Dynamics of Dual Networks: Strain Rate and Temperature Effects inHydrogels with Reversible H‑BondsXiaobo Hu,† Jing Zhou,† William F. M. Daniel,† Mohammad Vatankhah-Varnoosfaderani,†

Andrey V. Dobrynin,*,‡ and Sergei S. Sheiko*,†

†Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3290, United States‡Department of Polymer Science, University of Akron, Akron, Ohio 44325-3909, United States

*S Supporting Information

ABSTRACT: Combining high concentration of reversiblehydrogen bonds with a loosely cross-linked chemical networkin poly(N,N-dimethylacrylamide-co-methacrylic acid) hydrogelsproduces dual-network materials with high modulus andtoughness on par with those observed for connective tissues.The dynamic nature of the H-bonded cross-links manifests itselfin a strong temperature and strain rate dependence of hydrogelmechanical properties. We have identified several relaxationregimes of a hydrogel by monitoring a time evolution of the time-average Young’s modulus ⟨E(t)⟩ = σ(t)/ε̇t as a function of the strain rate, ε̇, and temperature. At low temperatures (e.g., 3 °C),⟨E(t)⟩ first displays a Rouse-like relaxation regime (⟨E(t)⟩ ∼ t−0.5), which is followed by a temporary (physical) network regime(⟨E(t)⟩ ∼ t−0.14) at intermediate time scales and then by an associating liquid regime (⟨E(t)⟩ ∼ t−0.93) at the later times. Withincreasing temperature to 22 °C, the temporary network plateau displays lower modulus values, narrows, and shifts to shortertime scales. Finally, the plateau vanishes at 37 °C. It is shown that the energy dissipation in hydrogels due to strain-induceddissociation of the H-bonded cross-links increases hydrogel toughness. The density of dissipated energy at small deformationsscales with strain rate as UT ∼ ε̇0.53. We develop a model describing dynamics of deformation of dual networks. The modelpredictions are in a good agreement with experimental data. Our analysis of the dual network’s dynamics provides generalframeworks for characterization of such materials.

1. INTRODUCTION

The introduction of reversible (physical) cross-links to apermanent (chemical) network allows for effective control ofthe network mechanical properties in both linear (modulus)and nonlinear (extensibility and toughness) deformationregimes. Such dual polymer networks are employed in abroad range of applications including self-assembly, self-healing,shape-memory, molding, and tissue engineering.1−14 Thisbroad variety of applications is driven by the network abilityto evolve by breaking and re-forming physical cross-links onexperimentally relevant time scales (seconds to hours).15−23

Because of the dynamic nature of dual networks, theirmechanical properties not only are determined by the networkstructure24 but also depend on deformation conditions, i.e.,strain rate and temperature.25−33

In strain-rate-controlled experiments, an increase indeformation speed entails faster dissociation of physical cross-links, which requires a higher mechanical stress,34,35 resulting ina corresponding increase in network modulus and toughness. Ifthe strain rate, ε̇, is larger than the inherent (stress-free)dissociation rate constant, kp, of the physical cross-links (ε̇ >kp), the network deformation process leads to significantdissipation of the mechanical energy and an increase ofapparent toughness (Figure 1). At slower strain rates, such thatε̇ < kp, the dissociation−association of physical cross-links does

not require any mechanical stimulation, and the amount ofenergy dissipation is negligible. At these deformationconditions, the same material behaves as a soft elastic networkand possesses a low toughness (Figure 1). In other words, dualnetworks with physical cross-links could be either rigid-and-tough or soft-and-weak depending on the deformation strainrate, ε̇. Yet, in both cases, the networks remain highlyextendable and elastic due to the loose chemical network. Asimilar level of control over network’s mechanical propertiescan be achieved by changing temperature, which shifts thedissociation rate constant of the physical cross-links withrespect to an applied strain rate. Note that temperature has adual effect: in addition to changing the thermal energy in theBoltzmann factor, a temperature variation changes thedissociation energy of physical cross-links, which causes thecorresponding shifts in the equilibrium constant and concen-tration of the physical cross-links.Herein, we report strain rate and temperature dependence of

both the small deformation property (modulus) and largedeformation properties (strength and toughness) of poly(N,N-dimethylacrylamide-co-methacrylic acid) hydrogels. The de-

