MWCNTs polymer nanocomposite with enhanced thermomechanical properties and electrical insulation for effective encapsulation

This study presents the effect of the variation in weight fraction of multiwall carbon nanotubes (MWCNTs) in polymer with the objective of enhancing the thermo-mechanical properties along with the electrical insulating properties. Polymer multi-walled nanocomposites (PMWCNC) and MWCNTs/Al2O3 bi-layer nanocomposites were prepared by solution mixing method with ultrasonication and magnetic stirring, then molded in vertical sandwich molds, made of acrylic and aluminum sheet as per ASTM standards. The tensile strength of PMWCNC was enhanced by 32%, 23%, 15%, and 5% compared to unmodified epoxy with the incorporation of 1 wt%, 0.75 wt%, 0.5 wt%, and 0.25 wt% of MWCNTs. The dispersion morphology of MWCNTs in epoxy was observed with field emission-scanning electron microscope (FE-SEM). The thermogravimetric analyzer (TGA) investigation found that increasing the weight percentage of MWCNTs resulted in improved thermal stability. The enhanced electrical conductivity of PMWCNC caused by the addition of MWCNTs was countered through the deposition of a thin film layer of alumina-filled polymer nanocomposite on the top surface of PMWCNC to retain the electrical insulation properties. The representative volume element (RVE) technique was employed to predict the effective modulus of nanocomposite based on the various constituent properties, weight fractions and interfacial behavior between MWCNTs and epoxy with the help of finite element analysis. Additionally, Modified Mori-Tanaka (MMT) micromechanics scheme was used to find the effective elastic modulus of the nanocomposite with the help of the MATLAB code. The elastoplastic behavior of polymer nanocomposites was also simulated in ANSYS APDL through the Voce model. The enhanced thermomechanical properties while retaining the electrical insulation properties suggest that the MWCNTs-based polymer would make the electronic chip more reliable.


