Analytical effective thermal conductivity model for colloidal porous composites and nanocomposites based on novolac/graphene oxide aerogels
Narges Nazari
Polymer Engineering Department, Faculty of Chemical Engineering, Tarbiat Modares University, Tehran, Iran
Search for more papers by this authorCorresponding Author
Ahmad Allahbakhsh
Department of Materials and Polymer Engineering, Faculty of Engineering, Hakim Sabzevari University, Sabzevar, Iran
Correspondence
Ahmad Allahbakhsh, Department of Materials and Polymer Engineering, Faculty of Engineering, Hakim Sabzevari University, Sabzevar, Iran.
Email: [email protected]
Ahmad Reza Bahramian, Polymer Engineering Department, Faculty of Chemical Engineering, Tarbiat Modares University, P.O.Box 14115-143, Tehran, Iran.
Email: [email protected]
Search for more papers by this authorCorresponding Author
Ahmad Reza Bahramian
Polymer Engineering Department, Faculty of Chemical Engineering, Tarbiat Modares University, Tehran, Iran
Correspondence
Ahmad Allahbakhsh, Department of Materials and Polymer Engineering, Faculty of Engineering, Hakim Sabzevari University, Sabzevar, Iran.
Email: [email protected]
Ahmad Reza Bahramian, Polymer Engineering Department, Faculty of Chemical Engineering, Tarbiat Modares University, P.O.Box 14115-143, Tehran, Iran.
Email: [email protected]
Search for more papers by this authorNarges Nazari
Polymer Engineering Department, Faculty of Chemical Engineering, Tarbiat Modares University, Tehran, Iran
Search for more papers by this authorCorresponding Author
Ahmad Allahbakhsh
Department of Materials and Polymer Engineering, Faculty of Engineering, Hakim Sabzevari University, Sabzevar, Iran
Correspondence
Ahmad Allahbakhsh, Department of Materials and Polymer Engineering, Faculty of Engineering, Hakim Sabzevari University, Sabzevar, Iran.
Email: [email protected]
Ahmad Reza Bahramian, Polymer Engineering Department, Faculty of Chemical Engineering, Tarbiat Modares University, P.O.Box 14115-143, Tehran, Iran.
Email: [email protected]
Search for more papers by this authorCorresponding Author
Ahmad Reza Bahramian
Polymer Engineering Department, Faculty of Chemical Engineering, Tarbiat Modares University, Tehran, Iran
Correspondence
Ahmad Allahbakhsh, Department of Materials and Polymer Engineering, Faculty of Engineering, Hakim Sabzevari University, Sabzevar, Iran.
Email: [email protected]
Ahmad Reza Bahramian, Polymer Engineering Department, Faculty of Chemical Engineering, Tarbiat Modares University, P.O.Box 14115-143, Tehran, Iran.
Email: [email protected]
Search for more papers by this authorFunding information: Tarbiat Modares University (Research group of Phase Change Materials, Grant No. IG-39710)., Grant/Award Number: IG-39710
Summary
The performance of porous composite materials in thermal energy storage and management applications can be engineered by controlling the relationship between the heat transfer mechanism and the structure of these materials. Analytical thermal conductivity models are essential tools to study and manage such structure/heat transfer relations in porous composite materials. This study develops an analytical thermal conductivity model for porous composites with colloidal matrix morphologies. The model developed here is a modified series-parallel model that considers important structural parameters such as the system's porosity, the colloidal size of the matrix, and the filler's aspect ratio. Moreover, essential effects in the structure of porous composites, including the gas-solid coupling effect and contact length of particles, are also included in the model developed here. In addition, this model can be used in a wide range of porosity and can predict the thermal conductivity of porous composites with appropriate accuracy by changing temperature, pressure, specific surface area, porosity, and other textural properties. Novolac/graphene oxide nanocomposite aerogels with different contents of graphene oxide (GO) nanosheets in the structure were prepared and used to study the validity of the data calculated using the developed model. Our results confirmed that the developed model in this study predicts the effective thermal conductivity of porous composite and nanocomposite structures with acceptable accuracy. More importantly, this model considers the structure's simultaneous presence of fillers and pores. As a result, it is an effective model for predicting the total thermal conductivity of porous composite and nanocomposite materials. Although the gaseous thermal conductivity contribution measured via the modified series-parallel model for porous composites (MSPC) model in novolac/graphene oxide nanocomposite aerogels decreased by around 79% with the incorporation of 15 wt.% GO, the effective thermal conductivity of nanocomposite aerogels was improved for more than 300%, compared to the neat novolac aerogel. Additionally, specific surface area and micropore surface area increased from 953.56 and 602.56 m2/g for neat novolac aerogel to 965.89 and 664.30 m2/g for the sample with 15 wt.% of GO respectively.
