S. Garrido Nuñez
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1
While the Discrete Element Method (DEM) provides high-fidelity insights into granular processes like high-energy ball milling, its computational cost can become prohibitive when exploring extensive parameter spaces required for scale-up. This limitation hinders the rapid design and optimization cycles crucial for emerging applications, like mechanochemistry. Surrogate modeling offers a promising path to overcome these computational barriers, yet existing approaches often struggle to accurately represent the complex, moving boundary conditions typical of milling equipment. In this work, we leverage a Signed Distance Function Graph Neural Network (SGN) surrogate tailored to the high-energy, moving-boundary regime of the Emax mill. Trained on DEM data, the SGN jointly predicts particle kinematics for recursive roll-out and a mechanochemistry-relevant global quantity, the global dissipated energy. The model exhibits strong generalization to unseen motion trajectories and moderate jar-shape edits without retraining, while operating with a timestep over 100x larger than required by DEM. In a CPU-only comparison, it achieves a minimum of 6.6× wall-clock speedup. This approach provides a powerful and promising technique for the simulation, analysis, and design optimization of high-energy ball milling equipment.
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While the Discrete Element Method (DEM) provides high-fidelity insights into granular processes like high-energy ball milling, its computational cost can become prohibitive when exploring extensive parameter spaces required for scale-up. This limitation hinders the rapid design and optimization cycles crucial for emerging applications, like mechanochemistry. Surrogate modeling offers a promising path to overcome these computational barriers, yet existing approaches often struggle to accurately represent the complex, moving boundary conditions typical of milling equipment. In this work, we leverage a Signed Distance Function Graph Neural Network (SGN) surrogate tailored to the high-energy, moving-boundary regime of the Emax mill. Trained on DEM data, the SGN jointly predicts particle kinematics for recursive roll-out and a mechanochemistry-relevant global quantity, the global dissipated energy. The model exhibits strong generalization to unseen motion trajectories and moderate jar-shape edits without retraining, while operating with a timestep over 100x larger than required by DEM. In a CPU-only comparison, it achieves a minimum of 6.6× wall-clock speedup. This approach provides a powerful and promising technique for the simulation, analysis, and design optimization of high-energy ball milling equipment.
Sodium borohydride (NaBH₄) is an attractive solid hydrogen carrier because it combines high gravimetric hydrogen capacity (~10.9 wt%) with stability and safe handling under ambient conditions, yet its large-scale use is constrained by the energy-intensive regeneration of the spent hydrolysis product sodium metaborate (NaBO₂). This thesis develops an energy-efficient mechanochemical pathway to regenerate NaBH₄ via high-energy ball milling, while simultaneously proposing a transferable methodology to make mechanochemical synthesis more reproducible, comparable across equipment, and scalable.
First, a fractional design of experiments quantifies the main and interaction effects of key operating variables (milling time, molar ratio, ball-to-powder ratio, and rotational speed), revealing that yield variability reported in the literature can largely be attributed to underreported or poorly controlled milling parameters and machine-specific characteristics. Using these insights, high regeneration yields reported in the literature are reproduced while operating at lower rotational speed, reducing specific energy demand and wear; the optimized procedure also enables direct production of a ready-to-use aqueous NaBH₄ solution, avoiding hazardous post-processing steps.
To connect operating settings to the “hidden” internal dynamics of the mill, the thesis employs Discrete Element Method (DEM) simulations and identifies a set of scale-independent mechanical descriptors that uniquely characterize milling conditions. Expressing experiments through these dimensionless groups collapses diverse conditions onto transferable master curves, providing a mechanical fingerprint that supports comparison across mills and scales. Building on this framework, the role of shear-versus-compression stressing is isolated: low fill ratios that enhance shearing substantially improve yield and enable record conversions (up to 94%), whereas higher fill ratios shift stressing toward compressive impacts and markedly reduce yield, producing practical guidelines to favor productive shear while limiting wasted energy.
Finally, data-driven models integrate chemistry and mechanics to accelerate discovery. A two-stage Gaussian-process-regression ensemble predicts out-of-sample yields with R² ≈ 0.83, enabling computational screening of operating windows before experimentation. In parallel, a graph neural network surrogate reproduces DEM-like particle trajectories with low error (MSE ≈ 2×10⁻⁴ m²) using time steps over 100× larger than DEM, and can dynamically predict energy dissipation, pointing to fast, accessible tools for mill design and reporting standardization. Together, the thesis delivers a validated route toward circular NaBH₄-based hydrogen storage and a general blueprint for reproducible, scalable mechanochemistry.