Received: November 8, 2016Revised: December 23, 2016Published: January 11, 2017

Article

pubs.acs.org/Macromolecules

© 2017 American Chemical Society 652 DOI: 10.1021/acs.macromol.6b02422Macromolecules 2017, 50, 652−659

signed materials integrate a loose permanent covalent networkand a dense H-bonded (physical) network, which undergoesrecurrent dissociation and reassociation during deformation.36

Because of the ambiguity of using the time−temperaturesuperposition principle for construction of master curve of thedual networks, our approach is based on analysis of theevolution of time-average Young’s modulus in both linear and

nonlinear deformation regimes of hydrogel films undergoinguniaxial extension in broad ranges of strain rates andtemperatures.

2. EXPERIMENTAL SECTION2.1. Materials. N,N-Dimethylacrylamide (DMAA), methacrylic

acid (MAAc), ammonium persulfate (APS), and N,N,N′N′-tetramethylethylenediamine (TEMED) were used as received(Sigma-Aldrich). Water was produced by distillation followed bydeionization to a resistance of 18 MΩ cm, followed by filtrationthrough a 0.2 μm filter to remove particulate matter.

2.2. Preparation of Dual-Network Hydrogels. The dual-network hydrogels were synthesized by a one-step copolymerizationof DMAA and MAAc with a total monomer concentration of 33 wt %.A mixed aqueous solution of DMAA and MAAc monomers with afeeding molar ratio of 4:6, together with 0.5 mol % APS (relative tothe total monomer concentration), was degassed with N2 for 20 min.TEMED was added to the solution, and the solution was thentransferred to a glass mold with a polydimethylsiloxane (PDMS)spacer to polymerize at room temperature under a N2 atmosphere for48 h. In this reaction, no additional chemical cross-linker was added. Alow fraction of chemical cross-links is produced in situ due to the chaintransfer reaction in copolymers with DMAA. Besides, the multipleintermolecular hydrogen bonds were stabilized by the hydrophobicinteractions due to the presence of the α-methyl groups of PMAAc.36

2.3. Characterization of Hydrogels. Tensile tests were carriedout using dynamic mechanical analysis (RSA-G2, TA Instruments)with an immersion clamps accessory. Samples with a thickness of 1.5mm were cut into dumbbell-shaped samples (DIN 53504-S3, 2 mm inwidth with an initial length L0 of 12 mm). The tensile deformation wasperformed within a broad range of strain rates from 0.00015 to 0.05s−1 at controlled temperature. In order to avoid water evaporation, allof the mechanical tests were carried out in silicone oil. Theengineering stress σ was estimated from the stretching force dividedby the cross-section area of the undeformed sample. The engineering

Figure 1. Schematic representation of stress−strain curves of dualnetworks at different strain rates. At low strain rate (ε̇ < kp), thenetwork behaves as a loose pure chemical network. With increasingstrain rate (ε ̇ > kp), the deformation process leads to significantdissipation of mechanical energy and, hence, an increase of bothapparent toughness and apparent modulus. Higher strain rate results inhigher dissipated energy and thus higher toughness and modulus. Thedissipated energy due to the dissociation of physical cross-links ismeasured as the area under the stress−strain curve after subtraction ofthe elastic energy stored in the chemical network.

Figure 2. Tough and elastic dual networks with H-bonds. (a) Chemical structure of dual networks with chemical cross-links and reversible H-bonds.Schematic representation of the initial dual-network state before deformation (i), stretching of polymer chains under mechanical loading (ii), and thedissociation and reassociation of H-bonds during deformation (iii). The chemical cross-links provide shape recovery, while the dissociation/reassociation of H-bonds controls dual-network toughness. (b) Stress−strain curves of tensile tests with repeated loading and unloading cycles (ε̇ =0.015 s−1, εmax = 0.5) of the same hydrogel specimen. All cycles were run at 22 °C in silicone oil. After each cycle, the samples were annealed for 1 hat 22 °C or 3 min at 37 °C in silicone oil. (c) Two loading and unloading cycles (ε̇ = 0.05 s−1, εmax = 6) of the same hydrogel sample with 4 h rest at22 °C in silicone oil. Both cycles were run at 22 °C in air, using samples coated with silicone oil.