REFERENCES
- 1Liu L, Corma A. Confining isolated atoms and clusters in crystalline porous materials for catalysis. Nat Rev Mater. 2020; 6(3): 244-263.
- 2Singh G, Lee J, Karakoti A, et al. Emerging trends in porous materials for CO2 capture and conversion. Chem Soc Rev. 2020; 49(13): 4360-4404.
- 3Oliveira ÉR, Nie L, Podstawczyk D, et al. Advances in growth factor delivery for bone tissue engineering. Int J Mol Sci. 2021; 22(2): 903.
- 4Chen X, Cheng P, Tang Z, Xu X, Gao H, Wang G. Carbon-based composite phase change materials for thermal energy storage, transfer, and conversion. Adv Sci. 2021; 8(9): 2001274.
- 5Bahru R, Shaari N, Mohamed MA. Allotrope carbon materials in thermal interface materials and fuel cell applications: a review. Int J Energy Res. 2019; 44(4): 2471-2498.
10.1002/er.5077 Google Scholar
- 6Zhu M, Huang J, Song M, Hu Y. Thermal performance of a thin flat heat pipe with grooved porous structure. Appl Therm Eng. 2020; 173:115215.
- 7Astanina MS, Rashidi MM, Sheremet MA, Lorenzini G. Cooling system with porous finned heat sink for heat-generating element. Transp Porous Media. 2020; 133(3): 459-478.
- 8Allahbakhsh A, Bahramian AR. Novolac-derived carbon aerogels pyrolyzed at high temperatures: experimental and theoretical studies. RSC Adv. 2016; 6(76): 72777-72790.
- 9Wang J, Chen Y, Feng Y, et al. Influence of porosity on anisotropic thermal conductivity of SiC fiber reinforced SiC matrix composite: a microscopic modeling study. Ceram Int. 2020; 46(18): 28693-28700.
- 10Yu H, Zhang H, Buahom P, Liu J, Xia X, Park CB. Prediction of thermal conductivity of micro/nano porous dielectric materials: theoretical model and impact factors. Energy. 2021; 233(15): 121140.
- 11Xu W, Zhang Y, Jiang J, Liu Z, Jiao Y. Thermal conductivity and elastic modulus of 3D porous/fractured media considering percolation. Int J Eng Sci. 2021; 161:103456.
- 12Noparvar-Qarebagh A, Roghani-Mamaqani H, Salami-Kalajahi M, Kariminejad B. Nanohybrids of novolac phenolic resin and carbon nanotube-containing silica network. J Therm Anal Calorim. 2016; 128(2): 1027-1037.
10.1007/s10973-016-5970-0 Google Scholar
- 13Wang T, Song Q, Zhang S, et al. Simultaneous enhancement of mechanical and electrical/thermal properties of carbon fiber/polymer composites via SiC nanowires/graphene hybrid nanofillers. Compos Part A Appl Sci. 2021; 145: 106404.
- 14Pan D, Dong J, Yang G, et al. Ice template method assists in obtaining carbonized cellulose/boron nitride aerogel with 3D spatial network structure to enhance the thermal conductivity and flame retardancy of epoxy-based composites. Adv Compos Mater. 2021; 5(1): 58-70.
10.1007/s42114-021-00362-6 Google Scholar
- 15Olenych IB, Aksimentyeva OI, Monastyrskii LS, et al. Effect of graphene oxide on the properties of porous silicon. Nanoscale Res Lett. 2016; 11(1): 43.
- 16Chao X, Tian W, Xu F, Shou D. A fractal model of effective mechanical properties of porous composites. Compos Sci Technol. 2021; 213: 108957.
- 17Wang S-L, Jin Z, Li J-N, et al. Theoretical modeling of thermal conductivity of alumina aerogel composites based on real microstructures. J Taiwan Inst Chem Eng. 2021; 120: 150-160.
- 18Wang XJ, Niu XH, Wang XX, Qiu XW, Istikomah N, Wang LB. Thermal conductivity of porous polymer materials considering pore special-shape and anisotropy. Express Polymer Letters. 2021; 15(4): 319-328.
- 19Chaichi M, Bahramian AR. Theoretical relation of the structure and thermal properties of gradient thermal insulator aerogels using fractal geometry. Microporous Mesoporous Mater. 2022; 333: 111722.
- 20Chen Y, Li D, Xie X-Q, Gao Y, He Y-L. Theoretical modeling and experimental validation for the effective thermal conductivity of moist silica aerogel. Int J Heat Mass Transf. 2020; 147: 118842.
- 21Liu H, Hu M, Jiao J, Li Z. Geometric optimization of aerogel composites for high temperature thermal insulation applications. J Non Cryst Solids. 2020; 547: 120306.
- 22Xu W, Lan P, Jiang Y, Lei D, Yang H. Insights into excluded volume and percolation of soft interphase and conductivity of carbon fibrous composites with core-shell networks. Carbon. 2020; 161: 392-402.
