Article Cite This: Macromolecules XXXX, XXX, XXX−XXX
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Dynamics of Supramolecular Self-Healing Recovery in Extension Zachary R. Hinton,† Aamir Shabbir,‡ and Nicolas J. Alvarez*,† †
Department of Chemical and Biological Engineering, Drexel University, Philadelphia, Pennsylvania 19104, United States Department of Chemical Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
‡
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S Supporting Information *
ABSTRACT: Self-healing materials are prized for their ability to recover mechanical properties after damage. Supramolecular polymer networks have been demonstrated to have the ability to recover without the need for extraneous material components or the use of external stimuli. Surprisingly, there is little quantitative measure of self-healing dynamics and recovery. In this work, we develop a tool using a filament stretching rheometer to probe self-healing dynamics in creep and constant rate of extension. We experimentally determine the effect of process time scales, τH and τW, on the degree of recovery for two distinct supramolecular architectures. These results are put into the context of molecular time scales such as disengagement time, the Rouse time, and bond lifetime. We find that entangled polymers undergo sequential healing, whereby at short times, dynamics are dominated by entanglement recovery followed by recovery of associations. For an unentangled polymer, recovery is seemingly dominated by association dynamics. Our experimental results are put into the context of leading theoretical models. We also introduce the importance of the measurement flow time scale on perceived material recovery. These initial results and reliable experimental tools begin to construct a framework for measuring, understanding, and predicting recovery of self-healing soft materials.
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INTRODUCTION Supramolecular networks are a diverse class of polymeric materials which are cross-linked via secondary interactions (often termed stickers or associations) such as hydrogen bonding,1−4 ionic5,6/metallic7,8 interactions, and steric assemblies9,10 (e.g., π−π stacking). These networks are highly promising as autonomic self-healing materials, i.e., materials which, after damage, can partially or fully recover mechanical strength without outside intervention.11−16 While many traditional self-healing polymers require the introduction of a reactive species to recover,17−24 some self-healing polymers recover intrinsically via polymer dynamics.11 Although in some applications these dynamics are enhanced using heat25,26 or solvent,27,28 materials that are both autonomic and intrinsic are highly desirable. When a supramolecular network is fractured, a nonequilibrium state is created consisting of stretched and dangling chains and unpaired associations. When the fractured surfaces are put into contact, both entanglements and associations re-form across the interface, in essence healing the material. Given sufficient time, the interface is said to achieve a steady state recovery. The rate at which the material approaches this steady state, i.e., original material properties, is critical to the efficacy of self-healing supramolecular networks. Little experimental data are available on self-healing dynamics. Moreover, it is not clear how best to measure self-healing recovery of viscoelastic materials. Typically self-healing dynamics are measured via mechanical testing.12,14 However, these are not standard techniques, and therefore the results are © XXXX American Chemical Society
mostly qualitative. Various measures of recovery have been made using shear rheology of entangled polymers,29 selfassembled gels,30−33 block copolymers,34 telechelic polymers,35,36 and ionomers;37 however, application of damage is difficult to interpret, measurements are often only characteristic of the applied flow, and systematic choices of parameters are seldom used. The field is in need of a controlled, reproducible technique to measure self-healing dynamics after controlled fracture as a function of material and process parameters. Experiments on supramolecular self-healing dynamics suggest that there are two important process time scales: the waiting time (τW) and the healing time (τH). τW is defined from the time of fracture to the time the material halves are recontacted. During τW, the two halves of the material evolve toward unique states which may differ from that of the undamaged material. Several measurements of self-healing recovery as a function of waiting time show that a material’s ability to heal is significantly decreased the longer the material halves remain separated.14,15,38 In fact, some sources suggest that at sufficiently long waiting times a material loses its ability to heal.3 τH begins when the two halves are recontacted, and the material recovers some degree of its undamaged mechanical properties. Mechanical testing of supramolecular networks shows that healed samples follow the same stress/ Received: November 14, 2018 Revised: February 20, 2019
A
DOI: 10.1021/acs.macromol.8b02423 Macromolecules XXXX, XXX, XXX−XXX
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stretching rheometry is that the damage to the interface is controllable and reproducible. Herein we define a robust measurement technique that can quantify self-healing dynamics as a function of τW, τH, and architecture using creep and constant rate of extension. We outline the fundamental parameters needed to quantify the rheological nature of selfhealing supramolecular polymer networks. We perform experiments on two well-studied hydrogen-bonding supramolecular networks: entangled poly(n-butyl acrylate)41,44,45 and unentangled poly(methoxyethyl acrylate).42 These polymers represent common supramolecular network architectures with varying: number of associations, molecular weights, number of entanglements, and relaxation times, which are useful for highlighting the robustness of our measurements and testing current models. We present our results in the context of the model developed by Stukalin et al. and test the generality of the model to entangled polymer architectures.13 Lastly, we also determine the importance of the measurement flow time scale on perceived recovery. The organization of the paper is as follows: (i) We first introduce the experimental protocol and test the importance of experimental parameters such as contact force and reproducibility on measured recovery. (ii) We examine the importance of τW for the two model polymers and compare the results with the model of Stukalin et al.13 (iii) We then examine the dependence of recovery on τH as a function of entanglements and number of associations. (iv) Finally, we show the dependence of measured recovery on the applied flow kinematics. Overall, this work defines a reproducible method to characterize healing dynamics in supramolecular systems and sets a foundation for our understanding of supramolecular recovery as a function of molecular parameters (time scales).
