Letter pubs.acs.org/macroletters
Telechelic Polymer Hydrogels: Relation between the Microscopic Dynamics and Macroscopic Viscoelastic Response Thomas Zinn,† Lutz Willner,‡ and Reidar Lund*,† †
Department of Chemistry, University of Oslo, Postboks 1033 Blindern, 0315 Oslo, Norway Jülich Centre for Neutron Science JCNS and Institute for Complex Systems ICS, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
‡
S Supporting Information *
ABSTRACT: Telechelic polymers, that is, hydrophilic polymers with hydrophobic end-groups, spontaneously form hydrogels consisting of interconnected micelles. Here we investigate the relation between the microscopic dynamics determining the connectivity, that is, the lifetime of the physical bonds and the resulting rheological properties. This is achieved by quantitatively relating the chain exchange kinetics measured by time-resolved small-angle neutron scattering (TR-SANS) and the mechanical response obtained from linear oscillatory shear measurements. The results show that the characteristic relaxation time obtained from rheology coincides exactly with TR-SANS at intermediate concentrations. The activation energy, Ea, is concentrationindependent and remain exactly the same as for TR-SANS. Upon crossing the melting point, a discrete change in activation energy is observed showing the contribution from the enthalpy of fusion to the release/debridging process. The results clearly show that the mechanical response and connectivity indeed are controlled by molecular exchange processes. The relaxation time at the lowest concentration is found to be faster in rheology as compared to TR-SANS, which can be quantitatively attributed to entropic forces arising from conformational deformation of bridging chains.
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Boltzmann constant. Annable et al.2,9 found that the rheological relaxation time follows an Arrhenius behavior with an activation energy that scales linearly with the length of the hydrophobic block. The latter is also known for the activation energy found in experiments on the molecular exchange kinetics of n-alkylPEO micelles using time-resolved small-angle neutron scattering (TR-SANS).10,11 Since we know that the residence time of the chains within the micelle is controlled by the interfacial energy of the hydrophobic block, the connectivity of a telechelic hydrogel, and thus, the rheological properties are likely to be governed by the same lifetime. Here we explicitly relate the macroscopic mechanical properties of hydrogels with the microscopic exchange kinetics of the bonds by combining TR-SANS with rheology. The TRSANS method is based on mixing proteated and deuterated micelles and observe the molecular exchange by simply measuring the decay in intensity. As well-defined model system we have taken monofunctional and difunctional poly(ethylene oxide), PEO, of 5 and 10 kg/mol end-capped with C22H45 groups: C22-PEO5 and C22-PEO10-C22. By the choice of these polymers we are able to tune the time scale such that we can directly compare the rheological relaxation properties of the
he microscopic dynamics and diffusion of associative polymers that form hydrogels play a key role in controlling their viscosity and flow behavior. A simple example are telechelic polymers composed of a hydrophilic main chain functionalized with hydrophobic end-groups. In water these materials self-assemble into hydrogels consisting of interconnected nanostructured transient networks of micelles.1 The mechanical properties of such materials are strongly determined by the concentration of bridges spanning two micelles and the lifetime of noncovalent physical bonds, that is, controlled by temporary cross-links. From dynamic mechanical studies in the linear regime, it is known that telechelic gels almost behave like simple Maxwellian fluids characterized by a single relaxation time.2,3 It is generally accepted that the mechanical relaxation directly reflects the lifetime of the physical bonds and is thus directly related to the molecular exchange kinetics in such systems.4−6 However, a clear quantitative experimental verification of the relation between the microscopic dynamics and macroscopic mechanical properties is still lacking. Combining dynamic light scattering (DLS) and linear rheology, Nicolai and co-workers found a slow Q-independent relaxation mode in DLS that displays the same activation energy as found for the viscoelastic relaxation.7 In the classical transient network theory by Tanaka and Edwards8 the lifetime of a bond, τbond, provides an Arrhenius relation τbond ∝ exp(Ea/kBT), where Ea is the activation energy for disengagement of a bridge and kB the © XXXX American Chemical Society
Received: October 27, 2016 Accepted: November 18, 2016
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DOI: 10.1021/acsmacrolett.6b00824 ACS Macro Lett. 2016, 5, 1353−1356
Letter
ACS Macro Letters
concentration shows no sign of crystal-scattering but rather resembles that of a gel with both repulsive and attractive interactions. This picture is more clearly seen in Figure 1b), where the concentration dependence of the scattered intensity is shown. As observed, the low Q scattering exhibits predominantly attractive interactions (increase in intensity at low Q) at low concentration, to a gradual development of a structure factor peak reflecting repulsive interactions. More quantitatively, the scattered intensity could be nicely described using a core−shell model reported earlier12 combined with a structure factor, S(Q,ϕ), for “sticky hard spheres”14 (details of data modeling can be found in the SI). As seen this model provides an excellent description of the experimental data yielding detailed structural parameters of the transient network such as P (the number of hydrophobic stickers in the core), Rc (core radius) and Rm (overall micellar radius). Values are summarized in Table 1.