Introduction
Plastic encapsulation is used to protect electronic chips from both external and internal environmental contamination, as well as thermal and mechanical overstress [1,2]. The majority of microelectronic industries use plastic packaging because it is lightweight, has better flame retardant properties, and is inexpensive [3][4][5][6]. Internally induced heat generation in an electronics chip is critical because it incorporates high temperatures that degrade physical performance, reliability, and lifetime. Due to the low thermal conductivity of polymers, it is difficult to effectively dissipate the heat generated by active devices [7][8][9][10][11]. To improve the thermo-mechanical reliability of microelectronic devices, modified polymers with conductive nano-fillers such as alumina, boron nitride (BN), silica, and diamond [12][13][14][15] have been studied. Graphene and MWCNTs can be envisioned as future encapsulant nanofiller due to their favorable properties like thermal conductivity of 3000-6000 W m −1 -K −1 and elastic modulus ∼1 TPa [16,17]. It has a two-dimensional sp 2 hybridized carbon atom with a large surface area and high aspect ratio in combination with a low density. When a small amount of graphene is mixed with epoxy, its thermo-mechanical properties are greatly influenced, but its functionality is hampered by its high electrical conductivity (107 S cm −1 ) [18][19][20][21]. It is difficult to achieve a homogeneous dispersion of MWCNTs in the polymer matrix due to the clustering form of MWCNTs. Agglomeration of MWCNTs is severe due to strong van der Waals forces between the MWCNTs fillers that cause cracks, pores, and pinholes in the composite [22,23]. To achieve uniform dispersion of nanoparticle reinforcement into the matrix, many techniques have been developed like solution compounding, melt blending, shear mixing, in situ polymerization, etc [24,25]. D An et al [26] D An et al [26] fabricated the boron nitride/reduced graphene oxide/nature rubber composites (BN/rGO/NR) with a loading of 4.9% volume fraction to improve the thermomechanical properties. The inplane thermal conductivity of polymer composites was 1.28 --Wm K , 1 1 which was 7.1 times higher than the NR. The polymer composite exhibited excellent tensile strength and good electrical insulation. According to J Zhou et al [27], a hybrid nanocomposite of PVA filled with boron nitride nanosheet and multiwalled carbon nanotubes achieved 11.49 --Wm K 1 1 at 20% weight fraction compared to.819 --Wm K 1 1 for pure PVA and had good electrical insulation properties. Z Sun et al [28] developed an electronic packaging material with graphenefilled polydopamine (PDA) and reported a 400% increase in thermal conductivity at 5 wt% of graphene in comparison to pure PDA. L R Viannie et al [29] prepare the MWCNT-polydimethylsiloxane composite using a solution mixing process with a weight fraction varying from 2% to 10% and found that the tensile strength reduces drastically as the weight fraction increases, which may cause the higher filler density. However, K Markad and A Lal [30] prepared MWCNT/epoxy hybrid nanocomposites by solution mixing method and observed an enhancement in tensile strength of 18%, 39%, and 26% with the incorporation of 0.4%, 0.6%, and 0.8% MWCNT nanocomposites as compared to pure unmodified epoxy. A A Allahdadian and M Mashayekhi [31] proposed a multiscale approach to predict the tensile strength and modulus of carbon nanotube-reinforced glass-epoxy composites and noticed that the improvement in tensile strength and modulus was 53% and 25%, respectively, at 0.5 wt% of CNT in comparison to a pure sample. Moisture impregnates the organic substrate due to a pinhole in the encapsulation material and causes oxidation on the cathode. To prevent moisture permeation, an atomic layer was deposited using the atomic layer deposition technique [32][33][34][35]. Nanocomposites with one weight percent MWCNTs/polypropylene composite showed the greatest improvement in tensile and flexural properties, while those with 1.5 weight percent MWCNTs/polypropylene composite showed the least improvement. Due to agglomeration, a higher proportion of MWCNTs in the composite could lead to the material losing its tensile and flexural strength [36,37]. Hiremnath and Shukla [38] reported the declination in glass transition temperature (Tg) of polymer nanocomposite with the addition of alumina nanorod in comparison with that of neat at one weight percent. Contreras et al [39] discovered that Tg increased as the weight percentage of silver/carbon nanoparticles in PMMA increased when compared to neat PMMA. As per Jarosinski et al [40], adding a 4 wt% graphene sheet to epoxy resin occurred in a 132% increase in thermal conductivity as well as a substantial improvement in electrical conductivity. Furthermore, for graphenebased polymer nanocomposites, experimental setup and characterization are costly and time-consuming processes. According to Gresil et al [41]Analytical and numerical approaches have attracted a lot of attention in the last few decades to investigate the effective properties of polymer nanocomposites. The Self-Consistent and Mori-Tanaka method micromechanics approach has been widely used for analytical models for predicting the effective properties of nanocomposite materials.
In this work, The MWCNTs/epoxy and bilayer MWCNTs-Al 2 O 3 /epoxy nanocomposites were prepared using a solution mixing technique including ultrasonication and magnetic stirring. The dispersion of filler in epoxy was revealed through morphological examinations of PMWCNC and bilayer MWCNTs-Al 2 O 3 /epoxy nanocomposites. In the experimental section, tensile behavior, thermal stability, and electrical conductivity of composites with varying weight fractions of MWCNTs were studied. The numerical and analytical section of this paper deals with the following parameters: (i) epoxy behaves as linearly isotropic and nonlinear elastoplastic; (ii) MWCNTs behave linearly isotropic and transversely isotropic; (iii) varying MWCNTs weight fractions in epoxy (iv) varying aspect ratios of MWCNTs; and (v) interfacial behavior between MWCNTs and epoxy. To the best of our knowledge, this is the first study that combines the enhanced thermomechanical properties and high electrical insulation of PWCNC with a thin film layer of Al 2 O 3 epoxy composite. The improved thermomechanical results raise the possibility of using MWCNTs-based encapsulation of flip chip in the near future. The schematic strategy of encapsulation of wire bounded bare die PGBA flip chip has been depicted in figure 1.

