed. Inset shows the fitting of the data to the Carreau equation (eq 2) for three different concentrations, X ) 0.8, 1, and 2.

a double peak profile, it is seen that the high-temperature process, associated with the random dilution limit, has a three times larger ∆H value than the one connected with the random field region, a feature opposite that observed in the case of the aerosil-LC systems. Figure 5 shows the N*-I transition temperature (TN*I) (obtained from optical microscopy as well as DSC data) dependence on the peptide concentration. The strong decrease with increasing concentration suggests the structural incompatibility between the host NLC and the guest peptide molecules, with the latter acting as impurities. The salient feature, however, is the additional peak temperatures (DSC) seen for X ) 2 and 4 composites but absent for the lower and higher concentrations, indicating that the crossover mentioned above can be seen only in the soft gel limits. 3.3. Steady-State Shear Measurements. The flow curves obtained for the “as loaded samples” are shown for gels with concentrations ranging over two decades and shear rates over nearly 6 decades (Figure 6). An essential feature for all the concentrations is that there is a strong change in the shear rate dependence of the viscosity η at higher shear rates appearing to mimic a Newtonian plateau. The missing Newtonian plateau at low shear rates for the composites, except for the X ) 10 material, is obvious and is reminiscent of the behavior in highly filled fluids and the consequent immobilization of the network.22 It should however be borne in mind that the defect network owing to the cholesteric structure of the medium may also be playing a role. In this context, the behavior of the 10% composite is interesting. It actually exhibits a plateau at very low shear rates, followed by a sudden drop in η values by nearly

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Figure 7. Effect of concentration on the viscosity at a very low shear rate (1 × 10-3 s-1). The line describes a power-law behavior with an exponent of 2.4 ( 0.2.

an order of magnitude, and then exhibits a variation that is similar to the other composites, and finally before exhibiting the high shear rate plateau has another drop in the value. Also notice that the η value for this composite at the lowest shear rate is comparable to materials which form strong gels. The strength of the gels with concentrations greater than 2% is also perhaps due to the cholesteric defect network being strongly aided by the hydrogen-bonded network of the GSC98 molecules. This effect could be so large for X ) 10 that there is a breakdown of the network at γ˙ ∼ 2 × 10-3 s-1. In fact, this concentration range is comparable to that in aerosil networks over which the nature of the gel changes over from weak to strong.20,21 A well-known expression for describing flow curves with a shear thinning feature is the Carreau equation23

η(γ˙ ) - η∞ ) ηo - η∞(1 + (λγ˙ )2)-N

(1)

Here η0 and η∞ are the viscosity values at zero and very large values of the shear rate. λ indicates the rate of a structural relaxation in the medium. It may be noted in Figure 6 that η∞ is not defined very well. Therefore, we neglect η∞ and rewrite eq 1 as

η(γ˙ ) ) ηo(1 + (λγ˙ )2)-N

Figure 8. Angular frequency dependence of the two moduli G′ and G′′ obtained with small strain amplitude. The low concentrations exhibit, above a certain value of ω, a frequency-dependent G′, which can be described by slope values between 1 and 2 (indicated by slope lines 1 and 2). The higher concentrations are essentially frequency independent over the entire range of ω. The inset in the bottom panel shows the concentration dependence of the exponent (x - 1) obtained from a power-law (ωx-1) fitting of the data (represented as solid lines in the main plot) in the low frequency regime. To depict the fitting in a better way, we have shown the data on an enlarged scale in the Supporting Information.

