Rheological Images of Dynamic Covalent Polymer Networks and

Feb 1, 2012 - determines the density of dynamic cross-links, thereby governing ... (12)N,N-Dimethylformamide (DMF), dimethyl sulfoxide (DMSO), acetic ...
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Rheological Images of Dynamic Covalent Polymer Networks and Mechanisms behind Mechanical and Self-Healing Properties Fuyong Liu,† Fuya Li,‡ Guohua Deng,*,‡ Yongming Chen,*,§ Baoqing Zhang,† Jun Zhang,† and Chen-Yang Liu*,† †

Beijing National Laboratory for Molecular Sciences, CAS Key Laboratory of Engineering Plastics, Joint Laboratory of Polymer Science and Materials, Institute of Chemistry, The Chinese Academy of Sciences, Beijing 100190, China ‡ School of Chemistry and Chemical Engineering, South China University of Technology, Guangzhou 510640, China § Beijing National Laboratory for Molecular Sciences, State Key Laboratory of Polymer Physics and Chemistry, Joint Laboratory of Polymer Science and Materials, Institute of Chemistry, The Chinese Academy of Sciences, Beijing 100190, China S Supporting Information *

ABSTRACT: In our previous work [Macromolecules 2010, 43, 1191−1194], we synthesized dynamic covalent cross-linked polymer gels through condensation of acylhydrazines at the chain ends of poly(ethylene oxide) (A2) and aldehyde groups in tris[(4-formylphenoxy)methy]ethane (B3) and reported reversible sol−gel transition and self-healing properties of the gels. For those dynamic gels, this paper examines the gelation kinetics and rheological behavior in pre- and postgelation stages and discusses the molecular mechanism underlying the mechanical and self-healing properties. The results showed that the condensation reaction before the critical gelation point can be treated as the pseudo-second-order reaction. The scaling exponent n (=0.75) for the frequency dependence of the complex moduli at the critical gel point, the exponent γ (=1.5) for the concentration dependence of the viscosity in the pregel regime, and the exponent z (=2.5) for the concentration dependence of the equilibrium modulus in the postgel regime were found to not exactly obey the relationship for covalent gels, n = z/(z + γ), possibly because of the dynamic nature of the gels. The terminal relaxation of the dynamic gels at high temperature (125 °C) accorded with the Maxwellian model, as often observed for transient associating networks. In contrast, at low temperature (25 °C) where this transient network reorganization was essentially quenched in a time scale of experiments (∼50 s), the uniaxial stress−strain behavior of the gel was well described by the classical model of rubber elasticity σeng = G(λ − 1/λ2) up to 300% stretch (as similar to the behavior of usual gels chemically cross-linked in a swollen state). Ultimately, the gel cut into two pieces was found to exhibit self-healing under ambient conditions in 8 and 24 h, respectively, when the edges of those pieces were coated and not coated with acid (catalyst for dynamic covalent bond formation).

1. INTRODUCTION The dynamic covalent bond is defined as a class of chemical bonds that can break and re-form under appropriate conditions.1−3 Dynamic covalent gels formed by such dynamic covalent bond not only have the stability of traditional covalent materials but also possess the environmental responsiveness of noncovalent supramolecular materials. The macroscopic properties of dynamic covalent gels can be tuned by adjusting the reactions involving such reversible covalent bond. Consequently, those dynamic gels are smart as supramolecular materials in response to external stimuli but have a higher stability because of the high strength of the reversible covalent bonds.4,5 Recently, one of the dynamic covalent bonds, acylhydrazone bond formed by the condensation of hydrazide with carbonyl group, has been receiving more attention. A series of polymers having main-chain dynamic covalent based on the acylhy© 2012 American Chemical Society

drazone bond have been synthesized by Lehn and coworkers.6,7 Polyacylhydrazones, the so-called dynamers,4,7 show the ability to exchange their components with outside monomers (to achieve spontaneous chemical modification of the original polymers).6,8 According to this exchange, the mechanical properties9 or the color/fluorescence10 of the original dynamers can be modified. Very recently, glycodynamers bearing side saccharide moieties were investigated by the Lehn group.11 In our previous work,12 bis(acylhydrazine)functionalized poly(ethylene oxide) (PEO) (A2) and tris[(4formylphenoxy)methyl]ethane (B3) were utilized to develop three-dimensional gel sustained by the dynamic acylhydrazone covalent bond. The gel possesses self-healing ability based on Received: November 7, 2011 Revised: January 23, 2012 Published: February 1, 2012 1636

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For this full characterization, we synthesized the dynamic gel utilizing acylhydrazone bonds and examined its reversible sol− gel transition and self-healing properties.12 In this paper, we make complete rheological characterization of this gel and discuss molecular mechanism(s) underlying its rheological properties. In the remaining part of this paper, we first explain the sample preparation and experimental conditions. Then, we discuss the gelation kinetics (including the effects of the gelator concentration and temperature), the mechanical properties of well-developed dynamic gel in relation to the properties of usual covalent gels, and the quantitative aspect of self-healing of the well-developed dynamic gel. Finally, the features of the dynamic covalent gel thus discussed are summarized as the conclusion of this paper.

the reversible dissociation and re-formation of those bonds and undergoes reversible sol−gel transitions according to the acidity in the system, as shown in Scheme 1. Scheme 1. Formation of Cross-Linked Polymer Gel Based on Reversible Covalent Acylhydrazone Bond

