NMR Characterization of PEG Networks Synthesized by CuAAC Using

Aug 29, 2013 - Two types of PEG network structures were prepared (i) by linking two three-arm star PEG oligomers together and (ii) by connecting three...
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NMR Characterization of PEG Networks Synthesized by CuAAC Using Reactive Oligomers Muhammad H. Samiullah,† Detlef Reichert,*,‡ Tatiana Zinkevich,‡ and Jörg Kressler† †

Institute of Chemistry, Martin Luther University Halle-Wittenberg, D-06099 Halle (Saale), Germany Institute of Physics, Martin Luther University Halle-Wittenberg, D-06099 Halle (Saale), Germany

‡

S Supporting Information *

ABSTRACT: Well-defined poly(ethylene glycol) (PEG) networks were synthesized using copper(I)-catalyzed azide− alkyne cycloaddition (CuAAC). Two types of PEG network structures were prepared (i) by linking two three-arm star PEG oligomers together and (ii) by connecting three-arm PEG star units with bifunctional linear PEG oligomers of different molar masses. End-group functionalization of PEG oligomers to azide and alkyne moieties was performed while for CuAAC the catalytic system of CuSO4 and sodium ascorbate in aqueous environment was used. The successful conversion of the precursors and the formation of networks were confirmed by 13C-MAS NMR and FTIR spectroscopy. Network defects like multiple links and dangling chain ends were quantitatively investigated by 1H double quantum (DQ) NMR spectroscopy. initiated thiol−ene “click” reactions allowing hydrogels to have a unique scaffolding ability with the mechanical moduli in the range of different body tissues. On the other hand, Elbert et al.24 synthesized tetrafunctional PEG hydrogels using CuAAC to produce nanogels which were used for protein adsorbing coatings. PEG hydrogels from “click” chemistry were also used recently to create multifaceted cell structure scaffold25 and drug delivery systems with anticipated and adjustable drug release and degradation rates26 and for various other applications.27 In this work, two types of PEG networks were synthesized using the CuAAC with CuSO4 and sodium ascorbate in water as a catalytic system. In the first case, two three-arm PEG oligomers end-group functionalized with azide and alkyne moieties, respectively, were joined together while in the second case, azide-functionalized three-arm PEG oligomers were reacted with alkyne-functionalized linear PEG chains. Different molar masses of linear PEG chains were used in order to vary the length of the PEG chains between two cross-linking points. FTIR and 13C-MAS NMR measurements were performed in order to examine the overall conversion of functional groups after the network formation. For the characterization of the network topology, in particular for the estimation of the amount of free (“dangling”) chain ends, we employed 1H-DQ NMR spectroscopy.

1. INTRODUCTION Cross-linked poly(ethylene glycol) (PEG) networks have long been used and developed for applications ranging from drug delivery systems1 and tissue engineering scaffolds2 to polymeric electrolytes3 and biosensor applications.4 Over the years, various methods have been developed for creating PEG networks;5,6 however, end-linking of functional precursors provides the best opportunity to have control over the internal structure of networks. A variety of different reactions have been used for this purpose;7−9 however, due to constraints like side reactions, slow reaction rates, or incomplete conversion, there has been an imminent search for better reaction systems. Quantitative coupling (“click”) reactions were found to be a better alternative compared to all previously used methods. Copper(I)-catalyzed azide−alkyne cycloaddition (CuAAC) results in triazoles which are hydrophilic in nature.10 This is a modified form of the Huisgen cycloaddition reaction11 developed independently by Meldal et al.12 and Sharpless et al.13 and possesses all those attributes like insensitivity toward various functional groups, fast reaction rates, and high yields, which makes it a preferable choice over various other existing reaction systems. Just after its emergence, it has been used extensively in various applications like self-healing materials,14 amphiphilic15 and triphilic block copolymers, 16,17supramolecular polymers,18dendrimers,19 etc. There have been already some efforts for synthesizing polymer networks via “click” chemistry.20,21 The first report was given by Hawker et al.,22 who synthesized PEG networks by CuAAC and characterized the mechanical properties of the formed PEG hydrogels. Recently, Malkoch et al.23 prepared orthogonally functionalized PEG hydrogels by simultaneous CuAAC and UV © XXXX American Chemical Society

2. EXPERIMENTAL PART 2.1. Materials. Three-arm PEG (1000 g/mol) from Sigma-Aldrich was used with each arm having a degree of polymerization of 6−7 Received: July 30, 2013 Revised: August 15, 2013

