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Vitrimers Designed Both To Strongly Suppress Creep and To Recover Original Cross-Link Density after Reprocessing: Quantitative Theory and Experiments Lingqiao Li,† Xi Chen,† Kailong Jin,† and John M. Torkelson*,†,‡ †

Department of Chemical and Biological Engineering and ‡Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States

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S Supporting Information *

ABSTRACT: Vitrimers form a promising class of dynamic polymer networks, but they have an Achilles’ heel: elastomeric vitrimers exhibit significant creep under conditions where permanently cross-linked, elastomeric networks exhibit little or no creep. We demonstrate that vitrimers can be designed with strongly suppressed creep and excellent reprocessability by incorporating a substantial yet subcritical fraction of permanent cross-links. This critical fraction of permanent cross-links, which has little or no detrimental effect on reprocessability, is defined by the gelation point of only permanent cross-links leading to a percolated permanent network. Via a modification of classic Flory−Stockmayer theory, we have developed a simple theory that quantitatively predicts an approximate limiting fraction. To test our theory, we designed vitrimers with controlled fractions of permanent cross-links based on thiol−epoxy click chemistry. We characterized the rubbery plateau modulus before and after reprocessing as well as stress relaxation of our original vitrimers. Our experimental results strongly support our theoretical prediction: as long as the fraction of permanent cross-links is insufficient to form a percolated permanent network, the vitrimer can be reprocessed with full recovery of cross-link density. In particular, with a predicted limiting fraction of 50 mol %, a vitrimer system designed with 40 mol % permanent cross-links achieved full property recovery associated with cross-link density after reprocessing as well as 65−71% creep reduction (for both original and reprocessed samples) relative to a similar vitrimer without permanent cross-links. In contrast, a system with 60 mol % permanent cross-links could not be reprocessed into a well-consolidated sample, nor did it recover full cross-link density; it failed by breaking at early stages of creep tests. The ability to predict an approximate limiting fraction of permanent cross-links leading to enhanced creep resistance and full reprocessability represents an important advance in the science and design of vitrimers.

I. INTRODUCTION At the end of use, conventional, covalently cross-linked polymeric materials or polymer networks cannot be recycled into high-value applications (e.g., tire-to-tire recycling) because the permanent cross-links prevent the spent networks from being reprocessed in the melt state.1−6 This outcome not only leads to losses in terms of sustainability but also is often accompanied by major economic losses because of the high economic value embodied in the original networks, especially if they were engineered or designed for critical applications. By allowing for structural rearrangement through dynamic chemistries, dynamic covalent polymer networks (DCPNs6) or covalent adaptable networks (CANs7) have shown great potential to be useful as high-value reprocessable polymer networks. Although the seminal study of reversible polymer networks using Diels−Alder reactions was reported nearly four decades ago by Kennedy and Castner,8,9 it has been only during the past 15 years or so that various dynamic chemistries have been employed in studies aimed at reprocessable polymer networks.3−6,10−44 There are two main categories of dynamic chemistry targeted toward DCPNs or CANs. The first is dissociative dynamic © XXXX American Chemical Society

chemistry, where under stimulus, such as elevated temperature, dynamic linkages break and later re-form upon removal of the stimulus, e.g., via the Diels−Alder reaction1,2,10 and alkoxyamine dynamic bonds.3,18 The original network may be melt-reprocessed as the polymer network transforms at high temperature to a combination of branched and linear chains, with cross-links being re-established upon cooling. The second is associative dynamic exchange chemistry in which the network structure rearranges by exchange of bonds while maintaining a constant number of bonds, e.g., via transesterification12 or transamination24 (see Scheme 1). Rarely, reprocessable polymer networks have been developed which exhibit the presence of both dissociative and associative dynamic chemistries.34 Dynamic polymer networks based strictly on associative dynamic exchange have been named vitrimers;12,16,29 above the glass transition temperature (Tg), these dynamic networks have been described as existing in a state intermediate to thermoplastics and thermosets.16,29 Received: April 30, 2018 Revised: May 29, 2018

