Chain Dynamics in Supramolecular Polymer Networks

Article pubs.acs.org/Macromolecules

Chain Dynamics in Supramolecular Polymer Networks Sebastian Hackelbusch,† Torsten Rossow,† Peter van Assenbergh,‡ and Sebastian Seiffert†,‡,* †

Institute of Chemistry and Biochemistry, Freie Universität Berlin, Takustrasse 3, D-14195 Berlin, Germany F-ISFM Soft Matter and Functional Materials, Helmholtz-Zentrum Berlin, Hahn-Meitner-Platz 1, D-14109 Berlin, Germany

‡

ABSTRACT: Supramolecular polymer networks consist of macromolecules that are cross-linked by transient physical interactions such as hydrogen bonding or transition metal complexation. The utility of these networks is based on their mechanical properties, which lay between those of permanent networks and that of mechanically entangled, viscoelastic polymer solutions, depending on the strength of transient chain cross-linking. To benefit from this interplay, it is necessary to understand it. To promote this understanding, we use a modular toolkit to form supramolecular polymer networks that exhibit greatly varying strength of transient chain crosslinking but that are all derived from the very same precursor polymer. This strategy allows the impact of the strength of transient chain cross-linking on the network dynamics and mechanics to be studied with high consistency. We follow this approach to evaluate the diffusive mobility of labeled tracer chains within these transient networks. Our results reveal that the concentration dependence of the tracer-chain diffusivity is in agreement with theoretical predictions derived from the “sticky reptation” model by Rubinstein and Semenov, provided the chain association is stronger than a certain threshold.

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INTRODUCTION Supramolecular polymer networks consist of macromolecules that are cross-linked by transient physical interactions1 such as multiple hydrogen bonding or transition metal complexation;2−7 they are useful for a plethora of applications as sensitive materials,8 including those as adaptive,9−12 selfhealing,13−15 shape-memory,16 controlled release,17 or soft adhesive substrates.18 The utility of supramolecular polymer networks is based on their mechanical properties, which lay between those of permanently cross-linked, rubbery elastic polymer networks and that of mechanically entangled, viscoelastic polymer solutions. The location between these two extremes is determined by the strength of transient chain cross-linking: whereas chain association by weak hydrogen bonding or hydrophobic interaction leads to viscoelastic liquids,19−24 strong multidentate metal complexation entails rubbery elastic, solidlike mechanics.25−30 Tailoring the microscopic supramolecular chain−chain interactions therefore tailors the macroscopic properties of supramolecular polymer networks.31 To benefit from this interplay, it is necessary to understand it. It is also necessary to go beyond and use this understanding to establish further, more sophisticated modeling of the function of supramolecular polymer networks in applications. For example, a particularly important class of application of these materials is that as self-healing scaffolds or coatings.13−15 In this class of application, use is made of the circumstance that if supramolecular polymer networks are ruptured, unassociated binding motifs are left behind that exhibit a tendency to reassociate if they are brought into contact. Tailoring this behavior relies on kinetic models for the self-healing, and the key to deriving these models is to understand the chain © XXXX American Chemical Society

dynamics in these networks. In addition to macroscopic healing, the transience of chain association in supramolecular polymer networks also causes temporal evolution of their microscopic topology, accompanied by changes of their mechanical properties.10,15,23,32 Understanding of this microstructural evolution is required to tailor these networks for applications, and again, the key to achieving this knowledge is to understand their chain dynamics. Different theoretical concepts have been developed to model the chain dynamics and mechanics of supramolecular polymer systems. In one theory, Cates focused on the dynamics of entangled “living” polymers that can continuously break and reassociate.33 In this picture, stress relaxation is modeled by the classical concept of reptation,34−37 but this mechanism may be abetted by reversible scission and recombination of the “living” chains. This concept of modeling leads to scaling laws for the relaxation time, τ, the viscosity, η, the living-chain diffusivity, D, and the plateau modulus, G0, of these transient networks as a function of the concentration of supramolecular building units:38 τ ∼ c1.2−1.5, η ∼ c3.5−3.7, D ∼ c−1.7, and, just as for semidilute networks of unbreakable polymers,36,37 G0 ∼ c−2.3. In a different theoretical approach, Leibler, Rubinstein, Colby, and Semenov extended the classical Rouse and reptation models to account for reversible association of “sticky” chains that consist of N segments and S sticky sites.39−41 These authors also derived scaling laws for the terminal relaxation time, τ, and the viscosity, η, of such transient polymer networks as a function of the polymer volume fraction, ϕ. Depending on the Received: February 20, 2013 Revised: July 6, 2013

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dx.doi.org/10.1021/ma4003648 | Macromolecules XXXX, XXX, XXX−XXX

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Table 1. Scaling Exponentsa for (a) the Relaxation Time, τ, (b) the Viscosity, η, and (c) the Chain Diffusivity, D, as a Function of Polymer Volume Fraction, ϕ, in Supramolecular Polymer Networks, Derived from the Sticky Rouse and Sticky Reptation Models by Rubinstein and Semenov40,41 Part a concentration range ϕ < ϕren ϕren < ϕ < ϕs ϕs < ϕ < ϕe ϕe < ϕ < ϕren ϕren < ϕ < ϕs ϕs < ϕ < ϕle ϕle < ϕ < 1

concentration range ϕ < ϕren ϕren < ϕ < ϕs ϕs < ϕ < ϕe ϕe < ϕ < ϕren ϕren < ϕ < ϕs ϕs < ϕ < ϕle ϕle < ϕ < 1

concentration range ϕ < ϕren ϕren < ϕ < ϕs ϕs < ϕ < ϕe ϕe < ϕ < ϕren ϕren < ϕ < ϕs ϕs < ϕ < ϕle ϕle < ϕ < 1

exponent α in τ ∼ ϕα (general form)

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Sticky Rouse Model, Overlapping but Unentangled Chains unrenormalized bond lifetime; transfer of intra- to intermolecular assocn (2 + 2z)/(3ν − 1) renormalized bond lifetime; transfer of intra- to intermolecualr association (6 + 7z)/(6ν − 2) renormalized bond lifetime; mostly intermolecular association z/(6ν − 2) Sticky Reptation Model, Overlapping and Entangled Chains unrenormalized bond lifetime; mostly intramolecular association (3 + 2z)/(3ν − 1) renormalized bond lifetime; transfer of intra- to intermolecular assocation (4 + 3.5z)/(6ν − 2) renormalized bond lifetime; mostly intermolecular association (1 + 0.5z)/(3ν − 1) renormalized bond lifetime; entangled strands between stickers (1.75 + 0.5z)/(3ν − 1) Part b exponent β in η ∼ ϕβ (general form)

comment

Sticky Rouse Model, Overlapping but Unentangled Chains unrenormalized bond lifetime; transfer of intra- to intermolecular assocn 1 + [(2 + 2z)/(3ν − 1)] renormalized bond lifetime; transfer of intra- to intermolcular association 1 + [(6 + 7z)/(6ν − 2)] renormalized bond lifetime; mostly intermolecular association 1 + [(z/(6ν − 2)] Sticky Reptation Model, Overlapping and Entangled Chains unrenormalized bond lifetime; mostly intramolecular association (3 + 3ν + 2z)/(3ν − 1) renormalized bond lifetime; transfer of intra to intermolecular association (4 + 3ν + 3.5z)/(3ν − 1) renormalized bond lifetime; mostly intermolecular association (1 + 3ν + 0.5z)/(3ν − 1) renormalized bond lifetime; entangled strands between stickers (1.75 + 3ν + 3.5)/(3ν − 1) Part c exponent γ in D ∼ ϕγ (general form)

