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Thermal conductivity of micro/nano-porous polymers: Prediction models and applications

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Abstract

Micro/nano-porous polymeric material is considered a unique industrial material due to its extremely low thermal conductivity, low density, and high surface area. Therefore, it is necessary to establish an accurate thermal conductivity prediction model suiting their applicable conditions and provide a theoretical basis for expanding their applications. In this work, the development of the calculation model of equivalent thermal conductivity of micro/nano-porous polymeric materials in recent years is summarized. Firstly, it reviews the process of establishing the overall equivalent thermal conductivity calculation model for micro/nanoporous polymers. Then, the predicted calculation models of thermal conductivity are introduced separately according to the conductive and radiative thermal conductivity models. In addition, the thermal conduction part is divided into the gaseous thermal conductivity model, solid thermal conductivity model and gas-solid coupling model. Finally, it is concluded that, compared with other porous materials, there are few studies on heat transfer of micro/nanoporous polymers, especially on the particular heat transfer mechanisms such as scale effects at the micro/nanoscale. In particular, the following aspects of porous polymers still need to be further studied: micro scaled thermal radiation, heat transfer characteristics of particular morphologies at the nanoscales, heat transfer mechanism and impact factors of micro/nanoporous polymers. Such studies would provide a more accurate prediction of thermal conductivity and a broader application in energy conversion and storage systems.

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References and notes

  1. J. Wu, F. Xu, S. Li, P. Ma, X. Zhang, Q. Liu, R. Fu, and D. Wu, Porous polymers as multifunctional material platforms toward task-specific applications, Adv. Mater. 31, 4 (2019)

    Google Scholar 

  2. B. H. Kreps, Energy sprawl in the renewable-energy sector: moving to sufficiency in a post-growth era, Am. J. Econ. Sociol. 79, 3 (2020)

    Google Scholar 

  3. S. K. Mangla, S. Luthra, S. Jakhar, S. Gandhi, K. Muduli, and A. Kumar, A step to clean energy — Sustainability in energy system management in an emerging economy context, J. Clean. Prod. 242, 118462 (2020)

    Google Scholar 

  4. X. Chang, Y. Xue, J. Li, L. Zou, and M. Tang, Potential health impact of environmental micro- and nanoplastics pollution, J. Appl. Toxicol. 40(1), 4 (2020)

    Google Scholar 

  5. F. A. Faize and M. Akhtar, Addressing environmental knowledge and environmental attitude in undergraduate students through scientific argumentation, J. Clean. Prod. 252, 119928 (2020)

    Google Scholar 

  6. S. Chu and A. Majumdar, Opportunities and challenges for a sustainable energy future, Nature 488(7411), 294 (2012)

    Google Scholar 

  7. L. Song, C. Jiang, S. Liu, C. Jiao, X. Si, S. Wang, F. Li, J. Zhang, L. Sun, F. Xu, and F. Huang, Progress in improving thermodynamics and kinetics of new hydrogen storage materials, Front. Phys. 6(2), 151 (2011)

    Google Scholar 

  8. Z. C. Tu, Abstract models for heat engines, Front. Phys. 16(3), 33202 (2021)

    Google Scholar 

  9. X. He, A review of material development in the field of carbon capture and the application of membrane-based processes in power plants and energy-intensive industries, Energy Sustain. Soc. 8(1), 34 (2018)

    Google Scholar 

  10. Y. Huang and X. Feng, Polymer-enhanced ultrafiltration: Fundamentals, applications and recent developments, J. Membr. Sci. 586, 53 (2019)

    Google Scholar 

  11. S. Wang, Y. Huang, C. Zhao, E. Chang, A. Ameli, H. E. Naguib, and C. B. Park, Theoretical modeling and experimental verification of percolation threshold with MWC-NTs’ rotation and translation around a growing bubble in conductive polymer composite foams, Compos. Sci. Technol. 199, 108345 (2020)

    Google Scholar 

  12. M. Hamidinejad, B. Zhao, R. K. M. Chu, N. Moghimian, H. E. Naguib, T. Filleter, and C. B. Park, Enhanced electrical and electromagnetic interference shielding properties of polymer-graphene nanoplatelet composites fabricated via supercritical-fluid treatment and physical foaming, ACS Appl. Mater. Interfaces 10, 36 (2018)

