Combination of Machine Learning and Artificial Neural Networks to Predict the Tensile Modulus of Thermoplastic Nanocomposites: The Role of Polymer/Particle Interphase

Document Type : Regular Article

Authors

1 Department of Chemical Engineering, Faculty of Petroleum and Chemical Engineering, Razi University, Kermanshah, Iran.

2 Polymer Research Center , Faculty of Petroleum and Chemical Engineering, Razi University , Kermanshah, Iran

Abstract
Polymer nanocomposites reinforced with multi-walled carbon nanotubes (MWCNTs) offer promising mechanical performance; however, predicting their tensile modulus remains challenging due to the complex interplay of multiple factors such as filler content, functionalization, and interphase quality. In this study, a dataset of 229 samples was compiled from the literature, augmented via cubic spline interpolation to 4,933 training points, and analyzed using six machine learning models, including SVR, Random Forest, Gradient Boosting Regressor, XGBoost, KNN, and Artificial Neural Networks (ANNs). The inclusion of the interphase modulus (Ei), calculated via an extended Ji model, proved critical for improving prediction accuracy. Among all models, Gradient Boosting Regressor and XGBoost achieved the best predictive performance (Test R² = 0.9868 and 0.9837, respectively), while ANN demonstrated competitive accuracy (Test R² = 0.9703) but higher sensitivity under cross-validation (Mean CV R² = 0.7486). Feature importance analysis using SHAP further confirmed the significant contribution of Ei to prediction outcomes. Overall, this work demonstrates that incorporating physically-informed features like interphase modulus, combined with robust machine learning pipelines, can substantially enhance the predictive modeling of nanocomposite mechanical properties, providing a valuable tool for material design and optimization.

