Facile tuning of the mechanical properties of a biocompatible soft material

Herein, we introduce a method to locally modify the mechanical properties of a soft, biocompatible material through the exploitation of the effects induced by the presence of a local temperature gradient. In our hypotheses, this induces a concentration gradient in an aqueous sodium alginate solution containing calcium carbonate particles confined within a microfluidic channel. The concentration gradient is then fixed by forming a stable calcium alginate hydrogel. The process responsible for the hydrogel formation is initiated by diffusing an acidic oil solution through a permeable membrane in a 2-layer microfluidic device, thus reducing the pH and freeing calcium ions. We characterize the gradient of mechanical properties using atomic force microscopy nanoindentation measurements for a variety of material compositions and thermal conditions. Significantly, our novel approach enables the creation of steep gradients in mechanical properties (typically between 10–100 kPa/mm) on small scales, which will be of significant use in a range of tissue engineering and cell mechanosensing studies.

. Thermophoresis of polystyrene nanoparticles. The fluorescence intensity, I, of the 200 nm polystyrene particles dispersed in the sodium alginate solution is monitored while a temperature gradient is imposed across the channel. The plot represents the gradient of fluorescent intensity across the channel, dI/dz, versus time. The thermophoretic drift becomes apparent after about 45 minutes. The average temperature was 38.9 ºC and the temperature gradient was 3.3 K mm -1 .

Estimation of actual temperature gradient
Temperature is monitored during experiment by two thermocouples placed beside the Joule heater and the cold-water channel (as shown in Figure 2a) that record Tout H and Tout C respectively. Use of the mock device (described in the main text) allows correlation of these values with the temperatures Tglass H and Tglass C, measured through a thin glass coverslip directly below the heating and cooling channels. In particular, we experimentally observed that temperatures measured on glass are approximately 1.13 times higher than the temperatures measured beside the bigger channels, since we are always performing experiments at an average temperature that is higher than ambient. This yields the relationship: Tglass H = 1.13* Tout H and Tglass C = 1.13* Tout C.
Subsequently, we evaluated the actual temperatures of the Joule heater and cold water to assess the influence of the glass coverslip. To do so we performed numerical simulations and evaluated the temperature drop across a 150 µm glass slide below the heater and cooler. The results are presented in Figure S2 and clearly show that the difference in temperature across the glass is negligible. Accordingly, we consider that the real temperature of the heater and cooler, TH and TC respectively, are the same as the temperature measured at the glass side, with TglassH = TH and TglassC = TC.

Estimation of the diffusion coefficient of sodium alginate
The diffusion coefficient of sodium alginate, D, can be estimated knowing its molecular size, the temperature of the sample and its viscosity. Specifically, D = kBT/6πhR, where kB is the Boltzmann's constant, h the viscosity and R the effective radius of the sodium alginate molecule. The average molecular size of alginate can be estimated through knowledge of its molecular weight, M, and its density, ρ =1.6 g/cm 3 , with its volume, V, being expressed as: Another parameter influencing mass diffusion is viscosity. The reported values for the viscosity of a 1% w/w sodium alginate at 25ºC lie between 4 and 12 cps (as stated in the specification sheet of the Sigma-Aldrich sodium alginate used for these experiments). Although the precise determination of the viscosity of sodium alginate is not the purpose of the current study, it is nevertheless worth noting that its exact value is difficult to predict a priori as it depends not only on the concentration of sodium alginate, but also on the relative abundances of the M and G groups, and in general also on the specific batch used to prepare the sample 2 .

Evaluation of mechanical properties by AFM
For each sample investigated, Young's moduli were measured at 6 to 8 points along the transverse direction, parallel to the concentration gradient, with each data point representing an average obtained from the evaluation of a matrix of 16 x 2 individual measurements within a 500 x 500nm 2 area. Figure S4. Example of measured force versus indentation curve for a calcium alginate sample prepared with a solution of sodium alginate 1% w/v exposed to a temperature gradient of 3.4 ºC/mm at an average temperature of 43 ºC (the overall elasticity behaviour is shown in Figure 3b of the main text). The red and blue curves represent the approach and retraction curves respectively. The dashed black line is the fit to the Hertz model for the approach curve. The obtained Young's modulus for this particular curve is 16.5 kPa. The spring constant of the cantilever used was 4.57 N/m and the radius of the silica colloidal sphere was 8 µm.