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First, a fractional design of experiments quantifies the main and interaction effects of key operating variables (milling time, molar ratio, ball-to-powder ratio, and rotational speed), revealing that yield variability reported in the literature can largely be attributed to underreported or poorly controlled milling parameters and machine-specific characteristics. Using these insights, high regeneration yields reported in the literature are reproduced while operating at lower rotational speed, reducing specific energy demand and wear; the optimized procedure also enables direct production of a ready-to-use aqueous NaBH₄ solution, avoiding hazardous post-processing steps.
To connect operating settings to the “hidden” internal dynamics of the mill, the thesis employs Discrete Element Method (DEM) simulations and identifies a set of scale-independent mechanical descriptors that uniquely characterize milling conditions. Expressing experiments through these dimensionless groups collapses diverse conditions onto transferable master curves, providing a mechanical fingerprint that supports comparison across mills and scales. Building on this framework, the role of shear-versus-compression stressing is isolated: low fill ratios that enhance shearing substantially improve yield and enable record conversions (up to 94%), whereas higher fill ratios shift stressing toward compressive impacts and markedly reduce yield, producing practical guidelines to favor productive shear while limiting wasted energy.
Finally, data-driven models integrate chemistry and mechanics to accelerate discovery. A two-stage Gaussian-process-regression ensemble predicts out-of-sample yields with R² ≈ 0.83, enabling computational screening of operating windows before experimentation. In parallel, a graph neural network surrogate reproduces DEM-like particle trajectories with low error (MSE ≈ 2×10⁻⁴ m²) using time steps over 100× larger than DEM, and can dynamically predict energy dissipation, pointing to fast, accessible tools for mill design and reporting standardization. Together, the thesis delivers a validated route toward circular NaBH₄-based hydrogen storage and a general blueprint for reproducible, scalable mechanochemistry.
...
Sodium borohydride (NaBH₄) is an attractive solid hydrogen carrier because it combines high gravimetric hydrogen capacity (~10.9 wt%) with stability and safe handling under ambient conditions, yet its large-scale use is constrained by the energy-intensive regeneration of the spent hydrolysis product sodium metaborate (NaBO₂). This thesis develops an energy-efficient mechanochemical pathway to regenerate NaBH₄ via high-energy ball milling, while simultaneously proposing a transferable methodology to make mechanochemical synthesis more reproducible, comparable across equipment, and scalable.
First, a fractional design of experiments quantifies the main and interaction effects of key operating variables (milling time, molar ratio, ball-to-powder ratio, and rotational speed), revealing that yield variability reported in the literature can largely be attributed to underreported or poorly controlled milling parameters and machine-specific characteristics. Using these insights, high regeneration yields reported in the literature are reproduced while operating at lower rotational speed, reducing specific energy demand and wear; the optimized procedure also enables direct production of a ready-to-use aqueous NaBH₄ solution, avoiding hazardous post-processing steps.
To connect operating settings to the “hidden” internal dynamics of the mill, the thesis employs Discrete Element Method (DEM) simulations and identifies a set of scale-independent mechanical descriptors that uniquely characterize milling conditions. Expressing experiments through these dimensionless groups collapses diverse conditions onto transferable master curves, providing a mechanical fingerprint that supports comparison across mills and scales. Building on this framework, the role of shear-versus-compression stressing is isolated: low fill ratios that enhance shearing substantially improve yield and enable record conversions (up to 94%), whereas higher fill ratios shift stressing toward compressive impacts and markedly reduce yield, producing practical guidelines to favor productive shear while limiting wasted energy.
Finally, data-driven models integrate chemistry and mechanics to accelerate discovery. A two-stage Gaussian-process-regression ensemble predicts out-of-sample yields with R² ≈ 0.83, enabling computational screening of operating windows before experimentation. In parallel, a graph neural network surrogate reproduces DEM-like particle trajectories with low error (MSE ≈ 2×10⁻⁴ m²) using time steps over 100× larger than DEM, and can dynamically predict energy dissipation, pointing to fast, accessible tools for mill design and reporting standardization. Together, the thesis delivers a validated route toward circular NaBH₄-based hydrogen storage and a general blueprint for reproducible, scalable mechanochemistry.
First, a fractional design of experiments quantifies the main and interaction effects of key operating variables (milling time, molar ratio, ball-to-powder ratio, and rotational speed), revealing that yield variability reported in the literature can largely be attributed to underreported or poorly controlled milling parameters and machine-specific characteristics. Using these insights, high regeneration yields reported in the literature are reproduced while operating at lower rotational speed, reducing specific energy demand and wear; the optimized procedure also enables direct production of a ready-to-use aqueous NaBH₄ solution, avoiding hazardous post-processing steps.
