High-Throughput Bayesian Optimization of Cement-Salt Hydrates Composites for Seasonal Thermochemical Energy Storage

This paper demonstrates that a high-throughput Bayesian optimization framework effectively accelerates the discovery of cost-effective cement-salt hydrate composites for seasonal thermochemical energy storage, identifying Pareto-optimal formulations that significantly improve specific energy and cost-performance balance compared to previous cement-based materials.

The Gist

Imagine you are trying to bake the perfect cake, but instead of flour and sugar, you are mixing cement and special salts to create a material that can "eat" heat during the summer and "spit" it out during the winter. This is called Seasonal Thermochemical Energy Storage. It's like a thermal battery that could keep your house warm all winter using heat collected from a sunny July day.

The problem? There are thousands of ways to mix these ingredients. You have different types of salts, different amounts of water, different amounts of cement, and different additives. Trying to find the perfect recipe by guessing and checking (the old "trial and error" method) would take years and cost a fortune.

This paper describes a smarter way to find the best recipe using a "digital chef" called Bayesian Optimization (BO).

The Digital Chef (Bayesian Optimization)

Think of the BO system as a super-smart, tireless assistant who loves to learn.

1. The Guessing Game: Instead of testing every possible combination (which would be like tasting every single cake in the world), the assistant picks a few promising recipes to test first.
2. The Taste Test: The team actually mixes these small batches of cement-salt paste, bakes them, and tests how much heat they can store.
3. The Learning Loop: The assistant looks at the results. "Oh, too much salt made the cake runny (it melted). Too little water made it crumbly. But this specific mix of Calcium Chloride and cement worked really well!"
4. The Next Move: Based on what it learned, the assistant immediately suggests the next best set of ingredients to test. It gets better and better at guessing the winners, skipping the bad recipes entirely.

The Two Goals: Power vs. Price

The team had two competing goals, like trying to buy a car that is both the fastest and the cheapest.

• Goal 1: Maximum Energy (The Fast Car): How much heat can the material store per kilogram?
• Goal 2: Minimum Cost (The Cheap Car): How much does the material cost to make per unit of energy stored?

Usually, the best energy storage materials are very expensive, and the cheap ones don't store much heat. The team wanted to find the "Goldilocks" zone—the best balance between the two.

The Discovery: New Ingredients

The researchers tested a huge variety of salts. While they already knew about some (like Magnesium Sulfate), they used their digital chef to explore ingredients that had never been tried in cement before: Lithium Chloride (LiCl), Calcium Chloride (CaCl2), and Zinc Nitrate (Zn(NO3)2).

Here is what they found:

• The Powerhouse (LiCl): The Lithium Chloride mix was the "Ferrari" of the group. It stored a massive amount of heat (about 458 kJ per kg), beating previous cement-based records by a factor of five. However, like a Ferrari, it was expensive to build.
• The Value Picks (CaCl2 and Zn(NO3)2): These mixes were the "reliable sedans." They didn't store quite as much heat as the Lithium one, but they were much cheaper to make. They offered a fantastic balance: good performance for a very low price.

The Results

By using this smart, data-driven approach, the team didn't just find one good recipe; they found a whole new family of materials.

• They discovered that cement (the stuff in your driveway) is actually a great "sponge" for holding these heat-storing salts, provided you get the recipe right.
• They identified a "Pareto Frontier," which is a fancy way of saying they found the absolute best trade-offs. You can't get more heat without paying more money, and you can't get cheaper materials without storing less heat. They found the perfect spots on that line.
• While these new cement-salt materials aren't quite as powerful as the most expensive, high-tech materials made of silica gel or expanded vermiculite, they are much cheaper.

The Bottom Line

This paper proves that you don't need to guess your way to better energy storage. By using a smart computer algorithm to guide the experiments, the team quickly found new, low-cost materials that store heat efficiently. It's like using a GPS to find the fastest route through a maze, rather than running into every dead end. These new cement-salt composites could be a practical, affordable way to store summer heat for winter use, helping us use renewable energy more effectively.

Technical Summary

Technical Summary: High-Throughput Bayesian Optimization of Cement-Salt Hydrates Composites for Seasonal Thermochemical Energy Storage

Problem Statement
Thermochemical energy storage (TCES) based on salt hydrates offers a promising solution for seasonal heat storage due to its high volumetric energy density and ability to store energy indefinitely without thermal losses. However, the practical deployment of these systems is hindered by the complex design of sorbent materials. The formulation of cement-salt composites involves a highly non-linear, combinatorial design space where performance depends on coupled variables: salt chemistry, salt loading, binder composition, and additive content. Traditional trial-and-error or one-factor-at-a-time experimental strategies are impractical for efficiently navigating this space, as a full exploration would require thousands of synthesis and characterization cycles over extended periods. Furthermore, existing cement-based TCES materials often suffer from low specific energy, while high-performance alternatives (e.g., silica gel or expanded vermiculite matrices) are often cost-prohibitive. There is a critical need for data-driven strategies to accelerate the discovery of cost-effective, high-performance cement-salt composites.

