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Mechanical properties and behavior of glass fiber-reinforced silica aerogel nanocomposites: Insights from all-atom simulations
Scripta Materialia 177 (2020) 65–68
Contents lists available at ScienceDirect
Scripta Materialia journal homepage: www.elsevier.com/locate/scriptamat
Mechanical properties and behavior of glass fiber-reinforced silica aerogel nanocomposites: Insights from all-atom simulations Sandeep P. Patil∗, Parag Shendye, Bernd Markert Institute of General Mechanics, RWTH Aachen University, Templergraben 64, Aachen 52062, Germany
a r t i c l e
i n f o
Article history: Received 27 August 2019 Revised 7 October 2019 Accepted 8 October 2019
Keywords: Glass fibers Silica aerogel Molecular dynamics Mechanical properties
a b s t r a c t The primary goal of this work is to understand the influence of the amount and dimensions of glass fibers in silica aerogel matrix on the mechanical properties using molecular dynamics (MD) simulations. By adding the glass fibers, the tensile strength, elastic modulus and compressive behavior of silica aerogel were significantly improved due to the resistance offered to bending and axial deformation of the fibers. Moreover, this work proposes a linear relationship between the elastic modulus and density of nanocomposites for particular fiber dimensions. The extraordinary mechanical performance of the proposed nanocomposites has a broad spectrum of mechanical-loading applications.
Enhancing the mechanical properties of low-density highlynanoporous materials, such as silica aerogel, relies on the characterization and fundamental understanding of their micro and nanostructure. Silica aerogel is defined as the network of interconnecting chains, wherein each chain is made of spherical nanoparticles of diameters of 5–10 nm. Due to the network of chains, silica aerogel possesses mainly meso-pores ( ∼ 2–50 nm diameter) and a very few micro-pores [1–4]. The mentioned characteristics provide silica aerogels extraordinary properties, such as high surface area, low density, high specific surface area and low thermal conductivity, which enabling its applications in many areas, for example, acoustic and thermal insulation, space technology, automotive industry, catalysis, gas filtering and electronic devices [5–10]. However, many above-mentioned and potential applications of silica aerogel are limited due to its low-tensile strength and brittle nature [11]. To mitigate the above limitations, recently, many researchers have been focusing on composites of silica aerogels by the addition of glass fibers. Parmenter and Milstein [12] studied the mechanical properties of native as well as fiber-reinforced silica aerogel using tension, compression, shear and hardness tests. As fiber percentage increases, the compressive strength, secant moduli and hardness increase, while the fracture strain decreases as the fiber reinforcement increases. Yuan et al. [13] reported glass fiber-reinforced silica aerogel composites using randomly dispersed glass fibers into silica aerogel powders. By adding the numberof glass fibers, the
∗
Corresponding author. E-mail address: [email protected] (S.P. Patil).
https://doi.org/10.1016/j.scriptamat.2019.10.010 1359-6462/© 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
© 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
strength of the composites was enhanced. However, thermal insulation property was declined. Liao et al. [14] prepared the laminated nanocomposites, wherein flexible silica aerogels were differently arranged with four glass fiber layers. The laminated designed structures can be tailored in order to achieve improved the mechanical properties of the nanocomposites. Wu et al. [15] investigated a proper technique to develop aligned fiber-reinforced aerogel composites for low thermal conductivity and significantly enhanced compressive and bending strengths compared to native aerogels. Li et al. [16] synthesized the glass fiber film/silica aerogel composites and investigated the thermal, mechanical and flammability properties of these composites with variation in H2 O: tetraethyl orthosilicate (TEOS) molar ratio. As the ratio increased from two to six, the composites showed significantly enhanced mechanical properties compared to the native silica aerogels, which was without imperiling their thermal properties. Zhou et al. [17] synthesized glass fiber-reinforced silica aerogel composites using methltrimethoxysilane (MTMS) and water glass co-precursor and performed different mechanical tests. As the molar ratio of MTMS/water glass increased, the mechanical strength and flexibility were significantly improved compared to pure aerogel. Maleki et al. [18] presented a detailed discussion on how to increase the strength and stiffness of silica aerogel using different reinforcement materials. In the last decade, many researchers have been working on the computational modeling of aerogels with especial attention to molecular dynamics (MD) simulations to investigate the mechanical and thermal properties [3,4,11,19–26]. In particular, the mechanical properties under large deformation [24], fracture mechanical properties [11], nanoindentation tests on pure [25] and
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S.P. Patil, P. Shendye and B. Markert / Scripta Materialia 177 (2020) 65–68
Fig. 1. Schematic representation of silica aerogel nanocomposites. (A) The GLF-SiO2 -L180 model with 25% weight of glass fibers. (B) The 32% weight of glass fiber models of three types of l/d ratios. To observe the random dispersion of glass fibers, silica aerogel matrix is represented in light gray.
