# The Effect of Silica Particle Size on the Mechanical Enhancement of Polymer Nanocomposites

^{1}

^{2}

^{3}

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## Abstract

**:**

_{2}micro/nanocomposites based on poly-lactic acid (PLA) and an epoxy resin were prepared and experimentally studied. The silica particles were of varying sizes from the nano to micro scale at the same loading. The mechanical and thermomechanical performance, in terms of dynamic mechanical analysis, of the composites prepared was studied in combination with scanning electron microscopy (SEM). Finite element analysis (FEA) has been performed to analyze the Young’s modulus of the composites. A comparison with the results of a well-known analytical model, taking into account the filler’s size and the presence of interphase, was also performed. The general trend is that the reinforcement is higher for the nanosized particles, but it is important to conduct supplementary studies on the combined effect of the matrix type, the size of the nanoparticles, and the dispersion quality. A significant mechanical enhancement was obtained, particularly in the Resin/based nanocomposites.

## 1. Introduction

_{2}, glass, Al

_{2}O

_{3}, Mg(OH)

_{2}, and CaCO

_{3}particles, carbon nanotubes, and layered silicates [1,2,3,4,5,6,7,8,9,10]. The reinforcing mechanism of polymer particulate composites has been the subject of numerous works in terms of micromechanical models for the evaluation of the elastic constants of the composites with varying volume fraction [10,11,12,13,14]. Simple equations are proposed to analyze the effects of size and density on the number [15], surface area, stiffening efficiency, and specific surface area of nanoparticles in polymer nanocomposites. Moreover, the effect of the nanosize of the nanoparticles, the adhesion between the matrix and nanofiller, and the interphase properties are also examined by introducing a number of equations. Polymer/particulate nanocomposites have been prepared and studied for a variety of properties, focusing mainly on the filler content, while the particle size also varied [16]. Nanocomposites based on polymethyl-methacrylate (PMMA) at a 0.04 volume fraction have also been studied. The particle diameters were 15, 25, 60, 150, and 500 nm. The mechanical properties were studied, and a Young’s modulus increment was detected with decreasing particle size. A systematic study on nanocomposites based on silica nanoparticles [17,18] has revealed that by decreasing the particle size, the composite’s properties are enhanced. Critical analysis of the experimental results and theoretical models of the mechanical properties, such as modulus, strength, and fracture toughness of polymer/particulate micro/nanocomposites, is also available in the literature [19]. Parameters such as filler/matrix adhesion, the filler’s loading and size, modulus, strength, and toughness have been extensively studied. Extended experimental and numerical studies have been performed [20] to define the effect of particle size on the elastic properties (modulus, tensile strength, fracture toughness) of the particulate composites. The size of the nanoparticles varied from macro (0.5 mm) to nano (15 nm) scale. It was discovered that the Young’s modulus of the composite increases as particle size decreases at the nanoscale, and that particle sizes at the microscale have little impact on the composite’s Young’s modulus. It was also discovered that particle size substantially impacts the composite’s tensile strength. Already, at a 1 vol % content, the tensile strength increased with decreasing particle size. The opposite trend could be obtained for 3 vol %.

_{2}fillers with a particle size of 15 nm, 200 nm, 500 nm, 1 μm, 2 μm, and 5 μm were selected to explore the effect of the particle size of fillers on the microstructures and physical properties of the microporous PLLA materials.

_{2}particles with varying average diameters from the nano to micro scale at the same weight fraction. The effect of silica size of the nanoparticles on the mechanical enhancement, namely, Young’s modulus, and tensile strength was analyzed, while the effect of the polymeric matrix type utilized on the mechanical properties was also studied. To the authors’ best knowledge, no previous extended research on the polymeric matrices has been done with a large variation of the silica size of the nanoparticles. Therefore, the novelty of the present work lies in both the development of composite materials with lower ecological impact and appropriate for industrial applications as well as in presenting new evidence regarding the competitive mechanisms between particle size effect versus agglomerate formation. The size effect of the particle was counterbalanced by agglomerations, revealing that the micro/nanoparticles’ dispersion formation quality plays a decisive role on the composite’s performance. Consequently, it was shown that the particles’ size effect cannot be studied separately but in combination with other parameters, such as matrix type, adhesion quality, and agglomerate formation.