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strain ε was estimated from the gap change (ΔL) divided by L0.Loading−unloading experiments were performed in order tocharacterize the hysteresis.

3. RESULTS AND DISCUSSION

3.1. Mechanical Properties of Dual Networks. Figure 2ashows the chemical structure of the dual-network hydrogelcomposed of N,N-dimethylacrylamide (DMAA) and meth-acrylic acid (MAAc) copolymers, which form low concentrationof covalent (chemical) bonds and high concentration of H-bonds (physical cross-links). Because of the presence of strong,dense, and reversible H-bonds, hydrogels can have a Young’smodulus of ∼30 MPa and fracture energy of ∼10 kJ m−2 (at 22°C, ε̇ = 0.083 s−1), which is similar to the mechanical propertiesof connective tissues such ligament and cartilage.36 Asmentioned in the Introduction, these values should be regardedas apparent properties that depend on the deformationconditions including temperature and strain rate. At the onsetof deformation (small strains ∼1%), both chemical andhydrogen-bond cross-links are largely intact, and their totaldensity determines the Young’s modulus of the dual-networkhydrogel. With increasing deformation, H-bonds start todissociate and then reassociate with new neighbors relaxingthe stress, while the chemical network strands remains strained(Figure 2a, i−iii). Both types of cross-links play distinct roles inthe mechanical response: the chemical cross-links control thenetwork elasticity and maintain the sample integrity at large

deformations, whereas the recurrent dissociation/reassociationof the H-bonds controls material’s rigidity and toughness bysupporting the external stress at a high level. Upon unloading,the stress stored in the strained covalent network facilitates thereverse dissociation/association of the transient H-bonds torestore both the original stress-free shape and mechanicalproperties (Figure 2a, iii to i). To explore this unique behavior,we performed cyclic loading−unloading tests in a broad rangeof maximum strains from 50 to 600%. Figure 2b shows thebehavior of a sample uniaxially extended up to a relatively lowstrain of 50% (ε = 0.5). The hydrogel exhibits pronouncedhysteresis (0.2 MJ m−3) and retains significant deformation (ε= 0.4) after unloading. The large hysteresis can be explained bysignificant energy dissipation due to the dissociation of H-bonds as illustrated in Figure 2a-iii. After resting in silicone oilat 22 °C for 1 h, the unloaded sample fully recovers its originalshape and mechanical properties as evidenced by the secondloading−unloading curve lying right on top of the first cycle(Figure 2b). Annealing at a higher temperature of 37 °C allowsfor much faster sample recovery (3 min) as verified by the thirdloading−unloading curve shown in Figure 2b. This is consistentwith a higher rate of H-bond dissociation with increasingtemperature. Both the shape and material properties are fullyrecovered even after very large deformations. Figure 2c showsan excellent elastic behavior of the rigid hydrogel (E ∼ 10 MPa)extended to a prerupture strain of 600% (ε = 6), which suggestsboth the robustness of the chemical network and reversibility of

Figure 3. Construction of the master curves for time-average Young’s modulus from stress−strain curves measured at different strain rates ε ̇, rangingfrom 0.000 15 to 0.05 s−1. Stress−strain curves measured at (a) 3 °C, (c) 22 °C, and (e) 37 °C. Within the limit of linear viscoelasticityapproximation, ⟨E(t)⟩ was extracted from the stress−strain relations in (a, c, e), ⟨E(t)⟩ = σ(t)/ε(t), where the true stress σ(t) = σeng(t)(1 + ε(t)).⟨E(t)⟩ is plotted as a function of time t = ε/ε ̇ at different temperatures: (b) 3 °C, (d) 22 °C, and (f) 37 °C.

