Borate Hydrogels

Article pubs.acs.org/Macromolecules

Strain Hardening Behavior of Poly(vinyl alcohol)/Borate Hydrogels Gang Huang,†,‡ Huanhuan Zhang,†,‡ Yulin Liu,†,§ Haijian Chang,†,∥ Hongwei Zhang,⊥ Hongzan Song,§ Donghua Xu,*,† and Tongfei Shi*,† †

State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China ‡ Graduate School of the Chinese Academy of Sciences, Beijing 100039, China § College of Chemistry and Environmental Science, Hebei University, Baoding 071002, China ∥ College of Materials Science and Engineering, Jilin University, Changchun 130025, China ⊥ Department of Food Science, Rutgers, The State University of New Jersey, 65 Dudley Road, New Brunswick, New Jersey 08901, United States S Supporting Information *

ABSTRACT: The large-amplitude oscillatory shear (LAOS) behavior of poly(vinyl alcohol) (PVA)/borate hydrogels was investigated with the change of scanning frequency (ω) as well as concentrations of borate and PVA. The different types (Types I−IV) of LAOS behavior are successfully classified by the mean number of elastically active subchains per PVA chain ( feas) and Deborah number (De = ωτ, τ is the relaxation time of sample). For the samples with Type I behavior (both storage modulus G′ and loss modulus G″ increase with strain amplitude γ, i.e., intercycle strain hardening), the critical value of strain amplitude (γcrit) at the onset of intercycle strain hardening is almost the same when De > ∼2 (Region 3), while the value of Weissenberg number (Wi = γDe) at γcrit is similar when De < ∼0.2 (Region 1). For intracycle behavior in the Lissajous curve, intracycle strain hardening is only observed in viscous Lissajous curve of Region 1 or in the elastic Lissajous curve of Region 3. In Region 1, both intercycle and intracycle strain hardening are mainly caused by the strain rate-induced increase in the number of elastically active chains, while non-Gaussian stretching of polymer chains starts to contribute as Wi > 1. In Region 3, strain-induced non-Gaussian stretching of polymer chains results in both intercycle and intracycle strain hardening. In Region 2 (∼0.2 < De < ∼2), two involved mechanisms both contribute to intercycle strain hardening. Furthermore, by analyzing the influence of characteristic value of De as 1 on the rheological behavior of PVA/borate hydrogels, it is concluded that intercycle strain hardening is dominated by strain-rate-induced increase in the number of elastically active chains when De < 1, while straininduced non-Gaussian stretching dominates when De > 1. nonlinear rheology properties of physical gels.11−15 As depicted in Scheme 1a, the cross-linker borate ion coexisted with boric acid and Na+ in water, and the complexation included two steps, i.e., monodiol and didiol complexation. Scheme 1b revealed various states of borate ion in the PVA/borate hydrogels, i.e., free, dangling, intrachain bound, and interchain bound state, wherein interchain bound borate was generally considered as the elastically active cross-linker.16 The strain hardening behavior of PVA/borate hydrogel was reported early in 1969;17 then Ahn’s group systematically investigated the strain hardening behavior of PVA/borate hydrogel by largeamplitude oscillatory shear (LAOS) experiments.18−22 In their work, the mechanism of strain hardening was thought to be the same as that of shear thickening, which had been proved as

1. INTRODUCTION Polymer hydrogels are three-dimensional polymeric networks capable of imbibing a large amount of water or biological fluids.1,2 One important subclass of polymer hydrogels is physical hydrogels, which are formed by transient cross-linkers such as multiple hydrogen bonding, ionic bonds, hydrophobic interactions, π−π stacking, metal−ligand coordination, host− guest interactions, dynamic covalent bond, etc.3,4 Physical hydrogels often exhibit rich nonlinear rheological properties, mainly including shear thickening, shear thinning, strain hardening, and strain softening, which are related to the characteristic changes of microstructure as a function of the deformation or flow imposed on the network.4 As a result, extensive experimental and theoretical research has been devoted to investigate the origin of shear thickening and strain hardening in the physical hydrogels at a molecular level.5−10 Poly(vinyl alcohol) (PVA)/borate hydrogels have been widely explored as a model system to study the linear and © XXXX American Chemical Society

Received: November 4, 2016 Revised: February 3, 2017

A

DOI: 10.1021/acs.macromol.6b02393 Macromolecules XXXX, XXX, XXX−XXX

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only explored the mechanism of strain hardening with Deborah number (De) much larger than 1. Xu et al. studied a metallosupramolecular polymer network during strain hardening by frequency sweep experiments, and the relaxation time (τ = 1/ ωc) of samples under different strain were obtained from the crossover frequency (ωc) of storage modulus (G′) and loss modulus (G″).25 Xu et al. observed that τ of the sample increased with strain during strain hardening, implying that the strain hardening was caused by strain-induced increase in the number of elastically active chains.25 By the frequency sweep experiments, no crossover of G′ and G″ can be observed when the lowest scanning frequency was larger than 1/τ, and this method only explored the mechanism of strain hardening when De < 1. In above work, the authors did not consider the effect of De (De < 1 or De > 1) on the mechanism of strain hardening of samples.8,25 In previous work about the strain hardening behavior of physical gels, the intercycle strain behavior, i.e., the increase of first harmonic G′ and G″ with strain amplitude (γ) between the different cycles of Lissajous curves during LAOS, was widely documented.18−22,25−29 However, the intracycle strain behavior, i.e., the change of viscoelastic properties with periodic strain γ(t) or periodic strain rate γ̇(t) in the cycle of the Lissajous curve, was seldom investigated.19,25 Xu et al. studied the distortion of elastic Lissajous curves in the aspect of ellipticity during strain hardening for a metallo-supramolecular polymer network, and the distortion was used to indicate the existence of non-Gaussian stretching of polymer chains during intercycle strain hardening.25 As discussed in this work, conclusions above might be arbitrary. Until now, there is few detailed analysis about the intracycle strain behavior of physical gels. The mechanism behind the intracycle strain behavior was still not explored, and the connection between intercycle and intracycle strain behavior was not built up. In this work, the effects of scanning frequency (ω), concentration of borate, and concentration of PVA on the LAOS behavior of PVA/borate hydrogels were explored. The LAOS behavior of PVA/borate hydrogels was analyzed by the Lissajous plot, stress decomposition, and Fourier transform (FT) rheology, etc.20,30 The mechanisms behind intercycle and intracycle strain behavior especially strain hardening behavior of the PVA/borate hydrogels were discussed.

