Tuning Cross-Link Density in a Physical Hydrogel by Supramolecular

Apr 4, 2014 - Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. ‡ ... network density leads to an increase in the storage and loss modul...
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Tuning Cross-Link Density in a Physical Hydrogel by Supramolecular Self-Sorting Marcel M. E. Koenigs,† Asish Pal,† Hamed Mortazavi,‡ Gajanan M. Pawar,† Cornelis Storm,‡ and Rint P. Sijbesma†,* †

Laboratory for Macromolecular and Organic Chemistry, and Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands ‡ Department of Applied Physics and Institute for Complex Molecular Systems Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands S Supporting Information *

ABSTRACT: Cross-link density is an important parameter for the macroscopic mechanical properties of hydrogels. Increasing network density leads to an increase in the storage and loss moduli of the gel and can be accomplished by either increasing the concentration of cross-linkers, or by reducing the fraction of mechanically inactive cross-links. Mechanically inactive crosslinks consist of loops in the network, which do not contribute to the mechanical properties. Suppression of loop formation is demonstrated in a system of semiflexible supramolecular rods of poly(ethylene glycol)−bis(urea) bolaamphiphiles. Use of a cross-linker which, due to self-sorting of its hydrophobic segments, preferentially connects different rods, increases the modulus of a hydrogel by a factor of 15 compared to a system without self-sorting. By using statistical-mechanical calculations, it is shown that this increase can be explained by the increased tendency of the cross-linkers to form bridges between the semiflexible rods and thus increasing the cross-link density in the supramolecular hydrogel.

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INTRODUCTION Hydrogels are cross-linked materials that absorb a substantial amount of water. They are of enormous economical importance due to their use as food additives, in the oil industry, and for biomedical applications.1−3 In all applications, their mechanical behavior is of paramount importance, and it is determined to a large extent by cross-link density. In physical hydrogels, the cross-links are reversible, and control over mechanical behavior can be obtained by tuning chemical structure to create well-defined and specific cross-linking interactions. Cross-links are formed by specific parts of the components through aggregation by noncovalent interactions, such as ion complexation and hydrophobic interactions.4 Specificity and additional strength of aggregation may be obtained by additional physical interactions such as hydrogen bonding. The combination of multiple noncovalent interactions gives highly desirable mechanical properties to natural hydrogelators such as collagen or actin.5,6 The recent realization that mechanical properties and forces play an important role in the behavior of cells has opened up new markets for materials with tunable mechanical properties, with considerable potential for use in, for instance, tissue engineering. Despite their attractive mechanical properties, the use of natural hydrogelators in biomedical applications is limited by biocompatibility issues. With the aim of gaining full control © 2014 American Chemical Society

over properties of biocompatible hydrogels, several synthetic approaches to physical hydrogels have been reported. Amino acids are popular building blocks in synthetic hydrogelators, both in engineered polypeptides7 and synthetic peptide amphiphiles8 because the chemical diversity of amino acids allows tuning of hydrophobicity and creates the possibility to engineer specific recognition motifs. Alternatively, hydrogelators have been developed with biocompatible poly(ethylene oxide) (PEO) as hydrophilic component and peptide9,10 or with fully synthetic motifs as aggregating parts.11 Gels composed of fully synthetic components give maximum freedom in designing specific interactions and can therefore lead to precisely controlled structures and functions.12 We, and others, have combined hydrophobic interactions with the hydrogen bonding recognition motif of the urea functional group in amphiphilic bis(urea) molecules that aggregate in water to form rodlike micelles and tubular structures.13−15 The reversible nature of the bonds within the rodlike micelles makes them suitable as platforms for reversible crosslinking. Moreover, the bolaamphiphiles reported by us do not gelate in the absence of cross-linkers, making them ideal Received: February 28, 2014 Revised: March 28, 2014 Published: April 4, 2014 2712

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reported in literature, where the hetero-cross-linker is used to influence the mechanical properties of the material.23−25 Here, we introduce heterobifunctional cross-linkers with self-sorting bis(urea) motifs and compare their cross-linking efficiency with homobifunctional cross-linkers by determining mechanical properties of the gels. The effects on gel modulus are compared to the predicted values using a standard statistical-mechanical approximation of the network topology, combined with the theoretical predictions from the semiflexible network model.