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Sticky Rouse Model, Overlapping but Unentangled Chains unrenormalized bond lifetime; transfer of intra- to intermolecular assocn −(2ν + renormalized bond lifetime; transfer of intra- to intermolecular association −(2ν + renormalized bond lifetime; mostly intermolecular association −(2ν + Sticky Reptation Model, Overlapping and Entangled Chains unrenormalized bond lifetime; mostly intramolecular association −(2ν + renormalized bond lifetime; transfer of intra- to intermolecular association −(2ν + renormalized bond lifetime; mostly intermolecular association −(2ν + renormalized bond lifetime; entangled strands between stickers −(2ν +

exponent α in τ ∼ ϕα (good solvent) 3.2 4.96 0.17 2.9 3.13 1.46 2.44 exponent β in η ∼ ϕβ (good solvent) 4.2 5.96 1.17 6.8 8.58 3.77 4.75 exponent γ in D ∼ ϕγ (good solvent)

2z + 1)/(3ν − 1) 3.5z + 2)/(3ν − 1) 0.5z + 1)/(3ν − 1)

−3.44 −5.19 −3

2z + 2)/(3ν − 1) 1.75z + 1)/(3ν − 1) 0.5z)/(3ν − 1) 0.5z + 0.75)/(3ν − 1)

−4.75 −3.36 −1.69 −2.67

a ν is the Flory exponent, with ν = 0.588 in the good-solvent limit. z accounts for excluded-volume interactions and governs the number of non-local contacts in a strand containing g monomers, where the number of contacts scales as g−z, with z = 0.225 in the good-solvent limit.40,41 With increasing concentration, intrachain associations are transformed into interchain associations, causing transition from one scaling behavior to another. Moreover, higher concentrations require renormalized bond lifetimes to be used, accounting for multiple dissociation and reassociation of the same sticky sidegroup. This causes further transitions between different scaling regimes. Both effects entail subdivision of the ϕ-range into seven subranges. In all tables, the concentration increases from the uppermost to the lowermost row, passing through these seven different scaling regimes, respectively. Scaling laws for D(ϕ) in part c are derived from the relation D ≈ R2/τ,35 with R the radius of gyration of the diffusing chain that scales as R ∼ ϕ−(ν−0.5)/(3ν−1) and τ the relaxation time that scales as summarized in part a.

considerable agreement to their experimental results.27,51 In contrast, the Rubinstein−Semenov model has been addressed by just a few investigations; these provide qualitative support52 but report discrepancies to its quantitative predictions.30 A major shortcoming of the existing studies on the dynamics of supramolecular polymer networks is that they have all been carried out with very different types of samples, each exhibiting its own specifity. This circumstance limits the comparability of these investigations, because each is based on samples that exhibit a different interplay between the effects of reversible cross-linking with that of the underlying nonassociative polymer physics. In the context of an extensive computersimulation study, Hoy and Fredrickson commented this interplay to be “beyond the reach of analytical theory”.53 Overcoming this limitation in experimental investigations

concentration range considered, which corresponds to different extent of chain overlap, entanglement, and association, different scaling exponents can be derived from this concept, as summarized for the scaling of τ(ϕ) and η(ϕ) in Table 1, parts a and b. These different theoretical models have been challenged by several experimental studies.7 Many of these studies rely on macroscopic rheology, focusing on how mechanical quantities such as the shear modulus, the viscosity, and the longest relaxation time of supramolecular polymer systems scale as a function of the concentration or molecular weight of their constituent supramolecular building blocks.27,30,42−52 However, no consistent picture has been derived to date. Whereas some experimental studies support the Cates model,14,42−50 both qualitatively and quantitatively, others question it, despite B


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Figure 1. Strategy of the present work. (A) A set of supramolecular poly(N-isopropylacrylamide) (pNIPAAm) networks that are cross-linked by different types of reversible chain association, but all formed from the same common precursor polymer, serves to study the dynamics and mechanics of transient gels. The starting material is an electrophilic, methacryl-succinimidyl (MASI) modified pNIPAAm copolymer, denoted p(NIPAAm-coMASI). The MASI moieties can be replaced by nucleophilic, amine-modified functionalities. This is done using the following motifs: (I) diaminotriazine (1), (II) cyanuric acid (2), and (III) terpyridine (3). After equipping the polymers with these motifs, they can be cross-linked through addition of complements like (I) bis-maleimide (4), (II) a Hamilton wedge (5), and (III) metal ions (here: Mn2+), yielding pNIPAAmbased supramolecular polymer networks with greatly varying type and strength of interchain cross-linking, all formed from the same starting material. (B) With these materials, two approaches are used to study the chain dynamics inside the networks. In one approach, fluorescently tagged tracer chains explore the supramolecular network matrixes by diffusing through them without tracer−matrix interactions, referred to as “non-sticky” tracers (left panel). In another approach, the fluorescently tagged chains are further functionalized with the same associable motifs that also form the supramolecular polymer network matrixes. These tracer polymers can bind to the network matrixes and are therefore referred to as “sticky” tracers (right panel). In both approaches, confocal fluorescence recovery after photobleaching serves to quantify the tracer-chain mobilities. In addition, the same gels are probed by macroscopic shear rheology (middle panel). Reproduced in part with permission from ref 31. Copyright 2013 The Royal Society of Chemistry.

requires systematic work that is based on a set of supramolecular polymer networks that are all derived from the same polymer, but that nevertheless exhibit different strength of transient cross-linking. This approach can ensure comparability of the results, which may then serve as a systematic check on the impact of the strength of reversible chain cross-linking on the properties of supramolecular polymer networks. On this basis, the applicability of the different theories to predict these properties can be appraised. Unfortunately, this has not yet been accounted for. In addition to this shortcoming, it is a particular limitation of the existing investigation of supramolecular polymer network dynamics that just very limited work has microscopically addressed these materials.49,51,54,55

Instead, the majority of the existing studies are based on macroscopic rheology on samples under macroscopic deformation. This is unfortunate, because macroscopic deformation can alter the sample structure, connectivity, and relaxation time scales.56 In this paper, we study the microscopic chain dynamics in semidilute supramolecular polymer networks, along with their macroscopic mechanics; we aim to assess both with unprecedented consistency. For this purpose, we employ a set of different supramolecular networks that are all derived from the same common precursor polymer. This is achieved by functionalizing the precursor polymer with different types of associating side groups in a modular principle, as illustrated in C


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Scheme 1. Amine-Functionalized Moieties and Cross-Linking Agents To Form Different Supramolecular Polymer Networks from One Common p(NIPAAm-co-MASI) Precursor As Illustrated in Figure 1A