Materials
The Huntsman Group provided Araldite CY-230 liquid epoxy resin and hardener (LY951). MWCNTs with an average diameter of 65 nm and an aspect ratio of more than 100 were bought from Sigma Aldrich. Alumina nanoparticles with an average diameter of 1 μm were also purchased from Sigma Aldrich.

Preparation of polymer nanocomposite
The sonication method was used to cast the nanocomposite sample. This is one of the most common solution mixing techniques for the casting of polymer nanocomposite [42][43][44][45]. The flow diagram of the process is presented in the figure 2. In this technique, a mold cavity has been prepared in the aluminum plate with a 5 mm thickness through wire EDM, and two acrylic sheets of the same dimension have been prepared through CO 2  laser machining. A mold cavity has been created by making a sandwich structure by tightening the nut and bolt. In this study, pure acetone (99.99%) was used as a solvent. To prevent MWCNT agglomeration, the required MWCNT was poured into 100 ml of acetone and sonicated for half an hour. After sonication for half an hour, the required quantity of epoxy was added based on weight fraction. The solution was sonicated again for 4 h to disperse the MWCNT throughout the epoxy. After uniform dispersion of MWCNT in epoxy, the solution was heated to a temperature of 60°C to evaporate the acetone and simultaneously stirred magnetically at 2000 rpm so that the particles did not settle down in the solution. This process was continued until all the acetone had evaporated. It took approximately 10 to12 h and then the solution was degassed to remove the entrapped air from the solution. The hardener (Ardur@951) is poured into the solution at a 1:10 ratio. The hardener was mixed into the solution very gently through magnetic stirrer for around 10-15 min. Finally, after mixing with the hardener, the solution was poured into the mold cavity. After 12 h of the casting of PMWCNC, the thin film of alumina composite solution was added to the top surface. The preparation of the alumina-based composite was carried out using the same preparation technique.

Characterization
The morphology and size of MWCNTs and alumina, as well as their dispersion in the nano-composites, were examined using a 5 kV field emission-scanning electron microscope (FE-SEM, Gemini SEM 500). The Novocontrol Spectroscopy Alpha Analyzer was used to measure electrical conductivity at room temperature (25°C ) with a bias voltage of 1 V and a frequency variation of 0.01 Hz to 1 MHz. Three types of samples (Neat epoxy, PMWCNC at 1 wt% of MWCNTs, and alumina deposited PMWCNC) were prepared in a circular shape with a 30 mm diameter.
The thermal stability of PMWCNC was measured over a temperature range of 30°C-600°C using a thermogravimetric analyzer (TGA, NETZSCH Technologies) at a constant heating rate of 20°C min −1 and under a nitrogen atmosphere with a gas flow rate of 20 cm 3 min −1 . The tensile test was performed according to ASTM standard D 638-02a. The dog-bone specimen's type-I was prepared in the specified shape for the different weight fractions of MWCNTs (0%, .25%, .50%, .75%, and 1%). The samples gauge a length of 50 mm, a narrow section width of 13 mm, and a thickness of 6.5 mm, respectively. The overall dimensions were 165 mm in length and 19 mm in width. At least five tests of each weight fraction were performed, and the average method was used to report the result with a 95% confidence level in a universal testing machine (Zwick-Roell Z050, 50 kN) at a crosshead speed of 5 mm min −1 .