building blocks to control cross-linking with specifically designed cross-linkers. Recent work from our group showed that segmented polymers of PEO and bis(urea) motifs have the potential to form injectable scaffolds for biomedical applications.16 The introduction of the bis(urea) recognition unit also was shown to give rise to the phenomenon of self-sorting.17 Bolaamphiphiles with different chemical structures form separate micellar populations in water, based on molecular self-recognition of the bis(urea) motif in mixtures of enantiomeric bolaamphiphiles or bolaamphiphiles with different spacing between urea groups.18,19 The aim of work described here is to gain maximum control over the mechanical properties of hydrogels by controlling the network topology with specific supramolecular interactions. In theoretical work, Storm et al. showed that any network created by suitable flexible cross-linking of semiflexible filamentous proteins in solution creates a viscoelastic network.20,21 Their theoretical model predicts that cross-linking bis(urea)-based rod-like micelles with a flexible linker provides similar viscoelastic properties. Hence, a system was designed to cross-link rods via a flexible linker. The cross-linkers are composed of two of the bis(urea) hydrophobic motifs also found in the bolaamphiphiles, connected by a flexible poly(ethylene glycol) linker (Figure 1). A cross-linker with two bis(urea) blocks can connect two micellar rods by incorporation of the bis(urea) into two separate rods.

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RESULTS Synthesis. A synthetic strategy was developed to prepare cross-linker molecules that combine two terminal hydrophobicbis(urea) blocks with a central hydrophilic PEO block (average molecular weight =8000) (See ESI). The synthetic strategy aims at cross-linkers with a segment sequence hydrophilic− hydrophobic- hydrophilic- hydrophobic- hydrophilic and provides cross-linkers with a single type of hydrophobic block (m = n). However, with this strategy hetero-cross-linkers cannot be obtained in a straightforward manner, and therefore we decided to prepare cross-linkers with a statistical mixture of U4U and U6U hydrophobic segments. The resulting mixture of cross-linker molecules is expected to contain 50% of 4 × 6 hetero-cross-linker and 25% of each homo-cross-linkers, 4 × 4 and 6 × 6, and is denoted as 4X6. The multistep synthesis (Scheme 1) was performed through reaction of the PEO derivative 1 with amine functionality with Scheme 1. Synthesis of PEO−Bis(urea) Cross-Linkers 6 × 6 and 4 × 4, and the Statistical Mixture of Homo and Hetero Cross-Linker 4 × 6

Figure 1. Structures of the bolaamphiphiles (UmU) and cross-linkers (mXn) . The numbers m and n designate the number of methylenes between the ureas.

However, such a cross-linker may also form intramicellar loops, thereby reducing cross-linking efficiency (Figure 2).22 Intramicellar loops will not contribute to the network density and will therefore decrease cross-linker efficiency. By making use of self-sorting, intramicellar loop formation may be suppressed and cross-linking efficiency may be increased by using cross-linkers that preferentially connect different rods. Cross-linking by heterobifunctional molecules has been

one of the isocyanato groups of 1,6-diisocyanatohexane. The excess 1,6-diisocyanatohexane was separated from the product by precipitation of the reaction mixture with hexane. Intermediate 2 with a single isocyanate group was reacted with PEO derivative 3 to give the cross-linker 6 × 6. Similarly, for the hetero-cross-linker, we separately synthesized two intermediates with single isocyanate group from 1,6-diisocyanatohexane and 1,4-diisocyanatobutane. They were mixed together and reacted with PEO derivative 3 to give statistical mixtures of cross-linkers, 6 × 6 (25%), 4 × 4 (25%), 4 × 6 (50%). The final products contained small fractions of crosslinker with an additional hydrophobic segment. Since the effect of these cross-linkers was deemed indistinguishable from that of

Figure 2. Limitation of cross-linking by formation of loops (left); suppression of loop formation in system of mixed bolaamphiphiles and hetero-cross-linker (right). 2713

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Figure 3. CryoTEM images of U6U (1 mg/mL) and a mixture of U6U (0.2 mg/mL) and 6 × 6 (0.1 mg/mL). The round darker features are artifacts caused by nonvitrified water.