To connect operating settings to the “hidden” internal dynamics of the mill, the thesis employs Discrete Element Method (DEM) simulations and identifies a set of scale-independent mechanical descriptors that uniquely characterize milling conditions. Expressing experiments through these dimensionless groups collapses diverse conditions onto transferable master curves, providing a mechanical fingerprint that supports comparison across mills and scales. Building on this framework, the role of shear-versus-compression stressing is isolated: low fill ratios that enhance shearing substantially improve yield and enable record conversions (up to 94%), whereas higher fill ratios shift stressing toward compressive impacts and markedly reduce yield, producing practical guidelines to favor productive shear while limiting wasted energy.
Finally, data-driven models integrate chemistry and mechanics to accelerate discovery. A two-stage Gaussian-process-regression ensemble predicts out-of-sample yields with R² ≈ 0.83, enabling computational screening of operating windows before experimentation. In parallel, a graph neural network surrogate reproduces DEM-like particle trajectories with low error (MSE ≈ 2×10⁻⁴ m²) using time steps over 100× larger than DEM, and can dynamically predict energy dissipation, pointing to fast, accessible tools for mill design and reporting standardization. Together, the thesis delivers a validated route toward circular NaBH₄-based hydrogen storage and a general blueprint for reproducible, scalable mechanochemistry.
In this study we investigate the mechanochemical regeneration of sodium borohydride (NaBH4) from a system comprising hydrated sodium metaborate ( [Formula presented] ) and magnesium hydride (MgH2). We explore the individual and joint impact of key operational parameters (rotational speed, milling time, ball-to-powder ratio (BPR), and molar ratio) on the regeneration yield. Furthermore, a method for quantifying chemical conversion is introduced relying only on water and thus, offering environmental benefits. This approach additionally facilitates the production and storage of a “ready-to-use” NaBH4 solution with minimal losses at room temperature. Notably, a yield of 90% is achieved, with a 20% reduction in rotational speed compared to prior literature. This research contributes to sustainable hydrogen storage and presents practical advancements in mechanochemical processes.
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In this study we investigate the mechanochemical regeneration of sodium borohydride (NaBH4) from a system comprising hydrated sodium metaborate ( [Formula presented] ) and magnesium hydride (MgH2). We explore the individual and joint impact of key operational parameters (rotational speed, milling time, ball-to-powder ratio (BPR), and molar ratio) on the regeneration yield. Furthermore, a method for quantifying chemical conversion is introduced relying only on water and thus, offering environmental benefits. This approach additionally facilitates the production and storage of a “ready-to-use” NaBH4 solution with minimal losses at room temperature. Notably, a yield of 90% is achieved, with a 20% reduction in rotational speed compared to prior literature. This research contributes to sustainable hydrogen storage and presents practical advancements in mechanochemical processes.
We compare the influence of tangential (shear) and normal (compressive) stress events on the mechanochemical regeneration of sodium borohydride NaBH4 from hydrated sodium metaborate [Figure presented] and magnesium hydride MgH2. Discrete element method (DEM) mechanical descriptors are used to design experiments that either maintain the mill at a constant rotational speed or maintain a constant total dissipation power, thereby separating stress distribution from net power input. Under constant power operation, a tangential rich regime achieves a record 94% conversion yield with 37.5% shorter milling time, 40% lower ball-to-powder ratio, and 34% reduced speed. However, this high yield requires such a substantial power consumption that the converted mass per Watt drops to only 0.090 gW−1, below both balanced (0.113 gW−1) and normal-bias (0.108 gW−1) cases. By contrast, a tangential bias at half the power (3 W) still delivers 84% yield and peaks at 0.185 gW−1, illustrating the often disregarded trade-off between absolute conversion and energetic productivity in mechanochemistry. Specific yield (conversion per Watt) likewise peaks at 0.28 W−1 and declines linearly with fill ratio (R2>0.99). Mechanochemical energy leverage analysis reveals that, at most, 1.7–3.7% of input mechanical work is theoretically recoverable on an enthalpy basis, 2.1–4.4% on a Gibbs free energy basis, and 4–8.7% when considering the fuel value of all available hydrogen. Our mill-agnostic framework provides a transferable blueprint for cross-platform optimization of mechanochemical processes.
...
