Effect of diffusive and ballistic aggregation on properties of gels

Effect of diffusive and ballistic aggregation on structural and fractal properties of gels was demonstrated in the poster

Predictive modeling and simulation of silica aerogels by using aggregation algorithms

Silica aerogels are highly porous solids with very low densities and thermal conductivities. Their high porosity results in a fractal morphology which has a strong influence on their mechanical properties. The geometric structure of silica aerogels can be described by diffusion-limited cluster-cluster aggregation (DLCA) models. In this work, the DLCA method is implemented to model silica aerogel networks and investigate the influence of different input parameters, as for example, varying particle sizes on their fractal properties. The resulting model networks are characterized for their fractal properties and compared with the small angle X-ray scattering (SAXS) results of silica aerogels. Furthermore, their mechanical properties are simulated using the finite element method. There, the effect of varying densities on their mechanical properties is examined. In addition, an artificial neural network (ANN) is trained based on the input parameters of the DLCA algorithm to predict the fractal properties of the silica aerogel model. By inverting the ANN it is possible to identify the necessary inputs to generate desired fractal morphologies with specific mechanical properties

Data-driven inverse design and optimisation of silica aerogel model networks

Silica aerogels are highly porous ultralight materials with extremely low density and thermal conductivity. These exceptional properties of silica aerogels are often accounted to microstructure morphology, thus making them of keen research interest for analysing their structure-property relationships. The classical approach for this involved the microstructure modelling of the silica aerogels with aggregation-based modelling algorithm viz., diffusion-limited cluster-cluster aggregation (DLCA) and then performing finite element method (FEM) on the generated representative volume element (RVEs). However, the process often requires large computation time and resources. The objective of this work was thus to introduce an artificial intelligence approach based on neural networks and reinforcement learning to eliminate the necessity of generating and simulating 3D silica aerogel models for predicting their structural and mechanical properties. To this end for the forward prediction of the elastic modulus and fractal dimension of the silica aerogels from DLCA parameters, an artificial neural network was developed. Furthermore, to reverse engineer the material and perform inverse material design, a reinforcement learning framework was developed, that is shown to have learned to determine appropriate DLCA model parameters as actions for a desired fractal dimension and elastic modulus

On the origin of power-scaling exponents in silica aerogels

The macroscopic properties of open-porous cellular materials hinge upon the microscopic skeletal architecture and features of the material. Typically, bulk material properties, viz. the elastic modulus, strength of the material, thermal conductivity, and acoustic velocity, of such porous materials are expressed in terms of power-scaling laws against their density. In particular, the relation between the elastic modulus and the density has been intensively investigated. While the Gibson and Ashby model predicts an exponent of 2 for ideally connected foam-like open-cellular solids, the exponent is found to lie between 3 and 4 for silica aerogels. In this paper, we investigate the origins of this scaling exponent. Particularly, the effect of the pearl-necklace-like skeletal features of the pore walls and that of the random spatial arrangement is extensively computationally studied. It is shown that the latter is the driving factor in dictating the scaling exponent and the rest of the features play a negligible or no role in quantifying the scaling exponent

Machine learning-based structure–property predictions in silica aerogels

The structural features in silica aerogels are known to be modelled effectively by the diffusion-limited cluster–cluster aggregation (DLCA) approach. In this paper, an artificial neural network (ANN) is developed for predicting the fractal properties of silica aerogels, given the input parameters for a DLCA algorithm. This approach of machine learning substitutes the necessity of first generating the DLCA structures and then simulating and characterising their fractal properties. The developed ANN demonstrates the capability of predicting the fractal dimension for any given set of DLCA parameters within an accuracy of R2 = 0.973. Furthermore, the same ANN is subsequently inverted for predicting the input parameters for reconstructing a DLCA model network of silica aerogels, for a given desired target fractal dimension. There, it is shown that the fractal dimension is not a unique characteristic defining the network structure of silica aerogels, and the same fractal dimension can be obtained for different sets of DLCA input parameters. However, the problem of non-uniqueness is solved by using a guided gradient descent approach for predictive modelling purposes within certain bounds of the input parameter-space. Model DLCA structures are generated from the constrained and unconstrained inversion, and are compared against several parameters, amongst them, the pore-size distributions. The constrained inversion of the ANN is shown to predict the DLCA model parameters for a desired fractal dimension within an error of 2%