Analytical and FEM simulation
The effective elastic and elastoplastic behavior of composites at various parameters was investigated using FEM and analytical methods. A total five different cases have been considered for the modeling of PMWCNC. In case 1, it is assumed perfect interfacing between polymer and MWCNTs without considering any thickness of the interphase layer, while in case 2, we have considered the thickness of the interphase layer between polymer and MWCNT for perfect interfacing. The elastic modulus of the interphase layer was investigated by using an averaging method of the Theocaris model [46]. In case 3, the elastic modulus of the PMWCNC was investigated utilizing the MT-scheme with aspect ratios ranging from 3 to 500. In case 4, the Voce model [47]was used for elastoplastic behavior through FEM analysis. Case 5 discusses the combined elastic modulus of the aluminafilled polymer that was deposited on a PMWCNC. The following five cases are discussed below in detail.
Case 1. Polymer and MWCNTs behave linearly elastic and isotropic and without interphase thickness between constituents.
In this, MWCNTs and polymer both are assumed to behave linearly elastic and isotropic. Properties of constituents were taken from table 1 for analytical and FEM analysis. The aspect ratio (L/D = 100) was kept constant while the fiber orientation was kept random throughout the simulation. In this case, the interface between MWCNTs and polymer was assumed perfect and neglected the interphase layer thickness between polymer and MWCNTs. Five different weight fractions ranging from 0 to 1% of MWCNTs are considered for the analysis.
Case 2. Polymer and MWCNTs are linearly elastic and isotropic with interphase thickness between constituents. In this case, the thickness of the interphase layer between MWCNTs and polymer has been considered for evaluation and all conditions were kept similar to case 1. The effective elastic modulus was also evaluated for axially aligned fiber through an analytical study. The average interphase elastic modulus was determined using the Theocaris model. Equation (2) was used to plot a graph of the interphase modulus versus interphase radius (r), and we chose adhesion exponent (n) = 6 for the evaluation of the average interphase modulus as shown in figure 3. The thickness of the interphase was considered 65 nm for the study that is equal to the average diameter of MWCNTs. Equation (1) was utilized to approximate the average interphase elastic modulus of the material. To obtain a more precise average interphase elastic modulus, the interphase layer was divided into three sublayers, with layer 1 located close to the MWCNTs and layer 3 located close to the matrix, as can be seen in the inset of figure 3. The average interphase properties of sublayers are presented in table 2.
Where E i is the young's modulus of interphase and ( ) E i r is the young's modulus of interphase that varies along the radius r. The symbols r i and r f represent the interphase and fiber radii, respectively.   In this case, the aspect ratio (L/D) ranged from 3 to 500, and other parameters were chosen in the same manner as in case 2. The Mori-Tanaka micromechanics was utilized to evaluate the effective elastic modulus at four different (0.25 wt%, 0.50 wt%, 0.75 wt%, and 1 wt%) weight fractions with varying aspect ratios.
Case 4. Polymer behaves as nonlinear elastoplastic and MWCNTs behave linearly elastic and transversely isotropic.
In this case, MWCNTs were modeled as linearly elastic and transversely isotropic, whereas the polymer was modeled as nonlinear elastoplastic. For the analytical and FE analyses, MWCNTs properties were taken from table 3, and polymer properties were collected from table 4. The interphase interaction between MWNCTs and the polymer was considered. The interphase layer thickness and characteristics were kept the same as in case 2. The aspect ratio was kept constant (L/D = 100) and the fiber orientation was random. The Voce model nonlinear isotropic hardening (equation (4)) was utilized to account for the behavior of nonlinear elastoplastic polymers. The von Mises yield criterion is combined with an associative flow rule to create the Voce hardening law for nonlinear isotropic hardening behavior. Von Mises equivalent stress (σ e ) can be defined in the term of deviatoric stress tensors (S and S ij ij ) as [48].
Voce model for nonlinear isotropic hardening: current yield stress (R) can be defined as [46] ( ) () Where s 0 is the initial yield stress of the material, R 0 is the initial value of isotropic hardening, ¥ R is the asymptotic value of isotropic hardening, and b is the material parameter. The plastic strain is denoted as e .
pl The nonlinear curve-fitting method was followed to find the material parameters. The true stress-equivalent plastic strain curve got through the tensile test of neat epoxy. The yield stress of neat epoxy has been observed at 21.72 MPa and other calculated material parameters have been reported in table 4. In this case, the alumina filled polymer nanocomposite thin film layer deposited on the PMWCNC was investigated. MWCNTs, alumina, and polymer were assumed linearly elastic. The constituent's properties have been taken from t for the numerical and FE analysis. The Interphase effect between MWNCT and polymer was taken into account. The Interphase effect was taken as negligible between alumina and polymer. The aspect ratio of MWCNTs was taken constant (L/D = 100) and the orientation of the fiber was taken randomly while alumina nanoparticles were considered spherical with an average diameter of 500 nm. The alumina-filled thin film layer of the polymer was deposited with a constant thickness ratio of 1:50 on the PMWCNC.