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the H-bonded cross-links in the physical network during theentire deformation process. In the next section, we analyzeindividual contributions of both networks at different stages ofthe deformation process as a function of the strain rate andtemperature.3.2. Time-Average Network Modulus. Characterization

of the mechanical properties of dual networks is not a trivialtask. Unlike the conventional polymer systems, where dynamicproperties are determined by one characteristic relaxation time,i.e., characteristic monomer relaxation time, τ0, associated withpolymer segmental motion, physical networks have anadditional relaxation process associated with the lifetime ofthe physical cross-links, τl. Both relaxation times have differenttemperature dependences and distinct activation energybarriers. This makes construction of a master curve using theconventional time−temperature superposition approach ambig-uous since the physical network structure changes withtemperature as well.20,37 Therefore, to characterize themechanical properties of the dual networks at smalldeformations, we use a linear viscoelasticity approximation tocalculate evolution of the time-average Young’s modulus duringuniaxial extension at a constant temperature. At a given strainrate, ε̇, the tensile stress increases with time as

∫ ∫σ ε ε τ τ ε= − ′ ′ = ̇ = ⟨ ⟩t E t t t E t E t( ) ( ) d ( ) ( ) d ( ) ( )t t

0 0(1)

where ε(t) = ε ̇t is a strain at time t and ⟨E(t)⟩ is the time-average network Young’s modulus:

∫σε

τ τ⟨ ⟩ = = −E ttt

t E( )( )( )

( ) dt

1

0 (2)

In the case of the power law dependence of the relaxationmodulus

ττ

≅+

α⎛⎝⎜

⎞⎠⎟E t E

t( ) 0

0

0 (3)

where E0 is the Young’s modulus at monomeric time scales; theintegration in eq 2 gives the following relation for the time-average modulus as a function of time

τ⟨ ⟩ ≅

α⎜ ⎟⎛⎝

⎞⎠E t E

t( ) 0

0

(4)

Thus, time-average modulus maintains the same power law asthe relaxation modulus in eq 3. However, for an exponential

relaxation behavior, ∼ −τ( )E t( ) exp t

l, the time averaging in

accordance with eq 2 results in linear decay of the time-averageYoung’s modulus (⟨E(t)⟩ ∼ t−1) on the time scales t > τl. Wewill apply the outlined formalism of the time averaged Young’smodulus to analyze stress−strain curves obtained for dualnetworks.Figures 3a,c,e show stress vs strain curves measured in a small

deformation range at different strain rates ranging from 0.00015to 0.05 s−1 and three different temperatures equal to 3, 22, and37 °C. As anticipated from mechanochemistry of physicalbonds,35 the stress level decreases with strain rate, resulting inthe different stress−strain behaviors. However, we were able tocollapse all data sets shown in Figures 3a,c,e by plotting thetime-average Young’s modulus ⟨E(t)⟩ = σ(t)/ε(t) as a functionof time t = ε/ε̇ in Figures 3b,d,f, respectively. Figure 3b (T = 3

°C) displays three different deformation regimes that can beidentified by using a scaling model of deformation of anassociating network with relatively strong reversible bonds (τl >τR) as shown in Figure 4 (eqs S1−S11). It is important to point

out that our scaling model for the time average Young’smodulus explicitly considers network relaxation processes at alltime scales (see Figure 4 and Supporting Information fordetails). In this respect it is different from the recentlydeveloped models of the reversible networks dynamics thatneglect strands’ Rouse modes.26,38−40 At short time scales (t =ε/ε̇ < 0.1 s), the modulus decreases with time as ⟨E(t)⟩ ∼t−0.45±0.03, which is attributed to the relaxation of networkstrands between H-bonded cross-links. This relaxation isconsistent with a Rouse dynamics of polymer chains (α = 0.5in eq 3), for which the time average network modulus scaleswith time as ⟨E(t)⟩ ∼ t−1/2 (eq 4). In the intermediate timerange, the modulus relaxation slows down as ⟨E(t)⟩ ∼ t−0.14,resulting in an apparent plateau due to the presence of a densephysical network of H-bonds. The high cross-linking densityresults in a high plateau modulus of around 108 Pa, whichcorresponds to the Young’s modulus of the physical network.After pausing at the temporary network plateau for a certaintime, the modulus continues its relaxation through recurringdissociation/reassociation of the H-bonds. In this regime, thesystem behaves as an associating liquid (⟨E(t)⟩ ∼ t−0.93), wherethe physical network continues breaking and rearranging into astress-relaxed configurations. Then the modulus will reach aplateau in the permanent chemical network regime at longertime (Figure 4). However, network deformation should beperformed at extremely small strain rates to achieve this regimeexperimentally. At a higher temperature of 22 °C (Figure 3d),the plateau seen in Figure 3b becomes an inflection and shiftsto shorter times. This is consistent with the physical networkmodel (Figure 4), which suggests a 2-fold effect of atemperature increase: (i) it results in a decrease of theconversion p of the associating groups, and (ii) it shortens the