2. EXPERIMENTAL SECTION 2.1.1. Materials and Sample Preparation. Materials. Bis(acylhydrazine)-functionalized PEO polymer (A2; Mn of PEO part = 2000 g/mol) and tris[(4-formylphenoxy)methyl]ethane (B3) were synthesized as described in our previous work.12 N,N-Dimethylformamide (DMF), dimethyl sulfoxide (DMSO), acetic acid (HAc), hydrochloric acid (HCl, ∼37 wt %), and triethylamine (TEA) were purchased from Beijing Chemical Reagent Factory and used as received unless specially stated. 2.1.2. Sample Preparation. The gelator mass concentration was defined as

The stimuli responsiveness and mechanical properties of the dynamic covalent gels are highly dependent on the network architectures and the chemical structure of gelators. We can rheologically investigate the gelation kinetics and thermodynamics, which helps us to fully understand a relationship(s) between structure and macroscopic properties of those gels. Specifically, rheological measurements in the linear regime can detect evolution of the microstructures during the gelation process. The structure of well-developed gels can be also examined with those measurements. Thus, rheological measurements serve as a powerful tool to investigate the relationship between microstructure and macroscopic performance of the dynamic gels.13−17 The bonding efficiency under a given set of conditions (concentration, temperature, etc.) determines the density of dynamic cross-links, thereby governing the equilibrium modulus of the well-developed gels. This efficiency is in turn determined by the bonding rate constant (k1) and the dissociation rate constant (kd), the parameters specifying the equilibrium constant Keq (= k1/kd). k1 determines the critical gelation time (tgel) and can be evaluated with a rheological method. kd can be also estimated rheologically as a dynamic relaxation frequency of the gels, as demonstrated by Craig and co-workers15,18 for the supramolecular networks formed by metal−ligand interactions and also by Scherman and coworkers19 for a polymeric material that utilizes the strong yet reversible cucurbit[8]uril-based 1:1:1 ternary binding motif in water. Gels can be stretched enormously without rupture. The stress−strain behavior of the cross-linked gels (and rubbers) has been studied extensively,20−22 and the molecular mechanism of their remarkable elasticity (of entropic origin) has been explored.23−25 The strands of dynamic gels can pass through each other on the dissociation of dynamic cross-links and are quite different from the strands in usual cross-linked gels. The terminal relaxation of such dynamic gels in the linear regime is well described by the Maxwell model with a single relaxation time.26−28 However, to the best of our knowledge, the rheological behavior of the dynamic gels in both linear and nonlinear regimes has not been fully characterized.

cgelator,wt% =

m A2 + m B3 × 100 (wt%) m A2 + m B3 + ms + mHAc

(1)

where mA2, mB3 ms, and mHAc are the masses of A2, B3, solvent, and HAc, respectively. The HAc volume fraction was defined as

ϕ HAc,vol% =

VHAc × 100 (vol%) Vs + VHAc

(2)

where VHAc and Vs are the volumes of HAc and solvent, respectively. 2.1.3. Samples for Rheological Tests. A2 and B3 were dissolved in DMF separately, and then prescribed volumes of the two solutions containing equimolar functional groups were mixed and HAc was added subsequently. This equimolar mixture was immediately loaded on the rheometer for the rheological tests explained later. 2.1.4. Samples for Tensile Tests. The mixed solution was cast into a dumbbell-shaped mold (length 25 mm, width 10 mm, thickness 1 mm; the length and the width of the middle (neck) part of the sample are 5 and 4 mm, respectively) designed according to the size of the tensile fixture geometry of a rheometer used. The mold containing samples was kept in a sealed glass case for 12 h to obtain the stable gel samples. 2.1.5. Self-Healing. The dumbbell-shaped gel samples were mechanically cut into two pieces with a blade, and the two pieces were brought into contact in the mold. The healing automatically occurred at room temperature. To avoid evaporation of DMF from the samples, the healing was conducted in the sealed glass case saturated with DMF vapor. For comparison, the cross sections of some samples were coated with HAc (catalyst for bond formation). 2.2.1. Rheological Measurements. Dynamic Measurements. Dynamic measurements in the linear viscoelastic regime were carried with a stress-controlled rheometer of TA Instruments (AR-2000ex). The lower fixture incorporated a Peltier plate, providing temperature control, while the upper fixture was equipped with a parallel plate fixture of a diameter of 40 mm. Prior to the measurements, a strain-sweep test was conducted at a fixed angular frequency, ω = 6.28 rad/s. For all cases, the linear response was confirmed at the strain amplitude less than 10%. Thus, the dynamic test was performed with 5% amplitude. For monitoring the gelation kinetics, the equimolar solutions of A2 and B3 were mixed and loaded in the rheometer, and the dynamic measurement at ω = 6.28 rad/s at 25 °C was started 5 min after the 1637

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solution loading to measure the storage and loss moduli, G′ and G″, as functions of the reaction time. In addition, for systems with the concentration in the vicinity of the critical gelation concentration cgel, the dynamic frequency-sweep measurements at ω = 1−100 rad/s were also made repeatedly (from low ω to high ω) during the gelation process at 25 °C. One scan lasts 50 s by controlling the number of data points per decade, and the data were interpolated to given reaction times t to construct a master plots of G′ and G″ against ω for those t. For the materials after completion of the reaction, the dynamic frequency-sweep test was made at ω = 0.1−100 rad/s. In particular, for well-developed gels (having the polymer concentration well above cgel), the test was made at several temperatures, T = 25, 50, 75, 100, and 125 °C. This test enabled us to examine the equilibrium modulus (Ge) that changed with T. 2.2.2. Tensile Measurement. For well-developed gels after completion of the reaction, tensile measurements were conducted at 25 °C with TA ARES-G2 rheometer utilizing its solid tensile fixture that gripped a dumbbell-shaped specimen. The deformation rate was set at 0.6 mm/s. The middle (neck) part of the dumbbell-shaped sample was prestretched to 6 mm to make sure that all samples had the same initial state. The test was made for neat (as prepared) gels and also for self-healed gels explained earlier.

