Numerical analysis of mechanical reliability of multi-coated phase change materials

Nanoencapsulated phase change materials (nePCMs) are nowadays under research for thermal energy storage purposes. NePCMs are composed of a phase change core surrounded by a shell that confines the core when molten. One of the main concerns of nePCMs when subjected to thermal processes is the mechanical failure of the passivation shell initially present in commercial metallic nanoparticles. In order to overcome this issue, multi-coated nePCMs, based on the synthesis of an additional coating by atomic layer deposition, appear to be as a candidate solution. With the objective of studying the influence of the composition and thickness of the additional nePCM shells on their probability of failure, a numerical tool combining a thermomechanical finite element model with phase change and Monte Carlo algorithms is developed. This tool also allows including the uncertainty of material and geometrical properties into the numerical analysis to account for their influence in the mechanical performance of nePCMs. In the present work, the mechanical reliability of SiO2 and Al2O3 coatings on Sn@SnOx nanoparticles is assessed by considering both deterministic and probabilistic failure criteria and Al2O3 coatings appear to have a better mechanical performance than their SiO2 counterparts. * Corresponding author: mondragn@uji.es E3S Web of Conferences 321, 02019 (2021) ICCHMT 2021 https://doi.org/10.1051/e3sconf/202132102019 © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/).


Introduction
Energy generation and conversion is one of the major concerns that society is facing nowadays. This tendency falls within the global context of transition from conventional energy sources towards renewable ones. Among the wide variety of available renewable sources, the focus is put on solar energy due to the enormous amount of energy that the Sun constantly delivers to Earth.
However, the main issue with solar energy is their dependence upon weather conditions for energy generation. On this ground, thermal energy storage (TES) systems are under research in order to decrease the eventual gaps between energy supply and demand, which may lead to instabilities in the operation of the electric grid.
More precisely, in the field of solar thermal energy, nanofluids based on molten salts are being studied as a candidate technology for TES purposes. Nanofluids are colloidal suspensions of nano-sized particles in a working fluid [1]. The potential of nanofluids to store energy normally was associated to their sensible storage capability but recently nanoencapsulated phase change materials (nePCMs) were used instead as the solid component of nanofluids. The use of nePCMs enhanced the thermal storage capability of the suspension by means of the contribution of latent heat [2,3].
NePCMs are normally composed of a phase change core wrapped in a shell made of another material with a higher melting temperature than the core. With regard to metallic nanoparticles, which are the object of study of the present work, their shell is normally made of an oxide layer formed by passivation [4,5].
An issue encountered when subjecting nanofluids with nePCMs dispersed in it to thermal cycles is the mechanical failure of their shell, which results in the leak of the molten core of nePCMs and the loss of thermal storage capability of the nanofluid. With regard to the mechanical failure of nePCM shells, the main difficulty in their synthesis is to determine which material and/or geometrical parameters exert the most significant influence on the mechanical failure of shells. In some previous works [6], it was found that the shell thickness as well as other material parameters such as the melting temperature or the thermal expansion coefficient of the core were some of the variables having more influence on the mechanical failure of nePCM shells. Since the initial oxide layer thickness formed by passivation is hard to control, the technique of atomic layer deposition (ALD) [7] appears to be as a possible solution to synthesise an additional coating of controlled properties and thickness on nePCMs. These nanoparticles with two different encapsulations often receive the name of multi-coated nePCMs and Figure 1 shows an image of these experimentally synthesised multi-coated nePCMs.
With regard to the synthesis of the shell thickness surrounding the core, a compromise must be reached between their mechanical strength and energy storage capability. Consequently, in order to systematically assess the mechanical performance of different nePCMs, to incorporate the measurement dispersion of material and geometrical parameters into the numerical analysis and to gain deeper insight into the causes of the failure of nePCMs, a numerical tool combining a thermomechanical finite element model with phase change with Monte Carlo (MC) simulations is presented in this work. More concretely, the performance of the following nePCMs (core@inner_shell@outer_shell) experimentally synthesised by ALD is assessed: Sn@SnO, Sn@SnO 2 @SiO 2 and Sn@SnO@Al 2 O 3 .