carboxyethylsulfanylthiocarbonylsulfanyl)propionic acid (TTC, 12.5 mg, 49.14 μmol, prepared as reported by Lowe et al.57), and N(methacryloxy)succinimide (MASI, 2.43 g, 13.27 mmol) are dissolved in 60 mL of dry DMF, and argon is bubbled through the solution for 20 min. After heating to 80 °C, 2,2-azobis(2-methylpropionitrile) (AIBN, 1.2 mg, 7.31 μmol) is added, and the solution is stirred overnight at 80 °C. The solvent is removed under reduced pressure, and the residue is dissolved in tetrahydrofuran (THF, 150 mL). After complete dissolution, the product polymers are isolated by precipitation in cold diethyl ether (1 L). Characterization by size exclusion chromatography reveals Mn = 61 kg mol−1, Mw = 104 kg mol−1, and Mw/Mn = 1.7. (PSS GRAM-1000/100−7 μm column, 70 °C, N-methylpyrrolidone eluent with 0.05 mol L−1 of lithium bromide and benzoic acid methylester as internal standard, using molecular weight calibration with polystyrene standards). This molecular weight ensures chain overlap and entanglement when gels are prepared at polymer volume fractions of 0.05−0.2. The amount of MASI in the copolymer, determined by 1H NMR (Bruker AC 700 spectrometer), is 4.8 mol % relative to the amount of NIPAAm repeat units. To prepare a set of supramolecular cross-linkable polymers from this precursor material, the stock of p(NIPAAm-co-MASI) is split into a set of substocks, and different supramolecular associable side groups are linked to them; this is achieved by replacement of the MASI moieties in each substock by different associable motifs. We use aminefunctionalized diaminotriazine (1) (prepared by a procedure of Zimmerman et al.58), amine-functionalized cyanuric acid (2) (prepared by a procedure of Reinhoudt et al.59), or aminefunctionalized terpyridine (3) (prepared by a procedure of Schubert et al.60) for this purpose, as shown in Scheme 1. To couple these groups to the polymer, p(NIPAAm-co-MASI) (1 g, 16.42 μmol) and DMAP (N,N-dimethylpyridin-4-amin; catalytic amount) are dissolved in 10 mL of DMSO, amine-functionalized derivatives of the desired side groups (1, 2, or 3, 1.2 eq per MASI group, respectively) are

Figure 1A. With this approach, we compare supramolecular polymer networks that are transiently cross-linked through either directed triple or sextuple hydrogen bonding or through tridentate transition metal complexation. This strategy allows the strength of chain−chain association to be varied within a range of association constants of K ≈ 102−1010 M−1 or −2.31 We study these different supramolecular polymer networks by probing the micrometer-scale mobility of fluorescently tagged linear chains that diffuse through them. We use two different types of tracer chains, as illustrated in Figure 1B. In one branch of experiments, the tagged tracer chains can bind to the supramolecular network matrixes by the same interactions that connect the matrix chains, thereby acting as “sticky” tracers. In another branch of experiments, the tracer polymers are “nonsticky” and cannot bind to the matrix networks. In addition to these microscopic studies, we probe the macroscopic mechanics of the same supramolecular networks by shear rheology, as also sketched in Figure 1B. The aim of this effort is to derive a picture on the impact of the strength of transient chain crosslinking on the dynamics and mechanics of semidilute supramolecular polymer networks. In particular, we aim to delimit the applicability of the Rubinstein−Semenov theory to model these properties.

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EXPERIMENTAL SECTION

Synthesis of Matrix and Tracer Polymers. The material basis for our investigations is a methacryl-succinimidyl (MASI) modified poly(N-isopropylacrylamide) (pNIPAAm) copolymer, denoted p(NIPAAm-co-MASI). This polymer is prepared by RAFT polymerization. For this purpose, NIPAAm (30 g, 0.27 mol), 2-(2D


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added, and the solution is stirred overnight at 60 °C. This procedure leads to replacement of the succinimidyl moieties by the desired supramolecular cross-linkable groups, bound to the polymer by amide linkages. The crude product is dialyzed against water. In the case of cyanuric-acid functionalization of the copolymer, 0.1 vol % of concentrated HCl is added to the water to ensure solubility of the cyanuric acid. The product polymers are isolated by lyophilization. Because of the presence of metals in common dialysis tubing, terpyridine-functionalized copolymers are purified by a different procedure: the solvent is removed in vacuo, the residue is redissolved in THF, and the product polymers are isolated by precipitation in cold diethyl ether. In all cases, the sidegroup functionalization leads to complete conversion of all MASI groups, as confirmed by 1H NMR spectroscopy. As a result, we obtain a set of polymers that can undergo reversible chain−chain association if complementary linkers are added. To dimerize the hydrogen-bonding moieties 1 or 2, we use bismaleimide (4) or Hamilton-wedge (5) linkers, as illustrated in Figure 1A (I and II) and detailed in Scheme 1. The synthesis of these linkers is detailed elsewhere.31 To achieve transition metal complexation of the terpyridine moieties 3, as also illustrated in Figure 1A (III), we add Mn(NO3)2. In addition to this set of supramolecular associable polymers that can be used to obtain different supramolecular polymer networks, another portion of the p(NIPAAm-co-MASI) precursor is used to prepare fluorescently tagged tracer chains. We prepare two sets of tracers. One set of tracers consists of pNIPAAm homochains that carry a small amount of a fluorescent label only, (S)-(+)-4-(3-aminopyrrolidino)-7-nitrobenzofurazan (NBD-apy, 6). Another set of tracers consists of 6-labeled pNIPAAm chains that exhibit additional functionalization with the same associating side groups that link the respective supramolecular network matrixes wherein the tracers are embedded. As a result, these tracers can transiently link or “stick” to their matrixes. To synthesize the unfunctionalized, “non-sticky” tracer polymers, p(NIPAAm-co-MASI) (1 g, 16.42 μmol) and a catalytic amount of DMAP are dissolved in 10 mL dioxane, and the fluorescent dye NBD-apy (6, 4.1 mg, 16.42 μmol) is added. The mixture is stirred for 24h at room temperature, and then all unreacted MASI-moieties are quenched by addition of N-isopropylamine (2 mL). After being stirred for another 24 h at room temperature, the mixture is poured into cold diethyl ether to precipitate the polymer. The degree of labeling is estimated by 1H NMR spectroscopy, denoting an average amount of one label per polymer chain. To synthesize the functionalized, “sticky” tracer polymers, the same labeling procedure is applied, but instead of quenching the unreacted MASI moieties with N-isopropylamine, they are reacted with the amine-functionalized cross-linkable side groups 1, 2, or 3. For this purpose, 1.25 equiv of either amine-functionalized diaminotriazine (1, 93.7 mg, 20.57 μmol), cyanuric acid (2, 117.3 mg, 20.57 μmol), or terpyridine (3, 150.3 mg, 20.57 μmol) is added and the solution is stirred for another three days at 60 °C. In the case of the triazine and cyanuric-acid functionalized polymers, the product polymers are purified by dialysis against water (three days, with water refreshment twice a day). For the terpyridinefunctionalized polymer, the work up is again different to avoid contamination with ions from the dialysis tubing. In this case, the solvent is removed under reduced pressure and THF is added. The resulting solution is then poured into cold diethyl ether to precipitate the polymer. The degrees of funtionalization and labeling are again investigated by 1H NMR: we determine an average of one fluorescent tag per polymer chain, whereas and the rest of the MASI moieties is confirmed to be completely substituted by the different cross-linkable, “sticky” side groups. Preparation of Supramolecular Polymer Networks with Embedded Fluorescent Tracer Chains. To prepare supramolecular polymer networks that contain either sticky or nonsticky fluorescent tracer chains, we dissolve each matrix polymer along with a portion of the nonsticky or the respective sticky tracer polymer in a stock solution. We prepare one solution for each of the different systems that are studied. Supramolecular chain cross-linking is then achieved by mixing each stock solution with a stock solution that contains the respective linker, using equal volumes of the polymer and the linker