A

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Figure 1. Scheme of the overall synthesis route selected for the formation of PEG networks. repeat units. Linear PEGs of molar mass of 300, 400, 1000, 2000, and 6000 g/mol were purchased from Fluka. For the precursor’s synthesis, propargyl bromide, sodium hydride, methane sulfonyl chloride, triethylamine, and sodium azide were purchased from Sigma-Aldrich and used as received. For the “click” reaction, CuSO4 and sodium ascorbate was purchased from Alpha Aeser. Solvents used for synthesis like THF and DMF were distilled and dried over calcium hydride. Two types of PEG networks were synthesized: “type A” networks formed by reacting two types of three-arm star PEG oligomers while “type B” networks were created by coupling three-arm star and linear PEG oligomers of different molar masses. Throughout this text, threearm star PEGs are denoted as PEG(S) and its modified species as PEG(S)-azide or PEG(S)-alkyne. All the linear PEG oligomers are denoted by their molar mass, e.g., PEG(400), etc., and its derivatives as e.g. PEG(400)-alkyne. The networks were represented by their respective precursors: e.g., a type A network of two three-arm star PEG(S) was named PEG(S-S) while type B networks made from PEG(S) and a linear PEG oligomers, e.g. PEG(400), are indicated as PEG(S-400). A comprehensive schematic overview of network formation is shown in Figure 1. 2.2. Synthesis. 2.2.1. Synthesis of Three-Arm PEG-Azide. The azide-functionalized, star-shaped PEG precursor was synthesized by reacting three-arm poly(ethylene glycol) (PEG(S)) with methane sulfonyl chloride and sodium azide.28,29 As a typical procedure, 10 g of PEG(S) (10 mmol) was dissolved in 150 mL of anhydrous THF together with 3.634 g (36 mmol, 3 × 1.2 equiv) of triethylamine, in a 500 mL flask. At 0 °C, 4.124 g (36 mmol, 1.2 equiv) of methane sulfonyl chloride diluted with 50 mL of THF was added dropwise into the reaction mixture. The reaction was allowed to proceed at room temperature overnight. After the reaction, precipitates were filtered and THF was removed via a rotary evaporator. Mesyl-PEG was obtained by extraction with DCM and water. The organic phase of

DCM was dried using sodium sulfate, and after solvent evaporation, white mesyl-PEG was obtained (yield 82%). In a second step, 5 g of mesyl-PEG and 1.95 g (30 mmol, 3 × 2 equiv) of sodium azide were added subsequently in 100 mL of anhydrous DMF, and the reaction was allowed to run for 36 h at 70 °C. Three-arm PEG(S)-azide was obtained after filtering the precipitates and drying (yield 87%). 1H NMR (CDCl3): δ (ppm); 3.64 (broad, (∼O−(CH2−CH2∼)), 3.38 (6H, (∼O−CH2−CH2−N3) (1H NMR spectrum of PEG(S)-azide is shown in Supporting Information). 2.2.2. Synthesis of Linear and Three-Arm PEG-Alkyne. Formation of linear and three-arm PEG-alkyne of different molar masses was achieved by following the methods already reported in the literature.30,31 In a typical case of PEG(400), 2.4 g (2 × 1.2 equiv) of sodium hydride/mineral oil mixtures was dissolved in 50 mL of anhydrous THF in a 500 mL flask. Then at 0 °C, a mixture of 10 g (25 mmol) of PEG(400) in 150 mL of dry THF was added dropwise to the sodium hydride/THF mixture. The system was stirred for about 30 min at 0 °C, and afterward 8.92 g of propargyl bromide (2 × 1.2 equiv), diluted with 50 mL of THF, was added dropwise to the reaction mixture. The reaction was allowed to proceed at 0 °C for another 2 h and then overnight at room temperature. Sodium bromide, produced during the reaction, was precipitated and filtered out after the reaction. The solvent was removed by vacuum, and the crude mixture was passed through a silica column. Initially, an ethyl acetate:dichloromethane mixture of 10:1 was used, while finally, a dichloromethane:methanol mixture of 10:1 was applied (yield 84%). 1H NMR (DMSO-d6): δ (ppm); 4.15 (4H, (∼O−CH2− CCH), 3.64 (broad, (∼O−(CH2−CH2∼)), 2.45−2.5 (2H, (∼O− CH2−CCH) hidden due to peak of DMSO at 2.50 ppm (1H NMR spectra of the PEG-alkyne precursors are shown in Supporting Information Figures S1−S7). B