## 2. Materials and Methods

#### 2.1. Materials

_{2}) is used as filler in this study in one weight concentration, namely 4 wt%, equivalent to a volume fraction V

_{f}= 0.025. In the micro scale, the average diameter of silica particles were chosen to be 1.5, 1.0, and 0.5 μm. All fillers were provided by Alfa Aesar (Kandel, DE). Regarding the nanosized particles, different batches of silica powder with a diameter size ranging between 13–22, 15–35, 18–35, and 55–75 nm, according to manufacturer’s specifications, were used, all provided by Nanografi Nano Technology (Talinn, EST). The nanofillers of diameters of 18–35nm, in particular, were surface treated by a KH550 silane coupling agent.

^{TM}Biopolymer 2003D, produced by NatureWorks LLC (Minnetonka, MN, USA), and was kindly supplied by the Greek Company M. Procos S.A. The selected grade 2003D has a density of 1.24 g/cm

^{3}and a MFR index equal to 6 g/10 min, measured at 210 °C at a load of 2.16 kg, according to ASTM-D1238-65T. Before use, the material was formed in pellet and dried at 45 °C for a minimum of 2 h in a desiccating dryer. The composites based on the thermoplastic matrix PLA were produced by a melt mixing of the fillers with the PLA matrix material, performed with a Brabender mixer. The temperature was set at 160 °C, and the rotation speed of the screws was 40 rpm. Hereafter, the materials were compression molded at 150 °C, using a thermo-press and a special mold of 1.5 mm thickness.

#### 2.2. Tensile Testing

^{−4}s

^{−1}. A laser extensometer—type cross-scanner by Fiedler Optoelektronik GmbH was used for the deformation measurement. The experimental setup is presented in detail in Ref. [28].

#### 2.3. Scanning Electron Microscopy (SEM)

#### 2.4. Dynamic Mechanical Analysis (DMA)

## 3. Results

#### 3.1. SEM Results

#### 3.2. Tensile Results

_{y}values after Equation (1), are presented in Table 3. Higher B values are exhibited by PLA/13-22 and PLA/15-35 from the PLA series. On the other hand, the epoxy Resin-based composites demonstrate high B values, particularly the Res/15-35 and Res/18-35, as well as the Res/0.5 composite. Parameter B seems to be affected by a number of factors, such as the filler’s surface modification, matrix type, particle size, and dispersion quality, but not in a regular way.

#### 3.3. Dynamic Mechanical Analysis (DMA)

#### 3.4. Modeling of the Effective Modulus Tensor

#### 3.4.1. Finite Element Analysis (FEA)

_{2}and Resin/SiO

_{2}composites at the various particle sizes under investigation have been generated using Digimat-FE. The RVE generation included incorporated spherical with agglomeration and also spherical with agglomeration and interphase SiO

_{2}particles, and their elastic modulus was evaluated using the Digimat-FE solver. After generating the RVE, it was exported to a Digimat FE solver by defining material properties, definition of boundary conditions, etc. to evaluate the resulting RVE elastic modulus using the finite element method. The matrix was treated as an isotropic material with a Young’s modulus equal to 3000 MPa for PLA and 2150 MPa for the Epoxy Resin. The Poisson’s ratio was equal to 0.28 for both matrices. The SiO

_{2}particles were also treated as isotropic materials with a Young’s modulus equal to 70,000 MPa and a Poisson’s ratio equal to 0.26. When the existence of an interphase between matrix and silica particles is assumed, the interphase’s modulus was taken equal to 20,000 MPa. In conventional composites, the RVE typically consists of a low number of reinforcing particles enclosed by matrix, and by applying appropriate boundary conditions to it, the effect of adjacent materials is covered. However, in the nanocomposites, due to the difference in the dimensions of the silica nanoparticles and matrix, the number of nanoparticles in the RVE is much more than one reinforcing part [42]. In our study, when the SiO

_{2}dimensions are in the nanoscale, a large number of nanoparticles should be included within the matrix for a correct RVE generation. The representative element is formed by entering the input parameters, including the geometric characteristics of the silica particles, the weight fraction of the nanotube, the elastic modulus of each phase, etc., in the Digimat-FE software. Representative volume elements (RVEs) of both procedures, without and with interphase, are illustrated in Figure 8, representatively, for 15–35 nm and 1.0 μm.