Scheme 1. (a) Dissociation of Sodium Tetraborate in Water and Two Steps of Complexation between Borate and PVA Chains; (b) Schematic Picture for the States of Borate in PVA/Borate Hydrogels

shear-induced association.18,23,24 At the same time, Ahn’s group had applied a general network model to understand LAOS behavior of complex fluids by using two parameters, i.e., the creation and loss rate of network junction, and the strain hardening behavior of PVA/borate hydrogels was predicated by setting the creation rate of network junction larger than loss rate.22 Until now, for PVA/borate hydrogels, the mechanism of strain hardening is still not clear, and it remains ambiguous whether the mechanism of strain hardening is really consistent with shear thickening or not. For some other physical gels, some specific experiments were performed to explore the mechanism of strain hardening. Determining the change of relaxation time during strain hardening was generally used to explore the underlying mechanism. Séréro et al. obtained the relaxation time (τ) of a hydrophobic associating network on step-strain experiments by fitting a shear relaxation function, and τ of the sample was observed to decrease with strain during strain hardening, implying that the strain hardening was caused by nonlinear stretching of the elastically active chains.8 By the step-strain experiments, the strain was generally applied at a shorter time than the relaxation time of the network, so this method actually

2. EXPERIMENTAL SECTION 2.1. Materials. Poly(vinyl alcohol) (98.0−98.8% hydrolyzed, Mw ≈ 61 000 g/mol) and sodium tetraborate decahydrate (Na2B4O7·10H2O) were purchased from Aldrich. The overlap concentration (ϕc) and critical concentration of entanglement (ϕe) of pure PVA aqueous solution were determined to be 0.022 g/mL and 0.088 g/mL at 25 °C (Part I in the Supporting Information). 2.2. Sample Preparation. Samples were prepared as following: Sodium tetraborate (SB) stock aqueous solution was prepared at room temperature. PVA solutions were prepared by dissolving PVA with deionized water in sealed vials for 2 h under 85 °C. Then SB stock solution was added to the cooled PVA solution at room temperature. After stirring for 4 h under 85 °C, the mixture remained under 85 °C without stirring for 12 h to remove trapped air bubbles. After cooling to room temperature, the samples with targeted concentrations of SB and PVA were prepared. In the following discussion, the concentration of SB (1%−5%) was defined as the molar ratio between sodium tetraborate (SB) and vinyl alcohol in PVA. The concentration of PVA in the samples ranged from 0.03 g/mL (semidilute unentangled regime) to 0.2 g/mL (semidilute entangled regime) in this work. 2.3. Characterization. Rheological experiments were carried out at 25 °C on a strain-controlled ARES G2 rheometer (TA Instruments) B


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Macromolecules with Peltier temperature control system, and cone−plate geometry (diameter of 20 mm, cone angle of 2°, truncation height 49 μm) was used. The flowable hydrogels can be easily loaded on the geometry, and after the edge was scraped, paraffin oil with low viscosity was used to seal the edge of samples to minimize the evaporation of water in samples. To erase the deformation history of sample during loading, the sample was left in the state of rest for 60 s (much longer than the relaxation time of sample) before each test. The influence of wall slip on the results of strain sweep experiments was excluded through series of strain sweep experiments with parallel plate geometry (25 mm) under different gaps.31 Strain sweep experiments were performed under different scanning frequencies from 0.1 to 50 rad/s. With fixed scanning frequency and strain amplitude, a series of oscillatory time sweeps were carried out. Oscillatory frequency sweeps ranging from 3 to 10 rad/s were carried out at strains that spanned from the linear response regime to the nonlinear one for 0.03 g/mL PVA aqueous solution with 2% SB. Linear oscillatory frequency sweeps ranging from 0.1 to 200 rad/s were applied at an appropriate strain within the linear response regime. Steady shear experiments were performed over a range of shear rates from 10−3 to 103 s−1. Both strain sweep experiments and a series of oscillatory time sweeps were used to study the strain hardening of PVA/borate hydrogels. In Part II of the Supporting Information, the comparison between strain sweep and series of oscillatory time sweep experiments is shown, and similar intercycle and intracycle behavior can be observed. However, the results of strain sweep experiments exhibited larger fluctuation than that of oscillatory time sweeps, probably because the sample was not totally relaxed from the previous oscillatory shear period in the nonlinear regime during strain sweep test. So, the intracycle strain behaviors of samples shown below were obtained from series of oscillatory time sweep.

Figure 1. Small-amplitude oscillatory shear: (a) storage modulus (G′) and loss modulus (G″) versus frequency (ω); (b) complex viscosity (|η*|) versus ω. Sample was 0.03 g/mL PVA aqueous solution with 2% SB.

3.2. Intercycle Strain Behavior. Classifying the Types of LAOS Behavior. To discuss the LAOS behavior of PVA/borate hydrogels clearly, four types of LAOS behavior were classified in this work:18,33 Type I: both G′ and G″ showed the linear strain regime, strain hardening regime, and strain softening regime at larger strain. For Type I behavior, the strain at the onset of strain hardening was defined as critical strain amplitude (γcrit), and the strain where modulus reached a maximum was defined as maximum strain amplitude (γmax). Type II: G′ and G″ showed the linear response regime, strain softening regime at intermediate strain, strain hardening regime, and strain softening at larger strain. Type III: G′ showed linear response regime and strain softening regime while G″ showed linear response regime, strain hardening regime, and strain softening regime. Type IV: G′ and G″ showed the linear response regime and strain softening regime. In this work, the behaviors of Types I−III were identified as intercycle strain hardening of G″ and/or G′. Influence of Scanning Frequency and Concentrations of SB and PVA. First, we studied the influence of scanning frequency (ω) on LAOS behavior of PVA/borate hydrogels. Strain sweep results of 0.03 g/mL PVA with 2% SB under different scanning frequencies are shown in Figure 2a as examples. In Figure 2a, only the behavior of Type I can be observed, where both γcrit and γmax changed with ω. A more detailed study about the onset of strain hardening will be discussed below. It is interesting to note that G′ and G″ started to decrease at one γmax as ω < 10 rad/s, while the γmax of G′ was smaller than that of G″ as ω ≥ 10 rad/s. The above phenomenon has been widely documented in other systems.27,29,34−37 Whether G′ and G″ started to decrease at the same strain amplitude was related to phase angle of material, and detailed discussions about such phenomenon are shown in Part IV of the Supporting Information. For γ > γmax, both G′

3. RESULTS 3.1. Linear Rheological Property. To understand the nonlinear LAOS behavior of PVA/borate hydrogels, the linear rheological properties of PVA/borate hydrogels were explored first. From the result of small-amplitude oscillatory shear (SAOS) for 0.03 g/mL PVA aqueous solution with 2% SB (Figure 1), the apparent relaxation time (τ) of the sample in linear response regime was determined as reciprocal of crossover frequency (ωc) of G′ and G″, τ ≈ 0.12 s. The dependence of complex viscosity (|η*|) on frequency is shown in Figure 1b, where |η*| remained constant as ω was less than ∼1.5 rad/s and then decreased with further increase of ω. At the same time, plateau modulus of the gel (GN) as 269 Pa was obtained from constant value of G′ at high frequency. According to the phantom network model, the plateau modulus of the gel (GN) can be expressed as32 G N = (1 − 2/f )νkBT