the cross-linkers with two bis(urea) groups, further separation was not attempted. Morphology. As shown before, the UnU bolaamphiphiles form long rod-like micelles that can be imaged with cryoTEM.13 The samples for TEM and rheology were prepared by mixing the respective dry compounds and dissolving them in deionized water under sonication at 40 °C. In the absence of bolaamphiphiles, the cross-linkers form ill-defined aggregates in solution (Figure S7). When a matching cross-linker was added to a solution of bolaamphiphiles, the length of the bolaamphiphiles rods significantly decreased from an average of over 1 μm to 30−300 nm. CryoTEM picture of the effect of 6 × 6 on a solution of U6U rods is shown in Figure 3. This is shown at a concentration of 1 mg/mL, since at higher concentrations the solutions become too viscous to yield properly prepared samples A decrease in rod length of U6U upon addition of crosslinker 6 × 6 was also deduced from small-angle X-ray scattering data (Figures S8 and S9). Rod dimensions were approximated by fitting the scattering profiles to the Kholodenko model for worm like micelles.26 The length of un-cross-linked rods exceeded 140 nm, the highest length that could be determined with the range of q values of the scattering wave vector. In the presence of 0.1 mg/mL of cross-linker, a decrease in the length of the rods, to an average length of 72.4 ± 0.4 nm was observed. This length is longer than the average distance between cross-links and will therefore have a limited influence on the mechanical properties. In the Kholodenko model, a measure for the stiffness is included that defines the part of the worm like micelle that can be seen as a straight cylinder. The fitted value of this parameter increases from 3.6 to 6.5 nm upon addition of the cross-linker, indicating that coupling of the rods also has an effect on their stiffness. This can be explained by seeing the rods coming closer to each other and therefore having more resistance to bending. Rheology. Linear and nonlinear rheological behavior of the cross-linked semiflexible rods was determined under oscillatory shear. All measurements were performed in a frequency independent regime shown in Figure S10. To ensure an even comparison the weight percentage of the gelators was kept constant. Typical concentrations were 1.0 wt % for the amphiphilic rods and 0.5 wt % for the cross-linker. Figure 4 shows a significant increase of the moduli upon adding cross-linker to the bolaamphiphiles. The storage modulus of the solution of bolaamphiphiles was around 0.08

Figure 4. Strain dependent storage and loss modulus, showing the effect of cross-linking at constant concentration of U6U (1 wt %) and 6 × 6 (0.5 wt %) respectively (ω = 0.1/s).

Pa, where the torque is close to the detection limit of the instrument. Therefore, not all data points are reliable, but an approximate value of the modulus can still be given. Mixing the rods and the matching cross-linker creates a visco-elastic network in water with a modulus that exceeds the values of the individual components. The network resulting from a solution of the cross-linker 6 × 6, which is an associative polymer, has a G′ = 4 Pa, giving a viscous liquid. In order to investigate the effect of molecular recognition on the rheology, 0.5 wt % of the 6 × 6 cross-linker was mixed with separate, 1 wt % solutions of nonmatching U4U bolaamphiphile rods and with matching U6U rods. Figure 5 shows the strain dependent measurement of the storage and loss moduli of these systems. The modulus of the system with matching cross-linkers (U6U + 6 × 6) increased approximately 75 fold compared to the solution of the cross-linker alone. Remarkably, upon addition of the nonmatching U4U bolaamphiphiles, storage and loss moduli decrease by a factor of almost 7. Half of the molecules of statistical hetero-cross-linker 4 × 6 contain two different bis(urea) motifs, which have been shown to self-sort in solution. Thus, incorporation of 4 × 6 in a system containing both bolaamphiphiles may be expected to preferentially cross-link between U4U and U6U micelles, and to have a decreased fraction of mechanically inactive loops as depicted in Figure 2. When 0.5 wt % of the hetero-cross-linker was dissolved together with 1 wt % of a 1:1 mixture of bolaamphiphiles U4U and U6U, a gel with a storage modulus of 6000 Pa was 2714