A

DOI: 10.1021/acs.macromol.8b00922 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules Scheme 1. A Dynamic Polymer Network May Change Its Structure through (a) Dissociative Dynamic Chemistry or (b) Associative Dynamic Exchangea

a These conceptual schemes represent the possible network topology changes enabled by different dynamic chemistries; the detailed mechanism for the dynamic chemistry employed in our model experimental system (transesterification, a type of associative dynamic exchange reaction) is shown in Scheme 2.

creep suppression. Very recently, Sumerlin and co-workers also demonstrated that adding permanent cross-links could improve structural integrity of vitrimers.44 However, we also recognize that materials would cease to be vitrimers if the level of permanent cross-links was sufficiently high that the vitrimers were no longer reprocessable. The critical level of permanent cross-links is associated with incipient percolation of permanent cross-links in a sample, thus eliminating the possibility that the network can be successfully reprocessed in the melt state into a robust material. This limiting condition of the incipient percolation of permanent cross-links is associated with the critical “gelation” point in the gelation theory by Flory and Stockmayer.51,52 Both Flory and Stockmayer were concerned with predicting the minimum level of branch unit incorporation to achieve a “gelled” or cross-linked polymer during step-growth polymerization.51,52 Here, we have taken a point of view which is the reverse of Flory and Stockmayer by asking: how high of a permanent cross-link density can be achieved in a vitrimer, just below the critical gelation point, that will strongly suppress creep while nevertheless allowing for effective melt-state reprocessability? This led us to derive a theoretical, quantitative prediction of the limiting fraction of permanent cross-links that can be present in vitrimers without sacrificing melt-state reprocessability. We have experimentally tested the theory by designing vitrimers based on thiol−epoxy “click” chemistry53,54 as shown in Scheme 2, which allows us to control the fraction of permanent cross-links and the fraction of dynamic cross-links, the latter with the capability to exchange (via transesterification) with each other in the network. Our tests provide strong experimental support for the validity of our Flory−Stockmayer-like theory that yields quantitative predictions for the limiting fraction of permanent cross-links leading to strong suppression of creep behavior in vitrimers while maintaining melt-state reprocessability. Additionally, our study shows that our methodology for incorporating both dynamic and permanent

Since the pioneering study by Leibler and co-workers in 2011,12 vitrimers have attracted substantial research interest.5,16,17,21,24,25,29,30,35−47 A particularly noteworthy study by Leibler, DuPrez, and co-workers demonstrated a case in which vitrimers could achieve full property recovery (rubbery plateau modulus) associated with cross-link density after multiple recycling steps.24 Despite the promise associated with vitrimers, these materials have an Achilles’ heel: numerous studies have shown the susceptibility of vitrimers to creep substantially under use conditions.16,17,24,29,38,39,45 (Creep is the tendency of a solid to deform continuously and permanently during exposure to mechanical stress.48) In a recent review article, DuPrez and co-workers stated, “For applications in typical vitrimer processing of rigid networks, the creep is highly undesirable for most applications where elastomers are typically used.”29 Creep behavior is a potentially important drawback that could prevent vitrimers from being developed for a wide variety of applications requiring robust network materials that exhibit limited or no creep in use. One study suggested that creep in vitrimers could be suppressed by carefully designed exchange reaction kinetics, with the elimination of creep at use temperatures below a topology freezing temperature of the vitrimer, Tv.29 However, other studies have shown that substantial creep is present at temperatures below the supposed Tv.16,45 Thus, there remains a need to develop a simple, efficient, and theoretically sound method to strongly suppress creep in vitrimers. Thermoplastics are generally capable of exhibiting significant creep at temperatures above their Tg. Because of their permanent network structure, conventional cross-linked polymers, e.g., rubber bands, exhibit no creep below their elastic limit and much less creep above their elastic limit than thermoplastics at temperatures above Tg. The latter fact led us to hypothesize that the presence of some fraction of permanent cross-links (cross-links that remain stable at processing conditions) in vitrimers should provide resistance to creep,49,50 with a greater fraction of permanent cross-links leading to greater B