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SDQ(τDQ) and the reference intensity Sref(τDQ), where τDQ is the variable length of the pulse sequence for multiple-quantum excitation and reconversion. SDQ(τDQ) is a rising function which contains the information on the residual dipolar coupling constant and its distribution. However, it is also affected by a relaxation decay which does not include information about the RDC. For a proper determination of the latter, the relaxation decay has to be separated from the dipolar information. To do so, the relaxation properties are experimentally accessible from the reference signal Sref(τDQ), providing the opportunity to remove relaxation effects in DQ signal SDQ(τDQ) by a point-by-point normalization, yielding the normalized DQ-built-up curve SnDQ(τDQ):

2.2.3. Synthesis of PEG Networks via CuAAC. CuAAC has been conducted in aqueous environment using the CuSO4 and sodium ascorbate system.32 In a typical case of PEG(S-400) network formation, 1 g (1 mmol) of PEG(S)-azide along with 0.6 g (1.5 mmol) of PEG(400)-alkyne and 0.2 mmol (30 mg) of CuSO4·5H2O were dissolved in 11 mL of deionized water and stirred at 40 °C for few minutes in a vial in order to make the reaction mixture homogeneous. After that, 0.3 mmol (60 mg) of sodium ascorbate, dissolved in small amounts of water, was added to the vial. Within a few minutes, the reaction mixture becomes a cross-linked gel which was washed with water for the next 4−5 days in order to remove the residual copper ions. The amount of water is critical in this process as the gelation time and final properties depend on that so all gels made initially have concentration of 15% w/v in water. However, samples with different concentrations of PEG oligomers, ranging from 15% to 75% w/v in water, were made and discussed in section 3.2. 2.3. Instrumentation and Measurements. 2.3.1. Fourier Transform Infrared Spectroscopy. ATR-FTIR measurements were performed on a Bruker Tensor VERTEX 70 equipped with golden gate diamond ATR. For the analysis, OPUS 6.5 software was used. All the measurements were performed at room temperature and within the range of 400−4000 cm−1. 2.3.2. Nuclear Magnetic Resonance Spectroscopy. Solution NMR spectra were recorded on a Varian Gemini 2000 (400 MHz). DMSOd6 was used as solvent for measuring the spectra of PEG(S)-alkyne while CDCl3 was used for PEG(S)-azide. 13 C-MAS single-pulse experiments were run on a BRUKER AVANCE 400 with a standard 4 mm VT-MAS probe. Typical MAS rates were about 8 kHz, and low-power decoupling was applied to remove the J-coupling. For reasons of signal intensity and sample handling, experiments were performed in the dry state for which the molecular mobility was sufficient to ensure an adequate spectral resolution. The low-field NMR experiments were performed on a Bruker minispec mq20 with a magnetic field of B0 = 0.47 T and 90° and 180° pulse lengths of 1.6−2.4 and 3.2−5.2 μs, respectively. The samples were swollen to equilibrium in D2O. Swelling increases the molecular mobility of the network chains, which ensures a sufficiently slow transverse relaxation of the 1H NMR signal and thus the ability to record data sets up to DQ evolution time well into the 100 ms range and beyond. The temperature was held at 27 °C by a standard BVT3000 temperature controller. Buildup curves of the longitudinal (T1) relaxation were measured by a saturation recovery experiment with a variable relaxation delay. The pulse sequence for the MQNMR experiment was described in detail in the literature.33 The relaxation delay between the scans was chosen to be 1 s, which is several times larger than the T1 of the network (T1 ≈ 0.3 s) but shorter than those of the residual water protons of the D2O (T1 ≈ 3 s, see Supporting Information). Thus, the signal of the latter is reasonably well suppressed in this experiment. Depending on the polymer concentration, the number of scans for each point in the MQ NMR experiment was varied between 512 and 2048. The details of the experimental procedure were well described in the literature33,34 and will thus only briefly summarized here. 1H MQ NMR is a robust and quantitative method for the analysis of the dynamics and structure in polymer networks. It permits the determination of residual homonuclear dipolar coupling (RDC) between the two protons in, for example, a CH2− group as well as the distribution of the RDCs. Couplings to more remote protons can be neglected in good approximation. Assuming the molecular mobility is fast compared to the static dipolar coupling (which is the case for polymer networks well above the Tg of the network chains), the RDC provides information about the degree of anisotropy of the molecular motion. Briefly spoken, the longer the network chain, the more isotropic is the reorientational motion of a given chain segment over a period which is short compared to the typical time of the NMR experiment and the smaller is the value of the RDC. Thus, the RDC becomes a measure of the anisotropy of the molecular dynamics. The 1H MQ experiment acquires two time-dependent signal intensity functions: the double-quantum (DQ) buildup curve

