Deep reinforcement learning for microstructural optimisation of silica aerogels.

Silica aerogels are being extensively studied for aerospace and transportation applications due to their diverse multifunctional properties. While their microstructural features dictate their thermal, mechanical, and acoustic properties, their accurate characterisation remains challenging due to their nanoporous morphology and the stochastic nature of gelation. In this work, a deep reinforcement learning (DRL) framework is presented to optimise silica aerogel microstructures modelled with the diffusion-limited cluster-cluster aggregation (DLCA) algorithm. For faster computations, two environments consisting of DLCA surrogate models are tested with the DRL framework for inverse microstructure design. The DRL framework is shown to effectively optimise the microstructure morphology, wherein the error of the material properties achieved is dependent upon the complexity of the environment. However, in all cases, with adequate training of the DRL agent, material microstructures with desired properties can be achieved by the framework. Thus, the methodology provides a resource-efficient means to design aerogels, offering computational advantages over experimental iterations or direct numerical solutions.

The Effect of Particle Necks on the Mechanical Properties of Aerogels.

Mechanical properties of open-porous materials are often described by constructing a cellular network with beams of constant cross sections as the struts of the cells. Such models have been applied to describe, for example, thermal and mechanical properties of aerogels. However, in many aerogels, the pore walls or the skeletal network is better described as a pearl-necklace, in which the particles making up the network appear as a string of pearls. In this paper, we investigate the effect of neck sizes on the mechanical properties of such pore walls. We present an analytical and a numerical solution by modeling these walls as corrugated beams and study the subsequent deviations from the classical scaling theory. Additionally, a full numerical model of such pearl-necklace-like walls with concave necks of varying sizes are simulated. The results of the numerical model are shown to be in good agreement with those resulting from the computational one.

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%.

Constitutive Modeling of the Densification Behavior in Open-Porous Cellular Solids.

The macroscopic mechanical behavior of open-porous cellular materials is dictated by the geometric and material properties of their microscopic cell walls. The overall compressive response of such materials is divided into three regimes, namely, the linear elastic, plateau and densification. In this paper, a constitutive model is presented, which captures not only the linear elastic regime and the subsequent pore-collapse, but is also shown to be capable of capturing the hardening upon the densification of the network. Here, the network is considered to be made up of idealized square-shaped cells, whose cell walls undergo bending and buckling under compression. Depending on the choice of damage criterion, viz. elastic buckling or irreversible bending, the cell walls collapse. These collapsed cells are then assumed to behave as nonlinear springs, acting as a foundation to the elastic network of active open cells. To this end, the network is decomposed into an active network and a collapsed one. The compressive strain at the onset of densification is then shown to be quantified by the point of intersection of the two network stress-strain curves. A parameter sensitivity analysis is presented to demonstrate the range of different material characteristics that the model is capable of capturing. The proposed constitutive model is further validated against two different types of nanoporous materials and shows good agreement.

Computational design of biopolymer aerogels and predictive modelling of their nanostructure and mechanical behaviour.

To address the challenge of reconstructing or designing the three-dimensional microstructure of nanoporous materials, we develop a computational approach by combining the random closed packing of polydisperse spheres together with the Laguerre-Voronoi tessellation. Open-porous cellular network structures that adhere to the real pore-size distributions of the nanoporous materials are generated. As an example, κ-carrageenan aerogels are considered. The mechanical structure-property relationships are further explored by means of finite elements. Here we show that one can predict the macroscopic stress-strain curve of the bulk porous material if only the pore-size distributions, solid fractions, and Young's modulus of the pore-wall fibres are known a priori. The objective of such reconstruction and predictive modelling is to reverse engineer the parameters of their synthesis process for tailored applications. Structural and mechanical property predictions of the proposed modelling approach are shown to be in good agreement with the available experimental data. The presented approach is free of parameter-fitting and is capable of generating dispersed Voronoi structures.

Physics-informed constitutive modelling of hydrated biopolymer aerogel networks.

