J. Phys. Chem. B 2008, 112, 8459–8465
8459
Structure and Dynamics of a Bisurea-Based Supramolecular Polymer in n-Dodecane Toshiyuki Shikata,*,† Takuya Nishida,† Benjamin Isare,‡ Mathieu Linares,§ Roberto Lazzaroni,§ and Laurent Bouteiller‡ Department of Macromolecular Science, Osaka UniVersity, Toyonaka, Osaka 560-0043, Japan, Laboratoire de Chime des Polyme`res, UMR 7610, UniVersite´ Pierre et Marie Curie-CNRS, 4 place Jussieu, 75252 Paris Cedex 05, France, and SerVice de Chimie des Mate´riaux NouVeaux, UniVersite´ de Mons-Hainaut/Materia NoVa, Place du Parc, 20, B-7000 Mons, Belgium ReceiVed: January 16, 2008; ReVised Manuscript ReceiVed: April 19, 2008
The structure and dynamics of a supramolecular polymer formed by a bisurea-type compound, 2,4-bis(2ethylhexylureido)toluene (EHUT), in an apolar solvent, n-dodecane (C12), were examined in detail. The EHUT/ C12 organo-gel system forms long, dynamic chain-like supramolecular polymers, which lead to an entangled network showing remarkable viscoelastic behavior with two major relaxation modes. A slow relaxation mode with an approximately constant relaxation time, τS, was observed in a flow region and the other, fast, relaxation mode with a time τF1 (99%) was purchased from Sigma-Aldrich (St. Louis) and was used as a solvent for the sample preparation without further purification. The concentration of EHUT, c, in the EHUT/C12 organo-gel system ranged from 4.0 to 90 mM for dynamic viscoelastic and dielectric measurements. To prepare completely transparent
10.1021/jp800495v CCC: $40.75 2008 American Chemical Society Published on Web 06/26/2008
8460 J. Phys. Chem. B, Vol. 112, No. 29, 2008 organo-gel samples, the preweighted EHUT and C12 were mixed in glass vials and stirred by hand with a spatula many times at about 80 °C. Then, samples were kept stationary at room temperature for more than 5 h for equilibration prior to the measurements. Methods. Dynamic viscoelastic measurements were performed with a conventional rheometer (Physica MCR301, Anton Paar, Graz) equipped with a cone-and-plate geometry of 20 mm radius and 4.0° cone angle. The measured angular frequency, ω, ranged from 0.01 to 100 s-1, and the applied shear strain amplitude was varied from 0.5% to 10% to determine the storage and loss moduli, G′ and G′′, in the linear viscoelastic regime at each measuring temperature from 0 to 60 °C. The measuring temperature was carefully controlled by using a Peltier system with an accuracy of 0.1 °C with nitrogen as a thermally conductive inert gas. The time-temperature superposition principle was employed to obtain master curves of G′ and G′′ over a wide scaled angular frequency range, ωaT, at the standard temperature Ts ) 25 °C. The aT value was a shift factor for G′ and G′′ along the ω axis necessary to obtain smooth master curves. The simplest type time-temperature superposition procedure, which uses only one shift factor, aT, for the entire frequency region, was not perfectly applicable to the obtained data. This is shown by the typically insufficient master curves for the EHUT/C12 system shown in the Supporting Information, which were obtained with a single aT. Consequently, two distinct shift factors (one for each relaxation mode) were determined for the EHUT/C12 organogel system as described later in detail. From the temperature dependence of aT, the activation energies for the slow and fast relaxation modes were determined for the EHUT/C12 organogel system at each concentration c value. Preliminary experiments of dynamic shear flow birefringence were carried out on the EHUT/C12 organo-gel system by using a homemade system equipped with a Senarmont optical arrangement24 to measure birefringence precisely over an ω range similar to the dynamic viscoelastic measurements at room temperature, ca. 25 °C. Samples sandwiched between two glass slides were subjected to dynamic shear strain with an amplitude γ0 ) 1.5% generated by the sinusoidal vibration of the upper glass slide at a constant small amplitude. The birefringence signals calculated from optical retardation observed at the same frequency as the applied shear strain were decomposed into inphase and out-of-phase components, ∆n′ and ∆n′′, against the shear strain, using a phase-sensitive technique with lock-in amplifiers.25 Finally, the in-phase and out-of-phase strain-optical coefficients, O′ ()∆n′(2γ0)-1) and O′′ ()∆n′′(2γ0)-1), of the system were determined as functions of ω. Dielectric measurements were performed at 25 °C with use of two measuring systems,26,27 over an angular frequency ω range of 10-2 to 6 × 106 s-1. For the lower ω range (10-2 to 104), we used a homemade measuring system with a fast Fourier transform analyzer (Hitachi, VC-2440, Tokyo), which is based on a precise impedance analysis technique.28 For the ω range of 102 to 6 × 106 s-1, we used an LCR meter (Hewlett-Packard 4284A, Palo Alto). The real and imaginary parts of the electric permittivity, ′ and ′′, were calculated from the electric capacitance, C, and the conductance, σ, of each sample as functions of ω according to the following: ′ ) CC0-1 and ′′ ) σ (ωC0)-1, where C0 is the electric capacitance of the empty electrode cell, ca. 18 pF. Molecular Simulations. Molecular mechanics and dynamics (MD) simulations were performed with the TINKER package29 and the MM3 force field,30 which has been recently reparam-
Shikata et al.