The concentrations of gelator, [A2] and [B3], control the gelation kinetics and affects the mechanical properties of gels. This kinetics was investigated by performing dynamic time sweep for samples with the gelator concentration ranging from 5.5 to 16.2 wt %. The storage modulus (G′) and loss modulus (G″) as a function of time are shown in Figure 1a. Similar time

3. RESULTS AND DISCUSSION 3.1. Gelation Kinetics of Dynamic Acylhydrazone Bond Gels. The condensation reaction of acylhydrazine and aldehyde groups, yielding acylhydrazone bonds, proceeds by a stepwise mechanism involving the formation of an intermediate hemiaminal.29 At low pH (achieved with HAc), hemiaminal formation is the rate-determining step.30 In addition, the water molecules generated by the dehydration of the hemiaminal were immediately absorbed by the HAc, so the reaction can be represented as Scheme 2.30 Scheme 2. Equilibrium for the Reversible Hydrazone Formation30

The rate equations for the above reaction can be written as d[A2] = −k1[A2][B3] + kd[A·B] dt

(3)

d[A·B] = k1[A2][B3] − kd[A·B] dt

(4)

Here, [A2] and [B3] are the molar concentration of the acylhydrazine group in A2 and molar concentration of the aldehyde group in B3, respectively, and [A·B] is the molar concentration of the characteristic functional group in product. k1 and kd are the bonding and the dissociation rate constants. At equilibrium, d[A2]/dt = d[A·B]/dt = 0. Thus, the equilibrium constant Keq is expressed in terms of k1 and kd as K eq =

k [A·B] = 1 [A2][B3] kd

Figure 1. (a) Dynamic storage G′ (solid symbol) and loss G″ (open symbol) modulus against time for samples with different gelator concentrations (5.5, 7.2, 8.0, 10.4, and 16.2 wt %). (b) Dynamic frequency spectrum at different times near the tgel for the sample with 5.5 wt % gelator and (c) for the sample with 7.2 wt % gelator. HAc volume fraction is 13.0 vol %.

evolution of G′ and G″ (increases of these moduli) was observed for different samples. At the beginning of the reaction, the system shows a liquidlike character, G′ being much smaller than G″. As the time progresses, G″ increases gradually whereas G′ shows a sharp increase in the vicinity of the gel point and becomes larger than G″. Finally, the sample shows solidlike behavior characterized with G′ ≫ G″ (G′ in this zone is equivalent to the equilibrium modulus Ge). As noted in Figure 1a, a characteristic time, tcross, defined as the time at which G′ =

(5)

The HAc catalyst plays an important role in the gelation kinetics. Thus, an effect(s) of its concentration on the reaction rate was examined at first, and the results are summarized in the Supporting Information. On the basis of those results, the HAc volume fraction was fixed at 13.0 vol % for the data shown in this paper. 1638

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processes. Thus, we utilize the real tgel data in the following argument for the gelation kinetics. In Figure 2, the tgel data are plotted against 1/[A2]0. We note that tgel is almost proportional to 1/[A2]0, which suggests that

G″, decreases, and the plateau of G′ increases with increasing gelator concentration. At low temperature, T = 25 °C, our gel had a very large Keq (= 8000 M−1), as explained later in section 3.3.1. For this case, the dissociation term kd[A·B] in eq 3 can be safely neglected in an early stage of gelation, and the rate equation for the reaction of equimolar functional groups ([A2] = [B3]) is satisfactorily approximated as d[A2] = −k1[A2][B3] = −k1[A2]2 dt

(6)

In fact, for such large Keq, the exact and approximate rate equations (eqs 3 and 6) gave indistinguishable time evolution of [A2] in a very wide range of time (including the range of time up to critical gelation), as explained in the Appendix. Thus, we made the analysis of gelation kinetics at low T on the basis of eq 6, as explained below. (However, it should be also noted that eq 6 becomes invalid at high T where the dissociation becomes important.) The extent of reaction is defined by p=1−

[A2] [A2]0

Figure 2. Dependence of tgel on reciprocal of the initial molar concentration of acylhydrazine groups in A2, 1/[A2]0. The solid line is a linear fit of the data. HAc volume fraction is 13.0 vol %.