- 23Zhou L, Sun X, Chen M, Zhu Y, Wu H. Multiscale modeling and theoretical prediction for the thermal conductivity of porous plain-woven carbonized silica/phenolic composites. Compos Struct. 2019; 215: 278-288.
- 24Kiradjiev KB, Halvorsen SA, Van Gorder RA, Howison SD. Maxwell-type models for the effective thermal conductivity of a porous material with radiative transfer in the voids. Int J Therm Sci. 2019; 145: 106009.
- 25Chu Z, Zhou G, Li R. Enhanced fractal capillary bundle model for effective thermal conductivity of composite-porous geomaterials. Int Commun. 2020; 113: 104527.
- 26Qiu L, Zou H, Tang D, Wen D, Feng Y, Zhang X. Inhomogeneity in pore size appreciably lowering thermal conductivity for porous thermal insulators. Appl Therm Eng. 2018; 130: 1004-1011.
- 27Zhang T, Zhang Y, Zhu H, Yan Z. Experimental investigation and multi-level modeling of the effective thermal conductivity of hybrid micro-fiber reinforced cementitious composites at elevated temperatures. Compos Struct. 2021; 256:112988.
- 28Kommandur S, Yee SK. An empirical model to predict temperature-dependent thermal conductivity of amorphous polymers. J Polym Sci B. 2017; 55(15): 1160-1170.
- 29Kosbe P, Patil PA. Effective thermal conductivity of polymer composites: a review of analytical methods. Int J Ambient Energy. 2021; 42(8): 961-972.
- 30Xu W, Zhang K, Zhang Y, Jiang J. Packing fraction, tortuosity, and permeability of granular-porous media with densely packed spheroidal particles: monodisperse and Polydisperse systems. Water Resour Res. 2022; 58(2):e2021WR031433:1-28.
- 31Qiu L, Guo P, Yang X, et al. Electro curing of oriented bismaleimide between aligned carbon nanotubes for high mechanical and thermal performances. Carbon. 2019; 145: 650-657.
- 32Swimm K, Reichenauer G, Vidi S, Ebert HP. Gas pressure dependence of the heat transport in porous solids with pores smaller than 10 μm. Int J Thermophys. 2009; 30(4): 1329-1342.
- 33Qiu L, Du Y, Bai Y, et al. Experimental characterization and model verification of thermal conductivity from mesoporous to macroporous SiOC ceramics. J Therm Sci. 2021; 30(2): 465-476.
- 34Thuras AL, Jenkins RT, O'Neil HT. Extraneous frequencies generated in air carrying intense sound waves. Bell Syst Tech J. 1935; 14(1): 159-172.
10.1002/j.1538-7305.1935.tb00688.x Google Scholar
- 35Ma H-S, Prévost J-H, Jullien R, Scherer GW. Computer simulation of mechanical structure–property relationship of aerogels. J Non Cryst Solids. 2001; 285(1–3): 216-221.
- 36Zeng SQ, Hunt A, Greif R. Transport properties of gas in silica aerogel. J Non Cryst Solids. 1995; 186: 264-270.
- 37Zhao J-J, Duan Y-Y, Wang X-D, Wang B-X. Experimental and analytical analyses of the thermal conductivities and high-temperature characteristics of silica aerogels based on microstructures. J Phys D Appl Phys. 2013; 46(1):015304.
- 38Chen G. Nonlocal and nonequilibrium heat conduction in the vicinity of nanoparticles. J Heat Transfer. 1996; 118(3): 539-545.
- 39Latré SK, De Pooter S, Buffel B, Brabazon D, Seveno D, Desplentere F. Comparative study of a cubic, kelvin and Weaire-Phelan unit cell for the prediction of the thermal conductivity of low density silica aerogels. Micropor Mesopor Mat. 2020; 301: 110206.
- 40Ren L, Pashayi K, Fard HR, Kotha SP, Borca-Tasciuc T, Ozisik R. Engineering the coefficient of thermal expansion and thermal conductivity of polymers filled with high aspect ratio silica nanofibers. Compos B Eng. 2014; 58: 228-234.
- 41Yang Y, Cao J, Wei N, et al. Thermal conductivity of defective graphene oxide: a molecular dynamic study. Molecules. 2019; 24(6):1103-1112.
10.3390/molecules24061103 Google Scholar
- 42Bahramian AR. Pyrolysis and flammability properties of novolac/graphite nanocomposites. Fire Saf J. 2013; 61: 265-273.
- 43Ha SM, Kwon OH, Oh YG, et al. Thermally conductive polyamide 6/carbon filler composites based on a hybrid filler system. Sci Technol Adv Mater. 2015; 16(6):065001.