strain curve as the pristine material, but break at a reduced stress/strain proportional to τH. The rate at which this recovery occurs appears to be dependent on both τW and the network architecture.14,15,26,38−40 At present there is a scatter of results testing the effects of τW and τH. What is really needed is a systematic study for various molecular architectures to build a general framework for self-healing dynamics. While experimental data are lacking, theorists have proposed models for supramolecular self-healing. For example, the comprehensive theoretical framework of Stukalin et al. predicts the number of associating bonds (“bridges”) formed across the fractured interface as a function of time for different unentangled architectures and varying τW and τH.13 The authors conclude that the mode and dynamics of recovery are uniquely determined by the value of τW, since it defines the state of the damaged surfaces before recovery. For high bond strength, ϵ, defined as ϵ ≫ 2kBT ln(N), where N is the number of monomers in a sticky segment, Stukalin and co-workers define four recovery regimes that are bounded by the relative value of τW to τR, the Rouse time of a dangling chain, τb, the average association lifetime, τeq, the equilibration time of open stickers, and τadh, the time to reach the undamaged state. For τW < τR, dangling chains do not have sufficient time to diffuse away from the fractured surface, and therefore associations readily recover to a subequilibrium state. For τH < τR, the degree of recovery is proportional to τH and constant for τR < τH < τeq. For τR < τW < τb, dangling chains diffuse away from the fractured surface, and paired associations do not have sufficient time to exchange partners. This regime is characterized by very little recovery with increasing τH until τH = τeq. For τb < τW < τeq, new dangling chains are available but are scavenged by associating groups within the respective network and are not available for bridging at the fractured surface. This leads to even slower recovery with τH until τH = τeq. Lastly, for τeq < τW < τadh, recovery is increasing with τH and results in the lowest degree of recovery. For τH ≫ τeq, the number of bridges is the same for all values of τW. While this model has broad implications on our understanding of healing dynamics, current experimental techniques are not able to validate the model. Recent rheological studies have quantified the important molecular time scales governing supramolecular polymer dynamics. These time scales are highly dependent on: the number, strength, and distribution of associating groups along the polymer backbone.41−45 For example, the longest relaxation time, λ, of a given polymer is strongly affected by the presence of associations. This is most evident in their linear viscoelastic response, which shows an increase in modulus proportional to τb at low frequency (i.e., long times). Surprisingly, in entangled polymer melts, the hydrogen bonds have little effect on polymer dynamics at times faster than the disengagement time τd.41 It is important to keep these molecular time scales in mind when building our understanding of supramolecular healing dynamics. Furthermore, these time scales are argued to be essential in the model of Stukalin and co-workers.13 We expect that the relative ratio of processing to molecular time scales is key to developing a general framework and understanding. In this work, we modify a filament stretching rheometer to study the self-healing dynamics of viscoelastic materials. The filament stretching rheometer has been previously used to measure the linear and nonlinear dynamics of polymers under a wide range of conditions.42,46−54 One advantage in filament
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EXPERIMENTAL SECTION
Materials. Four example networks were used in this work. Figure 1 shows the chemical structure of the backbone and associating group
Figure 1. Structure of the polymer chemistries used in this work.
chemistries of the two polymer systems used. Poly(n-butyl acrylate), nBA, was hydrolyzed to achieve random copolymers of nBA and poly(acrylic acid), AA, with varying concentrations of AA hydrogen bonding groups along the backbone. The details of this synthesis and rheological characterizations are available in previous works.41,45 The current work utilizes the reference or “pure” nBA (containing 3% PAA naturally41) and the synthesized nBA-AA (6%) and nBA-AA (38%) copolymers. These identical networks, except for number of associating groups, represent model entangled networks. The fourth network is a random copolymer of poly(methoxyethyl acrylate), PMEA, containing 3% 6-methyl-2-ureido-4[1H]pyrimidone-bearing methacrylate groups, or UPyMA, obtained via free radical polymerB
DOI: 10.1021/acs.macromol.8b02423 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules Table 1. Molecular Weights, Sticker Compositions, and Charactaristic Relaxation Times of the Polymer Networks polymer
Mw (kDa)
PDI
ns (stickers/chain)
Ms (kDa)
λ (s)
Z
ϵ/kBT
ln N
MEA-UPyMA (3%) nBA nBA-AA (6%) nBA-AA (38%)
32.1 166 161 134
2.9 1.375 1.375 1.375
2 49 90 615
16.0 3.4 1.8 0.2
3 × 10−6 1.06 1.16 3.37
0 5a 5a 5a
28.2 12.1 12.1 12.1
4.8 3.2 2.6 0.4
a
Note degree of entanglement is calculated without considering the effect of associations.