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materials were then cut into tension-film geometry for characterization. Creep Experiment. Both original and reprocessed samples were tested by creep experiments. Tension-film geometry samples were loaded with constant 0.2 MPa stress and put into an oven equilibrated at 150 °C. The sample length along the load direction was measured every 12 h, briefly releasing the stress for creep measurements. The load was immediately reapplied after each measurement. Stress Relaxation. Original samples were used for stress relaxation measurements. A TA Instruments ARES rheometer equipped with a torsion fixture was used to characterize the shear stress relaxation behavior of original samples at 160 °C with 5% initial strain. Dynamic Mechanical Analysis (DMA). Both original and reprocessed samples in tension-film geometry were tested using DMA. A TA Instruments 2980 dynamic mechanical analyzer operating in a strain-controlled mode (0.03% strain) at a frequency of 2 Hz upon heating at 3 °C/min (from 25 to 150 °C) was used to determine temperature-dependent tensile storage modulus, E′, tensile loss modulus, E″, and damping ratio tan δ values. Conversion. The conversion accompanying polymerization was characterized by Fourier transform infrared spectroscopy (FTIR, Bruker, Tensor 37) via the disappearance of the thiol peak at ∼2570 cm−1. For all samples synthesized in this study, the conversion was nearly unity as indicated by the disappearance of thiol peak in all FTIR curves shown in Figure S1.

Scheme 2. Experimental System Designed Using Thiol−Epoxy Click Reactions To Produce Vitrimers with a Controlled Fraction of Permanent Cross-Linksa

III. RESULTS AND DISCUSSION Theory Development and Derivation. Here, we explain the rationale behind our quantitative theory that describes the relationship between the fraction of permanent cross-links present in a vitrimer and the reprocessability of resulting materials leading to full property recovery associated with cross-link density (or being “fully reprocessable”). Our point of view is the reverse of Flory−Stockmayer (F−S) gelation theory.51,52 Developed more than 70 years ago, F−S analysis provides an approximate, quantitative prediction of the gel point based on the criterion of percolated network formation.51,52 In other words, conventional cross-linked polymers, which are not reprocessable, contain at least one percolated, permanent network structure. However, if we substitute some permanent cross-links in such a percolated network with dynamic crosslinks, the resulting network can convert into branched or even linear polymers through dynamic chemistry and thus become melt state reprocessable (see Scheme 1). We note that this statement is true regardless of the type of dynamic chemistry inherent within the network. For dissociative dynamic chemistries, dynamic linkages can reversibly break to convert the network structure into branched or linear chains. For vitrimers (resulting from associative dynamic exchange chemistries), although the total number of bonds in the system remains unchanged, the exchange between bonds leads to bonds breaking and re-forming simultaneously.29 Given that the dynamic bonds in vitrimers exchange with each other, the network structures are “broken” instantaneously and statistically, the consequence of which is indeed the same as the case of dissociative dynamic chemistry (see Scheme 1). Thus, regardless of the type of dynamic chemistry employed, the critical condition for a polymer network to be fully reprocessable is that permanent cross-links are insufficient to form a percolated permanent network in the material. We first present a generalized theoretical derivation based on a step-growth polymerization system shown in Scheme 3, where Af is the cross-linker with a functionality f (≥3). A2, B2, and D2 are bifunctional monomers with A, B, and D functional groups, respectively. Here, A groups can only react with either

a

Hexane dithiol leads to permanent cross-links between triepoxy cross-linkers; ester dithiol leads to dynamic cross-links between triepoxy cross-linkers. The network rearrangement is enabled by transesterification catalyzed by DMAP, which is a type of dynamic chemistry based on the exchange mechanism.

cross-links leads to full recovery of network cross-link density after reprocessing (or being “fully reprocessable”), which has rarely been reported in previous studies of dynamic polymer networks.3,24,34