#### 3.4.2. Analytical Model

**C**is the matrix stiffness tensor,

^{0}**I**the identity tensor,

**Φ**the effective particle volume fraction,

^{Σ}**S**is the Eshelby tensor, and

**T**is a tensor given by:

^{Σ}**Φ**and

^{Ρ/Σ}**Φ**are the volume fraction of nanoparticle and interphase inside the effective inclusion. Tensor

^{Ι/Σ}**T**, which, according to the double-inclusion method of Hori and Nemat-Nasser [45], is expressed as:

^{I}**A**defined as:

^{I}**C**is the elastic stiffness tensors of the interphase.

^{I}**S**for an isotropic spherical particle in an isotropic matrix are given by:

**ν**is the Poisson’s ratio of the matrix.

_{0}**Φ**,

^{Σ}**Φ**, and

^{Ρ/Σ}**Φ**as follows:

^{Ι/Σ}**Φ**is the particle volume fraction,

^{Ρ}**e**is the interphase thickness, and

**r**is the nanoparticle radius.

_{p}_{0}= 0.23, whereas the particles’ Poisson’s ratio was taken equal to 0.23, while the modulus of silica nanoparticles was taken equal to 70 GPa. The interphase modulus

**E**was varied between the matrix and silica nanoparticles’ moduli and was taken to be equal to 20GPa, similar to that utilized in the FE analysis. The interphase thickness is an additional parameter in the analytical model. In this analysis, the experimental results of the Resin/based composites were utilized. Calculations at various values of interphase thickness were performed to approximate the experimental values of Young’s modulus. In Figure 10, the Young’s modulus model calculated values with varying silica particles’ size and varying interphase thicknesses, which are depicted together with the experimental data of the Resin/based composites. More specifically, model calculations were made for three different interphase thickness e values, namely 5, 10, and 20 nm. It is shown that in the micrometer scale, the Young’s modulus is not significantly affected, exhibiting the same value at the three different SiO

_{i}_{2}diameters. Therefore, and for the reason of clarity, only the results for a diameter of 500nm are presented. Within the frame of the analytical mode, when selecting the interphase thickness, the interphase volume fraction ${\mathsf{\Phi}}^{\mathrm{I}/\mathsf{\Sigma}}$ could be hereafter evaluated on account of Equation (7) for the best approximation with the experimental Young’s modulus data. In Table 5, the calculated values of the interphase volume fraction, estimated by the analytical model, are presented comparatively with the ones obtained by the FE analysis.

_{2}particles. This result can be attributed to the fact that the analytical model works better in the case of larger particles.

## 4. Conclusions

_{2}composites based on PLA and epoxy Resin were prepared and experimentally studied. The silica particles were of varying size—from the nano to μm scale at the same weight fraction. Regarding PLA/composites, the highest mechanical improvement was exhibited by the PLA reinforced with silica nanoparticles of an average diameter equal to 0.025 (PLA/15-35) and 0.0265 nm (PLA/18-35). A Young’s modulus improvement was also obtained for PLA reinforced with silica particles with an average diameter of 0.5 μm. This is in accordance with SEM images, where uniform agglomerates of a moderate size of the order of 500 nm have been noticed.