stock solutions. We follow this approach and prepare supramolecular polymer gels with total volumes of 0.2 mL, respectively, each placed in a small glass vial with a gastight lid. We prepare the gels in two different solvents: dimethylformamide (DMF) and a mixture of chloroform and methanol (1:1). To prepare the DMF samples, both the polymers and linkers are dissolved in separate, properly concentrated DMF aliquots (0.1 mL, respectively) that are then combined. To prepare the chloroform−methanol samples, the polymers are dissolved in plain chloroform (0.1 mL), whereas the linkers are dissolved in plain methanol (0.1 mL); combination of both solutions yields supramolecular networks in a chloroform−methanol (1:1) environment. We prepare the samples such that their final polymer concentration spans the range of c = 50, 100, 150, 200, and 300 g L−1, where 5 g L−1 stems from the tracer, whereas the rest stems from the matrix in each case. The lower limit of this range is given by the overlap concentration of the precursor polymer that forms all networks in this work, which is c* = 45 g L−1 in DMF.31 The upper limit is chosen to be 300 g L−1, because it is impossible to prepare gel samples with homogeneous mixing of precursor polymers and crosslinkers at concentrations above. The linkers are used in stoichiometric amounts to the concentration of associable side groups in each sample. Fluorescence Recovery after Photobleaching (FRAP). To quantify the tracer-chain diffusive mobilities, temporally and spatially resolved fluorescence recovery after photobleaching (FRAP) profiles are recorded at (25 ± 0.1) °C. For this purpose, the supramolecular polymer network samples are placed on the sample stage of a confocal laser scanning microscope; this is done in their as-obtained state, leaving the samples inside the small glass vials wherein which they are prepared. We use a Leica TCS SP2 microscope with a 10× DRY objective of NA = 0.3. The low NA ensures that bleaching does not create any appreciable gradient in the z-direction; thus, we have to consider two-dimensional lateral diffusion only. In the scanning mode, the fluorophores are excited with the 488-nm line of an Ar-ion laser at 20% of its maximum power, whereas full-power irradiation with 6.2 mW at the object level is applied to bleach the fluorophore. Before bleaching, a stack of 10 images is scanned to record the prebleach situation. To bleach a spot pattern into the confocal plane, a chosen spot is irradiated for 0.1 s with the laser settings mentioned above. As a result, a Gaussian-shaped sink of the fluorescence intensity is created in this spot, with an initial bleach depth of ∼50% of the original fluorescence intensity and an initial e−1/2-radius of ∼4−5 μm in each case. After the bleaching, three series with 10−20 images each are recorded to document the subsequent fluorescence recovery process, with different temporal spacing between the images within each series. A typical temporal spacing between the single images is 0.3 s during the first series, 1 s during the second, and 5 s during the third; with settings like these, the ratio of the duration of scanning and the duration of bleaching exceeds 1000. The FRAP data are analyzed with a multicomponent diffusion model.61,62 In short, we record spatially (r) and temporally (t) resolved fluorescence intensity profiles, I(r,t), that are attenuated by a Gaussian sink in the bleached region around r = 0. This pattern smears out with time due to the diffusive exchange of bleached and unbleached fluorophores, characterized by an ensemble of translational diffusion coefficients Di in respective amounts Mi, with one D;M-pair for each diffusing species i. Quantitative analysis of these data sets yields distributions of diffusion coefficients.62 For all experiments discussed in this paper, these distributions spread across about one decade on the diffusivity scale. The exact shape of the D-distributions within this decade is not quantitative but depends on the mode of FRAP data analysis: whereas data evaluation with a damped Gauss−Newton fit tends to split each D-distribution into a group of single narrow modes, data evaluation with the maximum Entropy method yields a broad envelope instead.62 To prevent ambiguity, we average the Ddistributions on a logarithmic scale, yielding only one average tracerchain diffusivity for each sample; these averages are the same for both possible types of D-distribution fine structures. It is necessary to take the logarithmic rather than a linear average, because linear averaging would cause fast-diffusing fractions to dominate. E


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Preparation of Samples for Rheology. As with the FRAP samples, supramolecular polymer gels for shear experiments are prepared by dissolving each functionalized polymer in an independent stock solution and mixing these stock solutions with a set of corresponding stock solutions that contain the respective linkers, using equal volumes of the polymer and the linker stock solutions (0.4 mL, respectively) in each case. Again, we prepare each gel in two different solvents, dimethylformamide (DMF) and a mixture of chloroform and methanol (1:1), as detailed for the FRAP samples above. Also again, we prepare the samples such that their final polymer concentration spans the range of c = 50, 100, 150, 200, and 300 g L−1. Immediately after mixing the polymer and linker stock solutions, each sample is vortexed for about 2 s and then quickly placed on the rheometer. Rheology. Rheological studies are performed with a stresscontrolled Anton Paar Physica MCR 301 rheometer with cone− plate geometry (cone angle 1°, cone diameter 50 mm). Immediately after mixing the precursor polymer solutions and the cross-linkers, the resulting gels or polymer solutions are evenly distributed in the middle of the lower plate of the rheometer at 25 °C and the upper cone geometry is lowered. Excess sample is removed and a solvent trap is installed. For the first 30 min, each sample is monitored at a constant shear amplitude and frequency (γ = 0.01; ω = 1 Hz) to ensure equilibration. Then, a frequency sweep is recorded at constant strain amplitude (γ = 0.01; ω = 10−0.001 Hz) at 25 °C. After decreasing the temperature to 5 °C and allowing for equilibration for another 30 min, a second frequency sweep is recorded, followed by an amplitude sweep at the same temperature (γ = 0.001−1; ω = 1 Hz). We use the amplitude-sweep experiments to extrapolate the zero-shear viscosities of the supramolecular gels. This is done for all samples except for gels obtained by Mn(NO3)2-complexation of terpyridine-modified pNIPAAm (system III in Figure 1A) in chloroform−methanol; due to the high viscosities and considerable elastic contributions to mechanical response of these samples, their zero-shear viscosities are derived from creep tests at constant shear stress of τ = 0.1 Pa (T = 5°).

complementary to their sticky motifs. We employ bismaleimide (4) or Hamilton-wedge (5) linkers to dimerize the hydrogen-bonding moieties 1 or 2, as illustrated in Figure 1A (systems I and II) and detailed in Scheme 1. To achieve transition metal complexation of the terpyridine moieties 3, we add Mn(NO3)2, as also illustrated in Figure 1A (system III). The resulting supramolecular polymer networks exhibit marked differences in their strength of cross-linking. However, each network stems from the same original MASI-modified starting material. As a result, this strategy can serve as a consistent basis to systematically study the impact of the type and strength of interchain cross-linking on the dynamics of supramolecular polymer networks.31 To achieve this goal, we study the translational diffusive motion of two different kinds of linear tracer chains that are embedded within the networks. One set of tracers consists of pNIPAAm chains that carry a small amount of a fluorescent label only. Embedding these tracer polymers into the supramolecular network matrixes allows the tracer to freely explore the matrix network interior, thereby acting as a probe of its nanostructural topology. Another set of tracers consists of labeled pNIPAAm chains that exhibit additional functionalization with the same associating side groups that link the respective supramolecular network matrixes wherein which the tracers are embedded. As a result, these tracers can reversibly link or “stick” to the matrix and therefore act as labeled network chains that allow probing the transient network chain dynamics. The different supramolecular networks treated in this work are prepared and probed in two different solvents: dimethylformamide (DMF) and a mixture of chloroform and methanol (1:1). This strategy serves to cover opposite ends of a spectrum of solvent polarity.70 The Hildebrandt solubility parameter of a 1:1 chloroform−methanol mixture is calculated to be δchloroform−MeOH = 11.9 (cal cm−3)0.5 (arithmetic average of δchloroform = 9.3 (cal cm−3)0.5 and δMeOH = 14.5 (cal cm−3)0.5), whereas that of DMF is δDMF = 12.1 (cal cm−3)0.5.71 Both parameters are similar to that of pNIPAAm, δpNIPAAm = 11.2 (cal cm−3)0.5,72 indicating that both solvents provide good solvent conditions for this polymer. The parameter of the chloroform−methanol mixture is a slightly better fit to that of pNIPAAm than the parameter of DMF, indicating greater coil swelling in this solvent; this is in agreement to estimates of the hydrodynamic radius of the coils in both solvents by dynamic light scattering (DLS) and FRAP, denoting rH,DLS(CHCl3− MeOH) = 10.7 nm, rH,DLS(DMF) = 7.9 nm, rH,FRAP(CHCl3− MeOH) = 10.3 nm, and rH,FRAP(DMF) = 7.9 nm. Despite their similar ability to dissolve and swell pNIPAAm, chloroform−methanol and DMF cause marked differences in the association−dissociation equilibrium of the supramolecular cross-linkers that we use. A quantity that expresses the supramolecular binding affinity of the different cross-linking motifs is their association equilibrium constant, K, which relates the equilibrium concentration of associated supramolecular complexes to that of all unbound binding motifs. In our case, K = [ML]/([M] [L]) in case of equimolar association M + L → ML in systems I and II, whereas K = [ML2]/([M] [L]2) in case of 2:1 association M + 2L → ML2 in system III. This quantity has been determined by isothermal titration calorimetry in the context of another work.31 In addition to these estimates, we refer to literature data that are determined by other methods.73−76 The association of diaminotriazine and maleimide (system I) is weak, characterized by binding constants in the range of