on graphene-reinforced nanocomposites [27] of silica aerogel were previously investigated. Despite such vast literature on all-atom modeling of aerogels, the mechanical behavior and properties of glass fiber-reinforced silica composites have so far not been investigated. Due to the addition of glass fibers, the mechanical properties can be significantly improved. In the present work, silica aerogel nanocomposites were modeled by adding randomly dispersed glass fibers. The influence of weight percentage, as well as length to diameter ratio of dispersed glass fibers on the mechanical properties, were investigated. To the best of our knowledge, notably, glass fiberreinforced silica composites have never been investigated before in an all-atom study. This work utilized LAMMPS [28] (Large Scale Atomic/Molecular Massively Parallel Simulator) for carrying out MD simulations and OVITO [29] for visualizing the atomistic simulation data. The all-atom models of silica aerogel were created based on Vashishta interatomic potential [30,31]. Periodic boundary conditions were applied in three mutually perpendicular directions. Velocity Verlet integration algorithm was used with a constant step size of 0.5 fs. The atoms were initially supplied with a random velocity and assigned a temperature of 70 0 0 K. Later, the NVT (constant volume and constant temperature) ensemble was used to quench the sample to 300 K at 5 K/ps, which was followed by an energy minimization step. Finally, amorphous silica was generated when the sample was allowed to relax to atmospheric conditions (300 K and 1 bar). The obtained amorphous silica was instantaneously expanded to desired density ρ = 406 kg m−3 . Subsequently, the sample was heated to 30 0 0 K for 50 ps and relaxed again. Finally, the sample was quenched to 0 K and brought back to atmospheric conditions, which has resulted in the formation of silica aerogel. For a more detailed discussion on the construction of silica aerogel, the reader is referred to Patil et al. [24]. In this work, relatively high-density of silica matrix was studied because the low-density models are of high-dimensions as well as they exhibit high-variation in the complex structures for the same density. Therefore, the high-density models were considered for computing a wide range of MD simulations of weight percentages as well as length to diameter ratios on the available computational resources.
For modeling of fibers, the cylindrical shape of crystalline silica was modeled with fully coordinated silica rings at the edges. Due to such silica rings, unnecessary structural, chemical and electronic changes can be avoided [32]. The amorphous silica fibers were obtained by using the above-described heating treatment, i. e., heating to 70 0 0 K and cooling to 300 K at 5 K/ps. The interactions in glass fiber were defined by Vashishta et al. [30,31]. To prepare reinforced nanocomposites of silica aerogel, randomized coordinates were generated for every glass fiber, ensuring no intersections between them. Similarly, the empty spaces were created in the aerogel models at the respective places with 2 A˚ of extra tolerance all-around the dimensions of glass fiber. Once the combined models were constructed, we performed two cycles of annealing treatment accompanied by energy minimization to obtain the best conformations of energies of glass fiber silica aerogel nanocomposites. To define the interactions between glass fiber and silica aerogel matrix, Vashishta interatomic potential [30,31] was used. In this work, three types of length to diameter ratio (l/d), i. e., l/d = 3, 6 and 9, as well as various weight percentages of reinforced glass fibers in silica aerogel matrix were investigated (see ˚ and the Fig. 1). Here, the diameter of glass fiber was fixed to 30 A, ˚ length was varied from 90 to 270 A. Finally, the tension and compression simulations were performed on pure silica aerogel (Native-SiO2 ), glass fiber of l/d = 3 reinforced silica aerogel (GLF-SiO2 -L90), glass fiber of l/d = 6 reinforced silica aerogel (GLF-SiO2 -L180) and glass fiber of l/d = 9 reinforced silica aerogel (GLF-SiO2 -L270) with a time step size of 0.5 fs and using NVE (constant volume constant internal energy) ensemble. All the tests were carried out using a constant strain rate of 0.004 ps−1 [24]. Due to the highly complex structure of silica aerogel matrix as well as the randomness of glass fibers, six different MD simulations were independently performed for every analysis. In this work, the average resultant properties are presented, and the variation was determined based on the standard error deviation. In the present work, the mechanical behavior and properties of the pure silica and glass fiber-reinforced silica aerogel were investigated. Fig. 2A shows a comparison of the tensile stress– strain curves. The tensile strength of the pure silica aerogel was
S.P. Patil, P. Shendye and B. Markert / Scripta Materialia 177 (2020) 65–68
67
Fig. 3. Comparative analysis of variation in elastic moduli with standard error bars of native silica aerogel and the nanocomposites for the considered l/d ratios and varying amount composition of glass fiber reinforcement. Elastic modulus of pure silica aerogel is at ρ = 406 kg m−3 , which is a common point for all the linear fits (dotted lines).