(2)

The experimental data were fit to eq 2 by discarding the high shear rate part, which lies beyond the strong shear thinning region. The exponent N, which has a value of 0.35 ( 0.02 and 0.37 ( 0.02 for the two lower concentrations X ) 0.2 and 0.4, shows a marked increase for all other concentrations with the value lying in the range 0.6-0.66. The fit also provides information about the relaxation rate λ, which is experimentally taken to be the inverse of the γ˙ value at which there is a crossover from the low shear rate Newtonian plateau to the shear thinning behavior. Only for concentrations X ) 0.8, 1, and 2, there is a clear tendency of a low-rate Newtonian plateau (see inset of Figure 6). Therefore, λ can be unambiguously defined for these composites only, and the values obtained from the fit are 985 ( 54, 1669 ( 70, and 3863 ( 751 s, suggesting that the structural relaxation becomes slower with increasing concentration. As mentioned above, a clear saturation in the viscosity value at low shear rates is not seen for most of the composites. Therefore, we show in Figure 7 ηlow, the value determined at a low shear rate value of 1 × 10-3 s-1 plotted as a function of X. We observe a drastic increase in ηlow by more than 4 orders of magnitude when the concentration of GSC98 changes from 0.2 to 10%. On a double-logarithmic scale, the variation is nearly linear with a slope of 2.4 ( 0.2, a value which is much lower than that, for example, seen in associating polymers which exhibit a transient network developed by entanglements.24

3.4. Dynamic Characteristics. 3.4.1. Linear Viscoelasticity. Oscillatory linear viscoelastic experiments measure the response function, or the complex modulus, G*(ω) ) G′(ω) + G′′(ω), with G′ and G′′ representing the storage and loss moduli of the system. The advantage of these measurements is that since the deformation is small the finer details of the (gel) structure remain intact. The complex function mentioned above is strictly defined only within the linear response regime, and therefore an important practical experimental issue is the determination of its range of validity. We shall discuss later the limits of such a linear regime and also the nonlinear behavior. It suffices to mention here that for the angular frequency measurements the strain value employed retains the system in the linear response regime. Figure 8 shows the storage and loss moduli as a function of the angular frequency ω for six different concentrations, X ) 0.2, 0.8, 2, 4, 6, and 10. The composites with X < 4 exhibit, at low frequencies, a frequency-independent plateau suggesting that the material contains cooperative rearrangements as in rubber polymers. For these composites above a concentrationdependent frequency, a scaling regime is seen for both the moduli; noticeable is the fact that G′ remains greater than G′′ until the highest frequency of measurement, although there is a trend that at much higher values there may be a crossover. For gels 4% and above, the plateau region extends over the entire range of frequencies. These features are qualitatively similar to that of lightly cross-linked polymer bundle systems.25 Therefore, we checked to see whether quantitatively also the behavior is similar. For this purpose, we fitted the data in the scaling regime to a power-law of the type G′∼ωz. The fitted z value turned out to be in the range 1.0-1.7, which is much higher than 0.75, expected for the cross-linked polymers26 indicating that the comparison is only qualitative. A further feature to be noted is that even at the lowest frequency the liquid-like behavior (G′′

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> G′) is not seen, pointing to the fact that the structural relaxation times are very large, characteristic of gels. In the low and medium frequency regime, a soft glass rheology (SGR) model27,28 proposes a power-law dependence for both the moduli

G′(ω) ∼ ωx-1 and G′′(ω) ∼ ωx-1

(3)