    Google Scholar 

  13. Y. Huang, T. Gancheva, B. D. Favis, A. Abidli, J. Wang, and C. B. Park, Hydrophobic porous polypropylene with hierarchical structures for ultrafast and highly selective oil/water separation, ACS Appl. Mater. Interfaces 13, 14 (2021)

    Google Scholar 

  14. J. Zhao, G. Wang, Z. Chen, Y. Huang, C. Wang, A. Zhang, and C. B. Park, Microcellular injection molded outstanding oleophilic and sound-insulating PP/PTFE nanocomposite foam, Compos. Part B Eng. 215, 108786 (2021)

    Google Scholar 

  15. B. Zhao, M. Hamidinejad, C. Zhao, R. Li, S. Wang, Y. Kazemi, and C. B. Park, A versatile foaming platform to fabricate polymer/carbon composites with high dielectric permittivity and ultra-low dielectric loss, J. Mater. Chem. A 7(1), 133 (2019)

    Google Scholar 

  16. J. Zhao, G. Wang, L. Zhang, B. Li, C. Wang, G. Zhao, and C. B. Park, Lightweight and strong fibrillary PTFE reinforced polypropylene composite foams fabricated by foam injection molding, Eur. Polym. J. 119, 22 (2019)

    Google Scholar 

  17. J. M. Eagan, J. Xu, R. Di Girolamo, C. M. Thurber, C. W. Macosko, A. M. La Pointe, F. S. Bates, and G. W. Coates, Combining polyethylene and polypropylene: Enhanced performance with PE/iPP multiblock polymers, Science 355(6327), 814 (2017)

    Google Scholar 

  18. Z. Zhang, W. Li, and J. Kan, Behavior of a thermoelectric power generation device based on solar irradiation and the earth’s surface-air temperature difference, Energy Convers. Manage. 97, 178 (2015)

    Google Scholar 

  19. S. A. Khan, N. Sezer, S. Ismail, and M. Koç, Design, synthesis and nucleate boiling performance assessment of hybrid micro-nano porous surfaces for thermal management of concentrated photovoltaics (CPV), Energy Convers. Manage. 195, 1056 (2019)

    Google Scholar 

  20. J. Zhao, Y. Huang, G. Wang, Y. Qiao, Z. Chen, A. Zhang, and C. B. Park, Fabrication of outstanding thermal-insulating, mechanical robust and superhydrophobic PP/CNT/sorbitol derivative nanocomposite foams for efficient oil/water separation, J. Hazard. Mater. 418, 126295 (2021)

    Google Scholar 

  21. J. Zhao, Q. Zhao, L. Wang, C. Wang, B. Guo, C. B. Park, and G. Wang, Development of high thermal insulation and compressive strength BPP foams using moldopening foam injection molding with in-situ fibrillated PTFE fibers, Eur. Polym. J. 98, 1 (2018)

    Google Scholar 

  22. P. Gong, G. Wang, M. P. Tran, P. Buahom, S. Zhai, G. Li, and C. B. Park, Advanced bimodal polystyrene/multiwalled carbon nanotube nanocomposite foams for thermal insulation, Carbon 120, 1 (2017)

    Google Scholar 

  23. G. Wang, J. Zhao, G. Wang, H. Zhao, J. Lin, G. Zhao, and C. B. Park, Strong and super thermally insulating insitu nanofibrillar PLA/PET composite foam fabricated by high-pressure microcellular injection molding, Chem. Eng. J. 390, 124520 (2020)

    Google Scholar 

  24. J. Zhao, G. Wang, C. Wang, and C. B. Park, Ultra-lightweight, super thermal-insulation and strong PP/CNT microcellular foams, Compos. Sci. Technol. 191, 108084 (2020)

    Google Scholar 

  25. P. Gong, P. Buahom, M. P. Tran, M. Saniei, C. B. Park, and P. Pötschke, Heat transfer in microcellular polystyrene/multi-walled carbon nanotube nanocomposite foams, Carbon 93, 819 (2015)

    Google Scholar 

  26. G. Wang, J. Zhao, L. H. Mark, G. Wang, K. Yu, C. Wang, C. B. Park, and G. Zhao, Ultra-tough and super thermal-insulation nanocellular PMMA/TPU, Chem. Eng. J. 325, 632 (2017)

    Google Scholar 

  27. G. Wang, J. Zhao, K. Yu, L. H. Mark, G. Wang, P. Gong, C. B. Park, and G. Zhao, Role of elastic strain energy in cell nucleation of polymer foaming and its application for fabricating sub-microcellular TPU microfilms, Polymer (Guildf.) 119, 28 (2017)