Figure 2. Schematic of the sample forming, healing, and testing protocols used in this work. Constant position of the sample is held for the prescribed τH, after which the rheological characterization began. Two distinct rheological measurements were performed to probe recovery phenomena. Constant Hencky strain rate (ε̇H) experiments were conducted by continuous monitoring and control at the filament midplane.56 Strain rates were varied between 0.1 and 2.5 s−1. Creep experiments were conducted by maintaining constant stress, ⟨σzz − σrr⟩ = σ0, measured at the filament midplane. Creep stress was kept constant for all experiments at σ0 = 5 × 104 Pa. In constant rate of extension, stress growth coefficients, η̅ +(t), are calculated from measured stress and Hencky strain rate where η̅+(t) = ⟨σzz − σrr ⟩(t)/ε̇H. In creep, the compliance, J̅, is calculated from measured strain and the applied stress such that J̅(t) = εH(t)/σ0. η̅+(t) from creep experiments is calculated by smoothing J̅(t) and performing the
ization. The synthesis procedure and linear viscoelastic characterization for this system can be found in a previous work.42 Table 1 highlights the important characteristics of the melts used in this work as reported in previously, where Mw is the molecular weight and PDI is polydispersity index. The average number of hydrogenbonding groups, or stickers, per chain is represented by ns and is determined by NMR spectroscopy. Ms represents the molecular weight of the sticky segment, i.e., the equivalent length of a chain attached to one associating group, calculated as Mw/ns. The characteristic longest relaxation time of the melt is represented by λ. For nBA melts λ is the disengagement time, τd, determined by fitting a Baumgaertel−Schausberger−Winter (BSW) spectrum to small-amplitude oscillatory shear (SAOS) data.41 For MEA-UPyMA (3%), λ = τR, or the Rouse time, which is characteristic of the network backbone’s longest relaxation.42 The degree of entanglement, Z, is calculated using SAOS. The bond strength ϵ/kBT is a measure of the strength of a single associative group and is measured spectroscopically.55 There is a noticeable difference in ns between the unentangled and entangled networks; however, the relative bond strengths ϵ/kBT ln N, as defined by Stukalin et al. (see details in the Supporting Information), are of the same magnitude leading to favorable comparison. Extensional Rheology. Extensional rheology measurements were conducted using the VADER 1000 (Rheo Filament ApS). Cylindrical stainless steel sample plates with a diameter of 6 mm were used. The mass of each sample was on the order of 40 mg. Figure 2 illustrates the sample forming and testing procedure. Samples were first adhered to the top and bottom plates by heating the sample to 100 °C under nitrogen purge and applying a moderate force. Samples were then prestretched from an initial aspect ratio of Λ0 = L0/R0 = 0.167 to approximately Λ = 1.33, after which the sample was slowly cooled to room temperature (22.5 °C) and allowed to relax to zero stress. Filaments are then damaged by swiftly cutting the sample using a clean blade at the midpoint leaving two separate halves. The halves are maintained apart for some time, representing τW. The halves are then contacted at fixed approach velocity uc = 0.5 mm/s until the desired contact force, Fc, is achieved. The optimum Fc has been chosen by examining the stress at break for two τH for the most viscous network, MEA-UPyMA (3%), as shown in Figure S1 of the Supporting Information. As Figure S2 illustrates, there is a critical Fc required to achieve consistent measurements of the stress at break irrespective of τH. We have selected Fc = 10g such that consistency is achieved but excess deformation is not applied during recovery.
derivative where η ̅ +(t ) =
−1
( ) ∂J ̅ (t ) ∂t
. Linear viscoelastic envelopes
(LVE) are calculated using a multimodal Maxwell model fit to SAOS data.41,42 The LVE for η̅+(t) in constant rate of extension and creep are calculated separately according to eqs S7 and S9, respectively, with more details given in the Supporting Information. Creep compliance LVEs are calculated according to eq S8.53 Time−temperature superposition shift factors42,45 were used to shift all LVEs and relevant time scales to the testing temperature of 22.5 °C as necessary. All results are compared to the pristine material, defined as a sample which has been formed as described above but was kept intact before testing, representing the equilibrium state of the material. Properties at break are determined at the point where the filament begins to rupture and are denoted as η̅+break, σbreak, and εH,break for stress growth coefficient, the measured stress, and the strain at break, respectively. Additionally, we employ in our analysis both a stress (Rσ) and a strain (Rε) recovery fraction defined as σbreak and εH,break, respectively, normalized by that of the pristine material under the same flow conditions. It should be noted that the Rσ is equivalently calculated using η̅ +break for constant rate of extension experiments. To consistently compare results, creep experiments are also summarized using Rσ calculated with η̅+break; however, it is not equivalent to Rσ in terms of stresses in this case. This definition is necessary to account for the varying strain rates achieved as a function of time for different materials and degrees of recovery measured at the same stress. Examples of these transient strain rates are shown in Figure S6 for all melts. Using the healing protocol, we can achieve consistent transients for interfaces healed at identical conditions, as shown for example in Figure S3. Resulting σbreak and εH,break measurements have a standard deviation of 23% and 8%, respectively. C
DOI: 10.1021/acs.macromol.8b02423 Macromolecules XXXX, XXX, XXX−XXX
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Figure 3. Effect of τW on η̅+(t) (a, c) and stress−strain behavior (b, d) of nBA-AA (6%) and MEA-UPyMA (3%). To maintain detail at low εH, the pristine stress−strain curve for MEA-UPyMA has been omitted but can be seen in Figure 6d. The solid lines represent the LVE of the pristine network. The dash-dot line represents the LVE of pure nBA. Broken lines represent approximate η̅ +break and εH,break.