(1)

where f is the functionality of the cross-linkers, ν is the number density of elastically active chain, kB is Boltzmann’s constant, and T is absolute temperature. In order to compare with the result of the 11B NMR spectrum conveniently, ν0 is defined as the total number of borons per unit volume although only borate can form an effective cross-linker. Then, the fraction of elastically active chains (ν/ν0), i.e., the boron in interchain bound state, can be calculated as 0.4%. The 11B NMR spectrum of 0.03 g/mL PVA aqueous solution with 2% SB revealed didiol-complex boron accounted for 35% of total boron (Part III in the Supporting Information), indicating that most of bound boron was in the intrachain bound state. Results above were helpful to understand the structure reorganization of PVA/borate hydrogels during strain hardening in the following discussion. C


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Figure 2. Storage modulus (G′) and loss modulus (G″) versus strain amplitude (γ) in strain sweep experiments. (a) Strain sweep under different scanning frequencies (ω, 0.1−50 rad/s); sample was 0.03 g/mL PVA aqueous solution with 2% SB. (b) Strain sweep under 1 rad/s; samples were 0.03 g/mL PVA aqueous solution with different concentrations of SB (1%−5%). (c) Strain sweep under 1 rad/s; samples were different concentration of PVA aqueous solution (0.03−0.20 g/mL) with 1% SB.

feas = ν /n p = νM n /C PVANA

and G″ decreased; at the same time meniscus failure was observed (part V, video in Supporting Information). It was inferred that the strain softening at γ > γmax was related to rupture of network and/or sample loss in geometry.10,25,38 Second, we paid attention to the effect of SB concentration on LAOS behavior of PVA/borate hydrogels. In Figure 2b, strain sweep results of 0.03 g/mL PVA aqueous solution with different concentrations of SB under fixed scanning frequency (1 rad/s) are shown as examples. Type I behavior was observed for all samples, where both γcrit and γmax decreased as the concentration of SB was increased. Moreover, G′ and G″ started to decrease at the same strain. Third, the influence of PVA concentration on LAOS behavior of PVA/borate hydrogels was explored. In Figure 2c, strain sweep results (ω = 1 rad/s) of samples with different concentration of PVA aqueous solution and 1% SB are shown as examples. Type I behavior occurred in the concentration range of PVA from 0.03 to 0.06 g/mL, while Type II behavior was observed when concentrations of PVA were 0.08 and 0.10 g/mL (close to the critical concentration of entanglements ϕe as 0.088 g/mL). As the concentration of PVA solution further increased from 0.15 to 0.20 g/mL (semidilute entangled regime), Type IV behavior occurred. To understand the influence of scanning frequency, concentrations of SB and PVA on the LAOS behavior, more experimental results under different conditions were discussed (Part VI in the Supporting Information). What Controlled the Types of LAOS Behavior. To understand the LAOS behavior of the samples in a simple and clear way, two parameters are introduced here. One parameter is the mean number of elastically active subchains per PVA chain (feas):

(2)

where np is the number of PVA chains per unit volume, CPVA is the concentration of PVA solution, Mn is number-average weight of PVA, and NA is Avogadro’s number. Apparently feas is related with the concentrations of SB and PVA, so the influence of concentrations of SB and PVA on LAOS behavior can be simplified as the influence of feas on the LAOS behavior of samples. The value of feas for samples with different concentration of PVA and SB is shown in Part VI of the Supporting Information. Another parameter is the Deborah number De = ωτ, where ω is the scanning frequency and τ is the relaxation time of samples in the linear response regime. For samples with different concentrations of SB and PVA, i.e., the samples have different τ, it is more accurate to use the normalized scanning frequency De to evaluate the influence of scanning frequency on the LAOS behavior of samples. In this work, it was interesting to observe that four different types of LAOS behavior were all related with the value of feas and De. In Figure 3, when feas was less than around 4 (feas < ∼4), Type I behavior was observed. As feas increased, the LAOS behavior changed from Type I to Type II (or Type III) and then to Type IV, while the LAOS behavior changed from Type II to Type III can be distinguished by the value of De. According to the above discussion, the types of nonlinear LAOS behavior of PVA/borate hydrogels can be predicted by the parameters feas and De obtained in the linear rheological regime. In Figure 3, the blue dashed line feas = 0.093 represented the experimental lowest limit value of feas for Type I behavior. In addition, the experimental lowest limit value of De for Type I behavior was also obtained, which was about 0.01. A detailed D


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Figure 3. Depicting the different types of LAOS behavior by mean number of elastically active subchains per PVA chain ( feas) and Deborah number (De). Colors of symbols represented different concentration of PVA aqueous solution with 1% (○, ⊙, ●), 2% (□, ⊡, □, ■), 3% (△, ◬, △, ▲), 4% (◇, dotted ◇, ◇, ⧫), 5% (▽, ▽, ▼) SB. Open symbols (○, □, △, ◇, ▽), dot center symbols (⊙, ⊡, ◬, dotted ◇), “−” center symbols (□, △, ◇, ▽), and solid symbols (●, ■, ▲, ◆,▼) represented different types of LAOS behavior Type I, II, III, and IV, respectively. Red dashed line was used as guide line. Blue dashed line represented the experimental lowest limit value (0.093) of feas for Type I behavior.

Figure 4. Critical strain (γcrit) and Weissenberg number (γcritDe) at the onset of strain hardening versus the Deborah number (De) for samples with Type I behavior. The samples were different concentration of PVA solution with 1% (○), 2% (□), 3% (△), 4% (◇), and 5% (▽) SB. In the insets, the open squares and filled squares represent the results for 0.03 g/mL PVA solution with 2% SB under strain sweeps and a series of oscillatory time sweeps, respectively.