Keywords

Subjects


[1] Chanda M, Roy SK (2008) Industrial polymers, specialty polymers, and their applications. CRC press, NewYork.
[2] Tonelli AE, Srinivasarao M (2001) Polymers from the inside out: an introduction to macromolecules. MRS Bull 4:1024.
[3] Sharifzadeh E, Rahimi M, Azimi N, Abolhasani M (2024) Thermal management of photovoltaic panels using phase change materials and hierarchical ZnO/expanded graphite nanofillers. Energy 306:132324.
[4] Sharifzadeh E, Cheraghi K (2021) Temperature-affected mechanical properties of polymer nanocomposites from glassy-state to glass transition temperature. Mech Mater 160:103990.
[5] Sharifzadeh E, Mohammadi R (2021) Temperature/Frequencydependent complex viscosity and tensile modulus of polymer nanocomposites from the glassy state to the melting point. Polym Sci Eng 61(10):2600–15.
[6] Sharifzadeh E, Ghasemi I, Karrabi M, Azizi H (2014) A new approach in modeling of mechanical properties of binary phase polymeric blends. Iran Polym J 23(7):525–30.
[7] Sharifzadeh E (2021) Evaluating the dependency of polymer/particle interphase thickness to the nanoparticles content, aggregation/agglomeration factor and type of the exerted driving force. Iran Polym J 30(10):1063–72.
[8] Sharifzadeh E, Amiri Y (2020) The effects of the arrangement of Janus nanoparticles on the tensile strength of blend-based polymer nanocomposites. Polym Compos 41(9):3585–93.
[9] Groover MP (2010) Fundamentals of modern manufacturing: materials, processes, and systems. John Wiley & Sons, Danvers.
[10] Sharifzadeh E, Ghasemi I, Karrabi M, Azizi H (2014) A new approach in modeling of mechanical properties of nanocomposites: effect of interface region and random orientation. Iran Polym J 23(11):835–45.
[11] Sharifzadeh E, Karami M, Ader F (2023) Formation of nanoparticle aggregates and agglomerates in polymer nanocomposites and their distinct impacts on the mechanical properties. Polym Eng Sci 63(4):1303–13.
[12] Sharifzadeh E (2019) Modeling of the Mechanical Properties of Blend Based Polymer Nanocomposites Considering the Effects of Janus Nanoparticles on Polymer/Polymer Interface. Chin J Polym Sci 37(2):164–77.
[13] Mohammadi R, Sharifzadeh E, Azimi N (2024) Temperature-dependent storage modulus of polymer nanocomposites, blends and blend-based nanocomposites based on percolation and De Gennes’s self-similar carpet theories. Iran Polym J 33(7):877–90.
[14] Shameem MM, Sasikanth S, Annamalai R, Raman RG (2021) A brief review on polymer nanocomposites and its applications. Mater Today: Proc 45:2536–9.
[15] Hojatzadeh S, Sharifzadeh E, Rahimpour F (2023) An EBM based multi-stage mechanical model to predict the time-dependent creep behavior of semi-crystalline polymer nanocomposites. Mech Mater 184:104737.
[16] Huang J, Zhou J, Liu M (2022) Interphase in polymer nanocomposites. JACS Au 2(2):280–91.
[17] Rostami Z, Heidari N, Rahimi M, Azimi N (2022) Enhancing the thermal performance of a photovoltaic panel using nano-graphite/paraffin composite as phase change material. J Therm Anal Calorim 147(5):3947–64.
[18] Ghadami H, Sharifzadeh E, Azimi N (2024) A scaling theory to approximate the thermal conductivity of the interphase region in polymer nanocomposites. J Reinf Plast Compos 43(15-16):833–42.
[19] Azimi N, Sharifzadeh E (2025) Using binary-eutectic phase change materials and ZnO/aluminum nitride nanofillers to improve photovoltaic efficiency. Sol Energy Mater 284:113490.
[20] Sharifzadeh E, Azimi N, ZamanianFard A, Mohammadi R (2023) An energybased strategy to predict the thickness and content of randomly oriented nanolayers aggregates/agglomerates in thermoplastic polymer nanocomposites: experimental and analytical approaches. Polym Sci Eng 63(9):2733–44.
[21] Khanmohammadi S, Azimi N, Sharifzadeh E, Rahimi M, Azimi P (2023) An experimental study to improve cooling on a hot plate using phase change materials and high-frequency ultrasound. J Energy Storage 72:107930.
[22] Hojatzadeh S, Rahimpour F, Sharifzadeh E (2023) A study on the synergetic effects of self/induced crystallization and nanoparticles on the mechanical properties of semi-crystalline polymer nanocomposites: experimental and analytical approaches. Iran Polym J 32(5):543–55.
[23] Sharifzadeh E, Azimi N, Mohammadpour AH (2025) Aggregated/agglomerated and dispersed randomly oriented wavy CNTs in electrically conductive polymer nanocomposites: Impact of dispersion quality and polymer/particle interphase. J Mater Res Technol 35:858–68.
[24] Fu S, Sun Z, Huang P, Li Y, Hu N (2019) Some basic aspects of polymer nanocomposites: A critical review. Nano Mater Sci 1(1):2–30.
[25] Sharifzadeh E, Ader F (2025) Aggregation/agglomeration dependent percolation threshold of spherical nanoparticles in electrically conductive polymer nanocomposites. Polym Compos 46(3):2374–89.
[26] Sharifzadeh E, Azimi N, Mohammadi R (2023) Improved thermostimulative shape memory behavior of HDPE/PET immiscible blend-based polymer nanocomposite using amphiphilic Janus nanoparticles. Polym Compos 44(2):1161–74.
[27] Peigney A, Laurent C, Flahaut E, Bacsa R, Rousset A (2001) Specific surface area of carbon nanotubes and bundles of carbon nanotubes. Carbon 39(4):507–14.
[28] Bai J (2003) Evidence of the reinforcement role of chemical vapour deposition multi-walled carbon nanotubes in a polymer matrix. Carbon 41(6):1325–8.
[29] Ader F, Sharifzadeh E, Azimi N (2023) A novel strategy to predict the tensile strength of polymer/particle interphase based on De Gennes's self-similar carpet theory. Polym Eng Sci 63(10):3353–61.
[30] Rahimi Mir-Azizi Z, Sharifzadeh E, Rahimpour F (2022) Thermal analysis of ZnO/hollow graphene-oxide/polyester complex- and simple-structure nanocomposites: analytical, simulation and experimental approaches. Iran Polym J 31(6):717–27.