the gelation reaction up to tgel is satisfactorily treated as the second-order reaction and the above analysis based on eq 6 is basically valid. At the same time, we note minor deviation from the proportionality between the tgel data and 1/[A2]0. This minor deviation could be attributed to a small deviation of the equimolar condition of A2 and B3 and also to a competing reaction that forms intramolecular loops not contributing to the gelation. (In addition, eq 6 gives a large but finite tgel value even for a very small [A2]0 (cf. eq 9) while the rheologically determined tgel diverges if [A2]0 is smaller than the critical gelation threshold, which could also contribute to the minor deviation from the proportionality between tgel and 1/[A2]0 seen in Figure 2.) Nevertheless, the plots in Figure 2 demonstrate the basic validity of eq 6 (and eq 9) at times up to tgel, as explained above. Thus, we may evaluate the bonding rate constant k1 from those plots: k1 ≅ 0.03 s−1 M−1 (which corresponds to the solid line that fits the data points). For samples having 4.8−16.7 vol % HAc, k1 changed in the range of 0.003−0.043 s−1 M−1 (as evaluated from the tgel data shown in Figure S1a of the Supporting Information), which indicates that k1 increases with the HAc catalyst concentration. Levrand and co-workers30,37 found that k1 for the reaction of hydrazides and aldehydes at a fixed pH (= 2.47) varies in 0.0001−0.0012 s−1 according to a type of the substituting groups in hydrazides and aldehydes. In their case, the reactions between small molecules were treated as pseudo-first-order kinetics, which makes a contrast between their gel and ours, the latter containing the polymeric component. 3.2. Rheological Behavior of Gels and Sols after Full Reaction. Figures 3a and 3b show the ω dependence of the G′ and G″ data at 25 °C measured for the equimolar reaction mixtures (samples) of various gelator concentrations c after a sufficiently long reaction time. We first note that welldeveloped gels were formed at high c (≥4.2 wt %) to exhibit ω-independent G′ and much smaller G″ (not shown here for clarity of the plots). Those gels behave as elastic solids in the range of ω examined, and their G′ data are regarded as the equilibrium modulus Ge. The c dependence of those Ge data is shown in Figure 3c. (Note, however, that the gel samples stored in glass vessels flowed with their own weight at 25 °C in a time

(7)

where [A2]0 is the initial molar concentration of the acylhydrazine group in A2. Integrating eq 6, we can easily find that the time evolution of p is described by

1 = k1[A2]0 t + 1 1−p

(8)

Consequently, the critical gelation time tgel is specified as pc k1−1[A2]0−1 tgel = 1 − pc (9) where pc is the extent of reaction at the critical gelation point. For the case of the equimolar functional groups examined here, pc is estimated to be a constant independent of [A]0, pc ≅ 0.8, because the average degree of functional groups is f ̅ = 2.4 and pc = 2/f ̅ according to mean-field theory.31 Thus, the simple analysis predicts that tgel is proportional to 1/[A]0 (see eq 9). Utilizing the tgel data, we examine this prediction, as explained below. Experimentally, tgel is obtained as the time where G′ and G″ exhibit the critical gel behavior, G′ ∝ G″ ∝ ωn with n being the critical power-law exponent.32−34 This tgel was determined from the repeated frequency-sweep test as reported in the literature.32−34 In our test, each sweep took 50 s by adequately choosing the number of data points per decade, and the data were interpolated to a given time of reaction. As an example, Figures 1b and 1c show such isochronal data of G′ and G″ obtained for 5.5 and 7.2 wt % samples. The tgel is estimated to be 3350 and 2520 s for the 5.5 and 7.2 wt % samples, respectively.35 In relation to these results, a comment is made for tcross, an easily determined time at which G′ = G″ in Figure 1a. This tcross can be utilized as an apparent tgel,36 although the real tgel obtained for the G′ and G″ (>G′) data exhibiting the critical power-law behavior is always shorter than the apparent tgel. In fact, the difference between the two times was negligible for high concentration samples because the gelation was rapid for those samples. Nevertheless, the real and apparent tgel were very different for low-concentration samples exhibiting slow gelation 1639

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Typical gels are rheologically classified in three regimes characterized by the following scaling relationships.32,33,38,39 In the pregel regime η0 ∝ ε−γ

(10)

At the critical gel point G″ ∼ G′ ∼ ωn

(11)

G″(ω)/G′(ω) = tan δ = tan(n π/2)

(12)

In the postgel regime Ge ∝ εz

(13)

Here, η0 is the zero shear viscosity, ε is the relative distance of a variable q from the gel point qg: ε = |q − qg | /qg

(14)

q can be either the extent of reaction, the gelation time, the temperature, or the gelator concentration. γ, n, and z are the scaling exponents for the three scaling laws. In the simplest case, the exponents are expected to follow the relationship n = z /(z + γ)

(15)