SnDQ (τDQ ) =

SDQ (τDQ ) SRef (τDQ ) + SDQ (τDQ ) − k e−τDQ / T2

(1)

The exponential term in the denominator originates from the T2 decay of the fairly isotropically moving residual solvent (and sol) molecules as well as from free chain ends and is subtracted previously from the experimental Sref(τDQ) + SDQ(τDQ) (see Figure 2a). Since D2O is used for swelling (which does not contribute to the 1H signal), the amount of absorbed water is negligible (see Supporting Information), and the sol content is minimized by the preparation; the constant k is a good estimate of the amount of free (dangling) chain ends and will be used

Figure 2. (a) Subtraction of the signal from dangling chain ends (“exponential tail”) from the reference data set Sref(τDQ) for the type B sample PEG(S-400), yielding an amount of about 5.3% dangling ends. (b) 1H-DQ data for the type B sample PEG(S-400), obtained by crosslinking 15 mg of polymer/100 mL of water. Symbols represent the experimental data (after subtraction of the exponential tail from the reference data; see text) while the lines were calculated with the fitting parameter obtained from the two experimental data sets. The full line is the calculated DQ-built-up curve, clearly showing three components with different intensities and RDCs. C

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in the evaluation. SnDQ(τDQ) can then be fitted with the value of the RDC, D, as the only free parameter to SnDQ (τDQ ) =

1.5 1 (1 − e−(0.378·2πDτDQ ) cos(0.583·2πDτDQ )) 2

(2) In homogeneous and highly mobile systems, the ratio of the RDC and the well-known value of the static dipolar coupling of a completely rigid system is the dynamic order parameter which can be related to the length of network chains, Mc. In dry networks, the proportionality factor between dipolar coupling and Mc depends on the chain stiffness and on details of the spin dynamics of the monomeric unit33 and has to be determined for each polymer separately. In real systems with different length of network chains and different values of the dipolar couplings and relaxation parameters, both SDQ(τDQ) and Sref(τDQ) contain more than one component, which makes the normalization according to eq 1 impossible. Thus, the data processing requires a more sophisticated multiparameter fit which provides the relative intensities of the different components IA, IB, IC and which is described in detail elsewhere.34 We applied this approach and fitted the experimental data sets of SDQ(τDQ) and Sref(τDQ) (after subtraction of the exponential tail) with two components A and B and a remaining weakly coupled component C. According to our experiences, it is possible to extract reliable data only for the intensity as well as RDC of the most strongly coupled component (component A, corresponding to single links as defined in Figures 5a.1 and 5b.1) as well as of the RDC values of the second component (component B, corresponding to double links, Figures 5a.2 and 5b.2). These two components can be easily realized from the humps in the SDQ(τDQ) curve (open circles in Figure 2b) which translates into the steps of the theoretical (relaxation-free) curve (full line in Figure 2b). The position of these steps on the τDQ axis is an estimate of the inverse of the RDC, 1/D. Also, the relative intensities of the components are determined by the fit procedure; however, those of component B have to be considered with care, since this component is heavily affected by the onset of relaxation and the signal-to-noise ratio is weak. Component C is completely invisible in the SDQ(τDQ) curve (open circles in Figure 2b) due to relaxation; however, it must exist because the sum of the intensities of the two visible components A and B does not reach the theoretical values of 0.5. In summary, only component A (the most strongly coupled component) will be considered in the evaluation below. See also Supporting Information for a flowchart of the data processing. In swollen networks, however, the relation between RDC and MC becomes strongly preparation- and solvent dependent, as explained in the literature.34,35,39 We thus limit ourselves to the quantitative discussion of differences between the different samples and in particular to relative amounts of component A. We explicitly do not aim to determine the length of the networks chains from the experimental RDC values, for (i) the possible realizations are well determined by chemistry, i.e., the molar mass of the precursors and the efficiency of click chemistry, and (ii) we are most interested in the differences between the samples under investigation.

Figure 3. FTIR spectra of PEG(400)-alkyne, PEG(S)-azide, and PEG(S-400) (for reaction conditions see Experimental Part).