II. EXPERIMENTAL SECTION Materials. Tris(4-hydroxyphenyl)methane triglycidyl ether (triepoxy), 1,6-hexanedithiol (hexane dithiol, 97%) and 4-(dimethylamino)pyridine (DMAP, 99%) were purchased from Sigma-Aldrich. Ethylene bis(3-mercaptopropionate) (ester dithiol) was kindly supplied by Bruno Bock Thiochemicals. All chemicals were used as received. Synthesis. The starting compositions of reactants in all polymer networks are tabulated in Table S1. As a general procedure, triepoxy was first mixed with dithiol in a mixing cup (Max10, FlackTek), followed by adding a solution of DMAP dissolved in dithiol mixture. The resulting mixture was then well mixed using a SpeedMixer (FlackTek, DAC 150.1 FVZ-K) at 2500 rpm for 1 min. The mixture was then poured into a sample mold and sealed using two metal plates and clamps. The sample mold was cooled in an ice−water mixture and then allowed to warm to room temperature gradually. After reacting for 3 h at room temperature, the resulting solid materials were postcured at 80 °C for 12 h to ensure full conversion. Reprocessing. Reprocessing of the original (as-synthesized) materials was done by cutting them into millimeter-size pieces and hot pressing the pieces into ∼1.0 mm thick sheets using a PHI press (Model 0230C-X1). For each reprocessing cycle, samples were pressed at 160 °C for 8 h with 7 tons of ram force. The reprocessed C

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In order for no permanent network to percolate the system, the probability αp must be sufficiently small so that permanent chains are only linear or branched. Thus, according to our F−S-like analysis,51 αp must be smaller than the critical value for gelation, αc, where αc = 1/(f − 1), which is defined by the functionality of the cross-linker:

Scheme 3. General Step-Growth Polymerization Involving Different Monomers That Can Generate Permanent or Dynamic Cross-Links

rp2 ρSB2(k = 1) /k 1 < f−1 1 − rp2 (1 − ρ)SB2(k = 1) /k

As a check, we note that eq 6 reduces to the classic F−S expression52 (for the case of no gelation) when there is no D2 in the system (SB = 1, k → ∞), i.e., in the absence of dynamic bonds. Equation 6 quantitatively correlates conversion and monomer compositions that must be satisfied for a network containing both permanent and dynamic cross-links to be fully reprocessable. Specifically, with stoichiometric balance between A groups and B + D groups (r = 1) and in the limit of complete conversion (p = 1, SB = k/(k + 1)), eq 6 reduces to

B or D groups, and B and D groups can only react with A groups. Similar to F−S analysis, we assume that all the same functional groups have the same probability to react and that there is no intramolecular reaction. In our scheme, the bonds between A and D groups can reversibly break under reprocessing conditions; i.e., the A−D bonds are “dynamic”. In contrast, A−B bonds resulting from reaction as well as the bonds within the Af, A2, B2, and D2 monomers or structure units are “permanent”. As discussed above, the criterion for a network to be fully reprocessable is that no permanent network is percolated throughout the material; i.e., Af, A2, and B2 monomers must not react with each other to form a percolated network in the system under consideration. If we define the fractional conversion of initial A functional groups to be p, then the fractional conversion of B groups, pB, is given by (see Supporting Information for the full, detailed derivation) pB =

rpSB(k + 1) k

k

ρk+1 1 − (1 −

(1)

rpSB(k + 1) ρ k

(2)

where ρ is the fraction of all A groups present in Af monomers (cross-linkers). Similarly, the probability of having an Af−B2(−A2−B2)i−Af structure, pi, can be written as pi = (pSB)[(pB (1 − ρ))(pSB)]i (pB ρ) = pSB

rpSB(k + 1) rpS (k + 1) (1 − ρ)(pSB)]i B ρ k k

(3)

By summing pi over all possible values of i, we obtain the probability of cross-linker leading to another cross-linker by a chain consisting of only permanent bonds, αp: ÄÅ ÉÑi ∞ ÅÅÅ rpSB(k + 1) ÑÑ rpSB(k + 1) αp = ∑ pSBÅÅ (1 − ρ)pSBÑÑÑ ρ ÅÅ ÑÑ k k ÅÇ ÑÖ i=0 (4)