Here, we focus on the gelator concentration c and examine the above scaling relationships. The critical concentration cg can be accurately determined by focusing on loss tangent, tan δ.32,33 The c dependence of tan δ at various ω is shown in Figure 4a: tan δ is independent of ω for c = 3.7 wt %, and thus cg = 3.7 wt % according to the Winter−Chambon criterion (eq 12).32,33 The zero-shear viscosity η0 of the samples with c < cg (= 3.7 wt %) was obtained from steady flow measurements (cf. Figure S2 shown in the Supporting Information). Figure 4b presents the log−log plots of η0 against ε = |c − cg|/cg. Equation 10 with γ = 1.5 describes the data well. The Ge data (Figure 3c) are replotted against ε in Figure 4c (see filled circles). Those data are well described by eq 13 with z = 2.5. The above exponents, γ = 1.5 and z = 2.5, are close to the predictions by Martin et al. using a percolation model.40−42 If eq 15 is applicable to our dynamic covalent gels, n is predicted to be 0.63. However, the observed n value (= 0.75 for cg = 3.7 wt %; cf. Figure 3b) is larger than this prediction, which possibly reflected the dynamic covalent nature of our gel (that can relax through either the global motion of the self-similar gel network or slow thermal dissociation of the bonds). In relation to this point, we remember that a similar deviation from eq 15 has been noted for poly(vinyl chloride) (PVC)/bis(2-ethylhexyl) phthalate (DOP) gels systems (n = 0.75, γ = 1.5 ± 0.1, and z = 2.6 ± 0.1).16,43,44 Thus, eq 15 is not necessary valid for all physical gels. A further study is desired for this issue. 3.3. Mechanical Properties of Well-Developed Gels with High Gelator Concentration. As noted in Figure 3a, well-developed gels were formed after sufficiently long reaction of the samples with high gelator concentration (and at the HAc catalyst volume fraction = 13.0 vol %). The 2.5th power law relationship between the Ge data and the relative gelator concentration ε (Figure 4c) reflects the gel network structure at 25 °C. The temperature dependence of Ge and the tensile behavior of gels at 25 °C are examined below to further investigate the feature of the dynamic covalent bonds. 3.3.1. Effect of Temperature on Ge. For polymer melts, an increase of temperature (T) accelerates the segment and terminal relaxation processes but hardly affects the entangle-

Figure 3. (a) Dynamic storage (G′) modulus against frequency (ω) for the well-gelated samples with different gelator concentrations above the critical point. (b) Dynamic storage G′ (solid symbol) and loss G″ (open symbol) modulus against frequency for the samples around the critical point. The samples with 3.7 and 3.2 wt % gelator have been reacted for 24 h. The solid lines are a least-squares fit of the G′ and G″ data for the sample with 3.7 wt % gelator, and the slope = 0.75 was labeled. (c) Equilibrium modulus (Ge) as a function of gelator concentration. The error is estimated to be ±20%. HAc volume fraction is 13.0 vol %.

scale of a few days, which demonstrates that those samples behaved as dynamic covalent gels having a long but finite dissociation time at 25 °C, not as permanently cross-linked gels.) In Figure 3b, we also note that the mixture with the low c (3.2 wt %) behaves as a viscoelastic fluid with a well-defined relaxation time. This behavior suggests that the network was not fully developed throughout the system at such low concentration. Finally, for c = 3.7 wt %, G′ and G″ exhibit the power-law behavior (eq 11) characteristic of a critical gel.32,33 1640

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Figure 5. Dynamic storage G′ (solid symbol) and loss G″ (open symbol) against frequency (ω) at different temperatures. The solid curves are the predictions of the Maxwell model. Gelator concentration is 10.4 wt %, and HAc volume fraction is 13.0 vol %.

125 °C, the crossover point of G′ and G″ shifts to a higher frequency, and the well-known “terminal” regime (G′ ∼ ω2, G″ ∼ ω) is observed. The solid curves in Figure 5 show the results of Maxwellian fitting. The fit is well achieved,27,28 as noted for transient networks relaxing on the dissociation of the crosslinks.47−49 The flow of our dynamic gels at high T reflects the reversible nature of the acylhydrazone bond. Since the molar concentration of HAc is much higher than the gelator concentration, the water molecules generated in the reaction are mostly bounded to HAc (cf. Scheme 2). Therefore, the dissociation reaction of acylhydrazone bond can be treated as first-order, and the dissociation rate constant (kd) can be calculated from the crossover frequency of G′ and G″ (= terminal relaxation frequency for the Maxwellian relaxation) as kd = ωcross (see Figure 6a in ref 15. Thus, Figure 5 gives kd = 0.1 and 0.01 s−1 for the sample with 10.4 wt % gelator at 125 and 100 °C, respectively. This decrease of kd with decreasing T suggests that the dissociation governing the terminal relaxation becomes very slow at low T (= 25 °C, for example), which is in harmony with the observation explained earlier: The well-developed gels at 25 °C flowed with their own weight only in a time scale of a few days. Since the flow behavior was not experimentally detected in Figure 5 at low T, kd and the corresponding equilibrium constant Keq at low T cannot be accurately determined from the rheological data. Thus, NMR experiments were conducted to determinate the equilibrium constant Keq at 25 °C. (The results, 1H NMR spectra of free and bonded B3, are shown in Figures S3 and S4 of the Supporting g Information.) The Keq value thus obtained, 8000 M−1 at 25 °C, was very large, confirming that the dissociation is negligibly slow and the crosslinking reaction approached 100% conversion at 25 °C (as discussed earlier in relation to the gelation kinetics). 3.3.2. Tensile Properties of Gels at Low T. The tensile test was performed at 25 °C for the well-developed gels with the gelator concentration ranging from 5.5 to 16.2 wt %. Figure 6a presents plots of engineering stress (σeng) against extension ratio (λ = l/l0). The plots are similar to those seen for soft rubbers. The σeng and λ values at break increase with increasing the gelator concentration. In particular, σeng at break point reaches 0.32 MPa (true stress σtrue is 1.8 MPa) and λ at break exceeds 500% for the sample with 16.2 wt % gelator.