Fig. 2. (A) Comparison of tensile stress–strain curves of pure silica aerogel and nanocomposites of the GLF-SiO2 -L180 model. (B) Snapshots of the GLF-SiO2 -L180 model with weight of 25.82% of glass fiber at different strains during the tensile test. To understand the deformation and displacement of glass fibers, silica aerogel matrix is represented in light gray.
0.2 GPa. For the GLF-SiO2 -L180 models, as the weight percentages of glass fibers increased from 8.02 to 51.61%, the tensile strength was greatly improved from 0.25 to 0.442 GPa, respectively. However, the ultimate tensile strain was decreased from 0.25 to 0.19 for increasing the weight percentages of glass fibers. Similarly, for the GLF-SiO2 -L90 and GLF-SiO2 -L270 models, the tensile strength was increased, and the ultimate strain was decreased with increasing the number of glass fibers. One can note that as the l/d ratio increases, the trend of increase in the tensile strength was significantly improved. A detailed description of the tensile strength and ultimate strain versus weight percentages of glass fibers is presented in the Supplementary material. As the tensile load increases on the nanocomposite models, the randomly dispersed glass fibers were started to align in the direction of the loading (the snapshots at strain 0.10 and 0.24 in Fig. 2B). The resistance against deformation was mainly coming from the bending and axial pulling of glass fibers in the silica aerogel matrix. After the highest resistance to the deformation, the empty spaces (pores) in the models were joined together to find the minimum energy path, and one can observe this at a strain of 0.60 in Fig. 2B.
In case of the short length reinforcement (GLF-SiO2 -L90), there was a considerable amount of deformation resistance during the tensile loading was observed for the bending and axial pulling of glass fibers in the silica aerogel matrix, which was higher compared to pure silica aerogel. On the other hand, for large length reinforcement (GLF-SiO2 -L270), higher resistance to deformation was offered due to large length. Therefore, remarkably improved tensile strength and elastic modulus were observed for large length reinforcement nanocomposites compared to short length reinforcement nanocomposites. The variation in the mechanical properties is qualitatively in good agreement with the literature [12,15–17]. In our previous work, nearly linear stress–strain response of silica aerogel was reported up to 0.04 of tensile strain. Therefore, in this work, the elasticity modulus E values were obtained from the linear regime ( t ≤ 0.04) of the stress–strain curves simply by E = σt /t . Fig. 3 depicts the comparison of the elastic moduli of pure silica aerogel and nanocomposites. The elasticity modulus increases with an increase in l/d ratio and weight percentage composition of glass fibers in a silica aerogel matrix (see the Supplementary Material). For a particular l/d ratio, the E grows linearly with respect to ρ of the nanocomposite. Linear fits are presented on the elastic modulus versus density plot in Fig. 3. To end this, the proposed equation is
E = C + mρ
(1)
where C is the constant, and m is the slope of the linear fit. C values are −1.28, −2.55 and −3.76 GPa, and m values are 0.0071, 0.0102 and 0.0132 GPa/(kg m−3 ) for the GLF-SiO2 -L90, GLF-SiO2 L180 and GLF-SiO2 -L270 models, respectively. This newly proposed relation provides insights into the influence of fibers on the elasticity modulus at the nanoscale. Such a relation can be used to design the new nanocomposite for a particular application. Fig. 4A shows the stress–strain curves of pure silica aerogel and nanocomposites of the GLF-SiO2 -L180 models under uniaxial compression. The amount of glass fiber reinforcement has a significant influence on the mechanical performance. It was observed that the compressive stresses at particular strain increase with the weight percentages of glass fiber, which was an expected result. As the amount of glass fibers increases, the density of nanocomposites also increases. In the pure silica model, due to a lot of empty places, less deformation resistance was observed. However, as the amount of glass fibers increases, highly dense fibers restricted the easy deformation, which resulted
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The all-atom study reveals the nanomechanics during the tensile and compression tests on glass fiber-reinforced silica aerogel. The outcome of the investigation provides the understanding to design the nanocomposite for a particular application, wherein the well defined mechanical properties needed. The extension of this work is to conduct the experiments and all-atom simulations of the low-density aerogels ( ≤ 200 kg m−3 ) with variation in weight percentage of glass fibers. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments Simulations were performed with computing resources granted by RWTH Aachen University under project jara0201. Supplementary material Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.scriptamat.2019.10. 010. References
Fig. 4. (A) Compression stress–strain curves of pure silica aerogel and nanocomposites of the GLF-SiO2 -L180 model. Inset: Comparison of σ c – c curves for strain between 0.1 and 0.4 in enlarged view. (B) Snapshots of the GLF-SiO2 -L180 model with weight of 37.83% of glass fiber at different strains during the compression test. To understand the compression behavior of glass fibers, silica aerogel matrix is represented in light gray.