Figure 1. Angular frequency, ω, dependencies of storage and loss moduli, G′ and G′′, for EHUT/C12 at c ) 40 mM and varying temperature from 0 to 60 °C.
etrized31 to take into account the weak nonbonding interactions such as π-π stacking, and hydrogen bonds. We use periodic boundary conditions to perform calculations on an infinite tube, with a unit cell containing 48 molecules. For each system, we perform molecular dynamics simulations in the canonical ensemble (constant volume, temperature, and the number of molecules), with an equilibration time of 100 ps. Then during the next 50 ps, we extract several snapshots along the MD trajectory and optimize the geometry, which provides information about the total energy of the full system. Results Dynamic Viscoelastic Behavior. The typical linear dynamic viscoelasticity of the EHUT/C12 system is shown by the frequency dependence of G′ and G′′ for a solution at c ) 40 mM and various temperatures from 0 to 60 °C (Figure 1). The linear shear amplitude region in which the system shows a linear viscoelastic response is small, ca. 10 mM. However, when c e 10 mM, a single major relaxation mode is observed in the lower ωaT region. These different modes (Figures 3 and 4) are analyzed in detail below. Flow Birefringence Behavior. Preliminary experimental results of dynamic flow birefringence for EHUT/C12 at c ) 30
Structure and Dynamics of a Supramolecular Polymer
Figure 2. Mater curves of storage and loss moduli, G′bT and G′′bT, against scaled angular frequency, ωaT, for EHUT/C12 at varying concentrations ranging from c ) 4 to 90 mM determined at the standard temperature of Ts ) 25 °C.
mM and 25 °C are shown in Figure 5 as the ω dependence of the in-phase and out-of-phase components of the strain-optical coefficients, O′ and O′′. Interestingly, although the major fast relaxation mode F1 is clearly visible on the mechanical spectrum, it is not detected by the birefringence experiment. Presently, we have no suitable explanation for this discrepancy, which must be related to the structure and relaxation mechanisms of the formed supramolecular polymer. If we simply assume the stress-optical rule, O′ ) KG′ and O′′ ) KG′′, which has been widely accepted for polymer rheology,35 for the slow relaxation mode obviously detected in Figure 5, then the stress-optical coefficient is roughly estimated to be K ) -1.8 × 10-7 Pa-1 (ratio of the plateau value of O′ to that of G′). A negative value of the stress-optical coefficient, K, is a characteristic of supramolecular structures having aromatic rings perpendicular to the long axis. For example, an aqueous system of a cationic surfactant, cetyltrimethylammonium bromide (CTAB), with aromatic additives such as sodium salicylate (NaSal) forms stable, long threadlike micelles and shows remarkable viscoelastic behavior.36,37 The K value for CTAB:NaSal/W has been determined to be K ) -3.1 × 10-7 Pa-1 irrespective of CTAB concentration, and Sal- ions bearing a phenyl ring are known to be intercalated perpendicularly into the threadlike micelles.38,39 In the case of the DO3B/C10 organogel, it is well-known that the DO3B molecules, bearing a phenyl ring, are arranged perpendicularly to the long axis of the helically growing supramolecular polymer, owing to 3-fold hydrogen bond formation between amide groups.40 Also in this case, preliminary experiments yield a negative stress-optical coefficient, ca. K ) -4.6 × 10-8 Pa-1. These results strongly suggest that the phenyl rings of the EHUT molecules are arranged perpendicularly to the long axis of the supramolecular polymer in the EHUT/C12 system. Dielectric Relaxation Behavior. The dielectric relaxation behavior, ′ and ′′ vs ω, for the EHUT/C12 system at c ) 8.0 and 90 mM and T ) 25 °C is shown in Figure 6 as a typical example. Constant ′ values close to 2.0 were obtained independently of ω, while the relationship ′′ ∝ ω-1 was observed for ′′ in the low ω region. Basically, σ is expressed as σ ) σd(ω) + σdc, where σd(ω) corresponds to the ω dependent part of conductance σ, and is responsible for the dielectric dispersion. On the other hand, σdc is the direct current conductance due to the presence of ionic impurities in the solution resulting from both EHUT and C12. If the value of σdc