    Google Scholar 

  28. L. Wang, R. E. Lee, G. Wang, R. K. M. Chu, J. Zhao, and C. B. Park, Use of stereocomplex crystallites for fully-biobased microcellular low-density poly(lactic acid) foams for green packaging, Chem. Eng. J. 327, 1151 (2017)

    Google Scholar 

  29. B. Krause, H. J. P. Sijbesma, P. Münüklü, N. F. A. Van Der Vegt, and M. Wessling, Bicontinuous nanoporous polymers by carbon dioxide foaming, Macromolecules 34, 25 (2001)

    Google Scholar 

  30. S. N. Leung, and J. E. Lee, Tunable microcellular and nanocellular morphologies of poly(vinylidene) fluoride foams via crystal polymorphism control, Polymer Crystallization 2(1), 1 (2019)

    Google Scholar 

  31. S. Pérez-Tamarit, B. Notario, E. Solórzano, and M. A. Rodriguez-Perez, Light transmission in nanocellular polymers: Are semi-transparent cellular polymers possible? Mater. Lett. 210, 39 (2018)

    Google Scholar 

  32. S. Liu, R. Eijkelenkamp, J. Duvigneau, and G. J. Vancso, Silica-assisted nucleation of polymer foam cells with nanoscopic dimensions: impact of particle size, line tension, and surface functionality, ACS Appl. Mater. Interfaces 9, 43 (2017)

    Google Scholar 

  33. B. Notario, J. Pinto, and M. A. Rodriguez-Perez, Nanoporous polymeric materials: A new class of materials with enhanced properties, Prog. Mater. Sci. 78–79, 93 (2016)

    Google Scholar 

  34. B. Notario, J. Pinto, and M. A. Rodríguez-Pérez, Towards a new generation of polymeric foams: PMMA nanocellular foams with enhanced physical properties, Polymer (Guildf.) 63, 116 (2015)

    Google Scholar 

  35. Y. Zeng, R. Zou, and Y. Zhao, Carbon dioxide capture: Covalent organic frameworks for CO2 capture, Adv. Mater. 28, 3032 (2016)

    Google Scholar 

  36. L. Zou, Y. Sun, S. Che, X. Yang, X. Wang, M. Bosch, Q. Wang, H. Li, M. Smith, S. Yuan, Z. Perry, and H. C. Zhou, Porous organic polymers for post-combustion carbon capture, Adv. Mater. 29, 37 (2017)

    Google Scholar 

  37. X. Liu, G. J. H. Lim, Y. Wang, L. Zhang, D. Mullangi, Y. Wu, D. Zhao, J. Ding, A. K. Cheetham, and J. Wang, Binder-free 3D printing of covalent organic framework (COF) monoliths for CO2 adsorption, Chem. Eng. J. 403, 126333 (2021)

    Google Scholar 

  38. M. Wang, S. Zhou, S. Cao, Z. Wang, S. Liu, S. Wei, Y. Chen, and X. Lu, Stimulus-responsive adsorbent materials for CO2 capture and separation, J. Mater. Chem. A 8, 10519 (2020)

    Google Scholar 

  39. P. Puthiaraj, Y. R. Lee, S. Zhang, and W. S. Ahn, Triazine-based covalent organic polymers: design, synthesis and applications in heterogeneous catalysis, J. Mater. Chem. A 4(42), 16288 (2016)

    Google Scholar 

  40. Y. Zhang and S. N. Riduan, Functional porous organic polymers for heterogeneous catalysis, Chem. Soc. Rev. 41, 6 (2012)

    Google Scholar 

  41. Z. Ma, J. Zhuang, X. Zhang, and Z. Zhou, SiP monolayers: New 2D structures of group IV-V compounds for visible-light photohydrolytic catalysts, Front. Phys. 13(3), 138104 (2018)

    Google Scholar 

  42. M. Kilpatrick, R. D. Eanes, and J. G. Morse, The dissociation constants of acids in salt solutions(IV): Cyclohexanecarboxylic acid, J. Am. Chem. Soc. 75(3), 588 (1953)