hydrogel and the exchange dynamics of equivalent micelles determined by the TR-SANS method. The monofunctionalized PEO polymer, C22-PEO5, was synthesized by living anionic polymerization as already described in previous publication.12 The synthesis of the corresponding C22-PEO10-C22 polymer was accomplished by intermolecular coupling reaction of the C22-PEO5 via the terminal hydroxy groups followed by fractionation from chloroform/n-heptane as solvent/nonsolvent pair for purification and enrichment of the difunctional component. Details of the synthesis and characterization can be found in the SI. A characteristic feature of associative polymers in aqueous solution in the dilute regime is a phase separation into a dense, sometimes, turbid gel and a dilute phase on top.7,13 Laflèche and co-workers7 have shown that phase separation can be avoided by using blends of mono- and difunctionalized PEO. For our system, optically clear, homogeneous gels were obtained for mixtures containing 50% or less of the difunctional polymers. The nanostructure of the gels was characterized using an optimized Bruker NANOSTAR small-angle X-ray scattering (SAXS) instrument (RECX, University of Oslo). Figure 1
Table 1. Micelle and Transient Network Characteristics of C22-PEO10-C22/C22-PEO5 Mixtures for f tel = 0 and f tel = 0.5a Ea (kJ/mol)
τ0 (10−17s)
f tel
ϕ (%)
P
Rm (Å)
Rc (Å)
T < Tm
T > Tm
T < Tm
0b 0.5 0.5 0.5
1 2.5 5 7.5
45 53 53 53
112 110 114 114
18 19 19 19
100 100 99 101
67 70 68
1.98 0.843 1.98 1.7
a The SAXS data were obtained at 20 °C. The table further includes the main fit parameters Ea (below and above the n-alkane melting point Tm) and τ0 (below Tm) as obtained from rheology for f tel = 0.5 at ϕ = 2.5, 5, and 7.5%. Ea and τ0 of C22-PEO5 micelles ( f tel = 0) were obtained from TR-SANS. bMeasured at 25 °C.
As reported earlier,12 the scattering at high Q exhibits a discontinuity at the melting point which leads to a pronounced increase in scattered intensities due to the change in electron density of the C22H45 micellar core upon heating consistent with densities determined independently using an Anton Paar DMA5000 densitometer. The rheology was measured using an Anton-Paar MCR301 rheometer equipped with a Peltier system allowing for a precise heating and cooling between 10 and 50 °C. Representative data of the angular frequency, ω, and the dependence of the loss shear modulus G″(ω) are shown in Figure 2a) for the f tel = 0.5 mixture at ϕ = 5%. A comparison with the data for the monofunctionalized polymer of similar viscosity at ϕ = 7.5% is shown in the SI. It is obvious that the presence of telechelic polymers leads to a pronounced peak in the loss modulus which does not appear for pure micellar solution at f tel = 0. In order to quantify the spectra and to define the position of the maximum, ωmax, we have used the empirical Havriliak−Negami (HN) description15 which also takes into account the nonMaxwellian nature of the spectra6 (see SI for details). We also observe a high frequency contribution that can be assigned to PEO chain dynamics.6,16 In order to describe most of the main relaxation, we employed the HN-model although a simple peak position analysis would give essentially the same results. The mean relaxation time was calculated according to τrheo = 2π/ ωmax. In order to compare the mechanical relaxation time τrheo, with the microscopic lifetime of a bond, τbond, the chain exchange kinetics was determined from equivalent micelles at
Figure 1. SAXS curves for C22-functionalized PEOs (d-labeled PEO) in aqueous solution: (a) data for f tel = 0 (multiplied by a factor of 50) and f tel = 0.5 at ϕ = 7.5% measured at 20 and 40 °C, respectively, (b) data for f tel = 0.5 solutions with different concentrations at 20 °C. The SAXS pattern for the f tel = 0 at ϕ = 1% is added for comparison. Solid lines represent least-squares model fit curves.
