Design of Experiment (DoE)

How Importat Is It?

In materials research, resources like precursors, electricity for furnaces, and researcher time are limited. DoE is critical because it:

• Identifies Interactions: It reveals if the effect of one variable (e.g., temperature) depends on another (e.g., doping concentration).

• Maximizes Efficiency: It extracts the maximum amount of information from the minimum number of experiments.

• Reduces Noise: It accounts for experimental error and ensures that observed improvements are statistically significant.

• Predicts Performance: It creates mathematical models that can predict results for conditions not yet tested in the lab.

Identifying Independent and Dependent Variables

In a statistical study, variables are categorized to clarify cause and effect:

• Independent Variables (Factors): These are the parameters you actively manipulate. In battery research, these are typically synthesis conditions like calcination temperature, precursor ratios, or spinning voltage.

• Dependent Variables (Responses): These are the measurable outcomes. Examples include discharge capacity, half-wave potential (E1/2), fiber diameter, or specific surface area.

DoE Methods Available in Minitab

In Minitab, the choice of Design of Experiments (DoE) depends on our research stage and the nature of our materials. For example on my project (metal-air battery project), I can view these five options as a funnel that narrows down my research.

Screening Design

• The Goal: To identify the "vital few" factors from a large list of "trivial many."

• When to use: Use this at the very beginning of your research if you have 5 to 50 variables (e.g., different precursors, gas flow rates, stirring speeds, etc.).

• Battery Context: You have 10 different metal salts to test as a catalyst and want to see which 2 or 3 actually improve the oxygen reduction reaction (ORR).

Factorial Design

• The Goal: To study the "main effects" and "interaction effects" between factors.

• When to use: Use this when you have 2 to 5 important factors. It tells you if the effect of Temperature depends on the Doping Ratio (Interaction).

• Battery Context: Testing 2 levels of Temperature (Low/High) and 2 levels of Binder Concentration (Low/High). It is the most common "workhorse" design.

Response Surface Methodology

• The Goal: To find the optimal point (the peak or valley) and map the curvature.

• When to use: Use this at the end of your project when you have 2 to 3 critical factors and need the highest possible performance.

• Battery Context: You know Temperature and Doping matter most; now you want to find the exact coordinates (e.g., 615 °C and 7.2 wt%) for maximum power density.

Mixture Design

• The Goal: To optimize the proportions of ingredients in a blend.

• When to use: Use this when the factors are parts of a whole (they must sum to 100%). Changing one ingredient automatically changes the others.

• Battery Context: Optimizing the ratio of a ternary catalyst (e.g., %Pt + %Pd + %Ru) or the slurry for a separator (Alginate % + Ceramic filler % + Solvent %).

Taguchi Design

• The Goal: To make a product robust against noise and variation.

• When to use: Use this in industrial manufacturing to ensure the battery works well even if the environment (humidity/temp) changes. It focuses on the "Signal-to-Noise" ratio.

• Battery Context: Designing a separator that performs consistently even if the lab humidity fluctuates during the electrospinning process.

Factorial Design Case Study: Optimizing Electrospun Alginate Separators

1. Variables Identification

We will investigate the production of an alginate/PEO blend separator via electrospinning.

• Independent Variables (Factors):
  Voltage (kV): Low (15 kV) vs. High (25 kV).
  Flow Rate (mL/h): Low (0.1 mL/h) vs. High (0.5 mL/h).

• Dependent Variables (Responses):
  Average Fiber Diameter (nm): Measured via SEM imaging.
  Electrolyte Uptake (%): Affects the ionic conductivity of the battery.

2. Experimental Design: 2^2 Full Factorial

We use a 2^k Full Factorial Design, where k=2 factors.

• Choice: This design tests every possible combination of factor levels.

• Justification: It is the most efficient way to detect Interactions.
  For example, a high voltage might only be beneficial if the flow rate is also high; otherwise, it might cause "beading" on the fibers.

• Minitab Path: Stat > DOE > Factorial > Create Factorial Design

3. Sample Size Justification

For a 2^2 design, we have 4 unique combinations. We will perform 3 replicates for each combination, plus 3 center points.

• Total Runs: (4 x 3) + 3 = 15 runs.

• Justification: Replicates allow us to calculate Experimental Error (noise). Center points allow us to check if the relationship is linear or if we need to move to a more complex RSM design later.

4. Mock Dataset

5. Result