Information Figures S8−S13). The first peak at 2113 cm−1 belongs to the stretching vibration between two carbon atoms having a triple bond, while the second peak appears due to the stretching vibration between the terminal hydrogen and the carbon atom of the alkyne moiety. In the case of PEG(S)-azide, the presence of the azide group is evident by the peak at around 2100 cm−1. However, in the spectrum of the PEG(S-400) network, the respective peaks of azide and alkyne moieties vanished completely, assuming a complete conversion within the detection limits of FTIR spectroscopy (approximately 5%). This might indicate the successful formation of ideal PEG networks as shown in Figure 4, in which, according to IUPAC definition of perfect network, all network chains are connected on both ends to different network junctions.36 However, the absence of defects like dangling chain ends, inelastic loops, etc., in a network is fairly unlikely in practice: according to the Flory−Stockmayer theory of gelation,37 the critical conversion

3. RESULTS AND DISCUSSION 3.1. Formation of PEG Networks via CuAAC. Poly(ethylene glycol) or PEG networks were successfully synthesized by using “click” chemistry via the above-mentioned methods. FTIR spectroscopy is used to investigate each step of the network formation process. Alkyne and azide moieties have their distinctive peaks in the FTIR spectrum, and it was expected that these peaks disappear during the network formation. Figure 3 shows the FTIR spectra of the initial PEG(400)alkyne and PEG(S)-azide as well as the formed type B network, PEG(S-400). The PEG(400)-alkyne has two characteristic peaks at around 2113 and 3240 cm−1 (FTIR spectra of the PEG alkyne and PEG-azide precursors are shown in Supporting

Figure 4. Schematic cross-linking topologies leading to ideal networks made of either type A samples from the reaction of star-azide and staralkyne (a) and type B samples from star-azide and PEG-alkyne (b). D

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additional possible networks connection: in type A samples, in addition to “single links” (Figure 5a.1) we might have “double links”; i.e., two arms of a star oligomer are connected with two arms of one other star (Figure 5a.2) which, ultimately, only serves as a linear extension of network chain and leads to network defects, which only results in increasing the mesh size of the network loop. In type B samples, along with “single links” (Figure 5b.1) and “double links” (Figure 5b.2), the termination of a network chain is possible without leaving unreacted groups behind (Figure 5b.3), forming a dangling chain end which is not terminated by azide groups, as they are for type A networks. This makes it impossible to detect them by NMR and FTIR spectroscopy and will be discussed below. Two more issues deserve attention; the amount of solvent also plays a role since intramolecular reactions become more likely as the concentration of monomers decreases. Because the cross-linking reactions are carried out in solution, intramolecular reactions start way before the critical conversion is reached, and as these intramolecular reactions do not contribute in creating the infinite network, it basically increases the critical conversion limit of the whole system. So the moment the system reaches the gelation point, the overall conversion of functional groups is much higher than the limit calculated by the Flory−Stockmayer equation. Second, postgelation reactions also increase the final conversion of functional groups. Intramolecular and intermolecular reactions among the unreacted functional groups of the same network do happen, if the chains are in close proximity to each other. Finally, there is a possibility of diffusion of unreacted monomer into the network. As the size of these monomers is comparatively smaller than the network’s mesh size, they can easily penetrate into the network structure and can react with any other unreacted functional group present. Hence, the final conversion will be higher as compared to the theoretical conversion limit, but even after that, there will be a finite possibility of unreacted functional groups. However, they are far too small in number to be detected by either FTIR or MAS NMR spectroscopy. 13 C-MAS NMR spectroscopy is employed to study the structure of the synthesized networks. In particular, we were aiming to determine the amount of unreacted alkyne groups in type A samples, which are obviously hard to detect in FTIR spectra. Alkyne groups are easy to detect in 13C NMR spectra, while the resonances of carbons next to an azide group cannot be separated from those next to a triazole ring. Because of the high mobility in the swollen networks, direct polarization (single-pulse experiments) has to be applied. Figure 6 shows the 13C-MAS spectrum of the type B sample PEG(S-400). One can estimate that the intensity of the carbons labeled by the letters a−d in Figure 6 should be approximately 4.2% (relative to the CH2− main peak), assuming about 22 monomeric units (44 CH2− groups) per PEG(S) and 9 monomeric units (18 CH2− groups) per PEG(400), three triazole groups, and three linear chains attached to each star (counting 50% of each per star molecule so as to 3/(44 + 0.5·3·18) = 0.042). The carbon labeled e is one of the glycerol carbons and is expected to have an intensity of about 1.4% for this sample. As known from solution NMR spectra of the precursors and 13C-MAS spectra of partially reacted samples, resonances of unreacted functional groups should appear at around 81.2, 76.6, and 58.7 ppm (alkyne) and 50 ppm (azide). For all type B samples, there is no indication for such peaks in the spectrum, and from the signal-to-noise ratio one can conclude that the content of

at the gel point for type A and type B polymer networks can be estimated by the equation Xc =