- 44Kim J-H, Sin DH, Kim H, et al. Improved charge transport and reduced non-geminate recombination in organic solar cells by adding size-selected graphene oxide Nanosheets. ACS Appl Mater Interfaces. 2019; 11(22): 20183-20191.
- 45Tong Z, Liu M, Bao H. A numerical investigation on the heat conduction in high filler loading particulate composites. Int J Heat Mass Transf. 2016; 100: 355-361.
- 46Jafari Nejad SJ. A review on modeling of the thermal conductivity of polymeric nanocomposites. e-Polymers. 2012; 12(1):025.
10.1515/epoly.2012.12.1.253 Google Scholar
- 47Ha SM, Lee HL, Lee S-G, et al. Thermal conductivity of graphite filled liquid crystal polymer composites and theoretical predictions. Compos Sci Technol. 2013; 88: 113-119.
- 48Yu W, Xie H, Yin L, Zhao J, Xia L, Chen L. Exceptionally high thermal conductivity of thermal grease: synergistic effects of graphene and alumina. Int J Therm Sci. 2015; 91: 76-82.
- 49Guo JF, Tang GH. A theoretical model for gas-contributed thermal conductivity in nanoporous aerogels. Int J Heat Mass Transf. 2019; 137: 64-73.
- 50Alkhouzaam A, Qiblawey H, Khraisheh M, Atieh M, Al-Ghouti M. Synthesis of graphene oxides particle of high oxidation degree using a modified hummers method. Ceram Int. 2020; 46(15): 23997-24007.
- 51Shen C, Barrios E, Zhai L. Bulk polymer-derived ceramic composites of graphene oxide. ACS Omega. 2018; 3(4): 4006-4016.
- 52Khalaj M, Allahbakhsh A, Bahramian AR, Sharif A. Structural, mechanical and thermal behaviors of novolac/graphene oxide nanocomposite aerogels. J Non Cryst Solids. 2017; 460: 19-28.
- 53Hosseini MA, Malekie S, Ebrahimi N. The analysis of linear dose-responses in gamma-irradiated graphene oxide: can FTIR analysis be considered a novel approach to examining the linear dose-responses in carbon nanostructures. Radiat Phys Chem. 2020; 176: 109067.
- 54Chen J, Li L. Effect of oxidation degree on the thermal properties of graphene oxide. J Mater Res Technol. 2020; 9(6): 13740-13748.
- 55Lin S, Buehler MJ. Thermal transport in monolayer graphene oxide: atomistic insights into phonon engineering through surface chemistry. Carbon. 2014; 77: 351-359.
- 56Mahanta NK, Abramson AR. Thermal conductivity of graphene and graphene oxide nanoplatelets. 13th InterSoc Conf Therm Thermomechanical Phenom Electron Syst. 2012; 1-6.
- 57Mu X, Wu X, Zhang T, Go DB, Luo T. Thermal transport in graphene oxide – from ballistic extreme to amorphous limit. Sci Rep. 2014; 4(1):3909-3917.
10.1038/srep03909 Google Scholar
- 58Sabagh S, Arefazar A, Bahramian AR. Thermochemical erosion and thermophysical properties of phenolic resin/carbon fiber/graphite nanocomposites. J Reinf Plast Compos. 2016; 35(24): 1814-1825.
- 59Qiu L, Li YM, Zheng XH, et al. Thermal-conductivity studies of macro-porous polymer-derived SiOC ceramics. Int J Thermophys. 2013; 35(1): 76-89.
10.1007/s10765-013-1542-8 Google Scholar
- 60Xu W, Jia M, Gong Z. Thermal conductivity and tortuosity of porous composites considering percolation of porous network: from spherical to polyhedral pores. Compos Sci Technol. 2018; 167: 134-140.
- 61Xu W, Wu F, Jiao Y, Liu M. A general micromechanical framework of effective moduli for the design of nonspherical nano- and micro-particle reinforced composites with interface properties. Mater des. 2017; 127: 162-172.
- 62Zhai S, Zhang P, Xian Y, Zeng J, Shi B. Effective thermal conductivity of polymer composites: theoretical models and simulation models. Int J Heat Mass Transf. 2018; 117: 358-374.
- 63Chu K, Jia C, Tian W, Liang X, Chen H, Guo H. Thermal conductivity of spark plasma sintering consolidated SiCp/Al composites containing pores: numerical study and experimental validation. Compos Part A Appl Sci. 2010; 41(1): 161-167.
- 64Wang H, Tazebay AS, Yang G, Lin HT, Choi W, Yu C. Highly deformable thermal interface materials enabled by covalently-bonded carbon nanotubes. Carbon. 2016; 106: 152-157.
- 65Pan L, Wang J, Lu L, Qiu X. Modeling the effective thermal conductivity for disperse systems with high solid mass fractions. Int J Heat Mass Transf. 2016; 97: 719-724.