Equation 4 simplifies to αp =

rp2 ρSB2(k = 1) /k 1 − rp2 (1 − ρ)SB2(k = 1) /k

k ρ) k + 1


0.999), the stress relaxation results were well fit to stretched exponential decays. Notably, the best fits for samples with 0, 20, and 40 mol % permanent cross-links yielded σperm/σ0 values very close to zero (ranging from 0.003 to 0.046). Given that the relaxation data were limited to 8 h time frames, we believe these σperm/σ0 values are within error, consistent with σperm/σ0 = 0 or full stress relaxation at infinite time. When we performed constrained fits to eq 9 with σperm/ σ0 = 0, we also obtained excellent fits to data, with adjusted R2 > 0.999 for 0 and 20 mol % samples and a R2 = 0.997 for the 40 mol % sample (see Table S2). These results are consistent with the absence of percolated permanent network structures in the 0, 20, and 40 mol % permanent cross-link samples.

effectively illustrates a major difference in reprocessability. This difference is in accord with our approximate theoretical prediction of 50 mol % as the limiting fraction of permanent cross-links for reprocessability. In order to further test our theoretical prediction, we also investigated the effect of permanent cross-link fraction on the resulting stress relaxation behavior of original thiol−epoxy networks. We chose to use this method because many studies concerned with reprocessing of vitrimers have employed stress relaxation measurements on original samples to describe the capability of network rearrangement.12,16,17,21,24,25,29,36,38,40,42,43 Figure 3a shows stress relaxation behavior of original samples with different permanent cross-link fractions at 160 °C. Qualitatively, these results indicate that the rate of stress relaxation decreases with increasing fraction of permanent cross-links. In previous studies of this type,16,21,24,25,29,36,38,40,42,43 the characteristic relaxation time, τ*, of vitrimer systems was approximately estimated by the time scale required for the imposed stress to relax to its 1/e of its original value, consistent with the assumption of a single-exponential decay response. However, the stress relaxation of both vitrimers and polymers in general cannot be described quantitatively by a singleexponential decay or single relaxation time.48 Instead, stress relaxation of polymers can be well fitted to a Kohlrausch− Williams−Watts (KWW) stretched exponential decay:62−64 σperm σperm yz ij σ (t ) zz exp{− (t /t *)β } = + jjj1 − zz j σ0 σ0 σ 0 { k

(9)

where σ(t)/σ0 is the normalized stress at relaxation time t, τ* is a characteristic relaxation time, and β (0 < β ≤ 1) is the F

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value for samples with 60 and 80 mol % permanent cross-links, respectively. Both our reprocessing studies (Figures 1 and 2) and stress relaxation experiments on original vitrimers (Figure 3 and Table 1) indicate that the approximate, quantitative prediction of the limiting fraction of permanent cross-links from our modified F−S theory is supported by experiment. Taking this a step further, this critical condition for vitrimers being fully reprocessable is also meaningful to other DCPN systems containing both dynamic and permanent cross-links, regardless of the type of dynamic chemistry. (Dissociative dynamic chemistries and associative exchange dynamic chemistries have essentially the same effect on network structure, as mentioned earlier.) For example, in our previous study based on alkoxyamine dynamic bonds (a type of dissociative dynamic chemistry),3 we developed a DCPN containing some (relatively small) fraction of permanent cross-links. However, the resulting materials were reprocessed multiple times with full property recovery associated with cross-link density. Those results are consistent with our theory: as long as no percolated permanent network is formed in the system, the resulting materials are capable of being fully reprocessable. Thus, the quantitative prediction of critical permanent cross-link fraction allowing for full reprocessability represents a significant advance for the design of both associative dynamic networks and dissociative dynamic networks. Potentially of equal or even greater technological importance in the design of vitrimers is the role of critical permanent crosslink density in strongly suppressing creep. Figure 4a shows the creep behavior for original samples synthesized with 0, 40, and 60 mol % hexane dithiol or permanent cross-links. During the creep test, a constant 0.2 MPa stress was applied to all samples at 150 °C, which is ∼80 °C higher than their Tg values. In the case of the original vitrimer with 0 mol % permanent crosslinks, every cross-link comprises ester groups that can participate in transesterification to rearrange the network structure and change the sample shape. Therefore, major creep (ΔL/L0 = 0.169 after 48 h) along the employed force direction is observed over the experimental time scale. With increasing permanent cross-link fraction, creep behavior is greatly suppressed in the vitrimer with 40 mol % permanent cross-links (ΔL/L0 = 0.049 after 48 h), resulting in a 71% reduction in creep relative to the 0 mol % permanent cross-link vitrimer. Slightly greater