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polymer chains is not typically seen below ε = 1,57 and therefore insignificant recovery is expected to give a response which follows the LVE before breaking. While stress increases similarly for all τW ≤ 103 s, τW = 7 × 104 s shows different dynamics. Another important difference between MEAUPyMA and nBA-AA is that we observe an increasing η̅+break with increasing τW for τW ≤ 103 s for MEA-UPyMA. For τW = 7 × 103 s, we see that η̅+break starts to decrease again as observed in the case of nBA-AA (6%). Effect of τH on Recovery of Entangled Networks. For all subsequent healing measurements, we fix τW. For nBA-AA (6%), τW ≥ 103 s is used because recovery is no longer dependent on τW. Here τW ≈ τeq which, according to Stukalin et al., is expected to show a monotonically increasing number of bridges across the interface with increasing τH.13 For MEAUPyMA (3%) τW ≈ 103 s is used, at which time the maximum recovery with respect to τW is achieved. This gives τW ≈ τb, which is expected to give more complex bridge formation dynamics as a function of τH. From theory we expect the recovery of the mechanical properties of the network to be related to the number of interfacial bridges which have reformed. We use nonlinear extensional flow to probe the material properties using either constant stress or constant rate experiments. Typically tensile measurements are performed at constant velocity, which do not control the kinematics of the flow field. Using the VADER 1000, we control the kinematic flow and therefore are interested in comparing the recovery of the material in both flow fields.
RESULTS Effect of τW on Recovery. When a reversibly cross-linked network is damaged and contact is not immediately reestablished, both association and chain dynamics alter the state of the freshly damaged surfaces. We expect stress recovery to strongly depend on τW. According to Stukalin’s model,13 the recovery of the network should decrease with increasing τW for fixed τH. This is because at long τW, dangling chains have sufficient time to internalize stickers. Entangled Network. Figure 3a shows the effect of τW on η̅+(t) of nBA-AA (6%) for a fixed τH = 10 s, which is approximately 10λ, suggesting full relaxation of entanglements. For τW < 102 s, the network shows similar strain hardening behavior to the pristine network. For τW ≥ 102 s, η̅+(t) is significantly smaller than the pristine material response. More importantly, η̅+(t) is below the LVE for nBA-AA (6%). In fact, η̅+(t) appears to have no contributions from associating groups, i.e., follows the same response as pure nBA (dash-dot line). The same trends can be observed in Figure 3b in terms of measured stress versus applied strain. This figure highlights the dependence of εH,break on τW. For increasing values of τW the network becomes significantly more brittle and breaks at low Hencky strain. Unentangled Network. Figures 3c and 3d show the same experimental procedure as applied to MEA-UPyMA (3%). Unlike for nBA-AA (6%), η̅+(t) follows the LVE for all values of τW. The pristine MEA-UPyMA shows very little strain hardening compared to nBA-AA, and the network fractures at small strains for ε̇H = 0.1 s−1. Strain hardening in linear D
DOI: 10.1021/acs.macromol.8b02423 Macromolecules XXXX, XXX, XXX−XXX
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Figure 4. Effect of τH on creep response of entangled nBA networks in J̅(t) and η̅+(t). The solid lines represent the LVE of the pristine material for each plot. The dash-dot lines in (c)−(f) represent the nBA-AA (6%) LVE. The dash-dot-dot lines in (e)−(f) represent the nBA-AA (38%) LVE. Broken lines represent approximate η̅+ at break.