Analytical analysis
This section discusses the Modified Mori Tanaka (MMT) technique to determine the effective elastic modulus of a deposited alumina film layer on PMWCNC and the Mori Tanaka (MT) technique for the single-layer nanocomposite. The orientation of the nanofiller was assumed to be randomly oriented. The parametric studies were carried out for case 1, case 2, case 3, and case 5. The Poisson's ratio was assumed 0.3 in all cases of the polymer and CNT and the diameter of MWCNTs was assumed 65 nm. An in-house generalized MATLAB code was developed to simulate the problem. The Mori-Tanaka method is an analytical technique used to estimate the effective elastic modulus by determining concentration tensors. The modified Mori-Tanaka scheme is derived from the general Mori-Tanaka scheme. The generalized Mori-Tanaka method can be used to study a single layer of randomly oriented fibers in a nanocomposite with and without an interphase effect between the filler and matrix. The Modified Mori-Tanaka model [49] can be used to describe the combined stiffness matrix (C c ) for nanofiller with random orientation in a multilayer nanocomposite. The following equations describe the combined stiffness matrix for single-layer and multilayer nanocomposites with or without an interphase effect between the filler and the matrix.
The stiffness matrix of the nanofillers, matrix, and interphase are denoted by C , p C m and C , i respectively, and their respective volume fractions are denoted by V , p V m and V . i Equation (5) gives the effective stiffness tensor of randomly oriented nano composite considering without considering the effect of interphase while equation (6) considers the effect of interphase for single-layer composite. The effective stiffness tensor for a multilayer nanocomposite is derived using the modified Mori-Tanaka (MMT) scheme, as shown in equation (7), where 'l' represents the number of layers. In equations (8) and (9), T p and T pi are expressed in terms of Eshelby's tensor (S p ) of nanofiller, Identity Matrix (I ), and the elastic properties of the nano-filler and matrix, respectively. The Eshelby's tensor was calculated for the cylindrical shape of MWCNTs for different aspect ratios [50,51]. The curly bracket represents the average value of all possible orientations of MWCNTs. It is possible to calculate the effective stiffness tensor of an axially aligned fiber without the curly bracket in equations (5)- (7). The orientation of fiber in space in a generally anisotropic medium can be described by two Euler angles, j and q. The average combined effective modulus composite for the randomly oriented fiber can be defined as [52] ( was calculated from the above-derived equations (1)-(3). The combined effective modulus has been evaluated for cases 1-3 and 5 as explained in the modeling section.

FEM simulation
Finite Element Modeling has been done for the evaluation of material properties of nanocomposite for case 1, case 2, case 4, and case 5 using ANSYS research 19.1. MWCNT is modeled with equivalent solid fiber for this study. In this present study, the ANSYS APDL code was generated using MATLAB to create and analyze the RVE model with randomly oriented MWCNTs. The number of MWCNTs was estimated for different weight fractions by using the dimension and density of MWCNTs. Three-dimensional RVE randomly oriented PMWCNC models without and with an interphase layer are shown in figures 4(a) and (b) respectively. To discretize the RVE model, a 3D 8-Node Structural Solid (SOLID185) element was chosen. The discretized model of RVE is presented in figure 4(d). For the evaluation of different moduli of the nanocomposite, the periodic boundary conditions were applied as per table 5 and the periodicity of geometry has been represented in figure 4(c). Nodes of the remaining surfaces have been coupled with their normal direction to ensure that faces remain parallel during the deformation when force is applied. To calculate the effective modulus and plastic behavior of the composite, a strain magnitude of 0 to 0.05 was applied in with 20 steps in their respective directions. The effective modulus was calculated for various cases as described in this section.  figure 6(d), which is typical due to their high aspect ratio, which increases intermolecular forces. As a result, it is more difficult to  Table 5. Periodic boundary conditions applied to predict the elastic moduli.