We compare the influence of tangential (shear) and normal (compressive) stress events on the mechanochemical regeneration of sodium borohydride NaBH4 from hydrated sodium metaborate [Figure presented] and magnesium hydride MgH2. Discrete element method (DEM) mechanical descriptors are used to design experiments that either maintain the mill at a constant rotational speed or maintain a constant total dissipation power, thereby separating stress distribution from net power input. Under constant power operation, a tangential rich regime achieves a record 94% conversion yield with 37.5% shorter milling time, 40% lower ball-to-powder ratio, and 34% reduced speed. However, this high yield requires such a substantial power consumption that the converted mass per Watt drops to only 0.090 gW−1, below both balanced (0.113 gW−1) and normal-bias (0.108 gW−1) cases. By contrast, a tangential bias at half the power (3 W) still delivers 84% yield and peaks at 0.185 gW−1, illustrating the often disregarded trade-off between absolute conversion and energetic productivity in mechanochemistry. Specific yield (conversion per Watt) likewise peaks at 0.28 W−1 and declines linearly with fill ratio (R2>0.99). Mechanochemical energy leverage analysis reveals that, at most, 1.7–3.7% of input mechanical work is theoretically recoverable on an enthalpy basis, 2.1–4.4% on a Gibbs free energy basis, and 4–8.7% when considering the fuel value of all available hydrogen. Our mill-agnostic framework provides a transferable blueprint for cross-platform optimization of mechanochemical processes.
High-energy ball milling is a versatile method utilized in mechanochemical reactions and material transformations. Understanding and characterizing the relevant mechanical variables is crucial for the optimization and up-scaling of these processes. To achieve this, the present study delves into differentiating the contributions of normal and tangential interactions during high-energy collisions. Using Discrete Element Method (DEM) simulations, we characterize how operational parameters influence these energy dissipation modes, emphasizing the significance of tangential interactions. Our analysis also reveals how different operational parameters such as ball size, fill ratio, and rotational speed affect the mechanical action inside the milling jar giving rise to multiple operating zones where different modes of energy dissipation can thrive. Finally, we present master curves that generalize findings across a wide range of configurations, offering a tool for characterizing and predicting mechanochemical processes beyond the presented cases. These results provide a robust framework for improving mechanochemical reaction efficiency, and equipment design.
...
High-energy ball milling is a versatile method utilized in mechanochemical reactions and material transformations. Understanding and characterizing the relevant mechanical variables is crucial for the optimization and up-scaling of these processes. To achieve this, the present study delves into differentiating the contributions of normal and tangential interactions during high-energy collisions. Using Discrete Element Method (DEM) simulations, we characterize how operational parameters influence these energy dissipation modes, emphasizing the significance of tangential interactions. Our analysis also reveals how different operational parameters such as ball size, fill ratio, and rotational speed affect the mechanical action inside the milling jar giving rise to multiple operating zones where different modes of energy dissipation can thrive. Finally, we present master curves that generalize findings across a wide range of configurations, offering a tool for characterizing and predicting mechanochemical processes beyond the presented cases. These results provide a robust framework for improving mechanochemical reaction efficiency, and equipment design.
Mechanochemical synthesis faces reproducibility and scale-up challenges due to complex parameter interactions. This study employs machine learning (ML) to predict NaBH4 regeneration yield, integrating chemical experimental data and DEM (Discrete Element Method) derived invariant mechanical descriptors (Ēn, Ēt, fcol/nball). Various algorithms were evaluated, including a two-step modeling strategy to isolate the dominant effect of milling time in our process. Results demonstrate that a two-step Gaussian Process Regression (GPR) model achieves good predictive performance (R2 = 0.83), significantly outperforming single-stage models and providing valuable uncertainty estimates. Tree-based ensembles (XGBoost, RF) also benefit from the two-step approach and can enhance interpretability. This work establishes a framework for using ML to optimize mechanochemical processes, reducing experimental cost and offering a method to link mechanical milling conditions to chemical outcomes, thereby enabling predictive mechanochemistry.
...
Mechanochemical synthesis faces reproducibility and scale-up challenges due to complex parameter interactions. This study employs machine learning (ML) to predict NaBH4 regeneration yield, integrating chemical experimental data and DEM (Discrete Element Method) derived invariant mechanical descriptors (Ēn, Ēt, fcol/nball). Various algorithms were evaluated, including a two-step modeling strategy to isolate the dominant effect of milling time in our process. Results demonstrate that a two-step Gaussian Process Regression (GPR) model achieves good predictive performance (R2 = 0.83), significantly outperforming single-stage models and providing valuable uncertainty estimates. Tree-based ensembles (XGBoost, RF) also benefit from the two-step approach and can enhance interpretability. This work establishes a framework for using ML to optimize mechanochemical processes, reducing experimental cost and offering a method to link mechanical milling conditions to chemical outcomes, thereby enabling predictive mechanochemistry.