    Google Scholar 

  43. A. Chakrabarti and M. M. Sharma, Cationic ion exchange resins as catalyst, Reactive Polymers 20(1–2), 1 (1993)

    Google Scholar 

  44. R. Liu, Z. Yang, S. Chen, J. Yao, Q. Mu, D. Peng, and H. Zhao, Synthesis and facile functionalization of siloxane based hyper-cross-linked porous polymers and their applications in water treatment, Eur. Polym. J. 119, 94 (2019)

    Google Scholar 

  45. C. Gu, N. Huang, J. Gao, F. Xu, Y. Xu, and D. Jiang, Controlled synthesis of conjugated microporous polymer films: Versatile platforms for highly sensitive and label — free chemo — and biosensing, Angew. Chem. 126(19), 4950 (2014)

    Google Scholar 

  46. S. Luo, Z. Zeng, G. Zeng, Z. Liu, R. Xiao, P. Xu, H. Wang, D. Huang, Y. Liu, B. Shao, Q. Liang, D. Wang, Q. He, L. Qin, and Y. Fu, Recent advances in conjugated microporous polymers for photocatalysis: Designs, applications, and prospects, J. Mater. Chem. A 8(14), 6434 (2020)

    Google Scholar 

  47. Y. N. Jiang, J. H. Zeng, Y. Yang, Z. K. Liu, J. J. Chen, D. C. Li, L. Chen, and Z. P. Zhan, A conjugated microporous polymer as a recyclable heterogeneous ligand for highly efficient regioselective hydrosilylation of allenes, Chem. Commun. 56(10), 1597 (2020)

    Google Scholar 

  48. S. Kim and Y. M. Lee, Rigid and microporous polymers for gas separation membranes, Prog. Polym. Sci. 43, 1 (2015)

    Google Scholar 

  49. A. I. Cooper, Conjugated microporous polymers, Adv. Mater. 21(12), 1291 (2009)

    Google Scholar 

  50. F. Vilela, K. Zhang, and M. Antonietti, Conjugated porous polymers for energy applications, Energy Environ. Sci. 5(7), 7819 (2012)

    Google Scholar 

  51. J. Pinto, A. Athanassiou, and D. Fragouli, Surface modification of polymeric foams for oil spills remediation, J. Environ. Manage. 206, 872 (2018)

    Google Scholar 

  52. O. Oribayo, X. Feng, G. L. Rempel, and Q. Pan, Modification of formaldehyde-melamine-sodium bisulfite copolymer foam and its application as effective sorbents for clean up of oil spills, Chem. Eng. Sci. 160, 384 (2017)

    Google Scholar 

  53. M. R. El-Aassar, M. S. Masoud, M. F. Elkady, and A. A. Elzain, Synthesis, optimization, and characterization of poly (Styrene-co-Acrylonitrile) copolymer prepared via precipitation polymerization, Adv. Polym. Technol. 37(6), 2021 (2018)

    Google Scholar 

  54. A. Akelah, Functionalized Polymeric Materials in Agriculture and the Food Industry, Springer US, 2013

    Google Scholar 

  55. M. Noruzi, Electrospun nanofibres in agriculture and the food industry: A review, J. Sci. Food Agric. 96(14), 4663 (2016)

    Google Scholar 

  56. X. Meng, H. N. Wang, S. Y. Song, and H. J. Zhang, Proton-conducting crystalline porous materials, Chem. Soc. Rev. 46(2), 464 (2017)

    Google Scholar 

  57. S. Horike, D. Umeyama, and S. Kitagawa, Ion conductivity and transport by porous coordination polymers and metal-organic frameworks, Acc. Chem. Res. 46(11), 2376 (2013)

    Google Scholar 

  58. H. Xu, S. Tao, and D. Jiang, Proton conduction in crystalline and porous covalent organic frameworks, Nat. Mater. 15(7), 722 (2016)

    Google Scholar 

  59. P. M. Valetsky, M. G. Sulman, L. M. Bronstein, E. M. Sulman, A. I. Sidorov, and V. G. Matveeva, Nanosized catalysts in fine organic synthesis as a basis for developing innovative technologies in the pharmaceutical industry, Nanotechnol. Russ. 4(9–10), 647 (2009)

    Google Scholar 

  60. M. Sauceau, J. Fages, A. Common, C. Nikitine, and E. Rodier, New challenges in polymer foaming: A review of extrusion processes assisted by supercritical carbon dioxide, Prog. Polym. Sci. 36(6), 749 (2011)