1 r(falkyne − 1)(fazide − 1)

(3)

Here, r is the stoichiometric ratio of alkyne to azide functional groups and falkyne and fazide are the functionalities of the respective monomers. For type A networks, the critical conversion is 0.5 while for type B networks it is 0.71, which means that the gelation point reaches after 50% and 71% conversion, respectively, of all the functional groups present initially. It is then comparatively difficult for the remaining functional groups to react in the same way, as the mobility is hindered due to the dramatically increased viscosity. Thus, statistically, some unreacted groups and also dangling ends are expected in the final networks. As a matter of fact, the Flory−Stockmayer theory of gelation is based on two assumptions: i.e., equal reactivity of all functional groups and absence of intramolecular reactions. In our system the first assumption can be accepted, but the second assumption will not be valid. Intramolecular reactions are always present in curing and end-linking processes, and at best, one can only reduce their amount but never avoid them completely. Figures 4a and 4b demonstrate some possible ideal network structure of the type A and type B networks, respectively: all the reactive terminals of the oligomers units are connected to different junction points, forming “single links” between them. However, Figures 5a and 5b show

Figure 5. Examples of possible network chains for type A (a) and type B samples (b) (a.1) and (b.1): “single links”, leading to the intended network topologies of the ideal networks as shown in Figure 4. (a.2) and (b.2): chain extensions or “double links”. (b.3): chain terminations or “dangling ends” which exist only for type B samples. E

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is tempting and indeed sometimes done,38 it is an erroneous conclusion: in the system of three functional stars and linear chains (type B samples), the scenario shown in Figure 5b.3 forms structures in which the two free arms of a star at the dangling end are terminated by a linear chain. We just like to comment here that, indeed, dangling chains are as well present in type B samples but cannot be detected either by IR or by 13 C-MAS NMR. However, it can be done reliably by 1H-DQ NMR as it will be shown below. 3.2. 1H-DQ NMR Experiments. As shown above, FTIR and 13C-MAS NMR cannot provide information about the length of the network chains and about the network topology (see Figure 5). Depending on the precursor molecules (staralkyne/star-azide or star-azide/linear PEG-alkyne), ideal structures as shown in Figure 4 are expected. However, due to intramolecular reactions as discussed above, chain extensions like those shown in Figures 5a.2 and 5b.2 might appear, increasing the length of the network chains more than twice. Considering the short chain length of the stars (each arm has about 7 monomeric units only) and since the distance between the two free ends of a star is always comparable to the length of a linear PEG, such a topology is very likely to be formed. Other topologies (“multiple links”), leading to even longer chain extensions, are as well possible but hard to detect and to distinguish from each other. To quantify the relative amount of these network topologies, the1H-DQ-NMR technique is employed as described in the literature.33 Figure 2b shows as an example the data for the type B sample of PEG(S-400), swollen in D2O to equilibrium. In a first step (Figure 2a), an exponential tail (originating from almost isotropically moving PEGs) was subtracted from Sref(τDQ), yielding the relative intensity of the dangling ends k. The open symbols in Figure 2b are the SDQ(τDQ) and Sref(τDQ) (the latter after subtraction of the exponential tail), respectively, while the solid line is the net DQ-built-up curve SnDQ(τDQ) calculated from the fitting parameters of the two data curves. It can be seen that the experimental DQ-built-up curve SDQ(τDQ) contains discrete components which manifest themselves in the humps/maxima, and it decays away for longer τDQ by T2 relaxation. S nDQ (τ DQ ) contains at least three discrete components with different values of the RDC, the assignment of which is based on the considerations that the RDC is a measure of the degree of anisotropy of the reorientational motion of the CH2− groups in the polymer chains linking two network junctions: the longer the chain, the more degrees of conformational freedom exist and the more isotropic the molecular motion becomes. On the other hand, the crosslinking chemistry defines that the network chains can only have discrete lengths. Thus, the components with the strongest coupling (the SnDQ(τDQ) of which rises at smaller values of τDQ, see Figure 2b) must thus be assigned to the shortest network chains. The shortest possible connection of two network points in the present samples is the length of two arms (for the type A) or the length of two arms plus those of the linear PEG in case of type B (see Figures 5a.1 and 5b.1). Thus, this component in the SnDQ(τDQ) must unambiguously be assigned to the “single links”. The next component (next step in the SnDQ(τDQ) curve) must be assigned to the next chemically possible network-chain length which corresponds to topologies like those sketched in Figures 5a.2 and 5b.2 (“double links”). The SnDQ(τDQ) including these two components rises for the example shown in Figure 2b to about 0.38; however, theory requires that the asymptotic limit of SnDQ(τDQ) for long τDQ is