the Supporting Information), and a similar value of Wicrit (De < 1) and Wisscrit might implied that the strain hardening behavior of the samples at De < 1 needed to exceed a threshold strain rate. Compared to oscillatory strain sweep, a series of oscillatory time sweep were also used to study LAOS behavior of PVA/ borate. In the inset of Figure 4, open squares (results from oscillatory strain sweep) and filled squares (results from series of oscillatory time sweep) show the similar change trend with De. However, less fluctuation was observed in filled squares, indicating that series of oscillatory time sweep was a better choice to distinguish the onset of strain hardening. From the results of the inset in Figure 4, three regions are divided: Region 1 (De < ∼0.2): γcritDe remained constant; Region 3 (De > ∼2): γcrit was constant; Region 2 (∼0.2 < De < ∼2): both γcrit and γcritDe changed with De. Some other work also used the value of De and Wi to depict the rheological behavior of samples. Zhou et al. reported the Pipkin diagram of linear viscoelasticy, shear banding, and no shear banding of entangled wormlike micellar solution under LAOS by the value of De and Wi.41 More recently, Zhou et al. reported the Pipkin diagram of six different linear and nonlinear regimes of average polymer stretching dynamics of single polymer chain under large-amplitude oscillatory extension (LAOE) by the value of De and Wi.42 We noted that similar curves between De and the critical value of Weissenberg number were observed in the above two work and in our work,37,38 though the systems were totally different. And, it was observed that the characteristic value of De as 1, i.e., the relaxation time of sample and time scale of deformation was equal, cannot be used directly here to distinguish the transition of different regimes in the above

discussion about the lower limit of Type I behavior is shown in Part VI of the Supporting Information. For the sample with the experimental lowest limit value of feas for Type I behavior, is it a gel or not? The discussion in Part VII of the Supporting Information proved that the sample was a gel. As described by Flory, the condition to form a polymer network was that there is at least one interstrand cross-linker per polymer chain, i.e., feas > 1.39 However, as it was also known, the microscopic structure of polymer network is generally heterogeneous.40 Except the polymers incorporated into the network, individually free polymers and some polymer aggregates dissociated from the network also exist. In this work, to calculate the value of feas, PVA chains in all states are taken into account, indicating that feas inevitably underestimates the true average number of active subchains per PVA chain within the active network structure. Thus, the gel as feas < 1 implied that fraction of PVA chains participating in the active network structure was small, and there are a large proportion of “nonnetworked” fragments in the network. Relationship between Onset of Strain Hardening and De. For PVA/borate hydrogels with Type I behavior, the dependence of critical strain amplitude (γcrit) and Weissenberg number (γcritDe) on De are summarized in Figure 4. In Figure 4a, γcrit decreased monotonously until De was close to 1, while γcrit remained constant (about 0.3) as De was further increased. As shown in Figure 4b, the Weissenberg number (Wicrit = γcritωτ = γcritDe) at the onset of strain hardening was about 0.17−0.35 for all the samples when De < 1, while Wicrit increased sharply when De > 1. In addition, the Weissenberg number at the onset of shear thickening (Wisscrit = γ̇critτ) was in the range 0.12−0.38 under steady shear (shown in Part VIII of E


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Macromolecules Pipkin diagrams.37,38 However, the characteristic value of De as 1 was indeed important to the rheological behavior of PVA/ borate hydrogels, and this will be discussed below. Comparison between Strain Sweep and Steady Shear. According to the results in Figure 4, we inferred that strain hardening behavior as De < ∼0.2 (Region 1) was controlled by strain rate. Then, we compared the results from strain sweep and steady shear in Figure 5. For ω = 0.5 rad/s (De < ∼0.2,

Figure 6. (a) Normalized stress (σt/σ) and elastic stress (σ′t/σ) versus strain (γt/γ) at ω = 0.5 rad/s, γ = 15.74. (b) Normalized stress (σt/σ) and viscous stress (σ″t/σ) versus strain rate (γ̇t/γ̇) at ω = 0.5 rad/s, γ = 15.74. (c) σt/σ and σ′t/σ versus γt/γ at ω = 50 rad/s, γ = 1.96. (d) σt/σ and σ″t/σ versus γ̇t/γ̇ at ω = 50 rad/s, γ = 1.96. The sample was 0.03 g/mL PVA aqueous solution with 2% SB.

Figure 5. Shear viscosity η versus shear rate γ̇ from steady shear experiments (open symbol) and complex viscosity |η*| versus strain rate amplitude γω from strain sweep experiments (line). The sample was 0.03 g/mL PVA aqueous solution with 2% SB.

where γ is the strain amplitude of oscillatory shear and γt is instantaneous strain within a cycle. The elastic Lissajous plot in Figure 6a (ω = 0.5 rad/s, γ = 15.74) shows G′L < G′M, which corresponds to intracycle strain softening. While at ω = 50 rad/ s and γ = 1.96, the elastic Lissajous plot (Figure 6c) exhibits G′L > G′M, i.e., intracycle strain hardening. In the viscous Lissajous plot, the curve of mean stress versus strain rate represents the viscous part of stress decomposition, i.e., σ″(t) ∼ γ̇(t).30,44 Minimum-strain rate dynamic viscosity (η′M) and large-strain rate dynamic viscosity (η′L) are defined as30

Region 1), the strain-hardening curve can almost overlap shear thickening curve, implying that intercycle strain hardening for De < ∼0.2 might have the same mechanism as that of shear thickening under steady shear experiments. For ω ≥ 3 rad/s (De > ∼0.2, Regions 2 and 3), the value of |η*| in linear response regime was apparently lower than zero-shear viscosity, which was in accordance with the development of |η*| in SAOS (shown in Figure 1b). Besides, the region of strain rate where strain hardening occurred was apparently higher than that of shear thickening. So strain hardening for De > ∼0.2 might have different mechanism compared to shear thickening. 3.3. Intracycle Strain Behavior. If the periodic stress response σ(t) is plotted against periodic strain γ(t) (elastic Lissajous curves) or periodic strain rate γ̇(t) (viscous Lissajous curves), a linear viscoelastic response appears as an ellipse that contains two mirror planes (the major and minor axes of the ellipse), whereas a nonlinear viscoelastic response is characterized by Lissajous curves that deviate from ellipticity,20,38 as shown in Figure 6. To study the intracycle strain behavior of PVA/borate hydrogels, a simple introduction about the data analysis of Lissajous plot based on stress decomposition and Fourier transform (FT) rheology is described below. For a sinusoidal strain input γ(t) = γ sin(ωt), the stress response σ(t) can be decomposed into two parts, i.e., elastic stress σ′(t) and viscous stress σ″(t).43 In the elastic Lissajous plot, the mean stress versus strain curve can be obtained, which represents the elastic part of stress decomposition, i.e., σ′(t) ∼ γ(t).30,44 Smallstrain elastic modulus (G′M) and large-strain elastic modulus (G′L) are expressed as30

dσ ′t G′M = dγt

η′M =

dσ ″t dγṫ

η′L =

σ ″t γṫ

σ ′t γt

(5)

γṫ = ±γ ̇

(6)

where γ̇ is the strain rate amplitude of oscillatory shear and γ̇t is the instantaneous strain rate within one cycle. The viscous Lissajous plot in Figure 6b (ω = 0.5 rad/s, γ̇ = 7.9 s−1) shows η′L > η′M, which indicates intracycle strain rate-induced hardening. The viscous Lissajous plot at ω = 50 rad/s and γ̇ = 97.9 s−1 (Figure 6d) demonstrates η′L < η′M, i.e., intracycle strain rate-induced softening. The decomposition of stress can be rewritten by using the Fourier transform method:45 σ (t ; ω , γ ) = γ