Analysis and modelling
The numerical tool presented in this work combines a thermomechanical FE model with phase change with MC techniques.
The thermomechanical FE model was developed in a previous work [8] to study the thermal stresses Notice that the angular momentum balance is automatically satisfied by the symmetry of the Cauchy stress tensor.
The regularisation scheme called as enthalpy method presented in that same previous work [8] is used to run the numerical simulations performed in the present study. Regarding MC techniques, they are a class of numerical algorithms that make use of statistical samples to approach the solution of a model in a probabilistic sense. The general procedure to perform a MC analysis consists in: i) Defining the random parameters of the model and their distribution functions.
ii) Generating a sample of size N. iii) Performing N evaluations of the model.
Then, outputs are obtained by post-processing the results obtained from simulations. Further detail concerning MC techniques used in the present work can be found in the work of Forner-Escrig [6].
The performance parameter considered for the analysis of mechanical reliability of the nePCM shells is their Probability of Failure (POF), which can be evaluated by means of MC techniques as: where > @  With respect to boundary and initial conditions, the centre of the nePCM is mechanically fixed and a temperature value is prescribed on the external surface of the outer shell. Temperature is increased progressively with time varying from an initial value of 343 K until a value of 553.15 K, which is higher than the core melting temperature (498.65 K) of the aforementioned multi-coated nePCMs.

Results and discussion
With regard to the performance parameter, namely the POF of the nePCM shell, Figure 2 shows the stress distributions predicted by the numerical tool against a probabilistic failure criterion to also consider the influence of the tensile strength dispersion on the mechanical failure of the nePCM shells. POF is obtained by comparing the overlapping between stress distributions and failure criteria. For instance, for Sn@SnO 2 @SiO 2 nePCMs, the probabilistic failure criterion is obtained by comparing the intersection between the stress distribution and a distribution of tensile strength (in orange in Figure 2) which determines the POF of nePCM shells. The values of POF from Figure 2 for Sn@SnO nePCMs is 2.27%, for Sn@SnO 2 @SiO 2 nePCMs is 72.38% and the values for Sn@SnO@Al 2 O 3 nePCMs is 1.66%, according to the probabilistic failure criterion. Numerical studies performed by also considering deterministic failure criteria show the need to consider probabilistic ones because by using a deterministic critetion slightly underestimates the POF of nePCM shells, which may result in a remarkable loss of energy storage capability of nanofluids.
The influence of the shell thickness of the outer shell is examined as well, as depicted in Figure 3. This Figure shows the evolution of the mechanical POF of the shells with increasing shell thickness. It can be observed that the POF of the inner shells (SnO and SnO 2 ) remains nearly constant regardless of the value of the outer shell thickness. However, remarkable variations of POF of the outer shells occur when varying their shell thickness. For instance, POF of SiO 2 reduces from an initial value of 87.56% until a value of 72.38%. The same trend is observed for Al 2 O 3 , which exhibits a drastic reduction in POF from a value of 31.71% until a value of 1.66%. From these results it is noticed that Al 2 O 3 coatings present better mechanical strength than their SiO 2 counterparts. Furthermore, it is observed that encapsulation of nePCMs can contribute to improve their mechanical reliability but the shell thickness cannot be continuously increased because this could jeopardise the colloidal stability of the nanofluid since nanoparticles with bigger size could agglomerate and settle.

Conclusions
This work presents a numerical tool combining a thermomechanical FE model with MC techniques, which is used to assess the mechanical reliability of different nePCMs.
From the numerical simulations, the importance of considering a probabilistic failure criterion is stressed in order not to overestimate the mechanical strength of nePCM shells. Furthermore, Sn@SnO@Al 2 O 3 nePCMs exhibit the best mechanical performance since they are not expected to fail under thermal stresses while the POF of Sn@SnO 2 @SiO 2 is still high even for the largest value of shell thickness considered in this study.
In short, tuning the shell thickness of nePCMs can contribute to enhance their mechanical performance although this thickness cannot always be increased in order not to guarantee the colloidal stability of the nanofluids. Therefore, in order to carefully study the mechanical reliability of nePCMs, the numerical tool presented in this work can be employed to run numerical simulations with the aim of reducing the number of experiments to be conducted to determine the optimal properties of nePCMs.