into early densification and the very stiff σ c – c response were observed. Moreover, the glass fibers are randomly distributed and oriented in a silica aerogel matrix, which also caused higher bending and buckling resistance, and consequently resulted in higher overall stiffness. In summary, silica aerogel nanocomposites were modeled by adding randomly dispersed glass fibers. The influence of weight percentage, as well as length to diameter ratio of dispersed glass fibers on the mechanical properties, were investigated using MD simulations. In the tensile tests, as the weight percentages of glass fibers increases, the tensile strength, and elastic modulus were significantly improved. However, the ultimate tensile strain was decreased. Moreover, as the l/d of the fiber increases, the increasing trend of the mechanical properties was towering, this was the result of high-resistance to the bending and axial pulling of the glass fibers. Furthermore, the linear relationship was proposed between the elastic modulus and density of nanocomposites. In compression tests, compressive resistance increases with a weight percentage of the fibers, which was mainly due to bending and axial compression of the number of fibers.
[1] N. Hüsing, U. Schubert, Angew. Chem. Int. Ed. 37 (1-2) (1998) 22–45. [2] L. Roiban, G. Foray, Q. Rong, A. Perret, D. Ihiawakrim, K. Masenelli-Varlot, E. Maire, B. Yrieix, RSC Adv. 6 (13) (2016) 10625–10632. [3] W. Gonçalves, J. Morthomas, P. Chantrenne, M. Perez, G. Foray, C.L. Martin, Acta Mater. 145 (2018) 165–174. [4] S.P. Patil, P. Shendye, B. Markert, Materialia 6 (2019) 100315. [5] N. Hüsing, U. Schubert, Angew. Chem. 110 (1-2) (1998) 22–47. [6] L.W. Hrubesh, J Non-Cryst Solids 225 (1998) 335–342. [7] M. Koebel, A. Rigacci, P. Achard, Aerogels Handbook, Springer New York, 2011, pp. 607–633. [8] I. Smirnova, P. Gurikov, Annu. Rev. Chem. Biomol. Eng. 8 (2017) 307–334. [9] C.A. García-González, T. Budtova, L. Durães, C. Erkey, P. Del Gaudio, P. Gurikov, M. Koebel, F. Liebner, M. Neagu, I. Smirnova, Molecules 24 (9) (2019) 1815. [10] V.G. Parale, K.-Y. Lee, H.-H. Park, J. Korean Ceram. Soc. 54 (3) (2017) 184–199. [11] S.P. Patil, A. Rege, M. Itskov, B. Markert, J Non-Cryst Solids 498 (2018) 125–129. [12] K.E. Parmenter, F. Milstein, J Non-Cryst Solids 223 (3) (1998) 179–189. [13] B. Yuan, S. Ding, D. Wang, G. Wang, H. Li, Mater. Lett. 75 (2012) 204–206. [14] Y. Liao, H. Wu, Y. Ding, S. Yin, M. Wang, A. Cao, J. Sol-Gel Sci. Technol. 63 (3) (2012) 445–456. [15] H. Wu, Y. Liao, Y. Ding, H. Wang, C. Peng, S. Yin, Heat Transfer Eng. 35 (11-12) (2014) 1061–1070. [16] C. Li, X. Cheng, Z. Li, Y. Pan, Y. Huang, L. Gong, J. Non-Cryst. Solids 457 (2017) 52–59. [17] T. Zhou, X. Cheng, Y. Pan, C. Li, L. Gong, H. Zhang, Appl. Surf. Sci. 437 (2018) 321–328. [18] H. Maleki, L. Durães, A. Portugal, J. Non-Cryst. Solids 385 (2014) 55–74. [19] L.D. Gelb, J Phys Chem C 111 (43) (2007) 15792–15802. [20] J.S.R. Murillo, M.E. Bachlechner, F.A. Campo, E.J. Barbero, J Non-Cryst Solids 356 (25) (2010) 1325–1331. [21] J. Lei, Z. Liu, J. Yeo, T.Y. Ng, Soft Matter 9 (47) (2013) 11367–11373. [22] C.A. Ferreiro-Rangel, L.D. Gelb, J Phys Chem B 117 (23) (2013) 7095–7105. [23] C.A. Ferreiro-Rangel, L.D. Gelb, J Phys Chem B 119 (27) (2015) 8640–8650. [24] S.P. Patil, A. Rege, Sagardas, M. Itskov, B. Markert, J. Phys. Chem. B 121 (22) (2017) 5660–5668. [25] S.P. Patil, V.G. Parale, H.-H. Park, B. Markert, Mater. Sci. Eng., A 742 (2019) 344–352. [26] J. Morthomas, W. Gonçalves, M. Perez, G. Foray, C.L. Martin, P. Chantrenne, J. Non-Cryst. Solids 516 (2019) 89–98. [27] S.P. Patil, Molecules 24 (7) (2019) 1336. [28] S. Plimpton, J Comput Phys 117 (1) (1995) 1–19. [29] A. Stukowski, Model. Simul. Mater. Sci. Eng. 18 (1) (2009) 015012. [30] P. Vashishta, R.K. Kalia, J.P. Rino, I. Ebbsjö, Phys Rev B 41 (17) (1990) 12197–12209. [31] P. Vashishta, R.K. Kalia, A. Nakano, W. Li, I. Ebbsjö, Amor. Insul. Semiconduct. 33 (1996) 151–213. [32] S.T. Bromley, Nano Letters 4 (8) (2004) 1427–1432.