Table 1. Parameters Obtained from Fitting Stress Relaxation Curves to Experimental Data (at 160 °C) in Figure 3a Using Eqs 9 and 10 percentage of permanent cross-links (mol %)

σperm/σ0

τ* (s)

β

⟨τ⟩ (s)

adjusted R2

0 20 40 60 80

0.015a 0.003a 0.046a 0.166 0.382

1950 2500 3350 6740 8380

0.67 0.60 0.54 0.58 0.49

2580 3740 5780 10500 17200

>0.999 >0.999 >0.999 >0.999 >0.999

a Note: excellent fits of stress relaxation data were also obtained for samples containing 0, 20, and 40 mol % permanent cross-links when fits were done assuming that σperm/σo = 0, with adjusted R2 values >0.999 for the 0 and 20 mol % samples and equal to 0.997 for the 40 mol % sample. These excellent fits are consistent with these three samples being able to exhibit full stress relaxation at long times and not having a percolated permanent cross-link network structure.

In contrast, best fits of eq 9 to stress relaxation data for samples containing 60 and 80 mol % permanent cross-links resulted in σperm/σ0 values of 0.17 and 0.38, respectively, within error well above zero. These results are consistent with the presence of percolated permanent network structures in the samples with a fraction of permanent cross-links significantly exceeding our predicted limiting fraction of permanent crosslinks of 50 mol %. In addition to the important relationship between σperm/σ0 values and the limiting fraction of permanent cross-links for reprocessability of vitrimers, we note that the average stress relaxation time also exhibits an interesting correlation with the limiting fraction. For a stretched exponential decay, the average relaxation time, ⟨τ⟩,62,65,66 is given by τ=

τ *Γ(1/β) β

(10)

where Γ is the gamma function. As shown in Figure 3b and Table 1, ⟨τ⟩ exhibits a modest dependence on permanent cross-link fraction below the predicted limiting value of 50 mol % for reprocessability, with ⟨τ⟩ at 160 °C increasing by 3200 s from ∼2600 s to ∼5800 s for samples with 0 and 40 mol % permanent cross-links, respectively.67 However, ⟨τ⟩ increases much more substantially from 10 500 s to 17 200 s with increasing permanent cross-link fraction above the limiting

Figure 4. Relative displacement (change in sample length, ΔL, divided by the original sample length, L0) as a function of creep time measured at 150 °C with a constant loading of 0.2 MPa: (a) original thiol−epoxy networks with different fractions of permanent cross-links; (b) reprocessed thiol−epoxy networks with different fractions of permanent cross-links. (Note: the data for the sample with 60 mol % permanent cross-links are not present in (b) because that sample was unable to be reprocessed into a robust sample (see Figure 1b) due to the presence of percolated permanent network. As a result, the reprocessed sample with 60 mol % permanent cross-links broke in less than 1 h from the start of the creep test.) G

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i.e., rubber bands. Thus, we expect that any application of our modified F−S theory to dissociative dynamic networks containing a fraction of permanent cross-links will be relevant much more for reprocessability than for issues related to creep. Future studies applying our modified F−S theory to dissociative dynamic networks are worthy of consideration.