_{2}weight fraction. This mechanical improvement is also superior to that achieved in previous works. The specific epoxy resin appears to have better adhesion with the dispersed silica nanoparticles, whereas the mechanical improvement of the Resin/micro composites is very low at the same silica loading. In addition, an improvement of the yield stress was also obtained. These results are compatible with FE analysis, which premise an increased relative interphase volume fraction compared to that in the PLA/composites. In addition, the calculated interphase volume fraction for the microcomposites was quite low, which is in accordance with SEM observations, considering both the particles’ size and the interphase. In addition, a widely known analytical model was implemented, considering both the particles’ size and the interphase. Comparing the interphase volume fraction estimated by the two models, a lower deviation was obtained for the composites reinforced with silica particles at the micron scale.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Sinha Ray, S.; Okamoto, M. Polymer/layered silicate nanocomposites: A review from preparation to processing. Prog. Polym. Sci.
**2003**, 28, 1539–1641. [Google Scholar] [CrossRef] - Demjén, Z.; Pukánszky, B.; Nagy, J. Evaluation of interfacial interaction in polypropylene/surface treated CaCO3 composites. Compos. Part A Appl. Sci. Manuf.
**1998**, 29, 323–329. [Google Scholar] [CrossRef] - Leidner, J.; Woodhams, R.T. The strength of polymeric composites containing spherical fillers. J. Appl. Polym. Sci.
**1974**, 18, 1639–1654. [Google Scholar] [CrossRef] - Alexandre, M.; Dubois, P. Polymer-layered silicate nanocomposites: Preparation, properties and uses of a new class of materials. Mater. Sci. Eng. R Rep.
**2000**, 28, 1–63. [Google Scholar] [CrossRef] - Kim, M.H.; Park, C.I.; Choi, W.M.; Lee, J.W.; Lim, J.G.; Park, O.O.; Kim, J.M. Synthesis and Material Properties of Syndiotactic Polystyrene/Organophilic Clay Nanocomposites. J. Appl. Polym. Sci.
**2004**, 92, 2144–2150. [Google Scholar] [CrossRef] - Bikiaris, D.N.; Papageorgiou, G.Z.; Pavlidou, E.; Vouroutzis, N.; Palatzoglou, P.; Karayannidis, G.P. Preparation by melt mixing and characterization of isotactic polypropylene/SiO2 nanocomposites containing untreated and surface-treated nanoparticles. J. Appl. Polym. Sci.
**2006**, 100, 2684–2696. [Google Scholar] [CrossRef] - Alaei, M.H.; Mahajan, P.; Brieu, M.; Kondo, D.; Rizvi, S.J.A.; Kumar, S.; Bhatnagar, N. Effect of particle size on thermomechanical properties of particulate polymer composite. Iran. Polym. J. (Engl. Ed.)
**2013**, 22, 853–863. [Google Scholar] [CrossRef] - Georgiopoulos, P.; Kontou, E. Modeling of the elastic stiffness of biobased polymer nanocomposites. J. Reinf. Plast. Compos.
**2014**, 33, 942–952. [Google Scholar] [CrossRef] - Seon, H.A.; Seong, H.K.; Byoung, C.K.; Kwang, B.S.; Bong, G.C. Mechanical properties of silica nanoparticle reinforced poly(ethylene 2, 6-naphthalate). Macromol. Res.
**2004**, 12, 293–302. [Google Scholar] - Kontou, E.; Niaounakis, M. Thermo-mechanical properties of LLDPE/SiO2 nanocomposites. Polymer
**2006**, 47, 1267–1280. [Google Scholar] [CrossRef] - Benveniste, Y. A new approach to the application of Mori-Tanaka’s theory in composite materials. Mech. Mater.
**1987**, 6, 147–157. [Google Scholar] [CrossRef] - Dai, L.H.; Huang, Z.P.; Wang, R. Explicit expressions for bounds for the effective moduli of multi-phased composites by the generalized self-consistent method. Compos. Sci. Technol.
**1999**, 59, 1691–1699. [Google Scholar] [CrossRef] - Eshelbby, J.D. The determination of the elastic field of an ellipsoidal inclusion in an anisotronic medium. Proc. R. Soc. Lond.
**1957**, 241, 376–396. [Google Scholar] [CrossRef] - Mori, T.; Tanaka, K. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall.
**1973**, 21, 571–574. [Google Scholar] [CrossRef] - Ashraf, M.A.; Peng, W.; Zare, Y.; Rhee, K.Y. Effects of Size and Aggregation/Agglomeration of Nanoparticles on the Interfacial/Interphase Properties and Tensile Strength of Polymer Nanocomposites. Nanoscale Res. Lett.
**2018**, 13, 1–7. [Google Scholar] [CrossRef] - Blivi, A.S.; Benhui, F.; Bai, J.; Kondo, D.; Bédoui, F. Experimental evidence of size effect in nano-reinforced polymers: Case of silica reinforced PMMA. Polym. Test.
**2016**, 56, 337–343. [Google Scholar] [CrossRef] - Nielsen, L.E. Generalized equation for the elastic moduli of composite materials. J. Appl. Phys.
**1970**, 41, 4626–4627. [Google Scholar] [CrossRef] - Zamani Zakaria, A.; Shelesh-Nezhad, K. Quantifying the particle size and interphase percolation effects on the elastic performance of semi-crystalline nanocomposites. Comput. Mater. Sci.
**2016**, 117, 502–510. [Google Scholar] [CrossRef] - Fu, S.Y.; Feng, X.Q.; Lauke, B.; Mai, Y.W. Effects of particle size, particle/matrix interface adhesion and particle loading on mechanical properties of particulate-polymer composites. Compos. Part B Eng.
**2008**, 39, 933–961. [Google Scholar] [CrossRef] - Cho, J.; Joshi, M.S.; Sun, C.T. Effect of inclusion size on mechanical properties of polymeric composites with micro and nano particles. Compos. Sci. Technol.
**2006**, 66, 1941–1952. [Google Scholar] [CrossRef] - Pustak, A.; Leskovac, M.; Denac, M.; Švab, I.; Pohleven, J.; MakaroviÄ, M.; Musil, V.; Šmit, I. Interfacial and mechanical properties of polypropylene/silica nano- And microcomposites. J. Reinf. Plast. Compos.
**2014**, 33, 851–861. [Google Scholar] [CrossRef] - Siraj, S.; Al-Marzouqi, A.; Iqbal, M.; Ahmed, W. Impact of Micro Silica Filler Particle Size on Mechanical Properties of Polymeric Based Composite Material. Polymers
**2022**, 14, 4830. [Google Scholar] [CrossRef] - Dittanet, P.; Pearson, R.A. Effect of silica nanoparticle size on toughening mechanisms of filled epoxy. Polymer
**2012**, 53, 1890–1905. [Google Scholar] [CrossRef] - Chen, Y.; Han, L.; Dong, L. Effect of silica particle size on the microstructure and physical properties of microporous poly(L-lactic acid) produced by uniaxial stretching. Polym. Test.
**2019**, 79, 106051. [Google Scholar] [CrossRef] - Dekkers, M.E.J.; Heikens, D. The effect of interfacial adhesion on the tensile behavior of polystyrene–glass-bead composites. J. Appl. Polym. Sci.
**1983**, 28, 3809–3815. [Google Scholar] [CrossRef] [Green Version] - Spanoudakis, J.; Young, R.J. Crack propagation in a glass particle-filled epoxy resin—Part 1 Effect of particle volume fraction and size. J. Mater. Sci.
**1984**, 19, 473–486. [Google Scholar] [CrossRef] - Amdouni, N.; Sautereau, H.; Gerard, J.F. Epoxy composites based on glass beads. I. Viscoelastic properties. J. Appl. Polym. Sci.
**1992**, 45, 1799–1810. [Google Scholar] [CrossRef] - Charitos, I.; Mouzakis, D.; Kontou, E. Comparing the rheological and reinforcing effects of graphene oxide on glassy and semicrystalline polymers. Polym. Eng. Sci.
**2019**, 59, 1933–1947. [Google Scholar] [CrossRef] - Lau, K.; Gu, C.; Hui, D. A critical review on nanotube and nanotube/nanoclay related polymer composite materials. Compos. Part B Eng.
**2006**, 37, 425–436. [Google Scholar] [CrossRef] - Yang, J.; Sang, Y.; Chen, F.; Fei, Z.; Zhong, M. Synthesis of silica particles grafted with poly(ionic liquid) and their nucleation effect on microcellular foaming of polystyrene using supercritical carbon dioxide. J. Supercrit. Fluids
**2012**, 62, 197–203. [Google Scholar] [CrossRef] - Hsueh, C. -H Effects of Aspect Ratios of Ellipsoidal Inclusions on Elastic Stress Transfer of Ceramic Composites. J. Am. Ceram. Soc.