Figure 4. (a) Gelator concentration dependence of tan δ at different frequencies to determine cg according to the Winter−Chambon criterion. (b) Viscosity (η) as a function of the relative gelator concentration (ε = (c − cg)/cg, cg = 3.7 wt %), the error is estimated to be ±15% due to the very low viscosity. (c) Equilibrium modulus (Ge) as a function of the relative gelator concentration (ε = (c − cg)/cg, cg = 3.7 wt %). The shear modulus (Ge) obtained from the tensile test (section 3.3.2) are compared with Ge measured by small-amplitude oscillatory shear (SAOS) test. Solid line is a least-squares fit of the data, and the slope is labeled.

ment plateau modulus. In contrast, for our dynamic covalent gels sustained by acylhydrazone bonds, the hydrolysis reaction is significantly enhanced at high T,45,46 thereby reducing the association/dissociation equilibrium constant Keq and decreasing the equilibrium modulus Ge. In fact, this decrease of Ge at high T is noted in Figure 5 where the G′ and G″ data of the gel with the gelator concentration of 10.4 wt % at various T are plotted against ω. Clearly, G′ decreases with increasing T (which corresponds to the decrease of Ge) and shows the flow behavior in the experimental window at T ≥ 100 °C. G″ exhibits the corresponding behavior, the terminal peak associated with the cross with the G′ curve. In particular, at 1641

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is essentially quenched in the time scale (∼50 s) of the tensile test. In Figure 6c, the σeng−λ plot for the sample with 16.2 wt % gelator is shown in a wider range of λ (up to 5). The prediction of eq 16 with Ge = 0.052 MPa is shown with the solid curve. Clearly, the data follow the neo-Hookean relationship for λ < 3 and exhibit the hardening for λ > 3. Similar behavior has long been noted for swollen cross-linked rubbers in a wide range of λ52−54 (for example, Figure 5 in ref 54). In fact, Urayama and co-workers54,55 made extensive biaxial elongation tests to demonstrate that the gels showing the neo-Hookean behavior (followed by hardening at large λ) in uniaxial test do not exhibit the corresponding behavior in biaxial tests. Namely, the neoHookean relationship does not hold in a tensorial sense because of the interaction between the gel strands. The dynamic gel examined in this study behaves very similarly to the swollen chemical gels at least in the time scale of experiments (∼50 s) because the dissociation is essentially quenched at 25 °C (Keq = 8000 M−1). Thus, its apparent neo-Hookean behavior (Figure 6b) is to be interpreted in the same way as for the swollen cross-linked gels.54,55 Despite this similarity (at relatively short times) observed for our dynamic covalent gels and chemically cross-linked gels, we also note a difference in a very long time scale. This difference is most clearly demonstrated for the self-healing behavior occurring in a time scale of a day, as described below. 3.4. Self-Healing of Well-Developed Gels. In general, cracked dynamic gels can exhibit healing because of the reversibility of acylhydrazone bonds.12,56 In fact, the dynamic gel with 10.4 wt % gelator cut into two pieces exhibited the selfhealing when the two pieces are simply kept in contact for 7 h.12 In this study, the tensile test was performed on the gel with 16.2 wt % gelator to quantitatively evaluate this self-healing ability. For this purpose, dumbbell-shaped samples were cut into two pieces with a blade, the cut surfaces were brought together to allow self-healing at 25 °C for a given time (2−24 h) and with/without HAc coating at the cut surfaces, and healed specimen was subjected to the tensile test at 25 °C. The results of this test are shown in Figure 7. HAc works as a catalyst to accelerate the acylhydrazone bond formation. Even without this catalyst, the σeng−λ curve of the original sample (without blade-cutting) was almost recovered after self-healing for 24 h, as shown in Figure 7a. This recovery was observed in a shorter healing time, 8 h, in the presence of HAc (see Figure 7b). For both cases, the σeng−λ curves of the healed samples up to their break points were very close to that of the original sample, and the σeng and λ values at the break increased with the healing time. These results demonstrates that the acylhydrazone bonds are spontaneously reformed in a time scale of a day even at low T (25 °C), which distinguishes our dynamic covalent gels from usual chemically cross-linked gels. Recently, Leibler and co-workers57 designed a self-healing and thermoreversible rubber utilizing hydrogen bonds. For the supramolecular network plasticized with 11 wt % dodecane, σtrue at break point is about 3 MPa and strain at break exceeds 500%. The fractured material can almost recover its original properties after self-healing for 3 h at ambient temperature. Burattini and co-workers58 obtained a dimensionally stable and flexible material utilizing π−π stacking interactions. The 100% recovery of tensile modulus of the material was achieved in 5 min after healing at 50 °C. These two systems, based on the hydrogen bonding and π−π stacking, exhibit much faster self-

Figure 6. (a) Engineering stress (σeng) against extension ratio (λ) for the gels with different gelator concentrations. (b) σeng against λ − 1/λ2 for the gels with different gelator concentrations. The slope was labeled. (c) σeng against λ for gel with 16.2 wt % gelator and 13.0 vol % HAc. The solid curve is the prediction of classical model eq 14 with G = 0.052 MPa.