Figure 6. 13C-MAS spectrum of the type B sample PEG(S-400). Letters specify the carbon atoms at the triazole ring and the glycerol branch, respectively. The integrals are referenced to the CH2− main peak.

unreacted groups must be less than 0.1%. The small peak at 62 ppm could not be assigned; however, it was identified as originating from a CH2− group, and thus, it certainly does not belong to the functional groups of the precursors. Figure 7

Figure 7. CH and CH2− region of 13C MAS spectra of a type A sample (PEG(S−S), top) and a type B sample (PEGS(S-400), bottom). The resonances marked by arrows are from unreacted alkyne residues and are only present in the type A sample.

compares the CH/CH2− region of the 13C MAS spectra for the type A and type B samples, and it is obvious that for the former there are resonances originating from unreacted alkyne groups, yielding an upper limit for the fraction of dangling chains of about 10% (every 10th arm of a star terminated with an alkyne group is not part of the gel). It is a direct spectroscopic indication of the dangling ends in this sample which seems to be completely absent in the type B samples. We like to remind that the absence of unreacted end groups does not necessarily mean that there are no free chain ends. Though this assumption F

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is down to 10%), and its relative intensity depends weakly on the chemistry (type A or type B samples) as well as on the molar mass of the network chains. Also, there is always a relative intensity of about 5−10% of dangling ends (determined from the parameter k of the exponential tail, eq 1 and Figure 2a), except the largest molar mass for which it jumps up to about 30%. It is naturally to expect that the relative intensity of single links in type B samples is proportional to a probability that the two terminal linear PEGs connect with their unreacted ends to two different star molecules (forming a single link, Figure 5b.1), as opposed to the case in which they connect to the two free arms of just one other star, forming a double link (Figure 5b.2). This probability certainly depends on the chemistry, the concentration of molecules at the time of cross-linking, and conformational space available to the chains, i.e., on the molar mass of the linear PEGs. Figure 8 reveals a weak dependence of IA* as well as k on the molar mass of the network chains, in particular for network-chain length larger than about 2000 g/ mol. We like to note that for the longest network chains, the intensity of the single links decrease but those of the dangling ends strongly increase. One could speculate that this behavior is a consequence of the reduced conformational space of the chains for lengths larger than the entanglement length of about 2000 g/mol; however, we cannot support this assumption with further experimental evidence. Considering next the relation of IA* and k to the concentration of the monomers during crosslinking, Figure 9 reveals no significant dependence within the

0.5. Thus, there must be at least one more component with an even weaker dipolar coupling (smaller RDC), corresponding to a more isotropic motion and thus to longer network chains. Its RDC value cannot be determined since both SDQ(τDQ) and Sref(τDQ) have decayed away at τDQ larger than 100 ms. Since we cannot exclude higher order chain extensions like two double links in series, this last component might thus arise from such structures with longer network chains (“multiple links”). Thus, the relative signal intensity, i.e., the relative amounts of monomer units in single, double, and higher-order links for the sample PEG(S-400) is 26%, 50%, and 24%, respectively. The sum of these intensities corresponds to about 95% of the overall number of 1H spins of the sample; the remaining 5% is the amount of dangling ends which is given by the intensity of the exponential tail, k (Figure 2a). Normalization of all these data yields 5%, 25%, 47%, and 23% for the molar fractions of monomer units in dangling ends and single, double, and multiple links for this sample. We name these molar fractions Ii* = (Ii/(k + 1)) . It should be recalledas explained above that the 5% of dangling ends of type B samples cannot be detected by spectroscopic means. The relative intensities of single links (IA*) for samples with different length of linear PEG are shown in Figure 8 and

Figure 8. Dependence of the intensity of single links IA* and dangling ends k vs length of network chains for the type B samples (full symbols) with different length of network chains. The open symbols are from the type A sample. Figure 9. Dependence of intensities of single links IA* and dangling ends k in the 1H-DQ data of sample PEG(S-400) in dependence on the polymer concentration during cross-linking.