**1989**, 72, 344–347. [Google Scholar] [CrossRef] - Nakamura, Y.; Yamaguchi, M.; Okubo, M.; Matsumoto, T. Effects of particle size on mechanical and impact properties of epoxy resin filled with spherical silica. J. Appl. Polym. Sci.
**1992**, 45, 1281–1289. [Google Scholar] [CrossRef] - Kawaguchi, T.; Pearson, R.A. The effect of particle-matrix adhesion on the mechanical behavior of glass filled epoxies. Part 2. A study on fracture toughness. Polymer
**2003**, 44, 4239–4247. [Google Scholar] [CrossRef] - Le, T.T.; Le, M.V. Nanoscale Effect Investigation for Effective Bulk Modulus of Particulate Polymer Nanocomposites Using Micromechanical Framework. Adv. Mater. Sci. Eng.
**2021**, 2021, 1563845. [Google Scholar] [CrossRef] - Douce, J.; Boilot, J.P.; Biteau, J.; Scodellaro, L.; Jimenez, A. Effect of filler size and surface condition of nano-sized silica particles in polysiloxane coatings. Thin Solid Films
**2004**, 466, 114–122. [Google Scholar] [CrossRef] - Rodrigue, D.; Kavianiboroujeni, A.; Cloutier, A. Determination of the optimum coupling agent content for composites based on hemp and high density polyethylene. AIP Conf. Proc.
**2017**, 1914, 030003. [Google Scholar] [CrossRef] [Green Version] - Meng, Q.K.; Hetzer, M.; De Kee, D. PLA/clay/wood nanocomposites: Nanoclay effects on mechanical and thermal properties. J. Compos. Mater.
**2011**, 45, 1145–1158. [Google Scholar] [CrossRef] - Tsai, P.A.; Chiu, W.M.; Lin, C.E.; Wu, J.H. Fabrication and Characterization of PLA/SiO2/Al2O3 Composites Prepared by Sol-Gel Process. Polym. Plast. Technol. Eng.
**2013**, 52, 1488–1495. [Google Scholar] [CrossRef] - Piekarska, K.; Sowinski, P.; Piorkowska, E.; Haque, M.M.U.; Pracella, M. Structure and properties of hybrid PLA nanocomposites with inorganic nanofillers and cellulose fibers. Compos. Part A Appl. Sci. Manuf.
**2016**, 82, 34–41. [Google Scholar] [CrossRef] - Charitos, I.; Georgousis, G.; Klonos, P.A.; Kyritsis, A.; Mouzakis, D.; Raptis, Y.; Kontos, A.; Kontou, E. The synergistic effect on the thermomechanical and electrical properties of carbonaceous hybrid polymer nanocomposites. Polym. Test.
**2021**, 95, 107102. [Google Scholar] [CrossRef] - Turcsányi, B.; Pukánszky, B.; Tüdõs, F. Composition dependence of tensile yield stress in filled polymers. J. Mater. Sci. Lett.
**1988**, 7, 160–162. [Google Scholar] [CrossRef] - Maghsoudlou, M.A.; Barbaz Isfahani, R.; Saber-Samandari, S.; Sadighi, M. Effect of interphase, curvature and agglomeration of SWCNTs on mechanical properties of polymer-based nanocomposites: Experimental and numerical investigations. Compos. Part B Eng.
**2019**, 175, 107119. [Google Scholar] [CrossRef] - Boutaleb, S.; Zaïri, F.; Mesbah, A.; Naït-Abdelaziz, M.; Gloaguen, J.M.; Boukharouba, T.; Lefebvre, J.M. Micromechanics-based modelling of stiffness and yield stress for silica/polymer nanocomposites. Int. J. Solids Struct.
**2009**, 46, 1716–1726. [Google Scholar] [CrossRef] - Ju, J.W.; Chen, T.M. Micromechanics and effective moduli of elastic composites containing randomly dispersed ellipsoidal inhomogeneities. Acta Mech.
**1994**, 103, 103–121. [Google Scholar] [CrossRef] - Hori, M.; Nemat-Nasser, S. Double-inclusion model and overall moduli of multi-phase composites. Mech. Mater.
**1993**, 14, 189–206. [Google Scholar] [CrossRef] - Odegard, G.M.; Clancy, T.C.; Gates, T.S. Modeling of the Mechanical Properties of Nanoparticle/Polymer Composites; Jenny Stanford Publishing: Dubai, United Arab Emerites, 2017; pp. 319–342. [Google Scholar]
- Brune, D.A.; Biccerano, J. Micromechanics of nanocomposites: Comparison of tensile and compressive elastic moduli, and prediction of effects of incomplete exfoliation and imperfect alignment on modulus. Polymer
**2002**, 43, 369–387. [Google Scholar] [CrossRef]