[31] Azimi N, Sharifzadeh E (2025) Improved aggregation/agglomeration-dependent percolation theory to predict nanoparticle-aided electrical conductivity in polymer nanocomposites: A combination of analytical strategy and artificial neural network. Comput Mater Sci 246:113424.
[32] Ader F, Sharifzadeh E, Azimi N (2024) Unveiling the impact of percolation phenomenon on the microstructure of polymer nanocomposites based on the combination of scaling and percolation theories. Polym Compos 45(17):16280–92.
[33] Sharifzadeh E, Ader F, Moradi G (2024) Multi-layer structural representation of polymer/particle interphase region based on De Gennes’s scaling theory. J Reinf Plast Compos 1(1):1–14.
[34] Sharifzadeh E (2025) Energy-based characterization of polymer/particle interphase region as piled-up equilibrated molecular layers: The impact of different distribution patterns of adsorption energy. Polym Eng Sci 65(1):384–400.
[35] Ghasemi F, Sharifzadeh E (2026) An innovative analytical approach to define the dynamic electrical conductivity in polymer nanocomposites: The effect of nanoparticle network rearrangement. Comput Mater Sci 262:114384.
[36] Sharifzadeh E, Mohammadpour AH, Azimi N (2025) Frequency-Dependent Electrical Conductivity in Polymer Nanocomposites Based on the Impacts of Dispersion Quality and Polymer/Particle Interphase. Polym Compos 1(1):1–13.
[37] Mortazavian S, Fatemi A (2015) Effects of fiber orientation and anisotropy on tensile strength and elastic modulus of short fiber reinforced polymer composites. Compos B: Eng 72:116–29.
[38] Ghasemi S, Espahbodi A, Gharib N, Zare Y, Rhee KY (2023) A developed Takayanagi model to estimate the tensile modulus and interphase characteristics of polymer nanocellulose composites. Ind Crops Prod 206:117703.
[39] Bhuiyan MA, Pucha RV, Karevan M, Kalaitzidou K (2011) Tensile modulus of carbon nanotube/polypropylene composites–A computational study based on experimental characterization. Comput Mater Sci 50(8):2347–53.
[40] Feng J, Safaei B, Qin Z, Chu F (2023) Nature-inspired energy dissipation sandwich composites reinforced with high-friction graphene. Compos Sci Technol 233:109925.
[41] Alhijazi M, Safaei B, Zeeshan Q, Asmael M, Harb M, Qin Z (2022) An experimental and metamodeling approach to tensile properties of natural fibers composites. J Polym Environ 30(10):4377–93.
[42] Hojatzadeh S, Rahimpour F, Sharifzadeh E (2024) Isothermal crystallization kinetics of pure and surface-modified silica/high-density polyethylene nanocomposites. Polym Compos 45(4):3724–37.
[43] Pyzer-Knapp EO, Pitera JW, Staar PW, Takeda S, Laino T, Sanders DP, et al. (2022) Accelerating materials discovery using artificial intelligence, high performance computing and robotics. npj Comput Mater 8(1):84.
[44] Cheetham AK, Seshadri R (2024) Artificial intelligence driving materials discovery? perspective on the article: Scaling deep learning for materials discovery. Chem Mater 36(8):3490–5.
[45] Shah V, Zadourian S, Yang C, Zhang Z, Gu GX (2022) Data-driven approach for the prediction of mechanical properties of carbon fiber reinforced composites. Mater Adv 3(19):7319–27.
[46] Béji H, Kanit T, Messager T (2023) Prediction of Effective Elastic and Thermal Properties of Heterogeneous Materials Using Convolutional Neural Networks. Appl Mech 4(1):287–303.
[47] Champa-Bujaico E, Díez-Pascual AM, Redondo AL, Garcia-Diaz P (2024) Optimization of mechanical properties of multiscale hybrid polymer nanocomposites: A combination of experimental and machine learning techniques. Compos B Eng 269:111099.
[48] Rajaee P, Rabiee AH, Ashenai Ghasemi F, Fasihi M, Mahabadifar M, Nedaei Shekarab M (2024) XGBoost machine learning assisted prediction of the mechanical and fracture properties of unvulcanized and dynamically vulcanized PP/EPDM reinforced with clay and halloysite nanoparticles. Polym Compos 45(16):14799–815.
[49] Sharma H, Arora G, Kumar R, Debnath S, Siengchin S (2025) Data-driven insights into the high-temperature behavior of polymer/carbon nanotubes nanocomposites. Iran Polym J.
[50] Ho NX, Le T-T, Le MV (2022) Development of artificial intelligence based model for the prediction of Young’s modulus of polymer/carbon-nanotubes composites. Mech Adv Mater Struct 29(27):5965–78.
[51] Le T-T (2021) Prediction of tensile strength of polymer carbon nanotube composites using practical machine learning method. J Compos Mater 55(6):787–811.
[52] Bhuiyan MA, Pucha RV, Worthy J, Karevan M, Kalaitzidou K (2013) Defining the lower and upper limit of the effective modulus of CNT/polypropylene composites through integration of modeling and experiments. Compos Struct 95:80–7.
[53] Makireddi S, Shivaprasad S, Kosuri G, Varghese FV, Balasubramaniam K (2015) Electro-elastic and piezoresistive behavior of flexible MWCNT/PMMA nanocomposite films prepared by solvent casting method for structural health monitoring applications. Compos Sci Technol 118:101–7.
[54] Ji XL, Jing JK, Jiang W, Jiang BZ (2002) Tensile modulus of polymer nanocomposites. Polym Sci Eng 42(5):983–93.
[55] Zare Y, Rhee K (2020) A simple technique for calculation of an interphase parameter and interphase modulus for multilayered interphase region in polymer nanocomposites via modeling of young’s modulus. Phys Mesomech 23(4):332–9.
[56] Yanovsky YG, Kozlov G, Karnet YN (2013) Fractal description of significant nano-effects in polymer composites with nanosized fillers. Aggregation, phase interaction, and reinforcement. Phys Mesomech 16(1):9–22.
[57] Treacy MMJ, Ebbesen TW, Gibson JM (1996) Exceptionally high Young's modulus observed for individual carbon nanotubes. Nature 381(6584):678–80.
[58] Wong EW, Sheehan PE, Lieber CM (1997) Nanobeam Mechanics: Elasticity, Strength, and Toughness of Nanorods and Nanotubes. Science 277(5334):1971–5.
[59] Salvetat-Delmotte J-P, Rubio A (2002) Mechanical properties of carbon nanotubes: a fiber digest for beginners. Carbon 40(10):1729–34.