summarized in Table S1 (see Supporting Information). As stated above, these parameters result from a fitting procedure including 11 parameters.34 Extensive testing of this method reveals that the RDC and the intensity of the most strongly coupled component, IA* (corresponding to single links), are very reliable while those of the other two components are influenced by large errors. This can be also understood from Figure 2b: for the weakly coupled components, the signal is reduced by T2 relaxation down to below 50% of its original value, and the signal-to-noise of this part of SDQ(τDQ) is very low. Also, the values of the RDC depend on the degree of swelling of the sample. It increases the space between the network junctions, thus stretching the network chains, decreases the conformational degrees of freedom, and affects the RDC values which are a measure of the anisotropy of the molecular reorientations.35 All experiments are performed at swelling equilibrium, and thus, the degree of swelling is different for the different samples. Therefore, we will discuss here the intensities of component A (the single links), IA* only (Figure 8). It is evident that all samples consist of at most 20− 30% of single links (except of sample PEG(S-300) for which it

experimental error (see also Table S2 in Supporting Information). It should be noted at this point that recently a weak dependence of the latter was found for four-functional stars.34 However, the effect is very weak. We finally like to emphasize that our 1H-DQ NMR data show that the molar fraction of single links is in contrast to recent claims38 always far below 100%. The 1H-DQ data shown here are employed to characterize our materials. Without the necessity of making assumptions and models, the data clearly show that our networks are far from being ideal as shown in Figure 4. This is actually a result which is not unexpected. In addition, the data provide model-free quantitative information about the relative intensity of single links and dangling ends and about the existence of double and even higher-order “multiple” links. It should be emphasized that this method provides information on dangling ends even when they are invisible for spectroscopic methods, as it became G

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evident from the comparison of type A and type B samples in Figure 7 and as it is sketched in Figure 5b.3. The experimental parameter IA corresponds to the molar f raction of monomer units in single links. Sometimes it is desirable to recast this figure into the number f ractions of network chains. If we assume that components A, B, and C contain only single links, double links, and “double−double links” (two double links in series), the molar masses of which are 1, 4.2, and 7.4 kg/mol, and for example assuming the intensities of the components as shown in Figure 2b (IA = 0.26, IB = 0.50, and IC = 0.24), it would results in number f ractions of network links pA = 0.63, pB = 0.29, and pC = 0.08 (see Supporting Information for details). However, it is actually impossible to calculate their correct number fraction, since the relative amounts of the higher order links are not known: in addition to the “double− double links”, even longer chain extensions are possible as well. And they contribute heavily to the mass fraction, even if they are low in numbers. Furthermore, we cannot conclude from our experimental data to the size of the network loops or alternatively the volume of the voids between the network chains (mesh size), since the network chains forming a given loop can be of different length (in contrast to the ideal ones shown in Figure 4 which are formed by chains of unique length), and their distribution in a given loop is not accessible from our data. It is tempting to compare our data to simulations like refs 34 and 40. However, this simulation works with tetrafunctional cross-linkers while in our case, the functionality is three. Furthermore, ref 40 aims mainly to the dependence of different topologies on the ratio of cross-linker to precursors which in our case is a fixed number. Reference 34 presents dependencies of the molar fractions of the different components (as well as of the RDCs which we do not discuss; see above) on the concentration of the precursors during cross-linking. This was actually the motivation to run the experiments presented in Figure 9. However, since the effect is on the same order as the margin of error, we do not dare to discuss it in more detail.

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Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS J.K. thanks the DFG for financial support (FOR 1145). The authors thank Kay Saalwächter, Frank Lange, and Karsten Busse for helpful discussions.

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REFERENCES

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4. CONCLUSIONS We demonstrate the synthesis of well-defined PEG networks via CuAAC using two different sets of precursors: first by reacting two three-arm PEG oligomers together (type A) and second by reacting three arm PEG with a linear PEG chain (type B). FTIR and 13C-MAS NMR proved the formation of triazole moiety and about unreacted groups (leading to dangling ends) in type A samples. As a special case of trifunctional stars and type B samples, dangling chains are invisible for spectroscopy. The amount of dangling chain ends and network imperfections like double links were detected for both types of samples and studied by the 1H-DQ NMR technique. It turned out that for all different network-chain lengths and polymer concentrations during cross-linking the molar fraction of monomer units in single links never exceeds approximately 35% and that there is always a molar fraction of monomer units in dangling chain ends of up to 30%.

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AUTHOR INFORMATION

ASSOCIATED CONTENT

S Supporting Information *

Solution NMR and FTIR spectra of azides and alkynes of PEG oligomers, a flowchart-like instruction of the data processing, tables with the fitting parameters of the 1H-DQ experiments, conversion of the molar fractions, and a low-field T1 plot. This H

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