In situ mechanical reinforcement of polymer hydrogels via metal-coordinated crosslink mineralization

Biological organic-inorganic materials remain a popular source of inspiration for bioinspired materials design and engineering. Inspired by the self-assembling metal-reinforced mussel holdfast threads, we tested if metal-coordinate polymer networks can be utilized as simple composite scaffolds for direct in situ crosslink mineralization. Starting with aqueous solutions of polymers end-functionalized with metal-coordinating ligands of catechol or histidine, here we show that inter-molecular metal-ion coordination complexes can serve as mineral nucleation sites, whereby significant mechanical reinforcement is achieved upon nanoscale particle growth directly at the metal-coordinate network crosslink sites.

= 0 (1 + 2.5 + 14.1 2 ), where 0 is the stiffness of the gel without fillers (i.e., of the Mineral-Free gel) and is the estimated maximum volume fraction of filler in an In Situ gel. The volume fraction used in this estimate is an upper bound, assuming a 100% mineralization yield from the reactants put into the gel according to the reaction: 2Fe 3+ + Fe 2+ + 8OH -→ Fe3O4 + 4 H2O, resulting in 0.074 vol%. (b) The stiffness increase (∆ ) measured upon in situ mineralization is three orders of magnitude higher than that estimated by Guth-Gold theory for the incorporation of non-interacting particles in gels, which supports that the minerals formed in In Situ gels interact strongly with the matrix polymer network. In these polymer-free samples, iron oxide particles up to a size of ~ 50 μm can be observed (upper row). Nanoparticles, which typically agglomerate into larger particles 1 , are also observed (lower row). (b) EDS shows the essential elements (i.e., Fe, O) of iron oxide minerals. The atomic percentage of Fe was 15%, and that of O was 64%. The 7% higher atomic percentage of O than that expected of Fe3O4 (i.e., 57%) is attributed to residual H2O and/or the presence of other possible iron oxides of higher atomic fraction of O such as Fe2O3. We note that the Ex Situ gel samples are processed via first forming a dispersion of mineral precipitates (as shown in inset photo) by mixing all ingredients without 4cPEG, followed by later mixing with 4cPEG polymer solution. We observed and classified small spherical iron oxide particles of a few nanometers (< 3.5 nm) in diameter in both In Situ ×1 and ×5 gels, while larger particles (> 3.5 nm) are observed only in In Situ ×5 gels. Thin, cylindrical particles are also observed in both samples. We consider the small and large spherical particles (labeled as "Small" and "Large", respectively) to be Fe3O4, whereas the rod-like, cylindrical particles (labeled as "Rods") are likely side products or intermediates, possibly Fe(OH)2 2 . Quantitative image analysis of TEM micrographs revealed that the three types of particles display log-normal size distributions with calculated average radii of the Small and Large spherical particles of 1.4 (± 0.3) nm and 6.2 (± 2.5) nm, respectively, and an average length of 14.4 (± 5.3) nm and width of 3.3 (± 1.5) nm of the Rods. We note that extra-large species (labeled as "Aggregates", not included in the histograms), which appeared to be aggregates of the Large particles, were also observed in some TEM micrographs. Image analysis of these Aggregates revealed their average radius to be 23.4 (± 12) nm; a small sample size of aggregates led to a large standard deviation. Figure 4. Particle size histograms of In Situ × 1 gels of (a) spheres (Small), and (b) length and (c) width of cylinders (Rods), along with lognormal distribution fits (solid lines). In measuring the particles, we excluded instances below a certain pixel size to avoid counting noise, which caused the distributions to look cut off on the lower end. The mineral volume fraction in the hydrogels (Φmagnetic) calculated from the measured maximum magnetization (Mmax, blue bars), estimated saturation magnetization (Ms, red bars), and the 100% mineralization yield estimate (black diamonds). Magnetization values were obtained from the VSM measurement on dry gels. The saturation magnetization (Ms) was approximated using the linear extrapolation of the 1/H vs M curves in the high magnetic field (H) region (1/H < 2.05 × 10 -5 Oe -1 ) for the In Situ × 2 -5 that did not show a saturation under the measured H range (fitting data available in Supplementary  Figure 8). The Φmagnetic was calculated from the magnetization values as follows:

Supplementary
where is the volume of the mineral and ℎ is the volume of the whole hydrogel including the . The and is the mass (2.5 mg) and the density of the polymer (1.0 -1.2 g/mL), respectively.
is the volume of solvent (i.e., water) of the hydrogel (20 μL). , is the saturation magnetization of pure magnetite (86 emu/g) and is the measured magnetization of the dry gel samples. Note that the ℎ ≈ since ≫ . The Φmagnetic values derived from the magnetization data 9 were all consistently below those from the 100 % yield assumption, as expected, and showed a linear increase with repeating mineralization cycles (linear trends shown by dotted lines). In addition, the value of ~0.22 vol% and ~0.28 vol% obtained using the Mmax and the estimated Ms, respectively, for the In Situ × 5 are reasonably close to the Φmicroscopy ~0.29 vol% calculated from the TEM image analysis. While there could be some product loss from the sample washing step, we note that the Φmagnetic obtained from the magnetization analysis treats all minerals as magnetite, which thereby discounts any possible volume fraction of less magnetic side products or intermediates such as Fe(OH)2 or maghemites in agreement with the slightly higher volume fraction obtained from TEM image analyses, which includes all minerals. We also note that the very small sized particles may have a much smaller number of domains and magneto-crystalline anisotropy, which can respond differently to the external field, causing the deviance in the magnetization. Furthermore, since we used dehydrated instead of hydrated gels to prevent sample volume change during the multi-hour measurement, it is likely that the dehydration shortened interparticle distances in the gel, which could possibly form extrinsic magnetic anisotropy thereby inducing spontaneous magnetism. However, based on the superparamagnetic behavior lacking a coercivity in our dehydrated gels, such events were negligible to affect the magnetic properties.