J. Phys. Chem. B, Vol. 112, No. 29, 2008 8461 ) 2.3 × 10-15 S (or 4.3 × 1014 Ω) is assumed for the system at c ) 90 mM, the calculated σd(ω) diminishes to zero and yields a negligibly small ′′ over the ω range in which the solution shows the slow mode mechanical relaxation process S.28 Similar results were obtained for other solutions of EHUT/ C12 and also for the solvent, C12, with values of σdc slightly lower than the above value. These findings strongly suggest that there are no distinct dielectric dispersions in the EHUT/C12 system over the ω range examined. It is well-known that supramolecular polymers possessing a large total electric dipole moment along their long axis show distinctive dielectric dispersions at frequencies close to mechanical relaxation processes. For instance, this is the case for the supramolecular polymer formed in the DO3B/C10 system,26 and is due to the systematic parallel arrangement of dipolar groups, e.g., amide groups, along the chain axis. Some monourea compounds also show distinctive dielectric relaxation behavior in apolar solvents due to supramolecular construction.41,42 The fact that there are no dielectric dispersions in the EHUT/C12 system leads to the conclusion that the supramolecular polymer does not bear a finite total dipole moment along its long axis. Molecular Modeling. Molecular modeling was used to try and build supramolecular structures from EHUT molecules, which would account for all the experimental observations. First, the conformation of a monomer was probed with density functional theory (DFT) calculations. Because of the methyl group on the aromatic group, the ureido group in the ortho position cannot be coplanar with the aromatic group. This imposes a dihedral angle between the ureido group and the aromatic group of at least 50°. Second, based on infrared spectroscopy,13 it is known that all N-H groups are involved in hydrogen bonds. This means that to build a one-dimensional structure with all hydrogen bonds established, the two ureido groups of the bisurea monomers have to be either roughly parallel or roughly antiparallel to each other. Third, based on SANS experiments13 and the solvent effect23 described in the Introduction, it is known that the overall structure is tubular, with three molecules in the cross-section. With these constraints in mind, two different tubular structures were built, with ureido groups either antiparallel or parallel to each other. The unit cell contains 48 molecules, and the size of the box along the tube is 7.0 and 6.9 nm for the antiparallel and parallel tube, respectively. Molecular mechanics calculations were carried out to obtain minimized structures, which were then submitted to molecular dynamics simulations: the stable structures obtained are shown in Figures 7 and 8. In the figures large red and blue balls represent oxygen and nitrogen atoms, respectively, for enhancement to clarify the positions of the two atoms. The upper right pictures in Figures 7 and 8 schematically show the conformations of the basic three EHUT molecules including the location of hydrogen bonds in the tubular geometry, using simple ball and stick expression without atom enhancement. For both structures the ethyl-hexyl chains are pointing away from the tube, consequently we observe the formation of a cavity inside the tube with a diameter of about 7 Å. We observe that the aromatic groups are roughly perpendicular to the tube axis (85° and 67° on average, respectively), in agreement with the flow birefringence results. The calculated linear densities (0.66 and 0.68 Å-1, respectively) are in agreement with the experimental linear density derived from SANS (0.55 ( 0.12 Å-1).12,13 According to the calculations, both structures have a very similar stability (difference in total energy of ∆E ) 1.3 kJ mol-1 per molecule between the structures). In contrast, the dipole moment calculations show a very significant difference. The arrangement
8462 J. Phys. Chem. B, Vol. 112, No. 29, 2008
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Figure 3. Temperature dependencies of shift factors, aT and bT, to obtain the master curves of G′ and G′′ at c ) 40 (a) and 4 mM (b) for EHUT/C12.
Figure 4. Concentration, c, dependencies of magnitudes of relaxation strength of S, F1, and total modes, GS, GF1, and GT ()GS + GF1), and relaxation times, τS and τF1, at Ts ) 25 °C.