Contents lists available at ScienceDirect
Scripta Materialia journal homepage: www.elsevier.com/locate/scriptamat
Mechanical properties and behavior of glass fiber-reinforced silica aerogel nanocomposites: Insights from all-atom simulations Sandeep P. Patil∗, Parag Shendye, Bernd Markert Institute of General Mechanics, RWTH Aachen University, Templergraben 64, Aachen 52062, Germany
a r t i c l e
i n f o
Article history: Received 27 August 2019 Revised 7 October 2019 Accepted 8 October 2019
Keywords: Glass fibers Silica aerogel Molecular dynamics Mechanical properties
a b s t r a c t The primary goal of this work is to understand the influence of the amount and dimensions of glass fibers in silica aerogel matrix on the mechanical properties using molecular dynamics (MD) simulations. By adding the glass fibers, the tensile strength, elastic modulus and compressive behavior of silica aerogel were significantly improved due to the resistance offered to bending and axial deformation of the fibers. Moreover, this work proposes a linear relationship between the elastic modulus and density of nanocomposites for particular fiber dimensions. The extraordinary mechanical performance of the proposed nanocomposites has a broad spectrum of mechanical-loading applications.
Enhancing the mechanical properties of low-density highlynanoporous materials, such as silica aerogel, relies on the characterization and fundamental understanding of their micro and nanostructure. Silica aerogel is defined as the network of interconnecting chains, wherein each chain is made of spherical nanoparticles of diameters of 5–10 nm. Due to the network of chains, silica aerogel possesses mainly meso-pores ( ∼ 2–50 nm diameter) and a very few micro-pores [1–4]. The mentioned characteristics provide silica aerogels extraordinary properties, such as high surface area, low density, high specific surface area and low thermal conductivity, which enabling its applications in many areas, for example, acoustic and thermal insulation, space technology, automotive industry, catalysis, gas filtering and electronic devices [5–10]. However, many above-mentioned and potential applications of silica aerogel are limited due to its low-tensile strength and brittle nature [11]. To mitigate the above limitations, recently, many researchers have been focusing on composites of silica aerogels by the addition of glass fibers. Parmenter and Milstein [12] studied the mechanical properties of native as well as fiber-reinforced silica aerogel using tension, compression, shear and hardness tests. As fiber percentage increases, the compressive strength, secant moduli and hardness increase, while the fracture strain decreases as the fiber reinforcement increases. Yuan et al. [13] reported glass fiber-reinforced silica aerogel composites using randomly dispersed glass fibers into silica aerogel powders. By adding the numberof glass fibers, the
∗
Corresponding author. E-mail address: [email protected] (S.P. Patil).