In the classical theory of rubber elasticity,31,50,51 the engineering stress in uniaxial deformation is written in terms of λ and the equilibrium shear modulus (Ge): σeng = Ge(λ − 1/λ2)

(16)

The data in Figure 6a are redrawn in Figure 6b as plots of σeng against λ − 1/λ2. All four samples clearly obey the neoHookean relationship, eq 16, up to λ = 3 (300% stretch), after a moderate adjustment of the Ge value (increase, by a factor of 40%, from the Ge value obtained in the dynamic test; cf. Figure 4c). This adjustment was necessary because of unavoidable prestretching treatment in the tensile test that shifts the unstretched state. Despite the adjustment, the results seen in Figure 6b demonstrate basic validity of the neo-Hookean relationship for the dynamic gel at 25 °C where the dissociation 1642

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concentration dependence of the equilibrium modulus in the postgel regime were found to not exactly obey the relationship for covalent gels, n = z/(z + γ), possibly because of the dynamic nature of the gels. The terminal relaxation of dynamic gels at the high temperature (125 °C) was well described by the Maxwell model, as noted for transient associating networks. In contrast, at low temperature (25 °C) where this transient network dissociation (reorganization) was essentially quenched in the time scale of experiments (∼50 s), the stress−strain behavior of the gel was close to prediction of the classical model of rubber elasticity σeng = G(λ − 1/λ2) up to 300% stretch, as similar to the behavior of usual chemically cross-linked gels in a swollen state. Finally, the dynamic gel can completely recover to the original properties after self-healing for 24 h under ambient conditions. Coating HAc on two cut surfaces of gel material accelerated this healing.

Figure 7. (a) Engineering stress (σeng) against extension ratio (λ) for the gel self-healed different times. The dumbbell-shaped gels were cut into two pieces, and the two pieces were brought into contact together in the mold immediately (waiting time less than 1 min). The tensile test was performed at room temperature on ARES-G2. (b) Engineering stress (σeng) against λ for the gel self-healed different times with the cross-section coated with HAc after cutting off. Gelator concentration is 16.2 wt %, and HAc volume fraction is 13.0 vol %.

Figure 8. Evolution of [A2](t)/[A2]0 with time.

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APPENDIX. RIGOROUS AND APPROXIMATE SOLUTIONS OF THE RATE EQUATIONS OF GELATION The rate equations for the reaction shown in the Scheme 2 are specified as

healing compared to our dynamic gels. In addition, the bonding points in these systems are distributed along the whole backbone of polymers, and the bonding (cross-linking) density and the modulus are higher in those systems than in our gel, the latter being cross-linked only at the chain ends. Nevertheless, our dynamic covalent gels have some advantages: the gel with low solid content (16.2 wt % gelator) behaves, in a wide range of T, as a soft but tough material having a relatively high shear modulus (4.5 × 104 Pa) and a considerably large extensibility (λ ∼ 500% at break).

d[A2] = −k1[A2][B3] + kd[A·B] dt

(A1)

d[A·B] = k1[A2][B3] − kd[A·B] dt

(A2)

(Equations A1 and A2 are identical to eqs 3 and 4 in the text.) From eqs A1 and A2, we immediately find

4. CONCLUSIONS Mixing tris[(4-formylphenoxy)methy]ethane (B3) with an acylhydrazine end-capped poly(ethylene oxide) (A2) yielded a novel dynamic covalent cross-linked polymer gel with reversible sol−gel transition and self-healing properties. Gelation kinetics, rheological behavior at pre- and postgelation, and mechanical properties of polymer gels were investigated. The gelation kinetics was highly influenced by the gelator concentration (and also by the HAc catalyst content). The reaction before the critical gelation time can be treated as the pseudo second order, and the bonding rate constant k1 changed with the HAc content. The scaling exponent n (=0.75) for the frequency dependence of the complex moduli at the critical gel point, the exponent γ (=1.5) for the concentration dependence of the viscosity in the pregel regime, and the exponent z (=2.5) for the

d[A2] d[A·B] + =0 dt dt

(A3)

and thus [A·B] = [A2]0 − [A2]

at any time t

(A4)

Substituting eq A4 in eq A1, we find, for the equimolar reaction ([A2]0 = [B3]0) dx(t ) = −k1{x(t )}2 + kd{[A2]0 − x(t )} dt with x(t ) = [A2] at t 1643

(A5)