constant stress flow leads to noncreep behavior, as highlighted in Figure S5a,b and explained further in the Supporting Information. nBA-AA (6%) contains a moderate number of hydrogen bonding groups with an identical backbone to pure nBA. The compliance curves for this material are shown in Figure 4c. At low healing time, τH = 100 s, the material is more compliant than pure nBA, suggesting that frictional effects dominate and few associations are recovered. At τH = 101 s, the material has a compliance that is very similar to pure nBA for the same applied stress (see Figure 4a) but breaks at earlier time (lower strain). Increasing τH shows a drastic turnover in compliance, suggesting the recovery of associations across the fractured interface. Qualitatively above τH > 101 s, the compliance resembles a moderately cross-linked network, whereby crosslink density increases with τH.58 The similarity of compliance of nBA-AA (6%) to pure nBA at low τH is very clearly shown in Figure 4d in terms of η̅+(t). For τH = 100 s, strain hardening with respect to the pure nBA LVE (dash-dot line) is achieved. For τH = 101 s only slight strain hardening occurs with respect to pristine nBA-AA (6%) LVE, whereas τH ≥ 101 s shows
Creep. We first probe the effect of number of hydrogen bonding groups per chain on recovery dynamics using creep compliance, i.e., J̅(t), and calculate stress growth coefficients η̅+(t) as discussed in the Experimental Section. Figures 4a and 4b show the response for pure nBA. All compliance curves resemble a response typical of an amorphous polymer of low molecular weight. Furthermore, the shift of the compliance curve to higher times with τH is similar to a shift due to increasing molecular weight: suggesting increasing number of entanglements.58 Figure 4a shows that for τH ≤ 4 × 100 s the compliance curve is steeper than the pristine material response. For τH > 4 × 100 s the compliance curves follow the pristine material near the point of fracture. Nonlinear behavior is seen at long times for τH > 4 × 100 s. Figure 4b shows the corresponding η̅+(t) where the transition with τH is more noticeable. τH < 4 × 100 s shows a similar trend to the LVE of pure nBA, while τH > 2 × 101 s shows very similar strain hardening behavior to the pristine material. Note that in creep we expect that η̅+(t) approaches 3η0 faster than in constant rate of extension.53,59 However, at short experimental times creep η̅+(t) does not follow the creep LVE because start-up of the E
DOI: 10.1021/acs.macromol.8b02423 Macromolecules XXXX, XXX, XXX−XXX
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Figure 5. Effect of τH on nBA-AA (6%) under constant rate of extension, ε̇H = 0.1 s−1. The solid line represents the LVE for nBA-AA (6%) and the dash-dot line for pure nBA. Broken lines represent approximate η̅+break and εH,break.
Figure 6. Effect of τH on MEA-UPyMA (3%) in creep (a, b) and in constant rate of extension (c, d). Solid lines represent the MEA-UPyMA (3%) LVE. Broken lines represent approximate η̅+break and εH,break.
101 ≤ τH ≤ 6 × 101 s, J̅(t) further decreases with τH, approaching the nBA-AA (6%) LVE at long times (dash-dotdot line). For τH > 6 × 101 s, an order of magnitude increase in τH only slightly decreases J̅(t) as we slowly approach full recovery (see pristine response). The stress growth coefficients, η̅+(t), for the data set are shown in Figure 4f. It is clear that for short τH (≤2 × 101 s) the material is breaking at η̅+break approximately equal to 3η0 of pure nBA. For τH ≥ 6 × 101 s strain hardening is observed. The degree of strain hardening limited by η̅+break is increasing steadily with τH. Only for τH = 5
higher degrees of strain hardening. It is known that increased viscosity of this network is largely a function of degree of association;41 thus, reduced compliance and increasing η̅+break are directly proportional to recovery of hydrogen bonds with τH. Compliance curves for nBA-AA (38%) are shown in Figure 4e. As with the previous two networks, the compliance for short τH, i.e., τH ≤ 9 × 100 s, resembles that of pure nBA for σ0 = 5 × 104 Pa. At τH = 9 × 100 s the compliance is almost identical to the LVE of pure nBA (see dash-dot line). For 2 × F
DOI: 10.1021/acs.macromol.8b02423 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules × 104 s does η̅+(t) approach the LVE of pristine nBA-AA (38%) at long times, suggesting that full recovery requires much longer times. Constant Rate of Extension. A constant rate of extension (ε̇H) was used to measure recovery of nBA-AA (6%). Figure 5a shows η̅+(t) for varied τH and constant ε̇H = 0.1 s−1. At all τH, η̅+(t) follows a master curve (equivalent to the pristine response) up to the material breaking point. For τH ≤ 100 s, η̅+break is low and breaking occurs along the LVE. For τH > 100 s, much higher η̅ b+reak are obtained with behavior that is approximately the same as that of the pristine material. There is little difference between the η̅+break for measurements where τH ≥ 102 s. The stress−strain behavior in Figure 5b shows low εH,break for τH ≤ 100 s. For τH ≥ 102 s, high εH,break are achieved and are nearly identical to each other and to the pristine material. This behavior is fundamentally different from that seen for creep measurements. Whereas in creep both η̅+(t) and J̅(t) vary as a function of τH, in constant rate of extension, η̅+(t) is a master curve with varying η̅b+reak and εH,break. Additionally, recovery of the pristine material response is achieved at much shorter healing times, (τH ≈ 102 s), whereas in creep very little recovery of the material is observed for 2 orders of magnitude higher healing times. Effect of τH on Recovery of Unentangled Networks. We now explore a network composed of MEA backbones, which compared to the nBA based polymers is essentially free of entanglements. For example, the linear viscoelastic response of pure PMEA follows that of an unentangled melt.42 Figure 6a shows creep compliance for MEA-UPyMA (3%). For all τH, J̅(t) approximately follows the LVE. With increasing τH, increasing compliance is achieved; however, J̅(t) remains about an order of magnitude lower than the pristine material. The very low compliance is most likely due to the absence of reformed associations and the lack of entanglements to sustain the stress. Only when associations have sufficiently recovered (long τH) can the network distribute load continuously across the interface, leading to higher extensibility. η̅+(t) shown in Figure 6b all follow the LVE up to η̅+break which increases with τH. At no τH does strain hardening occur, and η̅+break is more than an order of magnitude lower than that of the pristine material. Figure 6c shows the effect of τH on MEA-UPyMA (3%) measured at constant rate of extension. η̅+(t) follows the pristine material response for all τH. With increasing τH, higher η̅+break are achieved; however, significant strain hardening is only achieved for τH > 103 s. Stress−strain curves (Figure 6d) highlight increasing εH,break with increasing τH. As with creep for τH < 103 s, healed responses are identical to the LVE up to η̅+break. However, unlike for nBA networks, the unentangled network exhibits the same qualitative behavior for both creep and extension, but the degree of recovery is different.