∑

|Gn*| sin(nωt + δn)

n odd

γt = 0

=γ

(3)

∑ n odd

G′L =

γṫ = 0

γt =±γ

G′n sin(nωt ) + γ

∑ n odd

G″n cos(nωt )

(7)

where |G*n| represent the intensities of n odd harmonic and δn is the corresponding phase angle of the n odd harmonic. G′1 and G″1 are the signals of first harmonic terms, and they are

(4) F


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Figure 7. (a) Normalized intracycle elastic modulus G′(ω,γt)/G′(ω,γt=0) versus instantaneous strain γt within one cycle (lines) and normalized intercycle first harmonic elastic modulus (G′1/G′1 lin) versus strain amplitude γ (open symbols). (b) Normalized intracycle dynamic viscosity η′(ω,γ̇t)/η′(ω,γ̇t=0) versus instantaneous strain rate γ̇t within one cycle (lines) and normalized intercycle first harmonic dynamic viscosity (η′1/η′1 lin) versus strain rate amplitude γ̇ (open symbols). Sample was 0.03 g/mL PVA aqueous solution with 2% SB. Scanning frequencies ranged from 0.1 to 50 rad/s. The original results were obtained from series of oscillatory time sweep experiments.

∼0.2, Region 1). In Region 1 (ω ≤ 1 rad/s), for a given scanning frequency, the growth curves of η′(ω,γ̇t)/η′(ω,γ̇t=0) under different strain rate amplitudes can almost overlap, and the threshold strain rate of intracycle strain rate-induced hardening (γ̇t crit) is the same as that of intercycle strain hardening (γ̇crit). As shown in Figure 7, whether intercycle strain hardening needs to exceed a threshold strain or strain rate is related to the type of intracycle behavior. For De < ∼0.2 (Region 1), intercycle strain hardening occurred with the constant value of γ̇crit, and samples exhibited intracycle strain rate-induced hardening. For De > ∼2 (Region 3), intercycle strain hardening occurred with the constant value of γcrit, and intracycle strain hardening was observed.

equal to storage modulus (G′) and loss modulus (G″) provided by a commercial rheometer. To investigate the change from G′M to G′L in the elastic Lissajous plot and the change of η′M to η′L in the viscous Lissajous plot, the other two parameters are used below. The intracycle elastic modulus G′(ω,γt) within elastic Lissajous plot is expressed as G′(ω , γt ) = G′1 + 3G′3 + 5G′5 −

4G′3 + 20G′5 γ2

γt 2 +

16G′5 γ4

γt 4

(8)

In the viscous Lissajous plot, the intracycle dynamic viscosity η′(ω,γ̇t) is defined as η′(ω , γṫ) =

G″1 − 3G″3 + 5G″5 4G″3 − 20G″5 2 16G″5 4 + γṫ + 5 4 γṫ ω ω3γ 2 ωγ

4. DISCUSSION 4.1. Mechanism of Intercycle Strain Hardening. Proposed mechanisms of intercycle strain hardening for polymer networks fall into either of the two following main categories: one is nonlinear high tension along chains that are stretched beyond the Gaussian range,6,8,46,47 and the other is the deformation-induced increase in the number of elastically active chains.5,10,48 Two mechanisms above can be investigated by the following experimental results: (1) the change in relaxation time of network during strain hardening; (2) the change in phase angle (δ) of samples during strain hardening; (3) the degree of strain hardening. The analysis of these results for 0.03 g/mL PVA aqueous solution with 2% SB during strain hardening is shown below as an example. Change of Relaxation Time during Strain Hardening. The relaxation time (τ) of the associative network is related to the

(9)

where the first-, third-, and fifth-order contributions for each signal were considered in eqs 8 and 9. Each line in Figure 7a represents the development of intracycle elastic modulus G′(ω,γt) (abbreviated as G′t for following discussion) within a oscillatory period. As shown in Figure 7a, G′t exhbits as intracycle strain softening for ω ≤ 10 rad/s (De < ∼2, Regions 1 and 2), while as intracycle strain hardening for ω ≥ 20 rad/s (De > ∼2, Region 3). With the treatment of the viscous Lissajous plot, the development of intracycle dynamic viscosity η′(ω,γ̇t) (abbreviated as η′t for the following discussion) within the viscous Lissajous plot is shown in Figure 7b, where η′t exhibits intracycle strain rate-induced softening as ω ≥ 3 rad/s (De > ∼0.2, Regions 2 and 3) and intracycle strain rate-induced hardening as ω ≤ 1 rad/s (De < G


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contribution of two factors should be taken into account: the network behaves more elastic-like due to stretching of polymer chains, and δ is supposed to decrease;31 partial rupture of the network due to overstretching of polymer chains will dissipate energy, and δ of material is supposed to increase.8,51 Thus, δ will exhibit nonmonotonous evolution in strain hardening region: δ decreases at the early stage of strain hardening due to stretching of polymer chains; δ increases at the late stage of strain hardening due to partial rupture of the network. The rupture of network at the late stage of strain hardening can be observed through oscillatory time sweep test with fixed scanning frequency and strain amplitude (shown in Part IX of the Supporting Information). Under different scanning frequencies, the change of δ during strain sweep is shown in Figure 9. Two categories of

density of cross-linkers in the network, and strain-induced increase in the number of elastically active chains can result in the increase of τ during strain hardening.32,49 For transient network, the non-Gaussian stretching of polymer chain can increase the dissociation rate (kd) of cross-linkers,50 and accordingly, the lifetime of single cross-linker decreases, which will cause the decrease of τ. At the same time, under overstretching of polymer chains during strain hardening, τ was also reported to decrease because of the partial break of the network.8 As shown in Figure 8, two strains in the linear

Figure 9. Phase angle (δ) versus strain amplitude (γ) for 0.03 g/mL PVA aqueous solution with 2% SB during strain sweep experiments. Scanning frequency was between 0.1 and 50 rad/s.

deformation can be divided: for ω ≤ 5 rad/s (De < 1), δ monotonously decreased in the regime of strain hardening; for ω ≥ 10 rad/s (De > 1), δ decreased at the primary stage of strain hardening and then increased sharply. The change of phase angle indicated that increasing in number of the elastic active chains caused the strain hardening as De < 1, while strain hardening as De > 1 was credited to non-Gaussian stretching of polymer chain. Degree of Strain Hardening. The degree of strain hardening of storage modulus (G′max/G′lin) and loss modulus (G″max/ G″lin) can be expressed by52

Figure 8. (a) Storage (G′) and loss modulus (G″) versus strain amplitude (γ) for 0.03 g/mL PVA aqueous solution with 2% SB during strain sweep experiments under different scanning frequencies (3, 5, and 10 rad/s). (b) G′ and G″ versus frequency (ω) for 0.03 g/mL PVA aqueous solution with 2% SB under different strain, and three different strains from linear to nonlinear regime were used.