    Google Scholar 

  61. J. Shokri and K. Adibki, in: Cellulose — Medical, Pharmaceutical and Electronic Applications, InTech, 2013

  62. Q. Fang, J. Wang, S. Gu, R. B. Kaspar, Z. Zhuang, J. Zheng, H. Guo, S. Qiu, and Y. Yan, 3D porous crystalline polyimide covalent organic frameworks for drug delivery, J. Am. Chem. Soc. 137(26), 8352 (2015)

    Google Scholar 

  63. L. Feng, C. Qian, and Y. Zhao, Recent advances in covalent organic framework-based nanosystems for bioimaging and therapeutic applications, ACS Mater. Lett. 2, 1074 (2020)

    Google Scholar 

  64. M. C. Scicluna and L. Vella-Zarb, Evolution of nanocarrier drug-delivery systems and recent advancements in covalent organic framework-drug systems, ACS Appl. Nano Mater. 3(4), 3097 (2020)

    Google Scholar 

  65. N. Yadav, K. Mishra, and S. A. Hashmi, Optimization of porous polymer electrolyte for quasi-solid-state electrical double layer supercapacitor, Electrochim. Acta 235, 570 (2017)

    Google Scholar 

  66. R. C. Agrawal, and G. P. Pandey, Solid polymer electrolytes: Materials designing and all-solid-state battery applications: an overview, J. Phys. D Appl. Phys. 41(22), 223001 (2008)

    Google Scholar 

  67. D. T. JrHallinan and N. P. Balsara, Polymer electrolytes, Annu. Rev. Mater. Res. 43(1), 503 (2013)

    Google Scholar 

  68. S. Kramer, N. R. Bennedsen, and S. Kegnæs, Porous organic polymers containing active metal centers as catalysts for synthetic organic chemistry, ACS Catal. 8(8), 6961 (2018)

    Google Scholar 

  69. I. Ro, J. Resasco, and P. Christopher, Approaches for understanding and controlling interfacial effects in oxide-supported metal catalysts, ACS Catal. 8(8), 7368 (2018)

    Google Scholar 

  70. S. H. Xie, Y. Y. Liu, and J. Y. Li, Synthesis, microstructures, and magnetoelectric couplings of electrospun multiferroic nanofibers, Front. Phys. 7(4), 399 (2012)

    Google Scholar 

  71. S. Ghasemi and A. Nematollahzadeh, Molecularly imprinted polymer membrane for the removal of naphthalene from petrochemical wastewater streams, Adv. Polym. Technol. 37(6), 2288 (2018)

    Google Scholar 

  72. K. Sanctucci and B. Shah, Association of naphthalene with acute hemolytic anemia, Acad. Emerg. Med. 7, 42 (2000)

    Google Scholar 

  73. A. Modak, M. Nandi, J. Mondal, and A. Bhaumik, Porphyrin based porous organic polymers: Novel synthetic strategy and exceptionally high CO2 adsorption capacity, Chem. Commun. 48(2), 248 (2012)

    Google Scholar 

  74. X. He, Q. Shi, X. Zhou, C. Wan, and C. Jiang, In situ composite of nano SiO2-P(VDF-HFP) porous polymer electrolytes for Li-ion batteries, Electrochim. Acta 51(6), 1069 (2005)

    Google Scholar 

  75. J. Y. Sanchez, F. Alloin, and C. P. Lepmi, Polymeric materials in energy storage and conversion, Molecular Crystals and Liquid Crystals Science and Technology A 324(1), 257 (1998)

    Google Scholar 

  76. M. Alamgir and K. M. Abraham, Li Ion Conductive Electrolytes Based on Poly(vinyl chloride), J. Electrochem. Soc. 140(6), L96 (1993)

    Google Scholar 

  77. Y. Wu, J. Wang, K. Jiang, and S. Fan, Applications of carbon nanotubes in high performance lithium ion batteries, Front. Phys. 9(3), 351 (2014)

    Google Scholar 

  78. Y. Huang, P. Liu, R. Hao, S. Kan, Y. Wu, H. Liu, and K. Liu, Engineering porous quasi-spherical Fe-N-C nanocatalysts with robust oxygen reduction performance for Zn-air battery application, ChemNanoMat 6(12), 1782 (2020)

    Google Scholar 

  79. J. Mandal, Y. Fu, A. C. Overvig, M. Jia, K. Sun, N. N. Shi, H. Zhou, X. Xiao, N. Yu, and Y. Yang, Hierarchically porous polymer coatings for highly efficient passive daytime radiative cooling, Science 362(6412), 315 (2018)