Results and discussion
Effective elastic molii u(0, y, z) u(a, y, z) v(x, 0, z) v(x, b, z) w(x, y, 0) w(x,y,c) distribute the filler particles evenly because they tend to agglomerate together more easily. Morphological studies suggest that the dispersion of more than 1 wt% of MWCNTs in a polymer may lead to agglomeration. Figure 7(a), suggests the Al 2 O 3 particles appear to be evenly distributed without clumping together. However, the larger surface area of alumina fillers may contribute to agglomeration at higher loadings. The deposition of Al 2 O 3 filled nanocomposite on the PMWCNC seems perfect and uniform layer produced as seen in figure 7(b). The micrograph of a fractured cross-section ( figure 7(b)) reveals no evidence of delamination in the deposited alumina layer (1) on the PMWCNC (2). The average thickness of the thin film layer deposited on the 5 mm thick PMWCNC for the studies was100 μm. Figure 8 shows a double logarithmic plot of electrical conductivity versus frequency for the PMWCNC with 1 wt% MWCNTs, the bilayer MWCNT-Al 2 O 3 nanocomposite, and neat epoxy. Electrical conductivity of composites increases with frequency due to increased charge carrier transportation [53][54][55]. It is observed from  figure 8 that Electrical conductivity of neat epoxy and bilayer composite is almost the same while the electrical conductivity of PMWCNC is very high compared to neat epoxy and bilayer composite and hence it is a good indication for our desired encapsulation materials. The PMWCNC at low frequency is an excellent electrical insulator, and that indicates that the PMWCNC is suitable for encapsulation at the lower frequency [56]. A total of five tests were performed at each weight fraction to evaluated the effective electrical conductivity. The average value obtained from the test with 95% confidence level were taken for the analysis.

Thermal stability
The TGA scanned results of MWCNTs modified epoxy under N 2 environment are shown in figure 9. This result illustrates the various composites at different weight percentage. Initial thermal degradation is a crucial property of polymer-based electronic encapsulant materials and the graph shows that the biggest improvement in thermal stability occurs when the nanofiller was indeed incorporated. Neat epoxy loses its initial 5% of weight at 293.66°C, while the 1 wt% MWCNTs composite loses the same amount of weight at 371.13°C. However, it appears that the initial 5% weight loss at 0.25 and 0.50 wt% MWCNTs is accompanied by a nominal increment in temperature compared to neat epoxy. Adding 1 wt%, 0.5 wt%, and 0.25 wt% MWCNTs to epoxy raises residual weight by 29%, 25%, and 15%, respectively, compared to 8% for neat epoxy. The good dispersion of  filler in the matrix can effectively impede the movement of molecular chains within the matrix. The enhanced thermal stability of epoxy containing MWCNTs nanofiller has a favorable tendency as an encapsulation material for electronic devices.

Tensile test
The tensile property is very important for encapsulant material to decide their mechanical properties. During the experiment, at least five tensile tests were performed for each weight fraction. Tensile strength and Young's modulus of nanocomposite is significantly affected by MWCNT content and incorporation. Figure 10 illustrates the variations in nanocomposite tensile strength and Young's modulus as a function of MWCNT concentration. It was found that pure/neat epoxy had an average elastic modulus of 2.3 GPa. It can be seen from figure 10(b) that at 1wt% of MWCNTs, the elastic modulus of polymer nanocomposite dramatically increased by 80%. Improvement in the tensile strength is very significant, which can also be seen in figure 10(a). The major enhancement in tensile strength was observed: 32%, 23%, 15%, and 5% tensile strength increases at 1%, 0.75%, 0.5% and 0.25% MWCNTs addition in the polymer composite.