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the network. We achieve this by exploiting the self-sorting effect in a solution of mixed semiflexible rods. The design of the hetero-cross-linker is such that the two bis(urea) motifs have different methylene spacers. Mixing this with a mixture of two different self-sorting bolaamphiphiles creates a system where the cross-linker will preferentially bind between two rods. The driving force for this behavior is the difference in binding energy for the matching and nonmatching bis(urea) motifs. This difference can be determined by reviewing the previous self-sorting results of this system, according to eq 1.19 ⎛ [U 6U * in U 4Ur] ⎞ ⎜ ⎟ ⎝ [U 6Uf ] × [U 4Uf ] ⎠ k ΔG − = ln Keq = ln non − match = ln ⎛ [U 6U * in U 6Ur] ⎞ RT kmatch ⎜ ⎟ ⎝ [U 6Uf ] × [U 6Uf ] ⎠ U 6U * in U 4Ur = ln U 6U * in U 6Ur

Figure 5. Strain dependent storage and loss modulus, showing the effect of matching and nonmatching cross-linkers at constant concentration of U4U or U6U (1 wt %) and 6 × 6 (0.5 wt %), respectively (ω = 1.0/s).

(1)

Equation 1 calculates the difference in binding energy between matching and nonmatching. U6Uf is the number of free monomers, U6Ur is the number of rods, and U6U* is the number of molecules in the rods. From this, we determine that the difference in binding energy between the U4U and U6U motifs is −6.48 kJ/mol, which equals −2.6 kBT at room temperature. The net effect, therefore, is that we have lowered the energy of the bridge configuration thereby rendering it more likely to occur. In what follows, we use this value as a mismatch penalty: the energetic cost of nonmatched insertion of a linker bis(urea) domain. Each of these states is characterized by an energy which equals the number of mismatches (i.e., 0, −2.6 kBT or −5.2 kBT). Using standard statistical-mechanical techniques, we compute the probabilities of each of these states as

obtained. (Figure 6) This value is approximately 15 times higher than the modulus (390 Pa) obtained obtained with homo-cross-linker 6 × 6 in the same mixture of bolaamphiphiles.

P(state) =

) ⎛ 1 ⎞ −( ΔGk(state ) ⎜ ⎟e BT ⎝Z⎠

(2)

We then proceed to sum over all states that yield bridges, and repeat this procedure for the homo- and the heterosystem to determine the probability ratio of bridges between the hetero and homo systems which also gives the ratio of the number of bridges:

Figure 6. Strain dependent storage and loss modulus, showing the effect of homo-cross-linking or hetero-cross-linking at constant concentration of U4U + U6U (1 wt %) and 4 × 6 or 6 × 6 (0.5 wt %) respectively (ω = 1.0/s).

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Pbridge(hetero)

DISCUSSION Cross-link density is often only moderately controlled in viscoelastic networks. The addition of the homo-cross-linker to the bolaamphiphiles shows this phenomenon as well. Even though the molar ratio of the rods and the cross-linker can be determined, one of the possible drawbacks of the system with the homo-cross-linker is the possibility of looping of the flexible linker. In equilibrium, the probabilities of looping or crosslinking are determined statistically by the binding affinities. For homo-cross-linkers, this affinity must be the identical regardless of whether the linker loops back, or bridges to a neighboring rod. While the energetics are the same, the effect on mechanics is not. In the case of both ends of a linker connecting the same rod (i.e., a loop) it provides no contribution to the modulus of the system. When the connection is made between two different rods, the network structure is reinforced and the crosslink does contribute to the macroscopic properties, i.e., the modulus of the network. Since we want maximal control over the effective linking in a network, we seek to decrease the amount of loops formed in

Pbridge(homo)

= 1.37 =

Nbridge(hetero) Nbridge(homo)

(3)

In other words, at the exact same polymer concentration, the hetero-cross-linker system is 45% more effectively linked by the same amount of cross-linker−a powerful way to create densely connected gels without increasing their mass. To relate this figure to an increase in mechanical modulus, we note the relation between G′ and gel architecture for semiflexible systems−as is appropriate for the fairly rigid rods in our system. MacKintosh and co-workers27 derived that

G′ ∝

kBTLp 2 ζ 2Lx 3

(4)

where Lp is the persistence length of the rods, ξ is the mesh size of the gel, and Lx is the length between two linker molecules along the backbone of a polymer. We compare the homo and the hetero systems, which will have approximately similar persistence lengths. The cross-linking length, however, will scale as the inverse number of cross-linkers. The mesh size is a 2715