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RESULTS AND DISCUSSION Modular Formation of Supramolecular Polymer Networks. To achieve the highest possible consistency in the investigation of supramolecular polymer network dynamics, we base our study on a set of supramolecular networks with greatly varying strength of transient cross-linking, all derived from modified poly(N-isopropylacrylamide), pNIPAAm.31 This polymer is well-known for its thermo-responsivity in aqueous media;63 however, we do not use it due to this feature, but for its solubility in a variety of organic solvents, both polar and nonpolar. This property allows these polymers to be studied at different solvent conditions. Furthermore, pNIPAAm-based polymers can be functionalized in a modular principle:64 first, an electrophilic, methacryl-succinimidyl (MASI) modified pNIPAAm is prepared by radical copolymerization. This copolymer can then be modified by coupling nucleophilic amine-functionalized moieties to its backbone, leading to copolymers that are equipped with a defined type and content of custom functional groups. We employ this principle and prepare a set of precursor polymers that consist of the same backbone, exhibiting a common substitution pattern and molecular weight distribution, but functionalized with different types of cross-linkable side groups.31 We use cross-linking that is based on two different classes of supramolecular interactions: directed multiple hydrogen bonding of diaminotriazine (1) or cyanuric-acid (2) moieties on the polymer backbone,23,24,65,66 or tridentate transition metal complexation of terpyridine (3) moieties on the polymer backbone,67−69 as illustrated in Figure 1A and detailed in Scheme 1. Tetrafunctional cross-linking of these polymers is achieved by adding linkers that are F


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Figure 2. Tracer-chain diffusion in supramolecular pNIPAAm networks cross-linked by sextuple hydrogen bonding between cyanuric-acid side groups and Hamilton-wedge linkers (system II). (A, B) Spatially resolved fluorescence intensity profiles after a spot-pattern has been photobleached into samples that host fluorescently tagged linear tracer chains. (A) Nonsticky tracer chains that diffuse through the surrounding supramolecular network matrixes without interacting with them, apart from mechanical entanglement. (B) Sticky tracers that temporarily bind to the surrounding network, thereby exhibiting slower motion. Both data sets resemble polymer network concentrations of 100 g L−1 in a mixture of chloroform and methanol (1:1) at 25 °C. (C, D) Distributions of diffusion coefficients in these samples and in corresponding samples at other concentrations. The distributions are obtained by analyzing the data in panels A and B as well as their analogues at other concentrations by a method published elsewhere.62

K ≈ 102−103 M−1 in chloroform at 25 °C.73 This is due to the fragile triple hydrogen-bonding array of type DAD−ADA in these complexes. When the hydrogen-bonding array is extended to six adjacent bonds, the association strengthens. As a result, equimolar association of cyanuric-acid and Hamilton-wedge motifs (system II) occurs with K ≈ 104−105 M−1 in chloroform at 25−30 °C.74−76 Even stronger association is achieved by complexation of the terpyridine motifs to Mn(NO3)2 (system III). This salt forms complexes with K = 3.5 × 109 M−2 in chloroform−methanol at 25 °C, whereas DMF as the solvent acts as a strong competitor and leads to K = 3.1 × 102 M−2 only.31 We prepare and probe supramolecular polymer gels at concentrations of 50, 100, 150, 200, and 300 g L−1. The overlap concentration, c*, can be determined as c* = 3M/(4πRg3NA),77 where NA is the Avogradro number, M the number-average molecular weight, and Rg the radius of gyration, which can be derived from the hydrodynamic radius via Rg = 2.05 rH for

random coils in a good solvent.78 We follow this approach and estimate c* = 45 g L−1 in DMF and c* = 18 g L−1 in chloroform−methanol. Thus, the concentration range that we cover corresponds to 3−17c* in chloroform−methanol and to 1−7c* in DMF; this is the range of onset of chain entanglement.79 As an alternative to mass-per-volume concentrations, we can express the polymer content in our samples in terms of the polymer volume fraction, ϕ, which is 0.04, 0.08, 0.12, 0.15, and 0.21 in our sets of samples. Microscopic Tracer-Chain Diffusion. To probe the dynamics of tagged tracer chains within the different supramolecular polymer networks that can be formed with our approach, we employ the technique of fluorescence recovery after photobleaching (FRAP).80 With this method, a selected micrometer-sized region of a fluorescently labeled sample is irradiated by a brief but intense light pulse that photobleaches the fluorophores in the illuminated region. Subsequent observation of the temporal evolution of the bleaching pattern G


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serves to assess the dynamics of the labeled materials. We do this by recording spatially (r) and temporally (t) resolved fluorescence intensity profiles, I(r,t), that are attenuated by a Gaussian sink in the bleached region around r = 0. This pattern smears out with time due to the diffusive exchange of bleached and unbleached fluorophores, as shown in Figure 2 for a 100 g L−1 supramolecular pNIPAAm network cross-linked by sextuple hydrogen bonding between cyanuric-acid side groups and Hamilton-wedge linkers (system II) in chlorofom− methanol at 25 °C. In this figure, the left data set (panel A) displays three selected fluorescence recovery profiles of a nonsticky tracer, whereas the right data set (panel B) shows the corresponding profiles of a sticky tracer. Comparison of these profiles, which are recorded at the same time intervals after bleaching (0.3, 1.2, and 4.8 s), reveals that the nonsticky tracers exhibit faster diffusive spreading than the sticky tracers. This is because the diffusion of the nonsticky tracers is obstructed by mechanical entanglement with the surrounding supramolecular network matrix only, whereas the sticky tracers can also bind to it, thereby undergoing repeat reversible entrapment as they diffuse through the polymer network. The fluorescence intensity profiles I(r,t) that are recorded after photobleaching are characterized by an ensemble of translational diffusion coefficients Di in respective amounts Mi. This ensemble of D;M-pairs, one for each individually diffusing species i, can be derived from the I(r,t) profiles by a method detailed elsewhere.62 Parts C and D of Figure 2 show the Ddistributions that correspond to the I(r,t) profiles in parts A and B of Figure 2, along with the distributions obtained from the same gels at other concentrations. In both parts C and D of Figure 2, the tracer diffusivity decreases with increasing polymer network concentration. For the nonsticky tracers, this decrease is caused by stronger mechanical entanglement at higher matrix concentrations. For the sticky tracers, additional obstruction is caused by transient binding to the network matrix, which is more pronounced at higher matrix concentrations. As a result, the decrease of the tracer-chain diffusivity with increasing polymer-network concentration is more pronounced for the sticky tracers than it is for the nonsticky tracers. To simplify further comparison, we average each D-distribution on a logarithmic scale. As a result, we can discuss the dependence of just one average tracer-chain diffusion coefficient on the concentration of the different surrounding supramolecular polymer networks, c, as assembled in Figure 3. These D(c) relations differ markedly, depending on the strength of supramolecular chain association. When a simple topological entanglement network of unfunctionalized pNIPAAm chains hosts a nonsticky tracer, a trivial result is obtained. In this case, the scaling of D with c resembles the classical prediction of D ∼ c−1.75 for semidilute solutions of entangled polymer chains,35 as shown in Figure 3A (main panel, chloroform−methanol; inset, DMF). This result confirms that our sample concentrations cover the semidilute entangled regime. When weak supramolecular cross-linking connects the chains in the polymer matrix, a similar result is obtained. For example, if the network matrix is reversibly crosslinked by weak association of diaminotriazine side groups and bis-maleimide linkers (system I) in chloroform−methanol, characterized by an association constant in the range of K ≈ 102−103 M−1,73 both the sticky and nonsticky tracer chains exhibit the same scaling of D ∼ c−1.75, as shown in Figure 3B. There is just a slight downshift of the absolute values of D by a factor of about 1.5 in these reversibly associating networks as