response regime (γ = 0.03 and 0.3) and a strain in the nonlinear response regime (γ = 2.5) were used for the oscillatory frequency sweep experiments from about 3 to 10 rad/s, and the crossover frequency (ωc) was observed to fall down as the strain increased from 0.3 to 2.5. The increase of relaxation time of samples during strain hardening indicated that the mechanism of increase in the number of elastically active chains dominated here (De < 1). For the mechanism of strain hardening under higher scanning frequency as De > 1, it is impossible to use the same method shown in Figure 8 as the crossover frequency (ωc) of G′ and G″ cannot be directly obtained in the experimental range. Change of Phase Angle during Strain Hardening. The phase angle (δ, i.e., first-harmonic phase angle δ1) indicates the comparison of stored energy and dissipated energy as heat during deformation. If strain hardening results from an increase in the number of elastically active chains, the meshes in network will be more compact, and material tends to be more elastic-like with the reduction of δ.25 For strain hardening induced by non-Gaussian stretching of polymer chains, the

G′max /G′lin = (G″max /G″lin )(tan δ lin/tan δmax )

(10)

where δlin and δmax are the phase angle in linear regime and at the maximum strain, respectively. If the strain hardening behavior is caused by the increasing of the number of elastically active chains, δ will decrease during strain hardening; according to eq 10, G′max/G′lin > G″max/G″lin can be obtained.25 For strain hardening result from non-Gaussian stretching of polymer chain, δ will increase when the strain is approaching to γmax, which may induce δmax > δlin. According to eq 10, the value of G′max/G′lin might be smaller than that of G″max/G″lin.29,53 As shown in Figure 10, magnitudes of strain hardening of G′ and G″ were both related to De. When De < 1, G′max/G′lin > G″max/G″lin, which was consistent with the mechanism of increasing number of elastically active chains. When De > 2, G′max/G′lin < G″max/G″lin, which implied that the mechanism of non-Gaussian stretching of polymer chain dominated. When 1 < De < 2, it was known that δ decreased at the primary stage of strain hardening and increased again when strain was close to maximum strain (γmax), indicating that the mechanism of nonH


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Region 2 (∼0.2 < De < ∼2), S < 0, H < 0; Region 3 (De > ∼2), S > 0, H < 0. According to eqs 11 and 12, the value of the thirdharmonic phase angle δ3 can conflate the nature of viscous and elastic nonlinearity.20 As shown in Figure 11b, δ3 clockwise turned from the first quadrant to third quadrant as De increased, where the material changed from viscous-like to elastic-like, and Regions 1, 2, and 3 of De corresponded to quadrants 1, 4, and 3 of δ3, respectively. When De < ∼0.2 (Region 1), H > 0 represents the intracycle strain rate-induced hardening in viscous Lissajous curves. As shown in Figure 7b, the critical strain rate of intracycle strain rate-induced hardening (γ̇t crit) was close to that of intercycle strain hardening (γ̇crit). So, it is inferred that the intracycle strain rate-induced hardening had the same mechanism as intercycle strain hardening for De < ∼0.2, i.e., strain rate-induced increase in the number of elastically active chains. For instantaneous strain γt changed from 0 to γ, S < 0 means that intracycle elastic modulus G′t decreased; at the same time, instantaneous strain rate γ̇t changed from γ̇ to 0. Namely, for De < ∼0.2, H > 0 and S < 0 indicated that both intracycle dynamic viscosity η′t and intracycle elastic modulus G′t increased with instantaneous strain rate γ̇t. When De > ∼2 (Region 3), S > 0 corresponds to intracycle strain hardening in elastic Lissajous curves in accordance with intercycle strain hardening, and both behaviors were related to strain. Thus, intracycle strain hardening should follow the same mechanism as intercycle strain hardening for De > ∼2, i.e., strain-induced non-Gaussian stretching of polymer chains. For instantaneous strain rate γ̇t changed from 0 to γ̇, H < 0 means that the intracycle dynamic viscosity η′t decreased; simultaneously, the instantaneous strain γt decreased from γ to 0. Namely, for De > ∼2, S > 0 and H < 0 indicated that both η′t and G′t increased with instantaneous strain γt. When ∼0.2 < De < ∼2 (Region 2), H < 0 indicated that η′t decreased with γ̇t (increased with γt); however, S < 0 indicated that G′t increased with γ̇t (decreased with γt). It was inferred that both strain and strain rate can affect the strain behavior as ∼0.2 < De < ∼2, which is consistent with the phenomenon that both γcrit and γcritDe changed with De in Region 2. As a result, we can observe the more complex intracycle behavior in Region 2. For De < ∼0.2 (Region 1), intercycle strain hardening was similar to shear thickening under steady shear; thus, another characteristic strain rate with Wi = 1 should be considered, where Wi > 1 corresponds to orientation and non-Gaussian stretching of polymer chains in the polymer solution.54 For the intracycle strain rate-induced hardening, by the help of stress

Figure 10. Degree of strain hardening versus the Deborah number (De) for 0.03 g/mL PVA with 2% SB during strain sweep experiments under different scanning frequencies.

Gaussian stretching of polymer chain dominated here. However, the value of G′max/G′lin was larger than that of G″max/G″lin as 1 < De < 2. It was apparent that the above assumption that δmax > δlin may not keep correct under the mechanism of non-Gaussian stretching of polymer chain. The degree of strain hardening only compared the moduli at the maximum strain with the value in linear response regime, and this method failed to distinguish the two mechanisms of strain hardening when the assumption that δmax > δlin did not hold under the mechanism of non-Gaussian stretching of polymer chain. 4.2. Mechanism of Intracycle Strain Hardening. In the viscous Lissajous plot, intracycle strain rate-induced hardening ratio (H) was introduced to quantificate the degree of intracycle nonlinearity. Similarly, the intracycle strain−stiffening ratio (S) can express the degree of intracycle nonlinearity in the elastic Lissajous plot:30,44 H=

S=

4|G3*| sin δ3 + ... η′L − η′M = η′L η′L −4|G3*| cos δ3 + ... G′L − G′M = G′L G′L

(11)

(12)

where “...” represents the contribution of the fifth and even higher harmonic, which is much less than the contribution of the third harmonic. Similar to the dependence of γcrit and γcritDe on De, the development of S and H in Figure 11a can be classified into three regions by De: Region 1 (De < ∼0.2), S < 0, H > 0;

Figure 11. Intracycle nonlinearity parameters in intercycle strain hardening regime: (a) Development of intracycle strain rate-induced hardening ratio (H) and intracycle strain hardening ratio (S). Three regions were classified by De. (b) Polar plot of third-harmonic phase angle (δ3) versus strain amplitude (γ). (c) Development of H with strain rate amplitude (γ̇) in Region 1. The sample was 0.03 g/mL PVA aqueous solution with 2% SB. I