Table 2. Calculated Time Scales of the Assciating Polymer Networks nBA-AA (6%) τ0 τR τb τeq τadh
4 4 6 2 7
× × × × ×
−4
10 10−2 101 103 103
MEA-UPyMA (3%) 2 3 4 4 4
× × × × ×
10−10 10−6 102 106 107
of τW/τb. The normalized values of τR and τeq are indicated via arrows in Figure 7. According to Stukalin et al., we expect a plateau in recovery for τW/τb < 1 and a sudden decrease in recovery for τW/τb > 1. Ultimately for τW/τb > τeq/τb there is again no change in the amount of recovery for a constant τH. The physical argument is that for τW/τb > 1 the free associations begin to find internal partners, which means less associations are available to form bridges at the interface. For τW > τeq, an equilibrium number of free associations have found internal partners leaving an equilibrium number of free associations available at the interface for all increasing τW. Examining the recovery of nBA-AA (6%) shows for τR/τb < τW/τb < 1 recovery is constant with increasing τW. For 1 < τW/ τb < τeq/τb there is an overall decrease in recovery of stress and strain. For τW/τb > τeq/τb, no change in recovery is seen with increasing τW. The data suggest that the results for nBA-AA (6%) are in excellent agreement with the arguments made by Stukalin et al. Note that many other works have observed a decrease in recovery with τW, but no systematic study has shown the plateau regions.14,16,38−40,60−62 Interestingly, MEA-UPyMA (3%) data show an unexpected increase in stress and strain recovery for τW/τb < 1 followed by an expected decrease in recovery for τW/τb > 1. We hypothesize that this contradictory trend is possibly due to irreversible damage to the chemical bonds within the backbone during break. In both cases, the damaged samples were created by cutting the material with a razor blade. As a result, the damage surface is likely composed of broken chains.63 While open stickers are present at the interface, their effect on recovery is limited because of their low concentration in the case of MEA-UPyMA. Thus, we observe an increase in the recovery due to diffusion of nearby free associations to the interface on the time scale of λ/τb ≈ 3 × 10−1. We suspect that this is not observed in nBA-AA due to the much higher concentration of associating groups per chain and the faster diffusion of free associations, λ/τb ≈ 2 × 10−2. Effect of τH on Recovery. The effect of τH on recovery of nBA networks in creep can be evaluated by comparing η̅+break, as shown in Figure 8. While convention dictates a stress at break is more appropriate, constant stress measurements vary only in strain and strain rate, leaving stress growth coefficient for comparison. τH is scaled by λ, the characteristic longest relaxation time for the polymer melts, to highlight the role of entanglements. Recall that λ was shown to dictate the role of associations on extensional flow by Shabbir et al.41 For τH/λ < 10, all melts form a master curve of η̅+break, suggesting that all three melts are undergoing the same healing dynamics (i.e., reformation of entanglements across the interface). For τH/λ > 10, a plateau for pure nBA at the pristine material η̅+break is observed, which is indicative of full recovery of entanglements. For τH/λ > 10, both nBA-AA 6% and 38% show η̅ b+reak increasing substantially over pure nBA, approaching their own pristine values (dotted lines) with increasing τH. These
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DISCUSSION Effect of τW on Recovery. According to Stukalin et al., the recovery of associations depends strongly on the relative magnitude of τW compared to time scales of the polymer. The three important time scales of the polymer are the Rouse time τR, bond lifetime τb, and the equilibration time τeq. Critical time scales are calculated as described in Stukalin et al.13 (see eqs S2−S5 in the Supporting Information) and are reported in Table 2. Figure 7 summarizes relative recovery in terms of stress and strain of MEA-UPyMA (3%) and nBA-AA (6%) as a function G
DOI: 10.1021/acs.macromol.8b02423 Macromolecules XXXX, XXX, XXX−XXX
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Figure 7. Stress and strain recovery of MEA-UPyMA (3%) and nBA-AA (6%) as a function of τW/τb for τH = 10 s under constant rate of extension ε̇H = 0.1 s. Arrows indicate normalized polymer time scales (see Table 2) for MEA-UPyMA (3%) on the lower axes and nBA-AA (6%) on the upper axes.