https://doi.org/10.1016/j.scriptamat.2019.10.010 1359-6462/© 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
© 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
strength of the composites was enhanced. However, thermal insulation property was declined. Liao et al. [14] prepared the laminated nanocomposites, wherein flexible silica aerogels were differently arranged with four glass fiber layers. The laminated designed structures can be tailored in order to achieve improved the mechanical properties of the nanocomposites. Wu et al. [15] investigated a proper technique to develop aligned fiber-reinforced aerogel composites for low thermal conductivity and significantly enhanced compressive and bending strengths compared to native aerogels. Li et al. [16] synthesized the glass fiber film/silica aerogel composites and investigated the thermal, mechanical and flammability properties of these composites with variation in H2 O: tetraethyl orthosilicate (TEOS) molar ratio. As the ratio increased from two to six, the composites showed significantly enhanced mechanical properties compared to the native silica aerogels, which was without imperiling their thermal properties. Zhou et al. [17] synthesized glass fiber-reinforced silica aerogel composites using methltrimethoxysilane (MTMS) and water glass co-precursor and performed different mechanical tests. As the molar ratio of MTMS/water glass increased, the mechanical strength and flexibility were significantly improved compared to pure aerogel. Maleki et al. [18] presented a detailed discussion on how to increase the strength and stiffness of silica aerogel using different reinforcement materials. In the last decade, many researchers have been working on the computational modeling of aerogels with especial attention to molecular dynamics (MD) simulations to investigate the mechanical and thermal properties [3,4,11,19–26]. In particular, the mechanical properties under large deformation [24], fracture mechanical properties [11], nanoindentation tests on pure [25] and
66
S.P. Patil, P. Shendye and B. Markert / Scripta Materialia 177 (2020) 65–68
Fig. 1. Schematic representation of silica aerogel nanocomposites. (A) The GLF-SiO2 -L180 model with 25% weight of glass fibers. (B) The 32% weight of glass fiber models of three types of l/d ratios. To observe the random dispersion of glass fibers, silica aerogel matrix is represented in light gray.
on graphene-reinforced nanocomposites [27] of silica aerogel were previously investigated. Despite such vast literature on all-atom modeling of aerogels, the mechanical behavior and properties of glass fiber-reinforced silica composites have so far not been investigated. Due to the addition of glass fibers, the mechanical properties can be significantly improved. In the present work, silica aerogel nanocomposites were modeled by adding randomly dispersed glass fibers. The influence of weight percentage, as well as length to diameter ratio of dispersed glass fibers on the mechanical properties, were investigated. To the best of our knowledge, notably, glass fiberreinforced silica composites have never been investigated before in an all-atom study. This work utilized LAMMPS [28] (Large Scale Atomic/Molecular Massively Parallel Simulator) for carrying out MD simulations and OVITO [29] for visualizing the atomistic simulation data. The all-atom models of silica aerogel were created based on Vashishta interatomic potential [30,31]. Periodic boundary conditions were applied in three mutually perpendicular directions. Velocity Verlet integration algorithm was used with a constant step size of 0.5 fs. The atoms were initially supplied with a random velocity and assigned a temperature of 70 0 0 K. Later, the NVT (constant volume and constant temperature) ensemble was used to quench the sample to 300 K at 5 K/ps, which was followed by an energy minimization step. Finally, amorphous silica was generated when the sample was allowed to relax to atmospheric conditions (300 K and 1 bar). The obtained amorphous silica was instantaneously expanded to desired density ρ = 406 kg m−3 . Subsequently, the sample was heated to 30 0 0 K for 50 ps and relaxed again. Finally, the sample was quenched to 0 K and brought back to atmospheric conditions, which has resulted in the formation of silica aerogel. For a more detailed discussion on the construction of silica aerogel, the reader is referred to Patil et al. [24]. In this work, relatively high-density of silica matrix was studied because the low-density models are of high-dimensions as well as they exhibit high-variation in the complex structures for the same density. Therefore, the high-density models were considered for computing a wide range of MD simulations of weight percentages as well as length to diameter ratios on the available computational resources.