The important point to note is that the exponent, which represents a noise temperature, is the same for both the moduli. The model expects a small value for the exponent x - 1 in the case of soft materials. We have fitted the data of G′ and G′′ in the low frequency region to eq 3. The G′′ data having a slightly higher noise level in the low frequency regime lead to larger error bars when such a power-law fitting is performed. For X ) 0.2, the influence of the noise level is high enough to prevent the fitting being performed with any level of confidence. It may be remarked here that but for X ) 0.8 the mixtures have a negative slope for the loss modulus (G′′ decreases with increasing ω) in this range. For the sake of uniformity, the range (ω ) 0.1 to 1 rad/s) over which such a feature is seen for X > 0.8 was used for the fitting of both G′ and G′′ data to eq 3 (the quality of fitting can be judged from the data presented on an enlarged scale in the Supporting Information). The exponent values from the fit are shown in the inset of Figure 8b. The fact that the values are quite low (in addition to the negative slope of G′′ mentioned above, seen in experiments quoted in ref 27) is in agreement with the expectation of the SGR model,27,28 although the exponents for the storage and the loss moduli data are slightly different from each other. It may be pointed out with increasing concentration that while the exponent for the G′ data does not show any systematic variation the exponent for the G′′ data appears to decrease. The low value of the exponent is expected for physical networks, indicating that the strands of the hydrogen-bond dictated network dynamically break and form, a feature universal for a wide variety of “soft materials”, such as slurries, paints, microgels, foams, etc.29 The SGR model also expects that the exponent x - 1 is given by the ratio G′′/G′. From the data shown in Figures 8a and b, the ratio turns out to be 0.08 to 0.13 for the different concentrations. These values are definitely higher than the values of x - 1. At present, we do not know the exact reason for this discrepancy. Notwithstanding the fact that in the present system there is an additional defect network, caused by the cholesteric structure, the very presence of the anisotropic liquid crystal itself may also introduce the difference. It is interesting to notice a similar discrepancy in the data presented in ref 19 (although not commented upon by the authors) on a system made up of aerosil particles and a smectic liquid crystal with a defect network. More experiments on such systems are needed to clarify this issue. In the second set of measurements, the frequency dependence of the moduli was determined by preshearing the sample for 10 min at a shear rate of 5 s-1 for X < 2 composites and 500 s-1 for gels X g 2. It is well-known that such a treatment results in the alignment of the cholesteric structure, and therefore these results can be considered to be due to the defect network that gets formed even in pure cholesteric materials without any gelating substance. [It should be noted here that that the host material E7 is achiral, and therefore the peptide molecule plays a dual role of imparting chirality as well as initiating gelation in E7.] Figure 9 shows the frequency dependence of the storage modulus before and after the preshear treatment for three representative concentrations X ) 0.4, 2, and 4, and it is seen that applying preshear lowers the modulus.30 The applied

Figure 9. Frequency dependence of the storage modulus before (solid symbols) and after (open symbols) a preshear treatment. Although the basic behavior remains the same, application of preshear reduces the low-ω value by about an order of magnitude.

Figure 10. Concentration dependence of plateau modulus obtained before the preshear treatment. The line represents a power-law behavior with the index 2.43 ( 0.02.

Figure 11. Moduli (filled circles, G′; open circles, G′′) data, shown for a representative concentration X ) 0.8, can be quite well described over the entire range of γ using eqs 4 and 5, depicted as lines.

preshear diminishes the defects in the network bringing down the modulus. In the case of the X ) 10 gel, owing to its large strength, the applied preshear may be insufficient to cause this before any irreversible rupture takes place. We characterize the strength of the gel by the value of the plateau modulus G′plateau, taken here as the G′ value at the lowest frequency (0.1 rad/s). As seen in Figure 10, the concentration dependence of the gel strength is described by a scaling law: G′plateau ∼ X2.43(0.02. 3.4.2. Nonlinear Viscoelasticity. To establish the limits of the linear viscoelastic regimes, we performed the strain amplitude (γ) dependence of the storage and loss moduli. It may be mentioned here that most colloidal suspensions and polymer solutions show a simple yielding behavior, where both G′ and G′′ decrease monotonically as γ increases.31 In contrast, the strain-amplitude behavior of the gels studied here can be divided into two regimes as seen in Figure 11, for a representative concentration X ) 0.8. At low strain amplitudes G′ is nearly constant, suggesting a linear viscoelastic regime, where the frequency sweeps mentioned in the previous section were measured. Here G′ is higher than G′′, exhibiting the solid-like behavior of the gel. Above a critical strain amplitude (γc), determined by drawing tangents to the data in the low and high strain ranges, and found to be 0.03 for this concentration, both

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moduli become strain dependent with G′ decreasing and G′′ passing through a maximum before decreasing as well. Above γc, G′ crosses over G′′, signaling a deformation-driven transition from a viscoelastic solid to a viscoelastic liquid. It is interesting to note that the observation of a peak in G′′ and a monotonic decrease in G′ is a hallmark of soft glassy materials32 and is expected theoretically below a certain noise temperature.28 We analyzed the data using the following two empirical expressions.