Methodology
The authors developed a high-throughput, data-driven experimental framework based on Bayesian Optimization (BO) to guide the formulation of cement-salt hydrate composites. The methodology integrates adaptive experimental design with thermodynamic modeling:

• Design Space: The optimization explored a four-dimensional parameter space defined by:
  1. Salt Type: A categorical variable covering 11 hydrated salts, including common candidates (e.g., MgSO₄) and under-investigated salts (LiCl, CaCl₂, Zn(NO₃)₂).
  2. Salt Concentration: Defined as the ratio of dissolved salt to the maximum solubility at 20°C ($s/s_{max}$).
  3. Water-to-Cement Ratio ($w/c$): Ranging from 0.70 to 1.50.
  4. Additive-to-Cement Ratio ($a/c$): Ranging from 0.0 to 30.0 g/kg, utilizing an anti-settling additive to mitigate bleeding.
• Optimization Strategy: The campaign utilized two parallel BO pipelines targeting competing objectives: maximizing specific energy ($E_d$) and minimizing specific energy cost (an economic Key Performance Indicator, KPI). The workflow employed Gaussian Process (GP) surrogate models with Radial Basis Function (RBF) and Matérn kernels. Acquisition functions (Probability of Improvement, Expected Improvement, and Lower Confidence Bound) balanced exploration and exploitation.
• Experimental Protocol: Composites were synthesized via an in-situ method where salts were dissolved in water and mixed with cement and additives. Samples were cured, dried, and granulated. High-throughput water adsorption isotherms were measured at 20°C using a Dynamic Vapor Sorption (DVS) analyzer capable of processing 20 samples simultaneously.
• Thermodynamic Modeling: Experimental isotherms were fitted using the Dubinin–Astakhov (DA) equation. Using Polanyi's potential theory, isotherms were extrapolated to operating temperatures (40°C adsorption, 90°C desorption). Specific energy ($E_d$) was calculated based on the cycle uptake variation ($\Delta x_{cycle}$) and the isosteric heat of adsorption ($q_{st}$), derived via the Clausius–Clapeyron equation.

Key Contributions

• First Application of BO to Cement-Salt TCES: This study represents the first application of Bayesian optimization to the multi-objective design of cement-salt composites for TCES, demonstrating the efficacy of sequential learning in a constrained, multi-variable materials discovery problem.
• Expansion of Chemical Design Space: The study systematically investigated salts (LiCl, CaCl₂, Zn(NO₃)₂) that had been marginally explored or not previously reported in cement-based TCES systems, moving beyond the traditional focus on MgSO₄.
• Handling of Failure Modes: The framework successfully incorporated synthesis failures (e.g., deliquescence, inability to harden) into the optimization loop through penalization strategies, allowing the surrogate models to learn the boundaries of feasible formulations.
• Pareto-Optimal Discovery: The approach identified a set of non-dominated solutions that offer optimal trade-offs between high energy density and low material cost, revealing distinct high-performing regions in the combinatorial space.

Results
The BO-guided campaign successfully identified Pareto-optimal formulations based on LiCl, CaCl₂, and Zn(NO₃)₂:

• Performance: The best-performing formulation, based on LiCl (LiCl-S1), achieved a specific energy of approximately 458 kJ kg⁻¹ (based on replicate measurements). This represents an improvement of up to a factor of five compared to previously developed cement-based materials.
• Cost-Performance Trade-off: While LiCl-S1 offered the highest energy density, it came with a higher material cost. Conversely, CaCl₂- and Zn(NO₃)₂-based composites (e.g., CaCl₂-S2, Zn(NO₃)₂-S1) exhibited lower specific energies (150–161 kJ kg⁻¹) but significantly more favorable economic KPIs (3.2–7.6 USD kWh⁻¹), offering a balanced cost-to-performance ratio.
• Comparison with Literature: The optimized cement-based composites showed specific energies lower than state-of-the-art silica gel or expanded vermiculite systems (which can exceed 1000–2000 kJ kg⁻¹) but demonstrated superior economic viability due to the low cost of the cement matrix.
• Repeatability: Re-test analysis of Pareto-optimal samples confirmed the robustness of the screening workflow, with relative standard deviations (RSD) for specific energy generally below 5%.

Significance and Claims
The paper claims that Bayesian optimization is an effective strategy for accelerating the discovery of TCES materials, particularly in complex formulation spaces where synthesis constraints and multi-objective trade-offs are central. The study demonstrates that cement-salt composites, when optimized via BO, can achieve specific energies significantly higher than previous cement-based iterations, making them attractive candidates for seasonal storage applications where cost is a primary constraint.

The authors modestly note that while the specific energy of their materials remains below that of high-performance porous matrices like silica gel, the cost-to-performance balance of the optimized cement-based composites (particularly those based on CaCl₂ and Zn(NO₃)₂) is a distinct advantage. The work highlights that data-driven optimization can reveal promising chemistries and formulation boundaries that might be missed by conventional experimental design, paving the way for more efficient development of low-cost, seasonal thermal storage solutions. Future work is suggested to focus on cycling stability, sorption kinetics, and further refinement of additives and matrix modifications.