    Google Scholar 

  80. A. P. Raman, M. A. Anoma, L. Zhu, E. Rephaeli, and S. Fan, Passive radiative cooling below ambient air temperature under direct sunlight, Nature 515(7528), 540 (2014)

    Google Scholar 

  81. G. Sharma, B. Thakur, M. Naushad, A. Kumar, F. J. Stadler, S. M. Alfadul, and G. T. Mola, Applications of nanocomposite hydrogels for biomedical engineering and environmental protection, Environ. Chem. Lett. 16(1), 113 (2018)

    Google Scholar 

  82. W. Chen, S. Liu, Y. Dong, X. Zhou, and F. Zhou, Poly (m-phenylene isophthalamide)/graphene composite aerogels with enhanced compressive shape stability for thermal insulation, J. Sol-Gel Sci. Technol. 96(2), 370 (2020)

    Google Scholar 

  83. X. Han, J. Zhang, J. Huang, X. Wu, D. Yuan, Y. Liu, and Y. Cui, Chiral induction in covalent organic frameworks, Nat. Commun. 9, 1 (2018)

    Google Scholar 

  84. Z. Wang, G. Chen, and K. Ding, Self-supported catalysts, Chem. Rev. 109(2), 322 (2009)

    Google Scholar 

  85. C. Train, R. Gheorghe, V. Krstic, L. M. Chamoreau, N. S. Ovanesyan, G. L. J. A. Rikken, M. Gruselle, and M. Verdaguer, Strong magneto-chiral dichroism in enantiopure chiral ferromagnets, Nat. Mater. 7(9), 729 (2008)

    Google Scholar 

  86. S. G. Mosanenzadeh, S. Karamikamkar, Z. Saadatnia, C. B. Park, and H. E. Naguib, PPDA-PMDA polyimide aerogels with tailored nanostructure assembly for air filtering applications, Separ. Purif. Tech. 250, 117279 (2020)

    Google Scholar 

  87. S. Karamikamkar, H. E. Naguib, and C. B. Park, Advances in precursor system for silica-based aerogel production toward improved mechanical properties, customized morphology, and multifunctionality: A review, Adv. Colloid Interface Sci. 276, 102101 (2020)

    Google Scholar 

  88. Q. Qi, L. Ma, B. Zhao, S. Wang, X. Liu, Y. Lei, and C. B. Park, An effective design strategy for the sandwich structure of PVDF/GNP-Ni-CNT composites with remarkable electromagnetic interference shielding effectiveness, ACS Appl. Mater. Interfaces 12(32), 36568 (2020)

    Google Scholar 

  89. S. Liu, J. Gong, and B. Xu, Three-dimensionally conformal porous polymeric microstructures of fabrics for electrothermal textiles with enhanced thermal management, Polymers (Basel) 10(7), 748 (2018)

    Google Scholar 

  90. D. Reichenberg, Properties of ion-exchange resins in relation to their structure (III): Kinetics of exchange, J. Am. Chem. Soc. 75(3), 589 (1953)

    Google Scholar 

  91. B. Notario, J. Pinto, R. Verdejo, and M. A. Rodríguez-Pérez, Dielectric behavior of porous PMMA: From the micrometer to the nanometer scale, Polymer (Guildf.) 107, 302 (2016)

    Google Scholar 

  92. B. Zheng, X. Lin, X. Zhang, D. Wu, and K. Matyjaszewski, Emerging functional porous polymeric and carbonaceous materials for environmental treatment and energy storage, Adv. Funct. Mater. 30(41), 1907006 (2020)

    Google Scholar 

  93. H. Shin, S. Seo, C. Park, J. Na, M. Han, and E. Kim, Energy saving electrochromic windows from bistable low-HOMO level conjugated polymers, Energy Environ. Sci. 9(1), 117 (2016)

    Google Scholar 

  94. Y. Kim, M. Han, J. Kim, and E. Kim, Electrochromic capacitive windows based on all conjugated polymers for a dual function smart window, Energy Environ. Sci. 11(8), 2124 (2018)

    Google Scholar 

  95. S. Rashidi, J. A. Esfahani, and N. Karimi, Porous materials in building energy technologies — A review of the applications, modelling and experiments, Renew. Sustain. Energy Rev. 91, 229 (2018)