A. Scattering Models
The combined model referenced in the main text combines scattering contributions from star polymers, small and large spheres, cylinders, and aggregates. All fitting procedures are performed on the Igor Pro software using the Irena package 9 . Intensity measurements can be generally modeled by the following relation: Where I(q) is the overall scattering intensity, P(q) is the form factor, S(q) is the structure factor, (∆ ) 2 is the X-ray scattering contrast and is the volume fraction. (∆ ) 2 and are typically difficult to decouple from SAXS data without making explicit assumptions, and as such are treated here as a single scaling parameter, with the contrast held at (∆ ) 2 = 100 × 10 20 −4 across all form factors. Additionally, our data can be described explicitly through form factors alone, and thus S(q) is set to 1.
The scattering intensity for a sphere is thus described by: Where captures the scaling of the Guinier region described by , the radius of gyration of the correlation element -made of aggregations of primary populations -and captures the scaling of the power-law region scaled by a power of . A Beaucage model is used here as it is routinely used for modeling of scattering from fractal aggregates (see Fig. 2c). We note that no volume fraction parameters are explicitly stated here as the volume is accounted for in the Guinier parameter .

B. Model Parameters and Fit Results Discussion
The size parameters for the small and large sphere models, cylinder model, and the aggregate model in the combined fit are obtained a priori directly from TEM image analyses (see Supplementary Figure 4, 5). The only fitting parameter in the combined fit is (which scales the combined contribution of volume fraction and the contrast, (Δ ) 2 in Supplementary Equation 1, as Δ is set to a fixed value discussed above). We note that the estimated volume fraction of the minerals after fitting are in the same order of magnitude as the TEM predictions, despite the convolution in intensities due to the polymer scaffold and gel thickness effects.
We utilize two populations for the spheres, corresponding to the two populations identified in the TEM images. Single populations are adopted for the rods (cylinders) and aggregates. Mean values for 3 nm are used to construct the fits. Moreover, in accordance with the TEM statistics, we apply polydispersity to our size parameters (such that ℎ → 〈 ℎ 〉) and follow the log-normal distributions identified in the TEM images for the spheres and the rods. The standard deviation is obtained from TEM statistics for the sphere and cylinder models. For the aggregates, we set = 6.3 nm as the aggregates consist of clusters of the large-spheres (Fig. 2C), and obtain , and through fitting. is calculated from these values using assumptions of the Guinier-Porod model. This process yields = 17.89 nm for the aggregate radius which is in good agreement with TEM (Fig. 2C).
All fitting parameters are listed in Supplementary Table 1, and a compilation of the individual fits as well as the combined fit is shown in Supplementary Figure 1_scattering Step-strain (10 % strain) curves of In Situ mineralized samples (i.e., In Situ × 1 -5). As the hydrogel goes through more mineralization cycles, it relaxes slower.   14 to match the polymer concentration (125 mg/mL) used in our work. For calculating affine rubber elasticity of gels, we used the following equation:
To account for the existence of crosslinks with different functionalities ( ) in gels, we used phantom network theory as follows: where the modification of ( −2) → (1 −  14,17,18 . Here, we consider that the metal-coordinate crosslinking efficiency itself is not 100 % regardless of the covalent crosslinks, leaving many ligands elastically inactive, since the Gp of mineral-free Fe:catechol=1:3 gels with limited covalent crosslinking (Supplementary Figure 17) or mineral-free Ni/Cu:histidine=1:2 gels without any covalent crosslinks ( Figure 4) are all below the 51619 or 30912 Pa, respectively estimated for a perfect trisor bis-coordinated 4-arm network.
If we consider a 4-arm network ( 1 = 4) crosslinked by infinite functionality ( 2 → ∞), we get 92915 Pa from the calculation, which is theoretically the maximum modulus expected for a 4-arm phantom network crosslinked with heterogeneous functionalities. Thus, the Gp ~ 45000 Pa of In Situ gel is ~50% of the theoretical maximum modulus. It suggests that the fraction of the elastically active chains is increased in In Situ gels compared with Mineral-Free gels considering that the actual functionality cannot be infinite.
We also note another possible interpretation could be that the increase in the functionality solely resulted in the increase in Gp as the contribution of defects impairing the elasticity becomes less important in high functionality gels 15 . In this case, assuming the ~27% crosslinking efficiency of Mineral-Free gels stays the same in In Situ gels, the modulus expected for In Situ phantom network is ~25000 Pa, i.e., ~27% of 92915 Pa. Hence, this interpretation suggests that the measured Gp ~ 45000 Pa of In Situ gels are in the regime of affine network prediction.