I. Abstract of the Paper’s Core Research

This study focuses on a ternary aerosol conductive ink composed of silver, carbon nanotubes, and ethanol. We propose a hybrid optimization approach integrating mixture design, response surface methodology, and NSGA‑III multi‑objective genetic algorithms, simultaneously targeting low line resistivity and high print quality. The process encompasses experimental modeling, predictive validation, optimal parameter space screening, and physical verification. The key findings are as follows:

Establishment of a Ternary Ink-Mixing Experimental System

Within the volume fraction ranges of 40%–60% for silver ink, 20%–40% for CNT ink, and 20%–40% for ethanol, a vertex‑center mixture design was employed to generate 13 gradient formulations. The resistivity, edge roughness, and overflow area of each printed trace were quantitatively characterized, and a comprehensive index for evaluating line quality was established.

Accurate fitting of the second-order response surface model (ReSM)

A second-order mathematical model with dual responses was established using analysis of variance (ANOVA), achieving R² values of 0.9634 for electrical resistivity and 0.9321 for print quality. This model accurately captures both the individual effects of the three components and their interactive coupling among AB, AC, and BC, enabling precise prediction of printing performance for any given formulation.

Bi-objective Stepwise Optimization Strategy

The first step employs the satisfaction‑function method to determine the two‑dimensional optimal formulation window; the second step introduces the NSGA‑III non‑dominated sorting genetic algorithm with statistical uncertainty constraints, yielding multiple Pareto‑optimal solution sets that balance predictive accuracy and model robustness, thereby circumventing the limitations of a single optimal solution.

Significantly enhanced optimal ink performance

The optimal formulation (50.2% silver, 21.9% CNTs, 27.9% ethanol) yields a line resistivity as low as 2.29 μΩ·cm, a 32% reduction compared to pure silver ink. The traces exhibit smooth edges with minimal material overflow, and after repeated 6-mm bends, their electrical conductivity remains significantly more stable than that of conventional single‑component silver pastes.

General-Purpose Digital Optimization Framework

This hybrid multi-objective optimization framework is not limited to silver–carbon composite inks; it can be extended to ceramic, two-dimensional material, and polymer‑based aerosol functional inks across all categories, thereby establishing a standardized formulation development process.

II. Complete Experimental Procedure for Aerosol Ink Optimization

Raw Material Preprocessing: Commercial silver nanoparticle ink, single-walled carbon nanotube ink, and high-purity ethanol are proportioned according to a stepwise gradient; mechanical stirring for 10 minutes followed by ultrasonic treatment for 20 minutes ensures uniform dispersion.

Plasma cleaning of PI substrates , Standardized process for aerosol device fabrication: nozzle diameter 150 μm, carrier gas flow rate 42 sccm, sheath gas flow rate 60 sccm, printing speed 1 mm/s, deposition at room temperature;

Each group’s formulation was repeatedly printed to produce five sets of standard lines, followed by sintering at 200°C for 2 hours.

Performance Testing: Four-point probe measurements of resistivity, optical imaging for quantifying edge roughness and material overflow, and calculation of a comprehensive line‑quality metric;

Modeling Optimization: Hybrid design-based sampling → Response surface modeling → Preliminary screening based on desirability → NSGA-III multi-objective global optimization;

Samples were taken and printed both within and outside the optimal formulation range. Dual validation of optimized reliability through microstructural SEM morphology and electrical performance.

III. Five Core Advantages of Optimizing Ink for Aerosol Spraying Applications

Synchronize balanced conflict performance metrics and say goodbye to trial-and-error with a single variable.

It simultaneously meets the two seemingly contradictory requirements of low resistance and high linearity, without having to sacrifice one performance metric in favor of the other.

Quantify component interactions and identify the global optimal region.

Traditional single-factor experiments overlook the adverse effects of multi‑component interactions; this model precisely elucidates the synergistic and inhibitory effects among three components, thereby identifying a stable process window.

Output multiple Pareto solution sets to accommodate varying device requirements.

It is not limited to a single optimal formulation; you can freely select and tailor the ink blend according to your application priorities—whether prioritizing low resistance or high precision.

Significantly shorten the ink R&D iteration cycle and reduce consumable waste.

It reduces hundreds of ineffective trial‑and‑error experiments, leverages data‑driven predictive modeling, and cuts the cost of nano‑precious‑metal ink raw materials.

A universal modular optimization framework, compatible with AJP functional inks across all product categories.

Metals, two-dimensional materials, ceramics, and bio‑inks can all be integrated into a hybrid design–genetic algorithm workflow, thereby establishing a standardized development tool for the industry.

IV. Five Core Technological Innovations of This Study

Innovation 1: Hybrid Design—Response Surface—A New Paradigm of Hybrid Multi-Objective Optimization Based on NSGA-III

A ternary mixture experiment is integrated with a genetic algorithm incorporating uncertainty constraints to perform global formulation optimization for aerosol‑based conductive inks.

Innovation 2: A Two-Response Second-Order Predictive Mathematical Model

The effects of single-component and pairwise interactions among silver, CNTs, and ethanol on resistivity and line quality were fully quantified, with model-fitting accuracy exceeding 93%.

Innovative Three-Tiered Two-Step Optimization Approach

First, a satisfaction function is used to rapidly identify a feasible search interval; then, a genetic algorithm performs a global search, balancing computational efficiency with the completeness of the optimal solution.