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(6) Ono, T.; Nobori, T.; Lehn, J. M. Chem. Commun. 2005, 1522− 1524. (7) Lehn, J. M. Prog. Polym. Sci. 2005, 30, 814−831. (8) Skene, W. G.; Lehn, J. M. P. Proc. Natl. Acad. Sci. U. S. A. 2004, 101, 8270−8275. (9) Ono, T.; Fujii, S.; Nobori, T.; Lehn, J. M. Chem. Commun. 2007, 46−48. (10) Ono, T.; Fujii, S.; Nobori, T.; Lehn, J. M. Chem. Commun. 2007, 4360−4362. (11) Ruff, Y.; Buhler, E.; Candau, S. J.; Kesselman, E.; Talmon, Y.; Lehn, J. M. J. Am. Chem. Soc. 2010, 132, 2573−2584. (12) Deng, G. H.; Tang, C. M.; Li, F. Y.; Jiang, H. F.; Chen, Y. M. Macromolecules 2010, 43, 1191−1194. (13) Mours, M.; Winter, H. H. Macromolecules 1996, 29, 7221−7229. (14) Winter, H. H.; Morganelli, P.; Chambon, F. Macromolecules 1988, 21, 532−535. (15) Yount, W. C.; Loveless, D. M.; Craig, S. L. J. Am. Chem. Soc. 2005, 127, 14488−14496. (16) Li, L.; Aoki, Y. Macromolecules 1997, 30, 7835−7841. (17) Stadler, F. J.; Pyckhout-Hintzen, W.; Schumers, J. M.; Fustin, C. A.; Gohy, J. F.; Bailly, C. Macromolecules 2009, 42, 6181−6192. (18) Loveless, D. M.; Jeon, S. L.; Craig, S. L. Macromolecules 2005, 38, 10171−10177. (19) Appel, E. A.; Biedermann, F.; Rauwald, U.; Jones, S. T.; Zayed, J. M.; Scherman, O. A. J. Am. Chem. Soc. 2010, 132, 14251−14260. (20) Dossin, L. M.; Graessley, W. W. Macromolecules 1979, 12, 123− 130. (21) Jong, L.; Stein, R. S. Macromolecules 1991, 24, 2323−2329. (22) Ramzi, A.; Hakiki, A.; Bastide, J.; Boue, F. Macromolecules 1997, 30, 2963−2977. (23) Deam, R. T.; Edwards, S. F. Philos. Trans. R. Soc. London, A 1976, 280, 317−353. (24) Rubinstein, M.; Panyukov, S. Macromolecules 2002, 35, 6670− 6686. (25) Termonia, Y. Macromolecules 1994, 27, 7378−7381. (26) Tanaka, F.; Edwards, S. F. Macromolecules 1992, 25, 1516−1523. (27) McLeish, T. C. B. Adv. Phys. 2002, 51, 1379−1527. (28) Cates, M. E.; Fielding, S. M. Adv. Phys. 2006, 55, 799−879. (29) Sayer, J. M.; Peskin, M.; Jencks, W. P. J. Am. Chem. Soc. 1973, 95, 4277−4287. (30) Levrand, B.; Ruff, Y.; Lehn, J. M.; Herrmann, A. Chem. Commun. 2006, 2965−2967. (31) Rubinstein, M.; Colby, R. H. Polymer Physics; Oxford University Press: New York, 2003. (32) Winter, H. H. Polym. Eng. Sci. 1987, 27, 1698−1702. (33) Chambon, F.; Petrovic, Z. S.; Macknight, W. J.; Winter, H. H. Macromolecules 1986, 19, 2146−2149. (34) Takahashi, M.; Yokoyama, K.; Masuda, T.; Takigawa, T. J. Chem. Phys. 1994, 101, 798−804. (35) The error of tgel estimated is about ±10%, due to purity of A2 and B3 from different batches(such as the degree of functionalities, molecular weight distribution of PEO in A2) and humidity of testing environment. It is worth noting that the apparent slope of the modulus is always bigger than the real one, since the dynamic frequency sweep was performed from the low frequency to the high frequency. (36) Tung, C. Y. M.; Dynes, P. J. J. Appl. Polym. Sci. 1982, 27, 569− 574. (37) Levrand, B.; Fieber, W.; Lehn, J. M.; Herrmann, A. Helv. Chim. Acta 2007, 90, 2281−2314. (38) Winter, H. H.; Chambon, F. J. Rheol. 1986, 30, 367−382. (39) Martin, J. E.; Adolf, D.; Wilcoxon, J. P. Phys. Rev. Lett. 1988, 61, 2620−2623. (40) Martin, J. E.; Adolf, D.; Wilcoxon, J. P. Phys. Rev. A 1989, 39, 1325−1332. (41) Colby, R. H.; Gillmor, J. R.; Rubinstein, M. Phys. Rev. E 1993, 48, 3712−3716. (42) Lusignan, C. P.; Mourey, T. H.; Wilson, J. C.; Colby, R. H. Phys. Rev. E 1995, 52, 6271−6280.

Equation A5 is analytically solved to give ⎧ ⎫ ⎧ x(t ) − x * ⎫ 2 ⎬ = − (x * − x *)k t + ln⎨ [A2]0 − x 2* ⎬ ln⎨ 2 1 1 ⎩ x(t ) − x1* ⎭ ⎩ [A2]0 − x1* ⎭ (A6)

with 1 x1* = − {Q eq + (Q eq 2 + 4Q [A2]0 )1/2 } 2

(A7a)

1 {−Q eq + (Q eq 2 + 4Q [A2]0 )1/2 } 2

(A7b)

x2* =

and k Q eq = 1/K eq = d k1

(A8)

For Keq = 8000 M−1 (cf. section 3.3.1) and [A2]0 = 0.04, 0.13 M (in the range examined in Figure 2), the time evolution of x(t) = [A2](t) calculated from eq A6 is shown with the circles and squares in Figure 8. For comparison, the approximate solution utilized in section 3.1, 1/x(t) = k1t + 1/[A2]0 (equivalent to eq 8 in section 3.3.1), calculated for the same parameters (Keq = 8000 M−1 and [A2]0 = 0.04, 0.13 M) are shown with the curves. The approximate solution for those parameter values are close to the rigorous solution in the range of [A2](t)/[A2]0 ≥ 0.1667 (that corresponds to the range of p ≤ pc = 0.8333 focused in section 3.3.1 for discussion of tgel). Thus, the discussion of tgel on the basis of eq 6 in section 3.3.1 is reasonable for the above Keq and [A2]0 values at 25 °C.

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ASSOCIATED CONTENT

S Supporting Information *

Text giving additional experimental details for the effect of HAc catalyst concentration on gelation, for the viscosity of the samples with concentration below cg and for the determination of the Keq using NMR analysis. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (G.D.); [email protected] (Y.C.); [email protected] (C.Y.L.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by National Natural Science Foundation of China (Grants 20874109 and 20974034), PetroChina Innovation Foundation, and National High Technology Research, and Development Program of China (Grants 2009AA033601 and 2009AA034605).

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