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Macromolecules decomposition and Fourier transform (FT) rheology, it was possible to observe the contribution from non-Gaussian stretching of polymer chains as Wi > 1. Figure 11c displays the development of H versus strain rate amplitude in intercycle strain hardening regime, where H gradually deviated from zero and increased until γ̇a = 6.3−7.9 s−1; then it decreased as strain rate amplitude was further increased. For γ̇ = γ̇a, the value of Weissenberg number (Wia = γ̇aτa) can be calculated by using the apparent relaxation time (τa = 0.16 s, in Figure 8b) of the sample in strain hardening regime; thus Wia = ∼1. As shown in Part IX of the Supporting Information, for Wi > 1 (LAOS at ω = 0.5 rad/s and γ̇ = 7.92 s−1), the sample switched from one state to another within first cycle, and the new state was stable during LAOS.40 Thus, the decrease of H at Wi > 1 was not caused by the instability of structure of sample over time. When Wi > 1, the tension of polymer chains along the orientation direction increases, and the strain hardening in the elastic part begins to do more contribution. Conversely, the relative contribution of viscous part to strain hardening will decrease; thus, the value of H can be observed to decrease. According to above discussion, for De < ∼0.2, non-Gaussian stretching of polymer chains did contribute to the strain rate-induced hardening behavior when Wi > 1. 4.3. What Did De = 1 Mean? The influence of characteristic value of De as 1 on the rheological behavior of PVA/borate hydrogels was further discussed here. For intercycle strain hardening behavior, the monotonous decrease of first-harmonic phase angle (δ1) in strain hardening regime revealed that strain-rate-induced increase in the number of elastically active chains dominated as De < 1. While, for De > 1, δ decreased at the primary stage of strain hardening and then increased sharply at the late stage, which indicated that nonGaussian stretching dominated for De > 1. It seems that De = 1 can be used to distinguish the relative contribution of two strain hardening mechanisms for intercycle strain hardening behavior. When De < ∼0.2, H > S indicated that strain rate-induced viscous behavior dominated strain hardening. Conversely, for De > ∼2, S > H indicated that strain-induced elastic behavior dominated. So, it is inferred that the difference for the value of S and H might can be used to distinguish whether viscous behavior or elastic behavior dominate. For intracycle strain behavior, it was interesting to observed that the difference for the value of S and H can also be divided by De = 1 (Figure 12a). When De < 1, H > S, the viscous property of network should dominate. While S > H as De > 1, the elastic property dominate the strain hardening behavior. The magnitude relation between S and H is accordance with that of scaled third harmonic elastic Chebyshev coefficient (e3/ e1 = −G′3/G′1) and scaled third harmonic viscous Chebyshev coefficient (υ3/υ1 = G″3/G″1). Moreover, the magnitude of e3/ e1 and υ3/υ1 can be formulated as −2I3/1 sin(δ1 + δ3) e3 υ − 3 = e1 υ1 sin 2δ1

Figure 12. Intracycle nonlinearity parameters in intercycle strain hardening regime: (a) Development of intracycle strain rate-induced hardening ratio (H) and intracycle strain hardening ratio (S). The magnitude of H and S was classified by De = 1. (b) Polar plot of relative phase angle (δ1 + δ3) versus strain amplitude (γ).The sample was 0.03 g/mL PVA aqueous solution with 2% SB.

Supporting Information discussed how the magnitude relation between e3/e1 and υ3/υ1 affected the shape of the stress wave.

5. CONCLUSIONS The large-amplitude oscillatory shear (LAOS) behaviors of PVA/borate hydrogels were explored with the change of scanning frequency as well as concentrations of borate and PVA. The four different types (Types I−IV) of LAOS behavior were successfully classified by the mean number of elastically active subchains per PVA chain (feas) and Deborah number (De = ωτ, where τ is the relaxation time of samples in the linear response regime). By this method, the types of nonlinear LAOS behavior of PVA/borate hydrogels can be predicted by the parameters feas and De obtained in the linear rheological regime. For PVA/borate hydrogels with Type I behavior, the onset of intercycle strain hardening showed strong dependence on De. Three regions were involved: Region 1 (De < ∼0.2), critical strain rate amplitude γ̇crit remained constant; Region 3 (De > ∼2), critical strain amplitude γcrit was almost constant; Region 2 (∼0.2 < De < ∼2), both γcrit and γ̇crit changed with De. For PVA/borate hydrogels with Type I behavior, the types of intracycle behavior also exhibited clear dependence on De, and the three regions included: Region 1 (De < ∼0.2), intracycle strain rate-induced strain hardening (intracycle strain-rateinduced hardening ratio H > 0) and intracycle strain softening (intracycle strain hardening ratio S < 0); Region 2 (∼0.2 < De < ∼2), intracycle strain softening (S < 0) and intracycle strain rate-induced softening (H < 0); Region 3 (De > ∼2), intracycle strain hardening (S > 0) and intracycle strain rate-induced softening (H < 0). The analysis of the onset of intercycle strain hardening, types of intracycle behavior, and the comparison between strain sweep and steady shear revealed that strain hardening was controlled by strain rate in Region 1 and by strain in Region 3. In Region 2, both strain and strain rate affected the strain hardening behavior. The mechanism of intercycle and intracycle strain hardening was explored by analyzing the relaxation time, phase angle, degree of strain hardening, shape of Lissajous curves, results of stress decomposition, Fourier transform (FT) rheology, etc. For Region 1 (De < ∼0.2), both intercycle strain hardening and intracycle strain rate-induced hardening were mainly caused by the strain-rate-induced increase in the number of elastically active chains, while non-Gaussian stretching of polymer chains started to contribute as Wi > ∼1. In Region 3 (De > ∼2), both intercycle and intracycle strain hardening resulted from strain-induced non-Gaussian stretching of

(13)

where the normalized intensity of third harmonic wave I3/1 = | G*3|/|G*1| > 0, sin 2δ1 > 0. Thus, the value of relative phase angle (δ1 + δ3) can determine the magnitude relation between S and H. As shown in Figure 12b, δ1 + δ3 clockwise turned from second quadrant to third quadrant as De increased: for De < 1, 0° < δ1 + δ3 < 180° equaled to H > S; for De > 1, 180° < δ1 + δ3 < 360° corresponded to S > H. In addition, Part X of the J


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Macromolecules polymer chains. In Region 2 (∼0.2 < De < ∼2), two mechanisms above both contributed to intercycle strain hardening. De = 1 can be used to distinguish the relative contribution of two involved mechanisms for intercycle strain hardening behavior. When De < 1, the monotonic decrease of δ1 and larger value of intracycle strain-rate-induced hardening ratio (H) than intracycle strain hardening ratio (S) in the regime of strain hardening revealed that intercycle strain hardening was dominated by strain-rate-induced increase in the number of elastically active chains. When De > 1, the nonmonotonic change of δ1 and S > H in strain hardening regime indicated that strain-induced non-Gaussian stretching dominated. Looking ahead, the mechanistic understanding of the strain hardening behavior of these physical gels provides a foundation for further work in which the LAOS behavior can be controlled through the rational molecular-scale design of physical gels.

