Free-standing supramolecular hydrogel objects by reaction-diffusion

Self-assembly provides access to a variety of molecular materials, yet spatial control over structure formation remains difficult to achieve. Here we show how reaction–diffusion (RD) can be coupled to a molecular self-assembly process to generate macroscopic free-standing objects with control over shape, size, and functionality. In RD, two or more reactants diffuse from different positions to give rise to spatially defined structures on reaction. We demonstrate that RD can be used to locally control formation and self-assembly of hydrazone molecular gelators from their non-assembling precursors, leading to soft, free-standing hydrogel objects with sizes ranging from several hundred micrometres up to centimeters. Different chemical functionalities and gradients can easily be integrated in the hydrogel objects by using different reactants. Our methodology, together with the vast range of organic reactions and self-assembling building blocks, provides a general approach towards the programmed fabrication of soft microscale objects with controlled functionality and shape.

The only difference was either the use of agar (1 %, left) or calcium alginate (1 %, right).

RD-SA by drop deposition (Figure 2g)
To form letters by RD-SA, we used the following procedure. To make the chemically differentiated grid, we followed the procedure described in section The solutions and agar matrix were prepared using phosphate buffer of pH = 6.5. In short: the holder was placed on top of the agar gel prepared in the well formed by putting a Press-to-Seal TM silicone isolator on a glass slide and left to diffuse in a closed humidified environment for 8 hours. The time was kept intentionally short to prevent the formation of a dense supramolecular network, which would not allow the ConA to penetrate. Subsequently, the holder was removed and another Press-to-Seal TM silicone isolator was placed on top and the resulting well was filled with a buffered solution of ConA (2 mM, pH = 7). This well was closed with a glass slide to prevent evaporation and left to stand in a closed humidified environment for 12 hours. After this period, the sample was analyzed using fluorescence microscopy. To remove the non-bound ConA, the top glass slide was removed, the ConA solution was removed, and the sample was immersed into buffer (at least several mL) and left to stand for 72 hours, while buffer being refreshed every 24 hours. The final sample was again imaged by fluorescence microscopy. Images were analyzed with ImageJ to extract the fluorescence intensity profiles.

Formation of hybrid network materials for compression tests (Figure 3a/b)
Alginate gels containing H were prepared similarly to pure alginate gels, but now dispersing CaCO 3 powder in an aqueous solution of H instead of in water. 10 mL of this solution was added to a Petri dish and left to gelate. Then, we manually cut out a circular segment of agar (the central angle defining the circular segment was 110°) to make a reservoir (Supplementary Figure 5). The solution of A was placed in the reservoir and the reaction was left running for at least three weeks (until the patterned region was more than 1 cm wide).
Cylinders of 8 mm in diameter were punched out from the alginate/HA3 hybrid network region using a circular puncher and subjected to compression tests.

The kinetics of hydrazone formation, measured using one-step reaction
We explored how the reaction constant of hydrazone formation varies with pH. Since the formation of HA 3 is a three-step reaction, it would be complicated to investigate its dependence on pH. Therefore, we used a one-step reaction of monohydrazide H' with aldehyde A giving monohydrazone H'A (Supplementary Figure 6). This reaction can be easily followed using UV-VIS spectroscopy. Briefly, the absorbance of a well-mixed reaction mixture containing H' (60 μM) and A (60 μM) was measured at 308 nm until no significant change in absorbance was observed. The evolution of the concentration of H'A was obtained from the absorbance curve using a separately constructed calibration curve.

Dynamics of 1D pattern formation
To study the dynamics of 1D pattern formation, we performed a set of experiments using the basic configuration shown in Figure 2a in which the width of the 1D pattern increases over time. A plastic Petri dish was filled with agar at the desired pH and left to gelate. A 2 cm wide agar strip was made with two parallel cuts, at equal distance from the center. The outer agar segments were removed, creating two reservoirs. Before injecting buffer solutions of H and A in these reservoirs, the Petri dish was placed on a flat Plexiglass plate above a digital microscope camera. The recording started at the moment that the two solutions were injected. Images were taken every 10 minutes, over the course of 20 to 120 hours depending on experimental conditions. They were analyzed using ImageJ, extracting the intensity profile This was done for multiple lines in the same image and the resulting profiles were averaged to reduce noise. The resulting intensity profile was then normalized by subtracting the minimum intensity value from the raw intensity profile and subsequently dividing the resulting intensities with respect to the peak intensity. The width of the 1D pattern was determined as the distance between points where two slopes intersect a base line (Supplementary Figure 8b). This baseline was determined as the average value of the first ten points of the intensity profile. This was done for all images in a time lapse, yielding the evolution of the width of the formed 1D pattern.