Figure 5. Dependencies of in-phase and out-of-phase strain-optical coefficients, O′ and O′′, on ω for EHUT/C12 at c ) 30 mM. This figure also contains scaled KG′ and KG′′ data with a stress-optical coefficient of K ) -1.8 × 10-7 Pa-1.
with parallel ureido groups (Figure 8) leads to a large dipole moment (392.4 D along the tube direction for a segment of 48 molecules), whereas the arrangement with antiparallel ureido groups (Figure 7) leads to a vanishingly small dipole moment (-0.9 D along the tube direction for a tube of 48 molecules). Consequently, only the structure shown in Figure 7 is consistent with all the experimental data available. Discussion Relationship between Dynamic Behavior and Structure. The rheological experiments described above also yield useful information about the dynamics of the self-assembled tubes. Coming back to the master curve shown in Figure 2, the
Figure 6. Dependencies of real and imaginary parts of electric permittivity, ′ and ′′, on ω for EHUT/C12 at c ) 8 and 90 mM and 25 °C.
Figure 7. Optimized tubular geometry for an EHUT supramolecular polymer chain determined by molecular mechanics and dynamics. The calculations were initiated from the monomer conformation with antiparallel ureido groups. The ethylhexyl side chains were included in the calculations, but replaced by methyl groups on the figure, for clarity. Large red and blue balls represent nitrogen and oxygen atoms, respectively, for enhancement. The upper right picture schematically shows the conformations of the basic three EHUT molecules in the tubular geometry, using simple ball and stick expression without atom enhancement.
dependence of the shift factors log aT and log bT on the reciprocal absolute temperature, T-1, is shown in panels a and b of Figure 3 for the system at c ) 40 and 4 mM, respectively, as typical examples. The value of log bT very weakly depends on T-1, which indicates that the structure of the supramolecular polymer formed in EHUT/C12 is unchanged between 0 and 60 °C. If all the mechanical relaxation modes existing in the system
Structure and Dynamics of a Supramolecular Polymer
Figure 8. Optimized tubular geometry for another EHUT supramolecular polymer chain determined by molecular mechanics and dynamics. The calculations were initiated from the monomer conformation with parallel ureido groups. The ethylhexyl side chains were included in the calculations, but replaced by methyl groups on the figure, for clarity. The upper right picture schematically shows the conformations of the basic three EHUT molecules in the tubular geometry, using simple ball and stick expression.
are governed by an Arrhenius type temperature dependence via the same activation energy, a straight linear relationship between log aT and T-1 should be found. However, there is a breaking point in the plots as seen in Figure 3a,b. The reason for the breaking point in the relationship is that the two relaxation processes possess different activation energies. On the one hand, in the temperature region higher than Ts ) 25 °C (T-1 lower than 3.36 × 10-3 K-1), shifting of G′ and G′′ curves is successful only for the slow relaxation mode S with a characteristic time of τs found at the flowing region. On the other hand, in the region where T-1 is larger than 3.36 × 10-3 K-1, shifting is successful for the fast relaxation mode F1 with a characteristic time of τF1 found at a high ω range. Consequently, for solutions with two major relaxation processes (c > 10 mM), the activation energies for both the slow and fast processes are estimated from the slopes of the straight portions of breaking lines observed in Figure 3a as ES* ) 110-120 kJ mol-1 and EF1* ≈ 80 kJ mol-1, respectively. The same ES* value as 120 kJ mol-1 has been reported already.32–34 These values are much larger than the activation energies for flow found in other organo-gel systems such as DO3B/C10, i.e., E* ≈ 32 kJ mol-1.40 This is in agreement with the tubular structure proposed above (Figure 7): scission of the EHUT supramolecular structure involves breaking 12 hydrogen bonds (4 per monomer), whereas scission of the DO3B structure involves breaking only 3 amide hydrogen bonds. In solutions with c e 10 mM showing a single major relaxation process corresponding to the slow mode, a similar value of ES* ) 110-120 kJ mol-1 is determined, whereas another activation energy, EF2* ≈ 12 kJ mol-1, is determined for a minor viscoelastic process in a region of 101 < ωaT < 102 s-1 as seen in Figure 3b. The value of EF2* is identical with that of the viscosity of the solvent, C12.43 Although the solutions at c e 10 mM do not have the major relaxation mode F1 in the high ω region, they still obviously keep a minor fast relaxation mode (F2), which looks like a shoulder without a maximum in G′′bT curves. Indeed, the slopes of G′′bT curves against aTω are not 1.0 but close to 0.5 in a double logarithmic scale as seen in Figure 2 (a relationship G′′bT ∝ aTω means the vanishing of mechanical relaxation processes). As a reference, the relationship G′′bT ) ηsωaT for the solvent, C12, at 25 °C without any relaxation modes is shown in Figure 2 as a solid line. Differences between G′′bT for the system and ηsωaT for