An artificial Intelligence approach in the mechanical and morphological analysis of silica aerogels

Silica aerogels can be computationally modelled by means of the 3D diffusion-limited cluster-cluster aggregation (DLCA) algorithm. The structural and mechanical properties of the computationally modelled silica aerogels can be characterised by analysing the simulated models and performing finite element (FE) calculations. However, the modelling process of DLCA is “slow” and together with the FE simulations requires significant computational time. The objective of this thesis is to introduce a machine learning approach to eliminate the necessity of generating and simulating 3-d silica aerogel models for predicting their structural and mechanical properties. To this end, an artificial neural network (ANN) based on supervised learning is developed to perform a mapping between the DLCA model parameters, the aggregate's fractal dimension and it's stress-strain response. In the next step, the ANN is trained by data-sets consisting of 3-d network structures of silica aerogels, that are modelled by means of the DLCA algorithm with varying structural parameters, and their FE analyses. The trained ANN in combination with a reinforcement learning (RL) agent is then used to perform data driven structure property relationships on the silica aerogel aggregates. It was found that a artificial neural network can effectively map the DLCA input variables to the target material properties. The ANN had a R2 score of 0.841. For the inverse design of the aerogel micro-structure Reinforcement Learning as an optimisation problem was utilised. A soft actor critic agent was utilised to optimise the DLCA parameters so as to achieve the desired material properties of elastic modulus and fractal dimension. The RL agent was proven to be effective in predicting the DLCA input parameters and as compared to previous work done on the inversion of the neural networks, was also not dependent on the prior knowledge of the desired input space so as to constraint it

Intelligent Computational Micro-architectured Design of Aerogels for Battery Development

Aerogels belong to a class of ultra-light materials with open porous cellular microstructure and extremely low thermal conductivity, which are synthesized by replacing the liquid component of the gel with a gas phase. Due to an interesting combination of these properties, aerogels have often found their application in high temperature insulation and aerospace applications, most famously silica aerogels in the stardust collector by NASA. Recently, sulfur infiltrated carbon aerogels as the cathode, have been proven to be an effective alternate to the existing lithium sulfur batteries, with increased charge capacities [1]. The carbon aerogels are synthesized by the pyrolysis of organic aerogels e.g. resorcinol-formaldehyde (RF) aerogels. However, it’s development with desired permeability for effective sulfur infiltration is a challenge due to the iterative nature of the synthesis process. Thus, the development of digital twins could help accelerate the optimization and development time for aerogels with desired material properties. In this contribution, an artificial intelligence-assisted modeling technique is presented for architectured microstructure design of RF aerogels with desired permeability. The morphology of RF aerogel’s representative volume element (RVE) was shown to be modeled with a 3-parameter Gaussian random field algorithm (GRF) [2]. By applying a similar model strategy the absolute permeability of the computational models is estimated by means of a watershed image segmentation algorithm to develop pore network models (PNM). The PNMs help analyse the pore size distribution and the infiltration characteristics through the RVE (the maximum flow path and the absolute permeability). For the rapid analysis and reverse engineering of aerogels with desired microstructures, a machine learning framework is developed. The environment constitutes of a surrogate model (artificial neural network) that maps the GRF parameters to the aerogel morphology and the infiltration characteristics. The surrogate model thus acts as an intelligent digital twin, eliminating the need for iterative computational modeling and its post-processing for permeability analysis. Furthermore, in the environment, a reinforcement learning agent (deep deterministic policy gradient agent) works in combination with the surrogate model to optimise the parameters of the GRF to achieve the target material infiltration characteristics. This enables the prediction of the RF aerogel’s material properties without extensive and iterative computational modeling, thus accelerating the process of aerogel development. References 1. M. Nojabaee et al., J. Mater. Chem. A 9, 6508-6519 (2021) 2. C.J. Gommes et al., Phys. Rev. E 77, 041409 (2018