For modeling of fibers, the cylindrical shape of crystalline silica was modeled with fully coordinated silica rings at the edges. Due to such silica rings, unnecessary structural, chemical and electronic changes can be avoided [32]. The amorphous silica fibers were obtained by using the above-described heating treatment, i. e., heating to 70 0 0 K and cooling to 300 K at 5 K/ps. The interactions in glass fiber were defined by Vashishta et al. [30,31]. To prepare reinforced nanocomposites of silica aerogel, randomized coordinates were generated for every glass fiber, ensuring no intersections between them. Similarly, the empty spaces were created in the aerogel models at the respective places with 2 A˚ of extra tolerance all-around the dimensions of glass fiber. Once the combined models were constructed, we performed two cycles of annealing treatment accompanied by energy minimization to obtain the best conformations of energies of glass fiber silica aerogel nanocomposites. To define the interactions between glass fiber and silica aerogel matrix, Vashishta interatomic potential [30,31] was used. In this work, three types of length to diameter ratio (l/d), i. e., l/d = 3, 6 and 9, as well as various weight percentages of reinforced glass fibers in silica aerogel matrix were investigated (see ˚ and the Fig. 1). Here, the diameter of glass fiber was fixed to 30 A, ˚ length was varied from 90 to 270 A. Finally, the tension and compression simulations were performed on pure silica aerogel (Native-SiO2 ), glass fiber of l/d = 3 reinforced silica aerogel (GLF-SiO2 -L90), glass fiber of l/d = 6 reinforced silica aerogel (GLF-SiO2 -L180) and glass fiber of l/d = 9 reinforced silica aerogel (GLF-SiO2 -L270) with a time step size of 0.5 fs and using NVE (constant volume constant internal energy) ensemble. All the tests were carried out using a constant strain rate of 0.004 ps−1 [24]. Due to the highly complex structure of silica aerogel matrix as well as the randomness of glass fibers, six different MD simulations were independently performed for every analysis. In this work, the average resultant properties are presented, and the variation was determined based on the standard error deviation. In the present work, the mechanical behavior and properties of the pure silica and glass fiber-reinforced silica aerogel were investigated. Fig. 2A shows a comparison of the tensile stress– strain curves. The tensile strength of the pure silica aerogel was
S.P. Patil, P. Shendye and B. Markert / Scripta Materialia 177 (2020) 65–68
67
Fig. 3. Comparative analysis of variation in elastic moduli with standard error bars of native silica aerogel and the nanocomposites for the considered l/d ratios and varying amount composition of glass fiber reinforcement. Elastic modulus of pure silica aerogel is at ρ = 406 kg m−3 , which is a common point for all the linear fits (dotted lines).
Fig. 2. (A) Comparison of tensile stress–strain curves of pure silica aerogel and nanocomposites of the GLF-SiO2 -L180 model. (B) Snapshots of the GLF-SiO2 -L180 model with weight of 25.82% of glass fiber at different strains during the tensile test. To understand the deformation and displacement of glass fibers, silica aerogel matrix is represented in light gray.
0.2 GPa. For the GLF-SiO2 -L180 models, as the weight percentages of glass fibers increased from 8.02 to 51.61%, the tensile strength was greatly improved from 0.25 to 0.442 GPa, respectively. However, the ultimate tensile strain was decreased from 0.25 to 0.19 for increasing the weight percentages of glass fibers. Similarly, for the GLF-SiO2 -L90 and GLF-SiO2 -L270 models, the tensile strength was increased, and the ultimate strain was decreased with increasing the number of glass fibers. One can note that as the l/d ratio increases, the trend of increase in the tensile strength was significantly improved. A detailed description of the tensile strength and ultimate strain versus weight percentages of glass fibers is presented in the Supplementary material. As the tensile load increases on the nanocomposite models, the randomly dispersed glass fibers were started to align in the direction of the loading (the snapshots at strain 0.10 and 0.24 in Fig. 2B). The resistance against deformation was mainly coming from the bending and axial pulling of glass fibers in the silica aerogel matrix. After the highest resistance to the deformation, the empty spaces (pores) in the models were joined together to find the minimum energy path, and one can observe this at a strain of 0.60 in Fig. 2B.