of creep for nBA-AA 6% and MEA-UPyMA 3%. Figure 9 summarizes the stress and strain recovery of nBA-AA (6%) as a function of τH. Note that an additional data set is included in Figure 9 at ε̇H = 2.5 s−1 which is not reported in the Results section (but available in Figure S7). It is evident that for the selected range of τH measured stress recovery is much lower for creep (Rσ < 10%) than for constant ε̇H (Rσ > 40%). At constant rate, a sudden increase in Rσ occurs at τH ≈ 10λ, followed by relatively constant Rσ for long τH. We do not expect flow kinematics to impact degree of recovery when probed in the linear viscoelastic regime. However, the importance of association dynamics at very large time scales (low frequency) makes it very difficult to probe the LVE (see Shabbir et al.41,42). Thus, all strain-rates probe some nonlinear response of the melts. Figure 9 clearly shows that the nonlinear response and thus nonlinear measured recovery strongly depend on the time scale of the flow. In creep, a single stress probes a spectrum of retardation times,58,59,64 while the constant rate of extension is said to probe only relaxations occurring at time scales slower than the flow time scale. In unassociating linear polymers, rates of extension faster than the inverse Rouse time induce chain stretch and entanglements dominate the measurement.49,65,66 For nBA-AA, entanglements are argued to be fully recovered at about τH ≈ 10 s. The sharp increase in Rσ observed at τH ≈ 10 s suggests that the response is strongly dependent on the presence of entanglements and is relatively insensitive to recovery of associations, which gradually increase recovery.
Figure 8. η̅+break for all nBA networks measured in creep. Lines represent pristine material η̅+break for each network.
measurements show clearly that recovery is sequential, beginning with re-entanglement dynamics across the interface, followed by reassociation of hydrogen-bonding groups. Note that for the longest τH measurements are in the regime of τH > τadh; however, recovery is not complete as predicted by the work of Stukalin et al.13 This is likely due to the presence of entanglements which must repeatedly relax to free up associations at the interface, which is not accounted for in the original model. Effect of Applied Kinematics on Recovery. We now evaluate the role of kinematics on the measurement of recovery by comparing the results of constant rate of extension with that
Figure 9. Effect of τH on stress and strain recovery for nBA-AA (6%) in creep and constant rate of extension. Dotted lines indicate τH ≈ 10λ. H
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Figure 10. Effect of τH on stress and strain recovery for MEA-UPyMA (3%) in creep and constatnt rate of extension.
Table 3. Wi for All Kinematics and Networks in This Work
Figure 11. Summary of recovery for all networks with respect to (a) chain dynamics and (b) association dynamics. See legend in Table 3.
The measured recovery probed in creep is orders of magnitude smaller than in constant rate of extension. In creep, the response is characteristic of the entire material for a wide range of time scales (both long and short). While in constant rate of extension we focus on entanglement dynamics, creep is probing the sequential buildup of entanglements and associations equally. This is most clearly seen in the buildup of material compliance in Figure 4 where entanglement dynamics and association dynamics are distinguishable. Strain recoveries, Rε, in Figure 9b further highlight this phenomenon. For constant ε̇H and τH < 10 s, Rε is substantially lower than full recovery (Rε < 1). Further recovery shows an increase in Rε and then an immediate plateau of extensibility. In creep for τH < 10 s, Rε starts off higher than full recovery. Further recovery shows a decrease in Rε until again a plateau in extensibility is reached. The plateau in Rε supports the argument that entanglements are solely responsible for the extensibility of the network. Associations do however affect the stress required to achieve a degree of extensibility. This is better seen in the absence of entanglements. Figure 10a summarizes the stress and strain recovery as a function of τH for both creep and constant rate of extension for unentangled MEA-UPyMA (3%). Comparable trends in stress and strain recovery are observed for both creep and constant
rate experiments. These results show clear differences from nBA-AA (6%); namely, Rε is much lower and is steadily increasing as a function of τH. We argue that since hydrogen bonds rather than entanglements are responsible for stress buildup in MEA-UPyMA, all flows are probing the number of reassociated bonds. In other words, the measured recovery of MEA-UPyMA (3%) does not depend on the applied flow. Furthermore, the extensibility of an unentangled network is dependent on the number of associations, whereas an entangled network has a critical strain that is proportional to the number of entanglements. This clearly shows that stress and strain recovery do not always probe the same mechanisms or measure the true recovery of the material. Stress recovery is much more indicative of the material behavior than strain recovery. Furthermore, true and measured recovery are independent properties and measured recovery can depend strongly on the chemical structure, measurement technique, and kinematics of flow. Making correlations between measured recovery and true recovery is still a challenge and must be explored further. We now bring together all measured data of stress recovery for the different chemistries presented here. Figure 11a summarizes the stress recovery as a function of normalized healing time (τH/λ) for all networks and flows studied in this I