G )

G′′ )

Go′ (1 + γm /γc) Go′′γn /γc (1 + γm /γc)

(4)

(5)

Equation 4 is the more generalized version of the one used by Colby et al.,33 by the introduction of the exponent m. In fact, forcing m ) 1 (as in Colby’s) will make the fit decay slower than the data. To retain the general feature of eq 4 and also to account for the peak in the G′′ data, we have added the term γn/γc to the numerator of eq 5, the form of which is influenced by empirical equations, such as Cole-Davidson, employed to describe the dielectric dispersion data. The additional exponent n (* m) is necessitated by the observation that the G′′ profile is asymmetric about the peak point. The solid lines in Figure 11 show that the above expressions fit the data quite well (with m ) 0.58 ( 0.06, n ) 1.28 ( 0.03), supporting the soft glassy rheological character of the E7-GSC98 gels. Above the critical strain, the decay in the storage modulus could be described as G′ ∼ γ-ν′. In a similar fashion, the loss modulus beyond its peak point can be represented as G′′∼ γ-ν′′. A fit to these expressions yields ν′ ) 1.31 ( 0.01 and ν′′ ) 0.64 ( 0.01, i.e., ν′′∼ ν′/2, as observed even for soft glassy materials.34 Studying the general behavior of complex fluids subject to large amplitude oscillatory strain (LAOS), Hyun et al.35 classified the trends observed above γc into four categories: type I, strain softening (both G′ and G′′ decrease monotonically); type II, strain hardening (both G′ and G′′ increase monotonically); type III, weak strain overshoot (G′ decreasing monotonically, G′′ exhibiting a peak); type IV, strong strain overshoot (both G′ and G′′ exhibiting peaks). Figure 12 shows the LAOS behavior for different concentrations. For convenience of presentation, the data sets have been normalized by taking the ratio G′/G′o (upper panel) and G′′/G′′o (lower panel), where G′o and G′′o are the plateau and maximum values, respectively. It is seen that all the concentrations, except X ) 0.2, display the type III or weak strain overshoot behavior, whereas the type I feature is seen for X ) 0.2. In fact, a gentle strain hardening can be seen, especially for X ) 4 and 6 composites, at strain values lower than γc. For X ) 6, the value of G′ increases by about 30% when the strain value is increased from 10-4 to about γc [see inset (a) of Figure 12, upper panel]. The enhancement in G′ appears to be maximum for X ) 4 and decreases for higher as well as lower concentrations. In the nonlinear region (γ > γc), the data can be fit to a straight line (in the log-log scale). The slope of such a line (closed circles) is plotted as a function of concentration in inset (b) of Figure 12 (upper panel); the data show that the higher concentration composites have a similar nonlinear rheological behavior. The concentration dependence of this slope can, in fact, be described by a power-law, with an exponent of 0.2. The critical strain (open circles, inset (b)) on the other hand decreases with concentration and can also be expressed as power-law function with an exponent of 0.86.

3.4.3. Complex Viscosity. An important parameter that differentiates between a liquid and a gel is the behavior of the complex viscosity η* which can be determined from the small oscillation measurements using

η* )

(G′2 + G′′2)1/2 ω

(6)

In Maxwellian fluids, the Cox-Merz rule, by which η, the viscosity determined from steady state measurements, and η*, determined as above, are identical. This superposition is not applicable for weak gels as well as soft glassy systems, a feature that the SGR model also expects.28 Further, the frequency dependence of the complex viscosity can be described by a power-law

η* ∝ ω-p

(7)

Here, values of p close to zero suggest liquid-like behavior and, if close to 1, a solid-like response.36 Figure 13 clearly shows the failure of the Cox-Merz superposition for two representative concentrations, X ) 0.8 and 10. For fitting to eq 7, the data of η* over the entire frequency span were considered for X ) 10, whereas for X ) 0.8 it was limited to ω ) 10 rad/s, owing to a slope change above that frequency. Equation 7 describes the data well in both cases, and the p values obtained, 0.966 ( 0.003 and 0.952 ( 0.001, for X ) 0.8 and 10, respectively, establish the solid-like response of the system, a feature seen in well-formed gels (see, for example, ref 36). 3.4.4. Gel Collapse. Transient measurements showed that the GSC98-NLC gels can collapse and, more importantly, recover its rheological properties on very fast time scales (Figure 14).