Analytical and FEM simulation results
For cases 1, 2, 3, and 5 the modified MT Micromechanics method was employed, whereas FEM analysis was performed for cases 1, 2, 4, and 5. The micromechanics and FE procedures used to study the elastic modulus of PMWCNC were compared with the results predicted by Joshi et al [57], Liu and Chen [58], Chwal and Muc [59] and Arora and Pathak [60] . We used similar conditions in our study for validation of results as those taken in the published literature. Table 6 shows that the normalized axial modulus

Analytical and FEM simulation for case 1 and case 2
It is shown from case 1 and case 2 in table 7 that the interfacial effect between two constituents plays an important role in nanocomposite material to enhance their effective modulus. The Analytical and FE study were also compared with experimental results in figure 11. It was found that the effective modulus does not  correspond well with the experimental results when the interphase effect is ignored. However, when the interphase effect was considered, the FE and analytical results followed the experimental result pattern that can be seen in figure 11. The difference between the FE and analytical results was not greater than 7% in any case. Insights from the analytical study found that the orientationally aligned fiber has a greater impact on the normalized elastic moduli, which can be seen in figure 11. The elastic modulus increased by about 50% with aligned fibers compared to randomly oriented fibers. It was also revealed from cases 1 and 2 that the improvement in transverse modulus was relatively lower in comparison to the axial modulus, as can be seen in table 7.

Analytical analysis results for case 3
The evidence from figure 12 shows that the effective elastic modulus increases very rapidly up to the aspect ratio (L/D) 100, and after that variation in modulus is very unproductive. Therefore, we have chosen an aspect ratio (L/D) 100 for all other cases for effective modulus calculations. The log scale was applied to both axes of figure 12 in order to distinguish the initial normalized modulus up to 100 aspect ratio.

Analytical and FEM simulation results for case 5
Case 5 represents the normalized modulus of the thin film layer of alumina nanocomposite that was deposited on the PWCNC. The alumina-filled polymer was deposited on PMWCNC with a constant thickness ratio of 1:50. The nanofillers and polymer were modeled for linearly elastic and isotropic properties, and the constituent properties were taken from table 1. Figure 15 shows the negligible differences in normalized modulus between PMWCNC with and without a deposited alumina layer, which was homogenized using FEM and the modified Mori-Tanaka method.

Conclusions
This study presents the effect of the variation of MWCNTs) in polymer concerning their enhancement in thermo-mechanical properties with electrical insulating properties. The solution mixing approach were used for fabrication of the MWCNTs-polymer composite as well as a bilayer MWCNTs-Al 2 O 3 /epoxy composite. The incorporation of MWCNTs into the epoxy at various weight fractions of PMWCNC significantly enhances its thermomechanical properties. Salient conclusions drawn from this study are as follows: • The tensile strength of PMWCNC was improved by 32%, 23%, 15%, and 5% as compared to pure epoxy when MWCNTs were incorporated with epoxy at concentrations of 0.25 wt%, 0.50%, 0.75 wt%, and 1 wt%, respectively.
• Morphological studies have revealed that MWCNTs are evenly distributed throughout the polymer matrix and have the perfect interface between the layers of the bilayer composite.
• Thermo gravimetric analysis (TGA) examination shows the thermal stability of PMWCNC was increased with increasing the MWCNTs concentration.
• The increased electrical conductivity of PMWCNC due to the incorporation of 1 wt% of MWCNTs has been successfully countered by the deposition of a thin film-layered alumina composite on the PMWCNC to retain the electrical insulation properties.
• The RVE model was developed using MATLAB and the ANSYS APDL for FEM analysis in order to explore the effective elastic and plastic properties of composites containing randomly oriented MWCNTs in a matrix at different weight fractions. The interfacial effect between the CNT and the matrix was also considered.
• Using a modified Mori-Tanka analytical approach, the effective modulus of randomly oriented MWCNTs with different weight fractions and aspect ratios was estimated, with and without taking into account the interfacial effect between MWCNTs and epoxy. The analytical and FEM results obtained were consistent with the experimental results.
• This study demonstrates an improved thermomechanical performance with electrical insulation in MWCNTs as nanofiller in epoxy-based encapsulation materials and its potential use as an encapsulating material for electronic devices.