Figure 4. Scaling predictions for time dependence of the time-averageYoung’s modulus ⟨E(t)⟩ for dual dynamic networks (red solid line)and chemical networks (blue dash dotted line) is outlined for twonetwork systems for τl > τR = τ0N

2 (strong physical cross-links).Logarithmic scales. Ep = E0p/m is the plateau modulus of physicalnetworks, and Ec = E0/N is modulus of chemical network. N is degreeof polymerization of chemical network strands, τ0 is the characteristicmonomer time, m is the degree of polymerization of the spacerbetween associating groups, and p is degree of conversion of theassociating groups into physical cross-links.

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lifetime of physical cross-links, τl. The decrease in the physicalcross-link conversion and lifetime also shifts crossover to thechemical network regime to shorter time scales (Figure 4). Theonset of the chemical network plateau at ⟨E(t)⟩ ∼ 2 × 105 Pa isclearly seen in Figure 3d. As the temperature increases to 37 °C(Figure 3f), the time-average modulus decreases with time as⟨E(t)⟩ ∼ t−0.55±0.03 at short time scales and then shows a smallinflection followed by a faster decay (⟨E(t)⟩ ∼ t−0.91±0.05). Atlonger times (∼10 s), the modulus levels off at ⟨E(t)⟩ = 2 × 105

Pathe modulus of the permanent chemical network (Figure4). In other words, the H-bonds do not affect the networkmechanical properties at high temperatures.3.3. Energy Dissipation in Dual Networks. The

combination of the dense physical network and loose chemicalnetwork allows dual networks to dissipate large amount ofenergy upon deformation. In this section, we characterize dual-network toughness as a function of strain and strain rate. Figure5a displays a series of loading−unloading curves that weremeasure at an intermediate strain of εmax = 0.5 and differentstrain rates ranging from 0.000 15 to 0.05 s−1. The hysteresisarea between the loading and unloading curves of a gel givesthe energy dissipated per unit volume,17 which is directlyrelated to reversible dissociation of the H-bonded cross-linksand exhibit strong dependence on the strain rate. As shown inFigure 5b, the hysteresis increases with strain rate at a distinctpower law with exponent α = 0.53, which directly follows fromthe time dependence of the time-averaged Young’s modulus⟨E(t)⟩ shown in Figure 3d. Indeed, for deformation at aconstant strain rate, we can express stress in a physical networksystem in accordance with eqs 1−4 as

σ ε ετ ε ε≅ ̇ ∼ ̇E t( ) 0 00.53 0.47 0.53 0.47

(5)

This implies that the hysteresis area obtained from loading−unloading cycle (hysteresis or dissipated energy density) shouldalso scale with the strain rate as ε̇0.53 since

∮ σ ε ε ε= ∼ ̇U ( ) dTC

0.53(6)

The strain rate dependence weakens with the increasing strainrate (Figure 5b and Figure S2), which could be explained by thecrossover to the glassy regime at t < τ0 as shown in Figure 4 andtime dependence of the Young’s modulus given by eq 3. In theSupporting Information we have verified that the contributionof the elastic energy due to deformation of the chemicalnetwork (Figure 1) to the hysteresis area is negligibly small(Figures S1 and S2).

3.4. Yielding Instability and Temperature-DependentMechanical Properties. The mechanical properties of thedual network show a strong temperature dependence whichcontrols the dissociation rate of the H-bonds. This ismanifested in significant variations of the form of the ⟨E(t)⟩curves upon the temperature increase from 3 to 37 °C as shownin Figure 3. A similar behavior was observed for the yield stress(Figure 6). Figure 6a shows a series of tensile stress−straincurves measured at different temperatures and a constant strainrate of 1 s−1. At temperatures lower than 37 °C, the inherentdissociation rate constant, kp, of the hydrogen bonds is muchsmaller than the strain rate (kp ≪ ε ̇). As a result, the higherstrain rate tends to enhance the strain localization and thuspromote necking, which induces a significant drop in stress.