In case of the short length reinforcement (GLF-SiO2 -L90), there was a considerable amount of deformation resistance during the tensile loading was observed for the bending and axial pulling of glass fibers in the silica aerogel matrix, which was higher compared to pure silica aerogel. On the other hand, for large length reinforcement (GLF-SiO2 -L270), higher resistance to deformation was offered due to large length. Therefore, remarkably improved tensile strength and elastic modulus were observed for large length reinforcement nanocomposites compared to short length reinforcement nanocomposites. The variation in the mechanical properties is qualitatively in good agreement with the literature [12,15–17]. In our previous work, nearly linear stress–strain response of silica aerogel was reported up to 0.04 of tensile strain. Therefore, in this work, the elasticity modulus E values were obtained from the linear regime ( t ≤ 0.04) of the stress–strain curves simply by E = σt /t . Fig. 3 depicts the comparison of the elastic moduli of pure silica aerogel and nanocomposites. The elasticity modulus increases with an increase in l/d ratio and weight percentage composition of glass fibers in a silica aerogel matrix (see the Supplementary Material). For a particular l/d ratio, the E grows linearly with respect to ρ of the nanocomposite. Linear fits are presented on the elastic modulus versus density plot in Fig. 3. To end this, the proposed equation is
E = C + mρ
(1)
where C is the constant, and m is the slope of the linear fit. C values are −1.28, −2.55 and −3.76 GPa, and m values are 0.0071, 0.0102 and 0.0132 GPa/(kg m−3 ) for the GLF-SiO2 -L90, GLF-SiO2 L180 and GLF-SiO2 -L270 models, respectively. This newly proposed relation provides insights into the influence of fibers on the elasticity modulus at the nanoscale. Such a relation can be used to design the new nanocomposite for a particular application. Fig. 4A shows the stress–strain curves of pure silica aerogel and nanocomposites of the GLF-SiO2 -L180 models under uniaxial compression. The amount of glass fiber reinforcement has a significant influence on the mechanical performance. It was observed that the compressive stresses at particular strain increase with the weight percentages of glass fiber, which was an expected result. As the amount of glass fibers increases, the density of nanocomposites also increases. In the pure silica model, due to a lot of empty places, less deformation resistance was observed. However, as the amount of glass fibers increases, highly dense fibers restricted the easy deformation, which resulted
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The all-atom study reveals the nanomechanics during the tensile and compression tests on glass fiber-reinforced silica aerogel. The outcome of the investigation provides the understanding to design the nanocomposite for a particular application, wherein the well defined mechanical properties needed. The extension of this work is to conduct the experiments and all-atom simulations of the low-density aerogels ( ≤ 200 kg m−3 ) with variation in weight percentage of glass fibers. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments Simulations were performed with computing resources granted by RWTH Aachen University under project jara0201. Supplementary material Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.scriptamat.2019.10. 010. References
Fig. 4. (A) Compression stress–strain curves of pure silica aerogel and nanocomposites of the GLF-SiO2 -L180 model. Inset: Comparison of σ c – c curves for strain between 0.1 and 0.4 in enlarged view. (B) Snapshots of the GLF-SiO2 -L180 model with weight of 37.83% of glass fiber at different strains during the compression test. To understand the compression behavior of glass fibers, silica aerogel matrix is represented in light gray.
into early densification and the very stiff σ c – c response were observed. Moreover, the glass fibers are randomly distributed and oriented in a silica aerogel matrix, which also caused higher bending and buckling resistance, and consequently resulted in higher overall stiffness. In summary, silica aerogel nanocomposites were modeled by adding randomly dispersed glass fibers. The influence of weight percentage, as well as length to diameter ratio of dispersed glass fibers on the mechanical properties, were investigated using MD simulations. In the tensile tests, as the weight percentages of glass fibers increases, the tensile strength, and elastic modulus were significantly improved. However, the ultimate tensile strain was decreased. Moreover, as the l/d of the fiber increases, the increasing trend of the mechanical properties was towering, this was the result of high-resistance to the bending and axial pulling of the glass fibers. Furthermore, the linear relationship was proposed between the elastic modulus and density of nanocomposites. In compression tests, compressive resistance increases with a weight percentage of the fibers, which was mainly due to bending and axial compression of the number of fibers.
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