**Figure 2.**SEM micrographs of PLA/SiO

_{2}nano-composites, (

**a**) PLA/13-22, (

**b**) PLA/15-35, (

**c**) PLA/18-35, (

**d**) PLA 55-75.

**Figure 3.**SEM micrographs of Resin/SiO

_{2}micro-composites, (

**a**) Resin/0.5, (

**b**) Resin/1.0, (

**c**) Resin/1.5.

**Figure 4.**SEM micrographs of Resin/SiO

_{2}nano-composites, (

**a**) Resin/13-22, (

**b**) Resin/15-35, (

**c**) Resin/18-35, (

**d**) Resin 55-75.

**Figure 5.**Tensile stress-strain curves of (

**a**) PLA/silica nanocomposites, (

**b**) PLA/silica micro-composites.

**Figure 6.**Tensile stress-strain curves of (

**a**) Resin/silica nanocomposites, (

**b**) Resin/silica micro-composite.

**Figure 7.**Master curves of storage modulus of the composites examined. (

**a**,

**b**) PLA/based silica composites, (

**c**,

**d**) Resin/based silica composites.

**Figure 8.**Representative RVEs of the composites examined: (

**a**) PLA/1.0 (

**b**) PLA/1.0/interphase (

**c**) PLA/15-35 (

**d**) PLA/15-35/interphase.

**Figure 9.**Young’s modulus by FE analysis with varying relative interphase volume fraction for all SiO

_{2}composites examined. Lines: Finite Element simulation; Points: Experimental data (

**a**) PLA/SiO

_{2}with particle’s diameter at the micro-scale, (

**b**) PLA/SiO

_{2}with particle’s diameter at the nano-scale, (

**c**) Resin/SiO

_{2}with particle’s diameter at the micro-scale, (

**d**) Resin/SiO

_{2}with particle’s diameter at the nano-scale.

**Figure 10.**Young’s modulus with varying particle radius, at various values of the interphase thickness. Points: Experimental results, Lines: Analytical model.

Specimen’s Designations | Matrix Type | SiO_{2}Fillerwt%/Vf | SiO_{2}Filler Diameter∅ [nm] |
---|---|---|---|

PLA | poly-lactic acid (PLA) | 0/0 | - |

PLA/13-22 | -//- | 4/0.025 | 13–22 |

PLA/15-35 | -//- | -//- | 15–35 |

PLA/18-35 * | -//- | -//- | 18–35 |

PLA/55-75 | -//- | -//- | 55–75 |

PLA/0.5 | -//- | -//- | 500 |

PLA/1.0 | -//- | -//- | 1000 |

PLA/1.5 | -//- | -//- | 1500 |

Resin ES-35 | bisphenol A—Epoxy- DGEBA | 0/0 | - |

Res/13-22 | -//- | 4/0.025 | 13–22 |

Res/15-35 | -//- | -//- | 15–35 |

Res/18-35 * | -//- | -//- | 18–35 |

Res/55-75 | -//- | -//- | 55–75 |

Res/0.5 | -//- | -//- | 500 |

Res/1.0 | -//- | -//- | 1000 |

Res/1.5 | -//- | -//- | 1500 |

Material/ Specimens | Young’s Modulus (MPa) | Modulus Increment% | Yield Stress (MPa) | Yield Strain | Tensile Strength (MPa) | Failure Strain |
---|---|---|---|---|---|---|