Kinetic model for HA3 formation
The formation of gelator HA3 proceeds in three consecutive steps as shown in Supplementary Figure 9. Assuming that the rate constants of the three steps k 1 , k 2 , and k 3 are independent and that they are first order in reactant concentration, the concentration of species in a well-mixed system without diffusion limitations changes in time according to: (1) (2) .

(5)
To validate this model and find the values of the rate constants, we performed a set of experiments in a system where diffusion plays no role. Briefly, we mixed solutions of H (20 mM) and A (120 mM) and measured the concentrations using HPLC to find the temporal concentration changes of A, HA, HA2 and HA3 (see reference 2 for complete experimental procedure details). We compared the experimental data with the concentration data obtained by solving the model equations using a MATLAB code using the same initial concentrations for A and H as in the experiment. We solved the set of equations for a wide range of reaction constants k1 and k3, while k2 was set to a value for which no significant amounts of the intermediate HA were observed (k2 was at least 1000 × higher than k1, k3), based on experimental observations. For each combination of rate constants k1 and k3, the goodness of fit between experimental and numerical data was determined as the sum of mean square errors in the concentrations of A, HA 2 and HA 3 (Supplementary Figure 10). The rate constants k1 and k3 that gave the smallest error are summarized in Supplementary Table 2 for two values of the pH, and are within one order of magnitude as the rate constant for the one-step reaction kH'A. The corresponding concentration data is in good agreement with the experimental data, suggesting the validity of the model assumptions.
Based on the linear dependence between -log kH'A and pH found for the one-step reaction, we assume that -logk1, -logk2 and -logk3 also linearly depend on pH as the HA3 reaction involves the same type of bond, but three times instead of once. Using the data in Supplementary

Reaction-diffusion model for 1D pattern formation
Having determined the rate constants and their dependency on pH, we developed a reaction-diffusion model to describe the formation of a 1D pattern in the basic experiment shown in Figure 2a. We hereby used the experimentally measured 1D pattern widths (Supplementary Section 6) to validated the model and to find the values of the diffusion coefficients. The reaction-diffusion model is based on Fickian diffusion and described by the following set of partial differential equations.  Table 3). Comparing the resulting pattern predicted by the model with that observed in experiments at pH=4, we observed that the simulated 1D pattern keeps increasing in width, while the experimental pattern reaches a plateau, as shown in Supplementary Figure 11a. By taking samples from the reservoirs, we excluded depletion of reactants as the underlying reason for the plateau. We hypothesized that the difference in dynamics is due to the gelation of HA3, which makes it harder for the reactants and intermediates to diffuse through the domain. We took into account the local dependence of diffusion coefficients on the local HA3 concentration using a stretched exponential function of the form with  the volume fraction of HA3 in the agar gel matrix modeled as 4 20

Supplementary Discussion
When comparing the width of the 1D pattern for different concentrations of H at a fixed ratio of H and A concentrations, low concentrations yield wider structures than high concentrations when compared at the same point in time (except for very short times (<20 hours)). This is understood, as higher concentrations yield tougher HA3 gels such that it takes longer for reactants and intermediates to diffuse through. This same effect in seen for a decreasing distance between the reservoirs, which yields tougher gels earlier on, slowing down the formation of the 1D pattern. The effect of pH was studied by varying the reaction rate constants in the model. We hereby used the experiment at pH = 4.0 as a benchmark, such that a 200-fold increase in reaction rates corresponds to a decrease in pH to 0.9.
Although the pH in our experiments cannot be decreased below 3.3 (as gelation does not occur for the agar and alginate/CaCO 3 /GDL systems) resulting in about 2 mm wide lines, the model does enable exploring how the width of the 1D pattern further decreases with pH. As can be seen in Supplementary Figure 12c, pH strongly influenced the line width, reaching 1.0 mm at pH = 0.9. In summary, the model demonstrates that the smallest patterns could be made using the highest concentrations of reactants possible, keeping the smallest feasible distances between reservoirs, while taking care that reaction rate constants are the highest possible (controlled by pH). Additionally, by knowing only the reaction rates and the diffusion coefficients of participating species, the model can be used to estimate minimum and maximum sizes of produced patterns and is not limited to the reaction used in this research.
In our case, the minimum size estimated using the model was in the order of 2 mm, and maximum size was in the order of 15 mm, thus spanning over approximately one order of magnitude.