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(3) Maeda, T.; Otsuka, H.; Takahara, A. Dynamic Covalent Polymers: Reorganizable Polymers with Dynamic Covalent Bonds. Prog. Polym. Sci. 2009, 34, 581−604. (4) Appel, E. A.; del Barrio, J.; Loh, X. J.; Scherman, O. A. Supramolecular Polymeric Hydrogels. Chem. Soc. Rev. 2012, 41, 6195− 6214. (5) Wang, S. Q. Transient Network Theory for Shear-Thickening Fluids and Physically Crosslinked Networks. Macromolecules 1992, 25, 7003−7010. (6) Marrucci, G.; Bhargava, S.; Cooper, S. L. Models of ShearThickening Behavior in Physically Cross-Linked Networks. Macromolecules 1993, 26, 6483−6488. (7) Tam, K. C.; Jenkins, R. D.; Winnik, M. A.; Bassett, D. R. A Structural Model of Hydrophobically Modified Urethane-Ethoxylate (HEUR) Associative Polymers in Shear Flows. Macromolecules 1998, 31, 4149−4159. (8) Séréro, Y.; Jacobsen, V.; Berret, J. F.; May, R. Evidence of Nonlinear Chain Stretching in the Rheology of Transient Networks. Macromolecules 2000, 33, 1841−1847. (9) Tripathi, A.; Tam, K. C.; McKinley, G. H. Rheology and Dynamics of Associative Polymers in Shear and Extension: Theory and Experiments. Macromolecules 2006, 39, 1981−1999. (10) Suzuki, S.; Uneyama, T.; Inoue, T.; Watanabe, H. Nonlinear Rheology of Telechelic Associative Polymer Networks: Shear Thickening and Thinning Behavior of Hydrophobically Modified Ethoxylated Urethane (HEUR) in Aqueous Solution. Macromolecules 2012, 45, 888−898. (11) Sinton, S. W. Complexation Chemistry of Sodium Borate with Poly(vinyl alcohol) and Small Diols. A 11B NMR Study. Macromolecules 1987, 20, 2430−2441. (12) Ahn, K. H.; Osaki, K. A Network Model for Predicting the Shear Thickening Behavior of a Poly(vinyl alcohol) Sodium-Borate Aqueous Solution. J. Non-Newtonian Fluid Mech. 1994, 55, 215−227. (13) Koike, A.; Nemoto, N.; Inoue, T.; Osaki, K. Dynamic Light Scattering and Dynamic Viscoelasticity of Poly(vinyl alcohol) in Aqueous Borax Solutions. 1. Concentration-Effect. Macromolecules 1995, 28, 2339−2344. (14) Narita, T.; Mayumi, K.; Ducouret, G.; Hébraud, P. Viscoelastic Properties of Poly(vinyl alcohol) Hydrogels Having Permanent and Transient Cross-Links Studied by Microrheology, Classical Rheometry, and Dynamic Light Scattering. Macromolecules 2013, 46, 4174− 4183. (15) Narita, T.; Indei, T. Microrheological Study of Physical Gelation in Living Polymeric Networks. Macromolecules 2016, 49, 4634−4646. (16) Cheng, A. T. Y.; Rodriguez, F. Mechanical Properties of Borate Crosslinked Poly(vinyl alcohol) Gels. J. Appl. Polym. Sci. 1981, 26, 3895−3908. (17) Schultz, R. K.; Myers, R. R. The Chemorheology of Poly(vinyl alcohol)-Borate Gels. Macromolecules 1969, 2, 281−285. (18) Hyun, K.; Kim, S. H.; Ahn, K. H.; Lee, S. J. Large Amplitude Oscillatory Shear as a Way to Classify the Complex Fluids. J. NonNewtonian Fluid Mech. 2002, 107, 51−65. (19) Hyun, K.; Nam, J. G.; Wihlem, M.; Ahn, K. H.; Lee, S. J. Nonlinear Response of Complex Fluids under LAOS (Large Amplitude Oscillatroy Shear) Flow. Korea-Australia Rheol. J. 2003, 15, 97−105. (20) Hyun, K.; Wilhelm, M.; Klein, C. O.; Cho, K. S.; Nam, J. G.; Ahn, K. H.; Lee, S. J.; Ewoldt, R. H.; McKinley, G. H. A Review of Nonlinear Oscillatory Shear Tests: Analysis and Application of Large Amplitude Oscillatory Shear (LAOS). Prog. Polym. Sci. 2011, 36, 1697−1753. (21) Lim, H. T.; Ahn, K. H.; Hong, J. S.; Hyun, K. Nonlinear Viscoelasticity of Polymer Nanocomposites under Large Amplitude Oscillatory Shear Flow. J. Rheol. 2013, 57, 767−789. (22) Sim, H. G.; Ahn, K. H.; Lee, S. J. Large Amplitude Oscillatory Shear Behavior of Complex Fluids Investigated by a Network Model: A Guideline for Classification. J. Non-Newtonian Fluid Mech. 2003, 112, 237−250.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.6b02393. Part I: concentration regime of pure PVA aqueous solution at 25 °C; Part II: comparison between strain sweep and series of oscillatory time sweep experiment; Part III: SAOS and 11B NMR spectra of PVA/borate hydrogels; Part IV: whether G′ and G″ started to decrease at the same strain; Part VI: strain sweep results of PVA/borate hydrogels; Part VII: zero-shear viscosity of samples; Part VIII: steady shear results of PVA/borate hydrogels; Part IX: time evolution of the Lissajous plot; Part X: shape of stress wave related to e3/e1 and υ3/υ1 (PDF) Part V: video of LAOS at {ω = 1 rad/s, γ = 20} (AVI)

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AUTHOR INFORMATION

Corresponding Authors

*(D.X.) E-mail [email protected]; Tel +86 (0) 431 85262516; Fax +86 (0) 431 85262969. *(T.S.) E-mail [email protected]; Tel +86 (0) 431 85262309; Fax +86 (0) 431 85262969. ORCID

Donghua Xu: 0000-0003-1828-1210 Tongfei Shi: 0000-0002-6763-2200 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (21274152, 51473168, 21234007, and 21674114). H.S. is thankful for the financial support by Open Research Fund of State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences (201507).

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Borate Hydrogels

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