Figure 5. Effect of strain rates on dissipated energy. (a) Loading−unloading cycles at different strain rates with a maximum strain εmax = 0.5. All testswere done at 22 °C in silicone oil. (b) Dependence of hysteresis (area under stress−strain curve during each loading−unloading cycle) on strainrates.

Figure 6. Effect of temperature on mechanical properties of dual networks. (a) Stress−strain curves up to rupture obtained at different temperaturesand the same strain rate of 1 s−1. Samples were thermally equilibrated in silicone oil and stretched in air. (b) The yield stress σeng

y and yield strain εy,

which were measured at different strain rates and temperatures (Figures S4 and S5), are plotted as − εε

σ̇⎜ ⎟⎛⎝

⎞⎠ln ln

Ey

engy

pversus σeng

y (1 + εy) (eq 9). From

the slope v/kBT and the intercept ln(1/τl), the values of the activation volume v = 12 ± 1 nm3 and the lifetime τl were obtained. Inset showstemperature dependence of the lifetime, τl. The line corresponds to τl = τ0 exp(Ea/RT) with activation energy (140 kJ mol−1).

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Lower temperature results in a larger stress decrease. We alsoconducted loading−unloading measurements at a strain rate of0.015 s−1 and temperatures between 10 and 37 °C (Figure S3).Similar to the effect of a strain rate decrease, the increase oftemperature results in decay of mechanical strength of the dualnetworks, including yield stress, fracture stress, and toughness(Figure S3). In contrast, the elongation at break exhibits asteady increase with temperature (Figure 6a). All theseobservations are consistent with the decrease in the conversionof H-bonds and with weakening of their strength at highertemperatures. This in turn results in lower energy dissipationduring deformation.The temperature/strain rate variations of the yield stress and

strain can be used to evaluate the mechanochemical parametersof the H-bond cross-links, including dissociation energy andactivation volume. We have extended the Eyring model ofstress-induced bond dissociation (renormalization of the bondlifetime τl) to describe yielding in physical networks (eqs S12−S19). Note that similar results can be obtained using theKramers’ rate theory as described in refs 38 and 40. In theframework of the Eyring’s approach, we can obtain the stress−strain relation during physical network deformation at aconstant strain rate:

∫σ ετ

τ σ τ= ̇ −⎛⎝⎜⎜

⎛⎝⎜

⎞⎠⎟⎞⎠⎟⎟t

tE

vk T

d ( )d

exp1

d exp( )

l

t

p0 B (7)

where Ep is the plateau modulus of the physical network and vis the activation volume. The maximum in the engineeringstress σeng(ε) = σ/(1 + ε) curve corresponds to the followingcondition for the true stress as a function of strain

σ

ε εσε

σε

=+

−+

=d

d1

1dd (1 )

0eng

2 (8)

After some algebra (see Supporting Information for details) wecan rewrite eq 8 in a form convenient for analysis of theexperimental data

εε

στ

σ ε− ̇ = +

+⎡⎣⎢⎢

⎤⎦⎥⎥E

v

k Tln ln ln(1/ )

(1 )

yl

engy

p

engy

y

B (9)

Knowing experimental values of the yielding stress σengy and

strain εy at different strain rates, we can use eq 9 to fit the dataand obtain the activation volume υ and the lifetime τl of H-bonds.

The Young’s modulus of the physical network, Ep, at differenttemperature is estimated from the plateau modulus (inflectionpoint) as shown in Figure 3b,d and Figure S4e (Table 1). Byusing the obtained values for σeng

y and εy from Figures S4a,b and

S5 (Table 1), we plot − εε

σ̇⎜ ⎟⎛⎝

⎞⎠ln ln

Ey

engy

pversus σeng

y (1 + εy) based

on eq 9. As shown in Figure 6b, the slopes v/kBT are all around3 MPa−1 for all the temperature, which gives a temperature-independent activation volume υ around 12 ± 1 nm3 (Table 1).This number is relatively large compared to mechanicalactivation of individual chemical bonds (∼0.1 nm3), whichmeans that yielding instability involves the cooperativemovement of a larger number of chain segments, suggestingactivation of larger species like clusters of hydrogen-bonds.41,42