Figure 3. Dependence of the tracer-chain diffusion coefficient, D, on the concentration of a surrounding supramolecular polymer network matrix, c, at T = 25 °C. Open symbols denote nonsticky tracers, whereas filled symbols refer to sticky tracers. (A) Unfunctionalized pNIPAAm in chloroform−methanol (main panel) and DMF (inset). (B) pNIPAAm network matrix cross-linked by weak association of diaminotriazine side groups and bis-maleimide linkers (system I) in chloroform−methanol. (C) pNIPAAm network matrix cross-linked by stronger association of cyanuric-acid side groups and Hamilton-Wedge linkers (system II) in chloroform−methanol. (D) pNIPAAm network matrix cross-linked by strong complexation of terpyridine side groups and Mn2+ cations (system III) in chloroform−methanol (main panel) and in DMF (inset). The dashed and dotted lines in Panel D denote the onset of chain overlap at 18 g L−1 (ϕ* = 0.016) and the onset of overlap of the chain segments between two sticky sites at 125 g L−1 (ϕs = 0.1). H


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Figure 4. Mechnical properties of supramolecular pNIPAAm networks cross-linked by either (A) sextuple hydrogen bonding between cyanuric-acid side groups and Hamilton-Wedge linkers (system II) or (B) complexation of terpyridine side groups with Mn2+ ions (system III). Panel A displays the viscosities of system II in a mixture of chloroform and methanol (1:1) as a function of the shear rate at 5 °C. Panel B shows the elastic (G′, full circles and diamonds) and viscous (G″, × and + symbols) parts of the complex shear modulus of system III in a mixture of chloroform and methanol (1:1) as a function of frequency. Gray data are recorded at 25 °C, whereas black data are recorded at 5 °C. The 5 °C data are shifted along the abscissa according to the principle of time−temperature superposition to superimpose with the 25 °C data. The inset plot shows G′ and G″ of the same system at a concentration of 200 g L−1 in DMF.

ions,81 the association constant decreases to only K = 3.1 × 102 M−2.31 As a result, both the sticky and nonsticky tracers diffuse with the same speed and both exhibit scaling of D ∼ c−2 in these weak networks, again with absolute values of D comparable to that in the other weakly associating systems, as seen in the inset plot in Figure 3D. The preceding scaling relations can be discussed in view of the different theories to model the dynamics of supramolecular polymer networks. This work focuses on supramolecular networks that are built from associating polymers with sticky side groups. The concentration range covered is the semidilute regime, with polymer volume fractions of 0.05−0.2. The sticky Rouse and sticky reptation models by Rubinstein and Semenov provide a close match to this experimental situation;39−41 thus, we focus on them to discuss our experimental results. These models provide a set of scaling laws for the concentration dependence of the longest relaxation time of a network of temporarily associating chains, τ, which is the Rouse or the reptation time depending on the concentration range, as summarized in Table 1a. From these relations, we derive scaling laws for the concentration dependence of the diffusion coefficient of linear chains that diffuse through the networks. We follow the approach by de Gennes and estimate the chain diffusivity as D ≈ R2/τ,35 with R the radius of gyration of the diffusing chain. R scales as R ∼ ϕ−(ν−0.5)/(3ν−1), yielding R2 ∼ ϕ−(2ν−1)/(3ν−1). Together with the tabulated scaling for τ(ϕ)

compared to the tracer diffusivities in plain pNIPAAm entanglement networks. If the supramolecular association is stronger, differences are more notable. For example, when matrixes that are cross-linked by association of cyanuric-acid side groups and Hamilton-Wedge linkers (system II) are probed in chloroform−methanol (K ≈ 104−105 M−1),74−76 scaling close to D ∼ c−1.75 is seen only for the nonsticky tracers, which explore these polymer matrixes without binding to them. By contrast, sticky tracers are slightly more decelerated in these networks, as shown in Figure 3C. This deceleration exacerbates with increasing polymer concentration, as also seen in Figure 3C. As a result, the D(c)-scaling changes to slightly more pronounced D ∼ c−1.8. This trend is markedly pronounced in networks with even stronger supramolecular cross-linking, for example, networks that are cross-linked by complexation of terpyridine moieties with Mn2+ cations (system III), exhibiting a cross-linker association constant of K = 3.5 × 109 M−2 in chloroform−methanol.31 These samples show shallow D ∼ c−1.5 scaling in case of the nonsticky tracers, with absolute values of D comparable to that of the preceding transient networks, but the sticky tracers are markedly decelerated and exhibit very steep scaling of D(c), as shown in Figure 3D. This is due to the strong binding between the network matrix and the sticky tracers, which drastically obstructs the tracer-chain motion. If these interactions are weakened by the use of DMF as the solvent, which is a good competitor for complexation of Mn2+ I


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(Table 1a), this serves to derive scaling relations for D(ϕ), as summarized in Table 1c. To discuss our experimental estimates of the tracer-chain diffusivities to the predictions derived from the Rubinstein− Semenov theory, it is necessary to delimit the concentration range covered in our experimental situation. A characteristic threshold in semidilute polymer solutions is the onset of chain entanglement, which is commonly appraised as 2−5c*.79 Our samples are at 3−17c* in chloroform−methanol and at 1−7c* in DMF; thus, we are likely in the entangled regime in chloroform−methanol, whereas the samples in DMF cover the boundary between the semidilute unentangled and the semidilute entangled regime. A second characteristic threshold that is relevant in view of the Rubinstein−Semenov model is the onset of overlap of the chain segments between two sticky groups, denoted by the volume fraction ϕs.41 This volume fraction can be estimated as ϕs ≈ (N/S)1−3ν, with N the degree of polymerization of the sticky chains, S their average number of sticky side groups, and ν the Flory exponent.30 We use this formula and calculate ϕs = 0.1. As our samples cover the range of ϕ = 0.05−0.2, we cover regimes below and above this threshold. A third characteristic quantity is the threshold for entanglement of the strands between stickers, ϕle. Our functionalized pNIPAAm chains carry an average of 4.8 mol % of stickers and have a number-average degree of polymerization of 465. Thus, the segments between stickers have a number-average degree of polymerization of 21. This is close to the persistence length of pNIPAAm, which has been reported to be 10 or even ∼30 segments.82,83 Therefore, we do not assume entanglement of the chain segments between the stickers. As a result, the supramolecular polymer gels treated in this work span the first and the second concentration subregime of the sticky reptation model. In these regimes, scaling relations of D ∼ c−4.75 and D ∼ c−3.36 are predicted for the sticky-tracer diffusivity, as summarized in Table 1c. This is in agreement to our findings of D(c) in the strongly associating system III. In this case, we can fit the sticky-tracer data below and above the characteristic volume fraction ϕs = 0.1 (∼125 g L−1) with separate scaling laws of D ∼ c−4.94 and D ∼ c−3.37, as illustrated in Figure 3D. Although these fits are supported by just a limited number of data points, the scaling in both these regimes is distinctly steeper than scaling to be expected in regimes below (last subregime of the sticky-Rouse domain, D ∼ c−3, row 3 in Table 1c) and above (third subregime of the sticky-reptation domain, D ∼ c−1.69, row 6 in Table 1c), supporting the above rationale. By contrast, if weaker association connects the network and tracer chains, the predictions of D ∼ c−4.75 and D ∼ c−3.36 are not confirmed. Instead, the tracer chains exhibit less hindrance on their diffusion, with scaling more similar to classical semidilutesolution-type D∼c−1.75, as observed in all other cases in Figure 3. Macroscopic Rheology. The above FRAP experiments shed light on the microscopic chain dynamics in our set of supramolecular polymer gels. To supplement a macroscopic picture, we probe them by shear rheology. This method yields estimates of the zero-shear viscosity, η0. Similar to the FRAP assessment, we determine this quantity as a function of the polymer concentration, c, and compare the scaling of η0(c) with the predictions by the Rubinstein−Semenov theory. To measure η0, we probe the different supramolecular gels by amplitude sweeps. In these tests, a shear-independent viscosity η0 is observed at shear rates smaller than ∼1 s−1, whereas shear-