Quantitative Validation of the Innovative 4 CNT Bridging Conductivity Enhancement Mechanism

It is clarified that a CNT loading range of 20% to 23% can significantly reduce the contact resistance between silver‑film particles without compromising the printed morphology.

Innovation 5: Standardized Digital Development Process for Reusable Aerosol Inks

A complete standardized workflow—comprising formulation experiments, modeling, optimization, and validation—has been established, enabling the direct application of this approach to the R&D of various additive‑based functional inks.

V. Current Industry Challenges and Corresponding Solutions

Challenge 1: The resistivity of the ink and the quality of the printed lines are mutually restrictive, making it impossible to optimize both simultaneously.

✅ Parallel optimization using a multi-objective genetic algorithm, yielding the optimal formulation range at the inflection point while balancing low resistivity and high precision in micro‑patterns.

Challenge 2: Traditional univariate experiments overlook the coupled interactions among multiple components, leading to a risk of local optima becoming distorted.

✅ The mixed-design approach covers all factorial interaction combinations, quantifies synergistic and inhibitory effects via response surface methodology, and achieves global optimization.

Challenge 3: Ink formulation development relies heavily on experience, requiring extensive trial-and-error experimentation and resulting in high consumption of precious-metal consumables.

✅ Data-driven predictive modeling enables proactive performance forecasting, significantly reducing the number of ineffective formulation trials and lowering R&D costs.

Challenge 4: Only a single optimal formulation is output, making it unable to accommodate the diverse requirements of different devices.

✅NSGA generates a Pareto-optimal solution set, enabling flexible selection based on the specific requirements of sensors, RF components, and microcircuits.

Challenge 5: There is no unified, universal framework for ink optimization, leading to redundant experimental setups across different materials.

✅ A modular hybrid optimization framework, compatible with metal, 2D, and ceramic aerosol inks, enabling direct reuse of modeling logic.

VI. Future Diversified Industrial Application Scenarios

1 Standardized Development of Flexible Strain-Sensing Ink

Rapid formulation screening of low-resistance, high-resolution conductive composite inks for the batch fabrication of wearable physiological-sensing electrodes.

2 RF micro‑interconnect line‑specific ink

It emphasizes the optimal balance of edge‑line precision and is used in millimeter‑wave MEMS microantennas and on‑chip interconnects.

3 Micro-supercapacitor composite electrode ink

High-throughput formulation optimization of carbon–metal composite slurries enhances the energy storage capacity and cycling stability of energy‑storage devices.

4 Laboratory Rapid Ink Development Platform

A single algorithm is compatible with all aerosol‑based functional inks, shortening the development cycle for new materials and composite inks.

5 Mass‑production ink for automotive and aerospace conformal circuits with non‑standard geometries

An optimal formulation that balances electrical conductivity with superior conformability to curved surfaces, meeting the stringent stability requirements of large-scale additive manufacturing.

Image and Text Guide

• Silver ink (Clariant, viscosity 8.3 cP), single-walled CNT ink (Nanolab NINK 1100, average length 1300 nm), and ethanol were formulated according to a mixture design, with volume fractions ranging from 40–60%, 20–40%, and 20–40%, respectively.
• Polyimide (PI) substrates were sequentially subjected to a 5‑minute cleaning step followed by a 3‑minute corona plasma treatment to enhance wettability; the ink formulation was mechanically stirred for 10 minutes and then ultrasonicated for 20 minutes to ensure uniform dispersion.
• Single-pass printing, with five replicates per experimental point; AJP settings: 150 μm nozzle, SFR 60 sccm, AFR 42 sccm, printing speed 1 mm/s, sintering at 200 °C for 2 h.

• Subject to the constraint that the sum of the volume fractions of all components equals 1, the experimental points are confined within a polyhedral region defined by silver at 40–60%, CNT at 20–40%, and ethanol at 20–40%.
• The overall center of mass was repeated three times to assess the system’s repeatability; the actual experimental data points are listed in Supplementary Table S2.
• A quadratic response surface model (ReSM) was constructed based on this design to characterize the causal relationships between compositional parameters and the electrical and morphological properties of printed conductive lines.

• CNTs act as conductive bridges that connect defects and grain boundaries in the deposition line, thereby reducing resistivity; however, an excessive amount of CNTs can fragment the silver particles into discontinuous clusters, leading to a resurgence in resistivity.
• Ethanol enhances the printability of inks, thereby improving line quality; however, excessive amounts can dilute the silver content and lead to excessive aerosol dispersion.
• The volume fractions of the components cannot vary independently, and the interactions among the constituents significantly influence both electrical conductivity and print quality.
  

• In Table 5, all three representative solutions lie on the Pareto front: Solution 1 (Silver 0.45/CNT 0.23/Ethanol 0.32) has a resistivity of 2.91 μΩ·cm and a mass of 0.91; Solution 2 (0.52/0.23/0.25) has values of 2.32 and 0.65; and Solution 3 (0.48/0.24/0.28) has values of 2.63 and 0.79.
• Compared with pure silver wires, the incorporation of CNTs and ethanol simultaneously enhances both mechanical flexibility and morphological characteristics; bending tests (with a radius of 6 mm and a strain of 1.04%) confirm the bridging conductive effect of the CNTs.
• The optimized ink exhibits a resistivity of 2.3 μΩ·cm, which is 32% lower than that of pure silver wire and 1.45 times the bulk silver resistivity.