PLA | 3000 ± 120 | - | 48.6 ± 3.5 | 0.02 | 36.9 | 0.056 |

PLA/13-22 | 3200 ± 140 | 7 | 47.8 ± 3.1 | 0.019 | 43.3 | 0.02 |

PLA/15-35 | 3600 ± 144 | 20 | 48.9 ± 3.0 | 0.018 | 48.6 | 0.02 |

PLA/18-35 | 3800 ± 185 | 27 | 43.0 ± 2.8 | 0.016 | 43.0 | 0.016 |

PLA/55-75 | 3202 ± 135 | - | 37.8 ± 2.8 | 0.015 | 31.0 | 0.04 |

PLA/0.5 | 3455 ± 131 | 15 | 45.8 ± 2.8 | 0.017 | 41.3 | 0.047 |

PLA/1.0 | 3250 ± 130 | 8 | 39.2 ± 2.4 | 0.018 | 32.0 | 0.025 |

PLA/1.5 | 3120 ± 123 | 4 | 41.0 ± 2.3 | 0.019 | - | 0.018 |

Resin ES-35 | 2150 ± 107 | - | 38.5 ± 3.2 | 0.03 | 20.0 | 0.17 |

Res/13-22 | 2800 ± 133 | 30 | 40 ± 3.3 | 0.024 | 22.5 | 0.07 |

Res/15-35 | 2600 ± 117 | 21 | 43 ± 2.1 | 0.028 | 20.0 | 0.09 |

Res/18-35 | 2900 ± 122 | 34.8 | 43 ± 3.0 | 0.028 | 25.0 | 0.08 |

Res/55-75 | 3450 ± 149 | 60 | 40 ± 2.1 | 0.027 | 26.0 | 0.13 |

Res/0.5 | 2470 ± 104 | 15 | 42.2 ± 2.8 | 0.028 | 20.0 | 0.085 |

Res/1.0 | 2380 ± 100 | 11 | 38 ± 4.0 | 0.028 | 23.6 | 0.08 |

Res/1.5 | 2500 ± 108 | 16 | 41.5 ± 2.5 | 0.026 | 25.0 | 0.07 |

Material | Interaction Parameter |
---|---|

PLA | - |

PLA/13-22 | 2.77 |

PLA/15-35 | 3.68 |

PLA/18-35 | - |

PLA/55-75 | - |

PLA/0.5 | 1.06 |

PLA/1.0 | - |

PLA/1.5 | - |

Resin | - |

Res/13-22 | 4.96 |

Res/15-35 | 7.86 |

Res/18-35 | 7.86 |

Res/55-75 | 4.96 |

Res/0.5 | 7.10 |

Res/1.0 | 2.91 |

Res/1.5 | 6.44 |

Material | Average Particle Diameter | Young’s Modulus Experim. | Young’s Modulus FEA | FEA Results Deviation from Experim. | Young’s Modulus FEA/Interphase | FEA/Interphase Results Deviation from Experim. |
---|---|---|---|---|---|---|

(nm) | (MPa) | (MPa) | (%) | (MPa) | (%) | |

PLA | - | 3000 | - | - | - | - |

PLA/13-22 | 17.5 | 3200 | 3128 | 2.25 | 3284 | 2.62 |

PLA/15-35 | 25.0 | 3600 | 3131 | 13.0 | 3585 | 0.41 |

PLA/18-35 | 26.5 | 3800 | 3197 | 15.8 | 3840 | 1.0 |

PLA/55-75 | 65.0 | 3202 | 3162 | 1.25 | 3226 | 0.75 |

PLA/0.5 | 500 | 3455 | 3205 | 7.23 | 3425 | 0.10 |

PLA/1.0 | 1000 | 3250 | 3177 | 2.25 | 3219 | 0.95 |

PLA/1.5 | 1500 | 3120 | 3161 | 1.31 | 3180 | 1.90 |

Resin ES-35 | - | 2150 | - | - | - | - |

Res/13-22 | 17.5 | 2800 | 2321 | 17.1 | 2819 | 0.67 |

Res/15-35 | 25.0 | 2600 | 2300 | 11.5 | 2690 | 3.46 |

Res/18-35 | 26.5 | 2900 | 2297 | 20.8 | 2982 | 2.82 |

Res/55-75 | 65.0 | 3450 | 2278 | 33.9 | 3400 | 1.45 |

Res/0.5 | 500 | 2470 | 2273 | 7.97 | 2446 | 0.97 |

Res/1.0 | 1000 | 2380 | 2280 | 4.2 | 2388 | 0.33 |

Res/1.5 | 1500 | 2500 | 2275 | 9.0 | 2496 | 0.16 |

Material | Interphase Volume Fraction (FEA) | Interphase Volume Fraction (analytical Model) |
---|---|---|

Resin | - | - |

Res/13-22 | 0.10 | 0.74 |

Res/15-35 | 0.08 | 0.63 |

Res/18-35 | 0.14 | 0.81 |

Res/55-75 | 0.23 | 0.88 |

Res/0.5 | 0.03 | 0.018 |

Res/1.0 | 0.025 | 0.017 |

Res/1.5 | 0.05 | 0.01 |

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## Share and Cite

**MDPI and ACS Style**

Kontou, E.; Christopoulos, A.; Koralli, P.; Mouzakis, D.E.
The Effect of Silica Particle Size on the Mechanical Enhancement of Polymer Nanocomposites. *Nanomaterials* **2023**, *13*, 1095.
https://doi.org/10.3390/nano13061095

**AMA Style**

Kontou E, Christopoulos A, Koralli P, Mouzakis DE.
The Effect of Silica Particle Size on the Mechanical Enhancement of Polymer Nanocomposites. *Nanomaterials*. 2023; 13(6):1095.
https://doi.org/10.3390/nano13061095

**Chicago/Turabian Style**

Kontou, Evagelia, Angelos Christopoulos, Panagiota Koralli, and Dionysios E. Mouzakis.
2023. "The Effect of Silica Particle Size on the Mechanical Enhancement of Polymer Nanocomposites" *Nanomaterials* 13, no. 6: 1095.
https://doi.org/10.3390/nano13061095