Hydration induces significant structural rearrangements in biopolymer aerogels, resulting in a completely different mechanical behaviour compared to the one in the dry state. A network decomposition concept was earlier introduced to account for these changes, wherein the material network was decomposed into an open-porous aerogel one and a hydrogel-like one. Recent experimental evidences have supported this idea of the formation of a hydrogel-like network. Using these observations as a basis, in this paper, we present a micromechanical model describing the effect of hydration on the structural and mechanical properties of aerogels. The aerogel network is modelled based on the mechanics of their pore-walls, while the hydrogel-like network is modelled based on the statistical mechanics of their polymer chains by means of the Arruda-Boyce eight-chain model. The influence of diverse structural and material parameters on the mechanical behaviour is investigated. The effect of different degrees of wetting, from a pure aerogel to a pure hydrogel-like state, is captured by the model. The results are shown to be in good agreement with available experimental data.

Influence of pore-size distributions and pore-wall mechanics on the mechanical behavior of cellular solids like aerogels.

The pore-size distributions play a critical role in the determination of the properties of nanoporous cellular materials like aerogels. In this paper, we propose a micromechanical model, and by further designing artificial normal pore-size distributions, we inspect their effect on the macroscopic stress-strain curves. We show that the location of the mean pore size as well as the broadness of the distribution strongly affects the overall macroscopic behavior. Moreover, we also show that by using different damage criteria within the proposed model, the elastic, inelastic, and brittle nature of the macroscopic material can be captured. The damage criteria are based on the different modes of deformation in the pore walls, namely, elastic buckling, irreversible bending and brittle collapse under compression, and combined bending and stretching under tension. The proposed model approach serves as a reverse engineering tool to develop cellular solids with desired mechanical properties.

Modeling and Simulation of the Aggregation and the Structural and Mechanical Properties of Silica Aerogels.

Mechanical properties of aerogels are controlled by the connectivity of their network. In this paper, in order to study these properties, computational models of silica aerogels with different morphological entities have been generated by means of the diffusion-limited cluster-cluster aggregation (DLCA) algorithm. New insights into the influence of the model parameters on the generated aerogel structures and on the finite deformation under mechanical loads are provided. First, the structural and fractal properties of the modeled aerogels are investigated. The dependence of morphological properties such as the particle radius and density on these properties is studied. The results are correlated with experimental small-angle X-ray scattering (SAXS) data of a silica aerogel. The DLCA models of silica aerogels are analyzed for their mechanical properties with finite element simulations. There, the aerogel particles are modeled as nodes and the interparticle bonds as beam elements to account for bond stretching, bending, and torsion. The scaling relation between the elastic moduli E and relative density ρ, E ∝ ρm, is investigated and the exponent m = 3.61 is determined. Backbone paths evidently appear in the 3-d network structure under deformation, while the majority of the bonds in the network do not bear loads. The sensitivity of particle neck-sizes on the mechanical properties is also studied. All the results are shown to be qualitatively as well as quantitatively in agreement with the experimental data or with the available literature.

Stability Studies of Starch Aerogel Formulations for Biomedical Applications.

Starch aerogels are attractive materials for biomedical applications because of their low density and high open porosity coupled with high surface areas. However, the lack of macropores in conventionally manufactured polysaccharide aerogels is a limitation to their use as scaffolds for regenerative medicine. Moreover, the stability under storage of polysaccharide aerogels is critical for biomedical purposes and scarcely studied so far. In this work, the induction of a new macropore population (1-2 µm) well integrated into the starch aerogel backbone was successfully achieved by the incorporation of zein as a porogen. The obtained dual-porous aerogels were evaluated in terms of composition as well as morphological, textural, and mechanical properties. Stability of aerogels upon storage mimicking the zone II (25 °C, 65% relative humidity) according to the International Council for Harmonization guideline of climatic conditions was checked after 1 and 3 months from morphological, physicochemical, and mechanical perspectives. Zein incorporation induced remarkable changes in the mechanical performance of the end aerogel products and showed a preventive effect on the morphological changes during the storage period.

Temperature-Dependent Stiffening and Inelastic Behavior of Newly Synthesized Fiber-Reinforced Super Flexible Silica Aerogels.

In recent years, flexible silica aerogels have gained significant attention, owing to their excellent thermal and acoustic insulation properties accompanied by mechanical flexibility. Fiber reinforcement of such aerogels results in a further enhancement of the strength and durability of the composite, while retaining the excellent insulation properties. In this paper, the influence of four different kinds of fibers within a flexible silica aerogel matrix is studied and reported. First, a description of the synthesis procedure and the resulting morphology of the four aerogel composites is presented. Their mechanical behavior under uniaxial quasi-static tension and compression is investigated, particularly their performance under uniaxial compression at different temperature conditions (50 °C, 0 °C, and -50 °C). The reinforcement of the flexible silica aerogels with four different fiber types only marginally influences the thermal conductivity but strongly enhances their mechanical properties.