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function of the polymer concentration, and scales as c−1/2.28 While it might appear that this concentration remains constant, there is a subtlety here: only those rods that are actually part of the meshwork contribute to the low-strain, low frequency modulus. This is where the heteronetwork receives another boost in modulus; because of the enhanced bridging, more rods are recruited into the network and the effective concentration rises as a result. With this recruitment effect, the concentration ratio between the homo- and hetero systems also becomes 1.37, and using eq 4 we may summarize the predicted relative increase in modulus as

The efficiency of the hetero-cross-linker in forming more bridges between the rods is shown by a factor of 15 higher modulus of the system than that with the homo-cross-linker. This shows that by using self-sorting and the resulting difference in binding energy of −6.5 kJ/mol, a highly efficient cross-linked system is obtained. Standard statistical mechanical calculations show that the difference in binding energy would result in a network topology whose G′ is increased by a factor of 9.2, very close to the experimental results. The difference in the cross-linking efficiency of the homo-cross-linker and heterocross-linker shows supramolecular control over the mechanical properties.

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3 ⎛ c(hetero) ⎞4 ⎛ Nbridge(hetero) ⎞ G′(hetero) ⎟ =⎜ ⎟⎜ G′(homo) ⎝ c(homo) ⎠ ⎜⎝ Nbridge(homo) ⎟⎠

S Supporting Information *

⎛ Nbridge(hetero) ⎞7 ⎟⎟ = ⎜⎜ ⎝ Nbridge(homo) ⎠ ≈ 9.2

ASSOCIATED CONTENT

Experimental details of synthesis, NMR, SAXS, cryoTEM, and rheological measurements and details of the statistical mechanical calculations. This material is available free of charge via the Internet at http://pubs.acs.org.

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(5)

This number agrees well with what we find experimentally in Figure 6: an increase of a factor of about 15 in mechanical modulus upon switching from the homo- to the hetero system. This illustrates the feasibility of mechanical control through designer cross-links: the system is highly dependent and responds strongly even to small changes in the energetics. Shen et al.24 have reported on the pronounced effect of heterobifunctional cross-linkers on the erosion resistance of physically cross-linked hydrogels, but the difference in modulus between systems with homo- and hetero-cross-linkers is about 20%. In recent work by Mes et al, an increase in modulus, of 10−30% compared to homo-cross-linkers was reported.23 However, direct comparison between homo-cross-linkers and hetero-cross-linkers is difficult, because additional parameters, such as solubility, are affected by the change in structure. The 15-fold increase in storage modulus as a result of the increased efficiency of the hetero-cross-linker shows that small molecular differences can have a great impact on the macroscopic properties of hydrogels, especially when important parameters such as the cross-linking density are targeted. The current work shows quantitatively that the increase can be attributed to the difference of 2.6 kBT in binding energy and using standard statistical mechanical calculations that this would give an increase of a factor 9.2 in the storage modulus. This closely matches our experimental result demonstrating that indeed, due to the effects of self-sorting of the different bis(urea) motifs and therefore the hetero-cross-linking, considerable increases in mechanical functionality may be obtained.

AUTHOR INFORMATION

Corresponding Author

*(R.P.S.) E-mail: [email protected]. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research forms part of the Project P1.04 SMARTCARE of the research program of the BioMedical Materials institute, cofunded by the Dutch Ministry of Economic Affairs. The financial contribution of the Nederlandse Hartstichting is gratefully acknowledged. This work was supported by the Ministry of Education, Culture and Science (Gravity program 024.001.035). Small angle X-ray experiments were performed at the European Synchrotron Radiation Facility (ESRF) in Grenoble at the high brilliance beamline DUBBLE BM26. The authors would like to thank G. Portale, W. Bras, I.K. Voets, M.A.J. Gillissen and I. de Feijter for assistance. P.H.H. Bomans and P. Besenius are kindly acknowledged for assistance with CryoTEM.

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CONCLUSION The cross-link density is an important parameter for the macroscopic mechanical properties of a viscoelastic network. However, in addition to the concentration of cross-linkers, the efficiency of the cross-linker has to be regarded. In the system with the homo-cross-linker it was shown that the semiflexible rods could be linked together into a viscoelastic network. The hetero-cross-linker suppresses looping, which is an intrinsic problem in physically cross-linked systems: the system is driven to an equilibrium state in which the probability of forming a loop is statistically larger when there is no preference for binding other rods. 2716

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