Based on the intercept ln(1/τl) of the fitting curves, the value oflifetime, τl, can be estimated for each temperature (Table 1),which is in the same order of magnitude to the experimentaldata in Figure 3. The apparent activation energy Ea = 140 kJmol−1 is obtained from the Arrhenius equation, τl = τ0 exp(Ea/RT), where R is the gas constant and T is the absolutetemperature (see inset in Figure 6b). This energy is lower thanthe dissociation energy of covalent bond (around 350 kJ mol−1)but much higher than the dissociation energy of an individualhydrogen bond in water. This suggests formation of clusters ofH-bonds that were observed during synthesis of thesehydrogels.36

4. CONCLUSIONSUnique mechanical properties of dual-network hydrogel andtheir dependence on the strain rate and temperature aremanifestations of the dynamics of reversible hydrogen bonds.In the limit of small deformations, modulus and toughness ofhydrogel decrease with decreasing strain rate or with increasingtemperature. In this deformation regime, the time-averageYoung’s modulus (⟨E(t)⟩) drops 3 orders in magnitude (from108 to 105 Pa) and demonstrates different relaxation regimes(see Figures 3). At low temperatures (3 °C), the time-averageYoung’s modulus ⟨E(t)⟩ first shows a Rouse-like relaxation ofstrands between physical cross-links, which is followed by aweaker time dependence due to a temporary plateau of physicalnetwork of H-bonds. The physical network plateau is followedby an associating liquid regime with ⟨E(t)⟩ ∼ t−1 as shown inFigure 4. With increasing temperature, both the conversion ofthe H-bonds and their lifetime decrease, resulting in shift of thecrossovers between different network relaxation regimes (see

Table 1. Yielding Parameters and the Fitting Results

T (°C) ε ̇ (s−1) σengy (MP) εy Ep (MPa) ν/kBT (MPa−1) ν (nm3) ln(1/τl) τl (s)

3 0.05 2.01 0.06 ± 0.01 100 3.2 ± 0.2 12 ± 1 −5.5 ± 0.1 244 ± 250.015 1.550.005 1.170.0015 0.910.0005 0.67

10 0.05 1.76 0.06 ± 0.01 80 2.9 ± 0.2 11 ± 1 −4.1 ± 0.1 60 ± 50.015 1.360.005 0.980.0015 0.65

22 1 1.56 0.07 ± 0.01 28 2.9 ± 0.1 11.8 ± 0.4 −1.3 ± 0.1 4 ± 10.5 1.370.15 0.990.05 0.690.015 0.39

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Figure 3). In particular, at 37 °C, we observe disappearance ofthe temporary plateau corresponding to physical networkregime and emergence of the plateau at longer time scaleswhich represents a chemical network regime.At lower strain rate or higher temperature, the chemical

network dominates the mechanical response, resulting in smallhysteresis of stress−strain curves during loading and unloadingcycle. This is exactly what one would expect in a regime wherethe H-bonds relax much faster than the experimental time scale.At higher strain rates and lower temperature, the dual networksexhibit significant energy dissipation due to strain-induceddissociation of the H-bond cross-links, which leads to thecorresponding increase in toughness. At small deformations thedissipated energy density first increases with increasingdeformation strain rate as UT ∼ ε̇0.53 and then begin tosaturate (see Figure 5b). The analysis of the yielding instabilityallows to estimate the mechanochemical parameters of the H-bonded cross-links such an activation volume of 12 nm3 and anapparent activation energy of 140 kJ mol−1. These values areconsistent with the clustering of H-bonds in the studiedhydrogels. Our approach to the analysis of mechanicalproperties of dual networks can be extended to describeother physical networks and guide the design of tough materialsfor specific applications and environmental conditions.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.macro-mol.6b02422.

Equations S1−S20 and Figures S1−S5 (PDF)

■ AUTHOR INFORMATIONCorresponding Authors*(A.V.D.) E-mail: adobrynin@uakron.edu.*(S.S.S.) E-mail: sergei@email.unc.edu.ORCIDSergei S. Sheiko: 0000-0003-3672-1611NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe gratefully acknowledge funding from the National ScienceFoundation (DMR 1407645 and DMR 1436201).

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