thinning occurs at higher shear rates, as shown for a set of supramolecular pNIPAAm networks cross-linked by sextuple hydrogen bonding between cyanuric-acid side groups and Hamilton-Wedge linkers (system II) in chloroform−methanol at 5 °C in Figure 4A. Similar behavior has been observed in other studies on supramolecular polymer networks, where shear-thinning is commonly addressed to shear-induced network rupture, network-chain disentanglement, and possible ejection of the sample from the rheometer.84−87 The scaling of η0 with c of our unfunctionalized pNIPAAm reference samples follows the classical prediction of η0 ∼ c3,88 as seen for the two lower data sets in Figure 5. There is just a

Figure 5. Dependence of the zero-shear viscosity, η0, on the concentration, c, of different pNIPAAm-based supramolecular gels at T = 5 °C.

difference between the absolute values of η0 by a factor of about 3 in these two data sets; this is due to higher coil swelling in chloroform−methanol than in DMF, in agreement to estimates of the hydrodynamic radius of the coils in both solvents by dynamic light scattering (DLS) and FRAP (rH,DLS(CHCl3− MeOH) = 10.7 nm, rH,DLS(DMF) = 7.9 nm, rH,FRAP(CHCl3− MeOH) = 10.3 nm, and rH,FRAP(DMF) = 7.9 nm). By contrast, if weak supramolecular chain association is added, for example, by association of diaminotriazine side groups and bis-maleimide linkers (system I) in chloroform−methanol, association of cyanuric-acid side groups and Hamilton-Wedge linkers (system II) in chloroform−methanol, or complexation of terpyridine moieties with Mn2+ cations (system III) in DMF, the viscosity increases. At c = 50 g L−1, all these different transient networks exhibit η0 values that exceed those in the unfunctionalized reference samples by a factor of about 2, in agreement with the corresponding decrease of the respective tracer-chain diffusivities in FRAP. Moreover, the scaling of η0(c) steepens to η0 ∼ c4 in these samples, as seen for the three upper data sets in Figure 5, again in agreement to the slightly steeper scaling of D(c) in the corresponding FRAP experiments. This finding can be viewed as a trend toward even steeper η0(c)-scaling predicted for sticky reptation in the concentration range ϕe < ϕ < ϕs by the Rubinstein−Semenov model (Table 1c). In consequence, we expect system III to show such steep η0(c)-scaling when it is cross-linked by Mn(NO3)2 in chloroform−methanol. We find η0 ∼ c5.7 for these transient gels, in qualitative agreement to this expectation. To add a more profound quantitative perspective, J


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we extend the discussion of the single parameter η0 in this particular case; this is done by considering the full time- or frequency-dependent viscoelastic spectra of these supramolecular gels: To quantify the complex viscoelastic properties of system III, we probe it by frequency sweeps and measure the elastic (full symbols, G′) and viscous (open symbols, G″) parts of its shear moduli. These tests demonstrate that G′ and G″ intersect at high frequencies, whereupon G′ exceeds G″ and tends to bend into a frequency-independent plateau, as shown for two concentrations in chloroform−methanol in Figure 4B. In basic polymer rheology, the frequency of G′−G″ intersection denotes the inverse of a characteristic relaxation time in a network of monodisperse entangled chains, τ, corresponding to the onset of macroscopic chain displacement and flow on longer time scales, which occurs with G′ ∼ ω2 and G″ ∼ ω1 according to the Maxwell model. For simplicity, we follow this picture in the present case and estimate τ100 = 12 ms for the 100 g L−1 and τ200 = 100 ms for the 200-g L−1 transient system III gels in Figure 4B (T = 25 °C), determined from their G′− G″ intersections. The corresponding sticky-tracer diffusion coefficients that have been estimated by FRAP are D100 = 0.03 μm2 s−1 and D200 = 0.002 μm2 s−1. Calculation with the Einstein−Smoluchowsky equation denotes mean-square tracerchain displacements of 720 nm2 and 400 nm2 in these two gels during their relaxation times, corresponding to linear displacements of 27 and 20 nm. This is both close to the hydrodynamic diameter of the tracer and matrix chains (∼20 nm), indicating the time scales of G′−G″ intersection in rheology to be those delimiting the regime of displacement of the constituent polymer chains by their own size. On longer time scales, stress relaxation leads to a drop of both G′ and G″. In our present set of samples, however, this does not occur with G(ω) scaling according to the Maxwell model (G′ ∼ ω2 and G″ ∼ ω1) but with both G′ and G″ apparently scaling close to ∼ω0.5. This finding denotes considerable deviation from single-exponential relaxation. To explain the latter finding, we address an argument based upon polydispersity: whereas un-cross-linked monodisperse polymer solutions display Maxwell-type G′ ∼ ω2 and G″ ∼ ω1 relaxation on time scales longer than τ, polydisperse samples exhibit shallower G′(ω) and G″(ω) due to multiexponential decay that causes broadening of the relaxation time spectrum.89,90 In the present supramolecular polymer gel system III, a percolated and elastically responding polymer network that exhibits a G′ ∼ ω0 plateau is present at time scales shorter than τ, whereas chain relaxation with a polydisperse relaxation time spectrum occurs on longer time scales. We postulate that the ability for transient association of the chains drags their relaxation, and that it does so more effectively for long chains with many associating side groups than for short chains with only few associating side groups. As a result, the intrinsic polydispersity of the sample (Mw/Mn = 1.7) is exacerbated, thereby broadening its relaxation time spectrum and leading to deviation from Maxwell-type G′ ∼ ω2 and G″ ∼ ω1 relaxation to shallower G(ω) in the low frequency range. Previous work has shown the same effect to occur and to be more pronounced if the extent and strength of transient chain association increases.52,91 When the preceding rationale is addressed to system III, we have to consider that its supramolecular chain association occurs with an average of two junctions per chain (chloroform−methanol, c = 200 g L−1), as determined in a previous

