A self-driving laboratory advances the Pareto front for material properties

Useful materials must satisfy multiple objectives, where the optimization of one objective is often at the expense of another. The Pareto front reports the optimal trade-offs between these conflicting objectives. Here we use a self-driving laboratory, Ada, to define the Pareto front of conductivities and processing temperatures for palladium films formed by combustion synthesis. Ada discovers new synthesis conditions that yield metallic films at lower processing temperatures (below 200 °C) relative to the prior art for this technique (250 °C). This temperature difference makes possible the coating of different commodity plastic materials (e.g., Nafion, polyethersulfone). These combustion synthesis conditions enable us to to spray coat uniform palladium films with moderate conductivity (1.1 × 105 S m−1) at 191 °C. Spray coating at 226 °C yields films with conductivities (2.0 × 106 S m−1) comparable to those of sputtered films (2.0 to 5.8 × 106 S m−1). This work shows how a self-driving laboratoy can discover materials that provide optimal trade-offs between conflicting objectives.


Supplementary Tables
Supplementary Table 1

Supplementary Methods
Calculation of the fuel to oxidizer ratio for the combustion synthesis reaction An idealized form for the combustion synthesis reaction studied here is: This assumes that the available oxidizers and fuels react fully with each other, and with additional atmospheric oxygen as needed to yield pure, metallic palladium. This idealized reaction is based on Jain's method 1 which calculates an overall fuel-to-oxidizer ratio on the basis of the oxidizing or reducing valence of each species involved in a combustion reaction. The reducing valences used are +4 for carbon, +1 for hydrogen, 0 for nitrogen, -2 for oxygen and +v for a metal forming a compound in which the metal has formal charge v (e.g. +2 for Pd).

Transformations from normalized optimizer variables to dimensional variables used by the robotics
As shown in Fig. 2, the optimizations performed here were cast in terms of normalized variables: • The fuel to oxidizer ratio, (dimensionless) • The fuel blend, x (dimensionless) • The total precursor concentration, C (mg/mL) • The annealing temperature, T ( °C) The values for these variables were chosen by the qEHVI optimization algorithm before each experiment. While the annealing temperature T chosen by the algorithm could be passed directly to the robotic hardware, the other variables ( , x, and C) required transformation into quantities suitable for execution by the robot. Specifically, a transformation was applied to these quantities to determine the required volumes of the Pd(NO 3 ) 2 , glycine, and acetylacetone stock solutions and water diluent required to form the precursor ink for each experiment. The transformations required that the total volume of ink required ink be specified (200 µL for the present experiments) and are expressed in terms of the following quantities: • The normalized variables introduced above ( , x, and C) • The total volume of ink to be mixed ( glycine R gly = 9 MM Gly = 75.07 C Gly = C stocks = 12 acetylacetone R acac = 24 MM Acac = 100.13 C Acac = C stocks = 12 The volumes of chemicals used are found by solving the following equations numerically:

Manual screening experiments
We qualitatively compared the decomposition temperatures of palladium combustion synthesis precursors using manual screening experiments. In these experiments, precursors containing glycine, urea, or acetylacetone as the fuel were drop cast onto glass substrates and allowed to dry in air. The dried precursors were then placed on a hotplate preheated to a specified temperature and observed by eye. Metallic films were never obtained for hotplate temperatures below 180 °C. The precursors containing glycine or acetylacetone exhibited a change in appearance earlier than those containing urea and were found to yield conductive films after annealing on a hotplate set to 350 °C. Conductive films were obtained from the urea-containing precursors only upon further heating.

Supplementary Figures
All figures containing numerical data were created in Python using the matplotlib library.
Supplementary Figure 1 | Photographs of typical drop casted films created by the robotic laboratory. The substrates are 3" × 1" glass microscope slides. A grey spray paint which is poorly wet by the precursors was used to define an 18-mm diameter circular well at the center of each slide. The precursors are dispensed into this well.

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Supplementary Figure 2 | Characterization of sputtered palladium films used for XRF calibration. Films of nominal thickness 10 nm, 50 nm, 100 nm, and 250 nm were deposited by sputtering and then characterized using XRF and profilometry. A linear relationship was observed between film thickness and XRF intensity. Note that the structure seen in panel a from 0 to 20 S m -1 is a result of predicted conductivities that are negative being clipped to 0 S m -1 . The amplitude of the experimental noise in the conductivity training data was estimated using a white noise kernel in the Gaussian process regression model. This noise estimate is plotted as a grey band spanning ±1 standard deviation.

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Supplementary Figure 8 | Model residuals as a function of sampling order. The conductivity residuals from the Leave-One-Out Cross-Validation (LOOCV) analysis are plotted as a function of the sampling order. The amplitude of the experimental noise in the conductivity training data was estimated using a white noise kernel in the Gaussian process regression model. This noise estimate is plotted as a grey band spanning ±1 standard deviation.