suppression of creep is evident in the original sample with 60 mol % permanent cross-links (ΔL/L0 = 0.034 after 48 h), resulting in an 80% reduction in creep relative to the 0 mol % permanent cross-link vitrimer. These results indicate that incorporation of permanent cross-links is an effective way to reduce creep in networks containing dynamic cross-links. Because vitrimers may be designed for recycling into highvalue products, a more critical test regarding our hypothesis on the suppression of creep in vitrimers by permanent cross-links involves the characterization of samples after reprocessing. Figure 4b shows the creep behavior for reprocessed vitrimers with 0 and 40 mol % permanent cross-links using the same creep test conditions as in Figure 4a. Results for the reprocessed samples are similar to those of the original samples (Figure 4a), consistent with recovery of network structure (and the results in Figure 2a). Importantly, in the case of the reprocessed sample with 40 mol % permanent cross-links, there is an excellent retention of creep suppression (ΔL/L0 = 0.058 after 48 h), resulting in 65% reduction in creep relative to the 0 mol % permanent cross-link system after reprocessing. This reduction in creep with the reprocessed sample is very close to the 71% reduction obtained in the original 40 mol % sample. In contrast to the excellent reprocessability and retention of creep suppression exhibited by the vitrimer with 40 mol % permanent cross-links, the sample with 60 mol % permanent cross-links not only exhibited poor reprocessability (Figures 1b and 2b) but also failed to withstand the relatively mild stress conditions employed in the creep experiment. Attempts to measure creep in the reprocessed 60 mol % samples failed because the samples broke within the first hour of being subjected to stress at 150 °C. As a result, we were unable to include any creep data for the 60 mol % sample in Figure 4b. This failure of the 60 mol % sample in the creep experiment is important in making evident the critical role of the limiting fraction of permanent cross-links in optimizing the combination of vitrimer creep resistance and reprocessability. When the fraction of permanent cross-links is close to but less than the limiting fraction, vitrimers remain fully reprocessable while exhibiting major suppression of creep in both original and reprocessed states. In contrast, when the fraction of permanent cross-links is significantly greater than the limiting fraction,68 reprocessing attempts may lead not only to rather poorly consolidated samples but also to failure in creep tests. Together, our modified F−S theory and experiments indicate that an effective approach both to retain vitrimer reprocessability with full recovery of cross-link density and to reduce the pain associated with the Achilles’ heel of vitrimers, i.e., creep, is to include a fraction of permanent cross-links near but less than the limiting fraction for reprocessability. Finally, it is important for us to note that although our theoretical prediction of the limiting fraction for vitrimers also applies for the reprocessability of dissociative dynamic networks, there may not be a direct analogue regarding creep in rubbery-state dissociative dynamic networks. Unlike associative exchange reactions, the nature of dissociative dynamic chemistry or simply any thermoreversible reaction allows for temperature regimes where the equilibrium fractional conversion associated with the reversible reaction is (to any truly significant digit) zero or unity.69 In temperature regimes where the reversible bonds serving as dynamic cross-links are effectively permanent and not dynamic, the measurable rubbery-state creep, if any, would be akin to the extremely minimal creep observed with conventional, permanently cross-linked rubber,

IV. CONCLUSIONS We demonstrated for the first time that creep behavior of vitrimers can be significantly suppressed by incorporating a fraction of permanent cross-links. On the basis of the quantitative, modified Flory−Stockmayer theory developed in this study, we easily determine an approximate, limiting fraction of permanent cross-links that can be present in a vitrimer while maintaining excellent reprocessability. As a result, by judiciously choosing the fraction of permanent cross-links incorporated in the vitrimer to be near but below the limiting fraction, major creep suppression can be achieved while maintaining reprocessability with full recovery of cross-link density. In contrast, if the fraction of permanent cross-links incorporated in a sample significantly exceeds the predicted limiting value, the sample is not fully reprocessable and may not exhibit the robustness necessary even to withstand creep characterization let alone to suppress creep. Our study provides a promising approach for limiting the deleterious effects associated with creep in vitrimer applications, particularly those related to elastomers. Besides its technological importance for vitrimer systems, our study also provides a scientific basis for understanding some of the behavior of DCPN or CAN systems that incorporate both dynamic and permanent cross-links.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b00922. Details of compositions used for synthesis; results of model fitting using a constrained condition; FTIR; full derivation of our modified F−S theory (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (J.M.T.). ORCID

Kailong Jin: 0000-0001-5428-3227 John M. Torkelson: 0000-0002-4875-4827 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge support of Northwestern University via discretionary funds associated with a Walter P. Murphy Professorship (J.M.T.), ISEN Fellowships (L.L.; X.C.), and a Terminal Year Fellowship (K.J.). We thank Prof. L. C. Brinson for generously providing access to the DMA instrument.

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REFERENCES

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H

DOI: 10.1021/acs.macromol.8b00922 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.8b00922 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.8b00922 Macromolecules XXXX, XXX, XXX−XXX