shows the scattered intensity, I(Q), normalized by concentration. I(Q) is plotted as a function of the scattering vector Q = 4π sin(ϑ/2)/λ, where λ is the wavelength and ϑ is the scattering angle. Figure 1a) shows the scattering curves of a 50% v/v mixture of C22-polymers ( f tel = 0.5) and for comparison for micelles formed by the pure (f tel = 0) monofunctionalized C22-PEO5 at 20 and 40 °C at a polymer volume fraction of ϕ = 7.5%. As can be seen the micelles of the monofunctionalized polymers exhibit the signature of a mesoscopic crystal with clear Bragg reflections that can be indexed to a bcc lattice. For f tel = 0.5 the scattering at the same 1354
DOI: 10.1021/acsmacrolett.6b00824 ACS Macro Lett. 2016, 5, 1353−1356
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ACS Macro Letters
Figure 3. Comparison of the relaxation time obtained by TR-SANS, τexch (ϕ = 1%), and oscillatory shear experiments, τrheo (ϕ = 2.5, 5, and 7.5%), in an Arrhenius representation above and below the n-alkane melting point of Tm = 29 °C determined from calorimetry. Inset: Concentration dependency of τ in a log−log plot for f tel = 0.5.
process, in agreement with earlier findings.11,19 Using the data for the heat capacity, Cp, reported in the SI, we obtain ΔHfus = ∫ Cp dT ≈ 26−29 kJ/mol, which coincides almost perfectly with the difference in the activation energy ΔEa = 30 kJ/mol. Hence, the crystalline-like packing inside the micellar cores leads to additional dynamic stability that is directly reflected in the rheological properties. The exact correspondence between the activation energies demonstrates very convincingly that the release process of the hydrophobic “stickers” from the core is the fundamental microscopic process governing the macroscopic mechanical properties in these physically associated networks. At 5% the relaxation times obtained from both experiments agree remarkably well, whereas at 2.5% the rheological relaxation is significantly faster (τrheo < τexch), while at 7.5%, the opposite is true, that is, τrheo > τexch. The molecular exchange kinetics of micelles is known to be independent of the concentration in the dilute regime10,20 but is slowed down at higher concentration as the micellar corona starts to overlap leading to a denser polymer network to diffuse through.21,22 Hence, at higher concentrations, it is likely that chain relaxation is slower due to increased chain overlap and topological interactions.6 Furthermore, it is found that τrheo scales approximately linearly with the polymer concentration which is stronger than what is predicted for homogeneous gel networks, τrheo ∼ ϕ2/3 (see inset in Figure 3).23 The faster rheological relaxation observed for the 2.5% solution points toward an entropic rather than an enthalpic contribution since the activation energies are identical in all cases. This might be due to the formation of “superbridges”, where more stress is carried inhomogeneously by fewer chains during deformation, which is also in agreement with the SAXS data that shows a less-defined network structure as well as the broader rheological spectra observed for the 2.5% solution (see SI). Inhomogeneous stretching of active “stress-bearing” chains will then lead to deformation from their spontaneous conformation which provides an entropic force. This was recognized by Tanaka and Edwards8 who calculated a bond lifetime under the influence of an elastic entropic spring force that exerts a “work”, W upon displacing the chain a distance Δx:
Figure 2. (a) Angular frequency dependence of the loss shear modulus G″ at different temperatures of a 50:50 mixture of C22-PEO-C22/C22PEO at ϕ = 5% (solid lines represent least-squares fit curves as obtained by Havriliak-Negami model. Inset: G′ (open symbols) and G″ (closed symbols) as a function of ϕ = 2.5, 5, and 7.5%. (b) TRSANS relaxation function R(t) as a function of time and temperature for f tel = 0 at ϕ = 1% in water. Inset comparison between the molecular exchange kinetics of f tel = 0 and f tel = 0.5 at 25°. Solid lines represent model fit-curves of R(t).