J. Phys. Chem. B, Vol. 112, No. 29, 2008 8463 C12 are assigned to the relaxation mode F2. The activation energy obtained above as E*F2 governs the temperature dependence of the fast relaxation F2 mode. The concentration dependence of the relaxation strength for the fast F1, slow S, and total modes (GF1, GS, and GT ) GF1 + GS) for the EHUT/C12 system, determined at Ts ) 25 °C, is plotted in Figure 4 in a double-logarithmic scale. Clearly, the proportionality to c2 is found in the entire c range for GT, in the range c > 30 mM for GF1 and in the range c < 10 mM for GS, respectively. The exponent of 2 for the relationship strongly suggests that the magnitude of each relaxation mode is proportional to the frequency of contacts (or entanglements) between supramolecular polymer chains formed in the system, because the contact is classified into the second order (chemical) reaction. These findings suggest that the total relaxation strength is proportional to the total density of entanglements of the supramolecular polymer chains, and some portions of entanglements working as the slow relaxation mode S are converted into the other entanglements for the fast relaxation mode F1 when c > 10 mM. The fraction of fast F1 mode increases with the frequency of contacts between supramolecular polymer chains. The magnitude of the total relaxation strength, GT ) GF1+ GS, in the mechanical behavior seen in Figure 4 is slightly smaller than that of other organo-gel systems such as DO3B/ C10 at the same c value. This means that the density of entanglements between chains of the formed supramolecular polymer for EHUT/C12 is lower than that of DO3B/C10 at the same c. In other words, the total sum length of the supramolecular polymer in EHUT/C12 is shorter than that in DO3B/C10. This is again in agreement with the structure proposed in Figure 7: because three monomers are contained in the cross-section of the supramolecular polymer chains in EHUT/C12, the linear density for EHUT/C12 (0.66 Å-1) is larger than that for DO3B/ C10 (0.28 Å-1).44 The dependence of τS and τF1 on c (Figure 4) is not as strong as that for the relaxation strength, and the relationship τS ∝ c0.6-0.8 is obtained approximately at c > 30 mM and Ts ) 25 °C as observed in a previous report.34 Although the same proportionality of τF1 ∝ c0.6-0.8 is found for the relaxation mode F1 and for the relaxation mode S, the magnitude of τF1 is almost 10-3 that of τS. Ducouret et al.34 have speculated that the relaxation mechanism for the slow mode S for the EHUT/C12 system is governed by a living polymer model proposed by Cates et al.45–47 for threadlike micelles systems formed by surfactant molecules in aqueous solutions. However, the constant values of τF1 ≈ 20 s and τS ≈ 0.02 s found in the c range lower than 30 mM as seen in Figure 4 cannot be explained by the living polymer model. A phantom-crossing model predicting relaxation times independent of the concentration of constituents would be more plausible for the mode S than the living polymer model. This phantom-crossing model has been previously proposed for aqueous threadlike micellar systems38,39 and organo-gel systems such as DO3B/C1040 which show a Maxwellian behavior with a single relaxation time. Exchange of hydrogen bonds at entanglement points could be the origin for the phantom-crossing process responsible for the entanglement release. Concerning the fast relaxation process, F1, we propose that it is due to “defects” in the structure. It is possible that some minor parts within the supramolecular polymer chains are composed of a more dynamic structure, such as a monomolecular (single-strand) filament structure. The interaction between the single-strand filaments, like entanglement formation and
8464 J. Phys. Chem. B, Vol. 112, No. 29, 2008 release, is presumably observed as the fast F1 mode. Such single-strand filaments have been demonstrated to be the major structure in chloroform or carbon tetrachloride solutions13 and on surfaces.48,49 From the above considerations, the overall structure of the supramolecular polymer chains in the EHUT/C12 system is an alternative connection of the thick tubular structure seen in Figure 7 and possibly single-strand filaments. The fraction of the more rigid tubular portion is much higher than that of the less rigid single-strand portion. Bending motions of semiflexible supramolecular polymer chains50 between entanglement points in the solvent, C12, feeling friction related directly to its viscosity, ηs, are possibly observed as the minor fast relaxation mode F2 with the relaxation time τF2, when the system possesses very little relaxation mode F1 at c < 10 mM. Conclusions A bisurea-type organo-gelator, 2,4-bis(2-ethylhexylureido)toluene (EHUT), dissolves in n-dodecane (C12) and makes an organo-gel system, EHUT/C12. EHUT/C12 contains long, stable supramolecular polymer chains, which build an entangled network showing remarkable viscoelastic behavior with two major mechanical relaxation modes. A slow relaxation mode with an approximately single relaxation time, τS, was observed in a flow region and the other, fast, relaxation mode with another relaxation time, τF1 (