Correlating Synthesis Parameters to Morphological Entities: Predictive Modeling of Biopolymer Aerogels.

In the past decade, biopolymer aerogels have gained significant research attention due to their typical properties, such as low density and thermal insulation, which are reinforced with excellent biocompatibility, biodegradability, and ease of functionalization. Mechanical properties of these aerogels play an important role in several applications and should be evaluated based on synthesis parameters. To this end, preparation and characterization of polysaccharide-based aerogels, such as pectin, cellulose and k-carrageenan, is first discussed. An interrelationship between their synthesis parameters and morphological entities is established. Such aerogels are usually characterized by a cellular morphology, and under compression undergo large deformations. Therefore, a nonlinear constitutive model is proposed based on large deflections in microcell walls of the aerogel network. Different sizes of the microcells within the network are identified via nitrogen desorption isotherms. Damage is initiated upon pore collapse, which is shown to result from the failure of the microcell wall fibrils. Finally, the model predictions are validated against experimental data of pectin, cellulose, and k-carrageenan aerogels. Given the micromechanical nature of the model, a clear correlation-qualitative and quantitative-between synthesis parameters and the model parameters is also substantiated. The proposed model is shown to be useful in tailoring the mechanical properties of biopolymer aerogels subject to changes in synthesis parameters.

Mechanics of Nanostructured Porous Silica Aerogel Resulting from Molecular Dynamics Simulations.

Silica aerogels are nanostructured, highly porous solids which have, compared to other soft materials, special mechanical properties, such as extremely low densities. In the present work, the mechanical properties of silica aerogels have been studied with molecular dynamics (MD) simulations. The aerogel model of 192 000 atoms was created with different densities by direct expansion of ß-cristobalite and subjected to series of thermal treatments. Because of the high number of atoms and improved modeling procedure, the proposed model was more stable and showed significant improvement in the smoothness of the resulting stress-strain curves in comparison to previous models. Resulting Poisson's ratio values for silica aerogels lie between 0.18 and 0.21. The elasticity moduli display a power law dependence on the density, with the exponent estimated to be 3.25 ± 0.1. These results are in excellent agreement with reported experimental as well as computational values. Two different deformation scenarios have been discussed. Under tension, the low-density aerogels were more ductile while the denser ones behaved rather brittle. In the compression simulations of low-density aerogels, deformation occurred without significant increase in stress. However, for high densities, atoms offer a higher resistance to the deformation, resulting in a more stiff response and an early densification. The relationship between different mechanical parameters has been found in the cyclic loading simulations of silica aerogels with different densities. The residual strain grows linearly with the applied strain (≥0.16) and can be approximated by a phenomenological relation ϵp = 1.09ϵmax - 0.12. The dissipation energy also varies with the compressive strain according to a power law with an exponent of 2.31 ± 0.07. Moreover, the tangent modulus under cyclic loading varies exponentially with the compressive strain. The results of the study pave the way toward multiscale modeling of silica as well as reinforced silica aerogels.

Micro-mechanical modelling of cellulose aerogels from molten salt hydrates.

In this paper, a generalised micro-mechanical model capable of capturing the mechanical behaviour of polysaccharidic aerogels, in particular cellulose aerogels, is proposed. To this end, first the mechanical structure and properties of these highly nanoporous cellulose aerogels prepared from aqueous salt hydrate melts (calcium thiocyanate, Ca(SCN)2·6H2O and zinc chloride, ZnCl2·4H2O) are studied. The cellulose content within these aerogels is found to have a direct relation to the microstructural quantities such as the fibril length and diameter. This, along with porosity, appears to influence the resulting mechanical properties. Furthermore, experimental characterisation of cellulose aerogels was done using scanning electron microscopy (SEM), pore-size data analysis, and compression tests. Cellulose aerogels are of a characteristic cellular microstructures and accordingly a network formed by square shaped cells is considered in the micro-mechanical model proposed in this paper. This model is based on the non-linear bending and collapse of such cells of varying pore sizes. The extended Euler-Bernoulli beam theory for large deflections is used to describe the bending in the cell walls. The proposed model is physically motivated and demonstrates a good agreement with our experimental data of both ZnCl2 and Ca(SCN)2 based cellulose aerogels with different cellulose contents.