Figure 12. Strain amplitude dependence of the normalized storage (upper panel) and loss (lower panel) moduli for X. Below a certain critical strain γc, G′ is independent of γ but exhibits a strong decrease above it. G′′ shows a similar signature only for X ) 0.2 but has a peak for all other X, corresponding to type I and type III behaviors discussed in the text. The higher concentration composites exhibit a weak strain hardening (G′ increasing as γ increases) just before γc, as in the example shown in the inset (a) for X ) 6. The G′ vs γ data in the nonlinear regime (i.e., above γc) have been fit to a straight line (in the log-log scale), the slope of which is shown as a function of X in inset (b). Inset (b) also shows that the critical strain γc decreases with X, in a power-law fashion.

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J. Phys. Chem. B, Vol. 114, No. 2, 2010 703 low concentration composites. However, for higher concentrations, although the return to the elastic state gets initiated when the strain value is reduced, there appear to be two stages in the complete recovery (see Figure 15). The detailed characterization of this aspect is in progress. 4. Conclusions

Figure 13. Frequency dependence of the complex viscosity η* determined from oscillatory measurements (open symbols) using eq 3 and the measured shear viscosity η (filled symbols). The lines represent fit to eq 4, and the exponent obtained, being nearly equal to a value of 1, suggests solid-like response of the system seen in well-formed gels. The fact that η* and η do not coincide indicates the breakdown of the Cox-Merz superposition.

We have performed calorimetric and extensive rheological measurements on an organogel system by a host nematic liquid crystal and a novel monodisperse peptide organogelator which is also liquid crystalline. The calorimetric data exhibit features similar to that of the random dilution to random crossover behavior seen in aerosil-liquid crystal gels. Apart from displaying the standard features of weak gels, the rheological measurements bring out the soft glassy characters of these composites. These materials also show a fast recovery to the gel state after the removal of a large strain. The elastic and viscosity parameters appear to be influenced by the defect network of the cholesteric liquid crystalline state as well as the network formed due to the hydrogen bonding among the peptide molecules. Supporting Information Available: The angular frequency dependence of the loss modulus for different concentrations is provided on an enlarged scale, along with a fit to eq 3. This material is available free of charge via the Internet at http:// pubs.acs.org.

Figure 14. Step strain measurements with an angular frequency of 1 rad/s for X ) 2 gel showing the rapid recovery of gel structure when the gel is subjected to a large oscillatory strain of 0.4 (regions indicated as High). The initial low strain amplitude is 3 × 10-3 (regions marked Low). The recovery to the gel state takes place within ∼ 20 s and is reproducible over repeated cycles of measurement.

Figure 15. Detailed view of the gel recovery after removal of the large strain. While for the low concentrations (X ) 0.2 and 0.8) most of the recovery takes place almost instantaneously upon removal of the large strain, for the X ) 6 composite there appear to be two time scales with a partial instant recovery and a slow increase (until about 200 s-1) toward an overall background variation that appears to be common for all X beyond about 300 s.

For these studies, the gel material was subjected to large amplitude oscillations with the strain values in the nonlinear regime (γ > γc) resulting in the breakdown of the gel structure. Subsequently, the strain amplitude was abruptly reduced to a very small value (γ < γο, to be in the LVR region) while monitoring G′ and G′′. As expected, at large strain values, G′ decreases by orders of magnitude and also becomes smaller than G′′. When γ is reduced to a small value, the recovery to the elastic state starts instantaneously, requiring less than 20 s. The recovery is indeed reproducible over repeated cycles of measurement. A point to be noted is that the recovery to the original values is nearly complete over very short time scales for the

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