f tel = 0 in dilute solution at ϕ = 1% by TR-SANS using the kinetic zero average contrast technique as described in detail in ref 17. The resulting data in terms of a dimensionless relaxation function, R(t), defined as R(t) = [(I(t) − I∞)/(I(0) − I∞)]1/2, where I(0) and I∞ is the intensity at t = 0 and after random mixing, are shown in Figure 2b). In agreement with previously published results,10 the data display a clear linear decay in a semilogarithmic representation demonstrating a single exponential decay with a uniquely defined relaxation time: R(t) ∝ exp(−t/τexch). As shown in the SI, the exchange rate of the difunctional polymers is significantly slower as both ends need to be released for a successful exchange event as has been found for triblock copolymer micelles.18 In Figure 3, the temperature dependence of the characteristic relaxation times τexch and τrheo obtained either by TR-SANS or rheology are compared in an Arrhenius representation. As seen times from both methods display parallel lines in all cases indicating identical activation energies, Ea. The data follow in all cases an Arrhenius equation: τexch,rheo = τ0 exp(Ea/kB T), where τ0 is the attempt time. Furthermore, the data can be divided into regions with two distinct slopes, indicating a discrete change of Ea from 100 to 70 kJ/mol below and above the melting point at 28−29 °C, as determined independently by calorimetry. The same can be found for the deuterated analogues (see SI). This reflects a significant contribution from the enthalpy of fusion associated with the expulsion 1355
DOI: 10.1021/acsmacrolett.6b00824 ACS Macro Lett. 2016, 5, 1353−1356
ACS Macro Letters τrheo = τbond·exp(W /kBT ) = τ0·exp(Ea /kBT ) ·exp(−Fent ·Δx /kBT )
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ACKNOWLEDGMENTS We are grateful for financial support through the SYNKNOYT program of the Norwegian Research Council (Grant No. 228573). Parts of this work are based upon experiments performed at the KWS2 instrument operated by JCNS at Heinz-Meier Leibnitz Zentrum (MLZ), Garching, Germany. Dr. Vitaliy Pipich, MLZ/JCNS, Forschungszentrum Jülich, is greatly acknowledged for help with TR-SANS experiments.
(1)
Here the entropic force of a Gaussian chain is, Fent = 3kB T·Ree/ (Rθee)2, with Ree and Rθee the end-to-end distance in the gel and in the unperturbed solution state, respectively. The latter can be estimated by assuming Rθee = √6·Rg and taking Rg = 0.215· 24 M0.583 which gives Rθee ≈ 113 Å. The end-to-end distance in PEO , the gel can be estimated from the SAXS data and model fit parameters, using the mean distance between micelles: d = (4π/ 3ϕ)1/3·Rm = 606 Å. The distance between two neighboring core surfaces is then Ree ≈ d − 2Rc = 570 Å. Inserting these values we obtain a force constant of Fent = 0.13kBT/Å. In the theory of Tanaka and Edwards, Δx, is assumed to be the characteristic length of a monomer. Here we use a Δx = 5 Å as a mean Kuhn length of a monomer. Inserting these values, we obtain a factor 1.9 reduction, that is, τbond ≈ 2·τrheo. This simple estimate is in remarkable good agreement with the experiments: τexch ≈ τbond ≈ 2.3·τrheo. At higher concentrations, we expect the degree of chain deformation to decrease since the intermicellar distance decreases with ϕ−1/3 and increased chain overlap is expected to slow down the dynamics further. The acceleration is thus expected to diminish with increasing concentration as the networks becomes more homogeneous and explains the reason why we observe an almost full overlap between the rheological and TR-SANS relaxation times at intermediate concentrations, which for the present systems seems to be around 5%. To conclude, the present work unambiguously shows that the mechanical relaxation found in telechelic polymer hydrogels is directly related to their molecular exchange kinetics controlling the connectivity. The activation energy obtained from TR-SANS and rheology are identical in all cases but the relaxation time is concentration-dependent. At the intermediate concentration, the relaxation times coincide exactly, but at the lowest concentration, the viscoelastic relaxation is faster than the molecular exchange. We attribute this to the additional entropic force exerted on the chains bridging the micellar cores in the network. Our results also directly demonstrate the stabilizing role of crystalline-packing of the micellar cores which leads to larger activation barriers and thus slower chain release rates and slowed rheological relaxation. This work sheds significant light into the molecular origin of the viscoelastic properties of selfassembled physical polymer gels as well as other supramolecular and biological networks.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsmacrolett.6b00824. Additional experimental details, figures, and analytical details (PDF).
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Reidar Lund: 0000-0001-8017-6396 Notes
The authors declare no competing financial interest. 1356
DOI: 10.1021/acsmacrolett.6b00824 ACS Macro Lett. 2016, 5, 1353−1356