study.31 Thus, the time scale for detachment of a sticky chain from the network and displacement by its own size is longer than the time for scission of the constituent cross-linking motifs alone. To provide quantitative support for this rationale, we estimate the time scales for cross-link scission and plain network chain relaxation. Previous work by Craig et al.27 and Scherman et al.92 argues that the relaxation time of a supramolecular polymer network reflects the intrinsic relaxation time of its constituent cross-linking complexes if their concentration is at the lowermost boundary at which a gel network can possibly be formed, denoted as the supramolecular gel threshold. We apply this concept to system III by probing 200-g L−1 gels cross-linked with 1, 0.5, 0.2, 0.1, or 0 equiv of Mn(NO3)2, as shown in Figure 6A−E. Addition of 0.2 equiv of Mn(NO3)2 still forms a weak gel with a plateau in G′ at frequencies above ω0 = 100 s−1 (Figure 6C). Increase of the Mn(NO3)2 content to higher values entails linear decrease of ω0,27 corresponding to linear increase of the relaxation time τ, as illustrated in Figure 6F. This finding is consistent with transient network models such as the theory by Jongschaap et al., predicting linear scaling of the time for segmental relaxation as a function of the number of cross-links that have to break for this process.93 By contrast, adding less than 0.2 equiv of Mn(NO3)2 does not entail further decrease of the relaxation frequency, as also shown in Figure 6F. The measurement with 0.2 equiv of Mn(NO3)2 therefore reflects the supramolecular gel threshold according to the above definition;27,92 this measurement denotes a relaxation time of τ0.2 Eq. = 10 ms (Figure 6C), which can be taken as a measure of the intrinsic breaking time of the constituent cross-links, τx‑link break. Chain relaxation in a nonsticky semidilute solution of the pNIPAAm precursor polymer occurs faster than the dissociation of the transient junctions system III; we estimate a plain− pNIPAAm chain relaxation time of τ = 4 ms in chloroform− methanol at c = 200 g L−1, as shown in Figure 6E. This is 2.5 times shorter than τx‑link break = 10 ms, causing deviation from single-exponential relaxation according to the Maxwell model that is exacerbated with increasing extent of supramolecular cross-linking,52,91 as seen in Figure 4B and 6A−D. Thus, the sticky reptation model is an appropriate concept to model the dynamics of these transient gels, as evidenced in Figure 3D. When the solvent is changed to DMF, however, the same gels exhibit G(ω) scaling in reasonable agreement to the Maxwell model, G′ ∼ ω2 and G″ ∼ ω1, as shown in the inset plot in Figure 4B. This finding suggests weakening of the supramolecular associations by the competing complexation of DMF,81 in agreement with the η0 ∼ c4 and D ∼ c2 scaling of this system. Despite the agreement of the upper rationale to previous results,52,91 it remains puzzling to quantitatively explain the apparent scaling of G′ ∼ G″ ∼ ω0.5 in system III at low frequencies in chloroform−methanol. As an alternative to our polydispersity-argument, it appears tempting to consider this as the signature of a critical gel at the verge of percolation;94 however, if this was true, then such scaling should be observed over the whole range of frequencies, and a plateau with G′ ∼ ω0 should be absent. As both is not the case in our present study, we refrain from addressing this argument and rather consider the course of G′ ∼ G″ ∼ ω0.5 in system III as just a pronounced deviation from Maxwellian single-exponential relaxation due to broadening of the relaxation time spectrum in the presence of supramolecular cross-linkers. Indeed, our results in Figure 6 show that whereas close-to Maxwellian scaling of G′ ∼ ω2 and K


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Figure 6. continued superposition to superimpose with the 25 °C data. (A) Stoichiometric equivalence (“1 Eq.”) of the concentration of cross-linker and sticky polymer side groups, c(Mn2+)/c(TPy) = 0.5, nominally allowing for complete conversion according to Mn2+ + 2TPy → Mn(TPy)22+ to form network junctions; reprinted from Figure 4B. (B−D) Understoichiometric concentration of cross-linker to sticky polymer side groups, c(Mn2+)/c(TPy) = 0.25 (“0.5 Eq.”, panel B), c(Mn2+)/c(TPy) = 0.1 (“0.2 Eq.”, panel C), and c(Mn2+)/c(TPy) = 0.05 (“0.1 Eq.”, panel D). (E) Nonsticky semidilute polymer solution without crosslinker. (F) Relaxation time, τ, at which G′(ω) = G″(ω), as a function of the concentration of cross-linker denoted by the equivalents of Mn(NO3)2 as defined above.

G″ ∼ ω1 is observed in these polymer samples when no crosslinker is added, gradual addition of cross-linker entails gradual flattening toward G′ ∼ G″ ∼ ω0.5 in the limit of equimolar cross-linker addition, in agreement to related observations in the literature.52,91 To further support or challenge this polydispersity argument, additional work that focuses on the use of monodisperse precursor polymers with determined and equal spacing of cross-linkable sites would be a good supplement. Such work is presently in progress in our group and will be reported in due course. First results do indeed indicate the effects addressed to polydispersity in this present paper to be absent in monodisperse systems.

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CONCLUSION We have introduced a model system to form supramolecular polymer networks with greatly varying strength of transient chain cross-linking, all derived from the same precursor polymer. This approach allows the impact of the cross-linking strength on the dynamics and mechanics of these networks to be studied separate from variation of other parameters. Chain cross-linking in these networks occurs in a heterocomplementary fashion, mediated by low molecular-weight linkers that are added separately. These linkers can freely move within the network if they are in their unassociated state, but stress relaxation requires the accompanying movement of chain segments attached to a specific cross-linking site after cross-link scission. This situation is a close match to the conceptual picture of the Rubinstein−Semenov model for transient polymer network dynamics. Thus, our system provides a basis to systematically challenge this model. Our results show good agreement to the predictions for the concentration dependence of the chain diffusion coefficient, provided the chain association occurs with association constants of K ≈ 109 M−2. By contrast, classical semidilute-solution-type chain dynamics is recovered at weaker chain association, for example, at transient cross-linking with K ≈ 104−105 M−1. These findings suggest the existence of a threshold strength of association between these two values that delimits the applicability of the Rubinstein−Semenov model to the range of stronger association. In a longer perspective, this knowledge can be a basis for further, more sophisticated modeling of the self-healing of supramolecular polymer networks, which relies on understanding the kinetics and mechanisms of chain rearrangement in transient polymer networks and therefore requires knowledge about which theoretical model best applies at which conditions.

Figure 6. Frequency-dependent elastic (G′) and viscous (G″) shear moduli of supramolecular pNIPAAm networks cross-linked by complexation of terpyridine side groups with Mn2+ ions (system III) as a function of cross-linker concentration. Key: G′, full circles; G″, × symbols; gray data, 25 °C; black data, 5 °C. The 5 °C data are shifted along the abscissa according to the principle of time−temperature L


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AUTHOR INFORMATION

Corresponding Author

*(S.S.) E-mail: seiff[email protected] or sebastian. seiff[email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS FRAP experiments were performed at Clausthal University of Technology, kindly hosted by Prof. W. Oppermann (Institute of Physical Chemistry). We thank Marlies Graewert (Max Planck Institute of Colloids and Interfaces, Golm) for performing SEC analyses. P.v.A. is a student at Wageningen University and participated in this work as a visitor to the Seiffert group at Helmholtz-Zentrum Berlin. S.S. is a Liebig fellow and S.H. is a doctoral fellow of the Fund of the Chemical Industry (Germany). T.R. is an Elsa-Neumann fellow of the state of Berlin. This work was supported by the Center for Supramolecular Interactions and the Focus Area NanoScale at FU Berlin, which is gratefully acknowledged.

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Chain Dynamics in Supramolecular Polymer Networks

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