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both associating polymers show a relatively flat recovery with increasing τW. Furthermore, for waiting times larger than τb, the experimental trends show a decreasing recovery due to the internalization of free associating groups. These two findings are in very good agreement with the arguments of Stukalin et al. However, we show for MEA-UPyMA (3%) that the creation of a free surface via cutting leaves behind very few free associations and thus an increase in recovery is observed until τW is on the order τb, which is not captured by the model of Stukalin et al. We argue that this is due to the irreversible damage to chains during the creation of the free surface, which has not been considered in previous works. For constant τW and varying τH, our data and analysis of unentangled, associating polymers validate the healing model presented by Stukalin et al. However, the recovery of entangled polymers is not so simple. The entangled polymer first shows recovery of entanglements followed by very slow recovery of associations, indicating a sequential healing process. The recovery dynamics of the entangled poly(n-butyl acrylate) does not agree with the scaling argument of Stukalin et al., suggesting that entanglement dynamics must be explicitly accounted for in a self-healing model. We note that the results here are for one specific entangled network, which restricts the generalization of our results. For example, nBA-AA has a large separation between entanglement dynamics and association dynamics. It would be interesting to see whether these trends still hold if entanglement and association dynamics were of similar time scales. One important result is the effect of flow kinematics on perceived healing recovery. The same material shows different stress and strain recoveries depending on the applied Wi. In high Wi flow, entanglements dominate the measurement, leading to high stress recoveries which remain constant for τH/ λ > 10. In low Wi flow, both entanglements and associations are contributing to the recovery of stress and strain. Recovery is consistently lower for low Wi kinematics. Overall, this work introduces a new tool that will allow for consistent and reliable results of self-healing dynamics for a wide range of supramolecular and viscoelastic materials. While we have demonstrated the tool on two unique supramolecular architectures, more experiments are needed to validate current models and develop new theoretical frameworks. Our future goal is to apply this technique to supramolecular chemistries that allow for systematic changes in association strength and number of entanglements. As our understanding grows, we can begin to think about engineering supramolecular systems with tailored properties.
work. Here we employ a Weissenberg number, Wi = λε̇H, to quantify the applied flow with respect to characteristic polymer relaxation. For creep, we use the asymptotic strain rate, defined as ε̇H =
∂εH ∂t t →∞
( )
to define the Weissenberg number. Note
that in creep experiments, the strain rate starts very high and decays in exponential manner with time (see Figure S6). We separate experiments into four regimes determined by applied flow (high vs low Wi) and three mechanisms of recovery: I and III represent dynamic relaxation of entanglements, II represents relaxed entanglements, and IV represents dynamic recovery of associations. For τH shorter than the characteristic relaxation time of the polymer, i.e., τH/λ < 10 (regimes I and III), the stress recovery is dominated by entanglement recovery with little to no recovery of associations. In regime II, the stress recovery of nBA-AA networks shows almost full recovery since only entanglements are probed at these Wi, as argued above. For τH/λ > 10 and low Wi (regime IV), associations are recovering with increasing τH. We can clearly see the effect of bond strength on the relative recovery when comparing MEAUPyMA and nBA-AA. The weaker associations of nBA-AA (despite the much larger number of associations per chain) recover much faster than MEA-UPyMA with regard to the backbone relaxation. This indicates that the time to recovery is more appropriately scaled by some multiple of the bond lifetime which Stukalin et al. argue is the equilibration time τeq. τeq is the time scale for equilibration of unpaired associations within the bulk network and accounts for both the number and strength of stickers as well as the relaxation time of the monomer. Figure 11b shows the relative stress recovery as a function of τH normalized by τeq. This figure clearly shows that the recovery of MEA-UPyMA is probed at very low values of τH/ τeq, and therefore the recovery is expected to be slow. What is surprising is the very low values of stress recovery for nBA-AA networks. This can be explained by bringing forth arguments from Stukalin et al. where the rate of recovery of bridges strongly depends on the relative τW. For nBA-AA, the waiting time is such that we are in the “adhesion-hopping regime”, which is the slowest recovery regime. Additionally, Stukalin’s model does not take into account recovery of entanglements which most certainly would slow down recovery. We expect that free associations only become available after some convoluted process that involves bond dissociation and reptation dynamics. Lastly, the argument that high Wi probes only entanglements is strengthened by this figure, since we do not expect full recovery of associations until some multiple of τeq.
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CONCLUSIONS In this work, we show that measuring and quantifying intrinsic, autonomic self-healing in associating networks is not trivial and depends on experimental conditions and material characteristics. We demonstrate the use of a filament stretching rheometer to measure self-healing recovery dynamics in terms of true stress and true strain: before, during, and after recovery. We confirm that self-healing dynamics depend nonintuitively on two key process time scales: the waiting time before recovery, τW, and the time of recovery, τH. Using nBA-AA (6%) and MEA-UPyMA (3%), we show that the evolution of recovery as a function of τW depends on the availability of free associations. When τW is on the order τb,
ASSOCIATED CONTENT
* Supporting Information S
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b02423. Experiments highlighting the role of contact force and measurement reproducibility; explanation of theoretical model parameters and calculation methods; experimental details for calculating stress growth coefficients in creep, linear viscoelastic envelopes, and time−temperature superposition; experimental results for high rate of strain experiments (PDF) J
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Nicolas J. Alvarez: 0000-0002-0976-6542 Present Address
A.S.: Coloplast, Hulebaek, Denmark. Notes
The authors declare no competing financial interest.
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