Reinforcement Learning for Tailored Development of Aerogels

Ever since Kistler developed the first ‘aerogels’, silica aerogels have been the interest of the scientific community due to their exceptional thermal insulation and lightweight characteristics and suitability for diverse applications [1]. Depending on the nature of synthesis and the application, ranging from thermal insulation in high-temperature applications to their application in lithium sulphur batteries, several intrinsic material characteristics may influence the structure-property relationships of the final aerogel product. However, designing aerogels for specific requirements remains a complex task due to the intricate and nanostructured morphology of the material. Given the recent advancements in the areas of materials research and artificial intelligence, deep reinforcement learning (DRL) provides a solution to such optimisation problems for developing aerogels for achieving targeted properties. With the ability to learn and extract complex patterns and relationships, it provides a data-driven approach to understand and optimise these materials. As such, an offline DRL approach in combination with a property predictor (surrogate model) is presented to optimise computationally designed aerogel microstructures for diverse application. The surrogate models act as intelligent digital twins, eliminating the requirement for iterative computational modelling and the subsequent post-processing. These computational microstructures are modelled with aggregation algorithms mimicking the sol-gel chemistry [2] and gaussian random field-based algorithms [3] to optimise the mechanical and the flow properties of the aerogel microstructures. References [1] M. A. Aegerter, N. Leventis and M. M. Koebel, Aerogels handbook, Springer Science & Business Media, 2011 [2] R. Abdusalamov, C. Scherdel, M. Itskov, B. Milow, A.Rege, J. Phys. Chem. B 2021, 125, 1944–1950. [3] C.J. Gommes, A.P. Roberts Phys. Rev. E, 2008, 77, 04140

A New Type Of Hybrid Aggregation Model And The Application Towards Silica (Aero)gels

A new type of hybrid aggregation model and the application towards silica (aero)gels Nina Borzęcka, Prakul Pandit, Ameya Rege Department of Aerogels and Aerogel Composites, Institute of Materials Research, German Aerospace Centre, Cologne, Germany Silica aerogel modelling requires acknowledging the complexity of their structure. The condensation of the classic particle aggregates type of aerogel is a complex phenomenon which result in their final nanostructured porous morphology. In order to understand the process, a comprehensive and multiscale approach is needed. A widely utilised, although significantly simplified approach for modelling sol-gel transition is diffusion or reaction limited cluster aggregation method (DLCA/RLCA). This type of numerical system can mimic random motion of primary/secondary particles and follow simultaneously the structure evolution and the kinetics of its formation. The model parameters such as concentration of secondary particles and sticking probability affect the process rate and the structural and fractal properties. As a consequence, we introduce a modelling approach, that takes into the consideration the numerical particle reactivity based on the experimental reaction rates. The comparison of numerical and experimental results provides data for model validation and discussion whether these improvements bring us closer to reflecting the real materials – silica aerogels. Which brings us to the question: Does such a modelling approach show potential for reverse engineering and product design

On the impact of aggregation mechanism in modelling fractal materials

In this contribution, the diffusive and ballistic nature of aggregate-formation in colloidal-like materials will be discussed. To this end, diffusion-limited and reaction-limited algorithms together with their cluster-cluster aggregation extensions will be considered. While the aggregating particles in such algorithms follow natural Brownian motion, an additional algorithm accounting for the linear motion of particles will also be analysed. The effect of these algorithms on the final network’s structural and fractal properties will be presented. Furthermore, the application of the diffusion-limited cluster-cluster aggregation approach to model the sol-gel process in synthesising silica aerogels will be illustrated. The use of the finite element method in describing the mechanical properties of the generated model silica aerogels will be elucidated at the end [1]. References 1. Abdusalamov, R., Scherdel, C., Itskov, M., Milow, B., Reichenauer, G., & Rege, A. (2021). Modeling and Simulation of the Aggregation and the Structural and Mechanical Properties of Silica Aerogels. The Journal of Physical Chemistry B 125, 1944-1950