    Google Scholar 

  96. W. Chen and W. Liu, Thermal analysis on the cooling performance of a porous evaporative plate for building, Heat Transf. Asian Res. 39(2), 127 (2010)

    MathSciNet  Google Scholar 

  97. N. Gupta and G. N. Tiwari, Review of passive heating/cooling systems of buildings, Energy Sci. Eng. 4(5), 305 (2016)

    Google Scholar 

  98. M. Dogru, M. Handloser, F. Auras, T. Kunz, D. Medina, A. Hartschuh, P. Knochel, and T. Bein, A photocon-ductive thienothiophene-based covalent organic framework showing charge transfer towards included fullerene, Angew. Chem. 125(10), 2992 (2013)

    Google Scholar 

  99. S. W. Park, Z. Liao, B. Ibarlucea, H. Qi, H. H. Lin, D. Becker, J. Melidonie, T. Zhang, H. Sahabudeen, L. Baraban, C. K. Baek, Z. Zheng, E. Zschech, A. Fery, T. Heine, U. Kaiser, G. Cuniberti, R. Dong, and X. Feng, Two-dimensional boronate ester covalent organic framework thin films with large single crystalline domains for a neuromorphic memory device, Angew. Chem. Int. Ed. 59(21), 8218 (2020)

    Google Scholar 

  100. Z. Lai, X. Guo, Z. Cheng, G. Ruan, and F. Du, Green synthesis of fluorescent carbon dots from cherry tomatoes for highly effective detection of trifluralin herbicide in soil samples, Chemistry Select 5(6), 1956 (2020)

    Google Scholar 

  101. M. D. Allendorf, R. Dong, X. Feng, S. Kaskel, D. Matoga, and V. Stavila, Electronic devices using open framework materials, Chem. Rev. 120(16), 8581 (2020)

    Google Scholar 

  102. F. Q. Huang, C. Y. Yang, and D. Y. Wan, Advanced solar materials for thin-film photovoltaic cells, Front. Phys. 6(2), 177 (2011)

    Google Scholar 

  103. S. B. Alahakoon, C. M. Thompson, G. Occhialini, and R. A. Smaldone, Design principles for covalent organic frameworks in energy storage applications, ChemSusChem 10(10), 2116 (2017)

    Google Scholar 

  104. G. A. Leith, A. M. Rice, B. J. Yarbrough, A. A. Berseneva, R. T. Ly, C. N. IIIBuck, D. Chusov, A. J. Brandt, D. A. Chen, B. W. Lamm, M. Stefik, K. S. Stephenson, M. D. Smith, A. K. Vannucci, P. J. Pellechia, S. Garashchuk, and N. B. Shustova, A dual threat: Redoxactivity and electronic structures of welldefined donoracceptor fulleretic covalentorganic materials, Angew. Chem. Int. Ed. 59(15), 6000 (2020)

    Google Scholar 

  105. J. Li, X. Jing, Q. Li, S. Li, X. Gao, X. Feng, and B. Wang, Bulk COFs and COF nanosheets for electrochemical energy storage and conversion, Chem. Soc. Rev. 49(11), 3565 (2020)

    Google Scholar 

  106. S. Lee, I. Y. Cho, D. Kim, N. K. Park, J. Park, Y. Kim, S. J. Kang, Y. Kim, and S. Y. Hong, Redox-active functional electrolyte for high-performance seawater batteries, ChemSusChem 13(9), 2220 (2020)

    Google Scholar 

  107. N. Liu, W. Li, M. Pasta, and Y. Cui, Nanomaterials for electrochemical energy storage, Front. Phys. 9(3), 323 (2014)

    Google Scholar 

  108. P. P. Mukherjee and C. Y. Wang, Direct numerical simulation modeling of bilayer cathode catalyst layers in polymer electrolyte fuel cells, J. Electrochem. Soc. 154(11), B1121 (2007)

    Google Scholar 

  109. X. A. Zhang, S. Yu, B. Xu, M. Li, Z. Peng, Y. Wang, S. Deng, X. Wu, Z. Wu, M. Ouyang, and Y. H. Wang, Dynamic gating of infrared radiation in a textile, Science 363(6427), 619 (2019)

    Google Scholar 

  110. Q. Peng, J. E, J. Chen, W. Zuo, X. Zhao, and Z. Zhang, Investigation on the effects of wall thickness and porous media on the thermal performance of a non-premixed hydrogen fueled cylindrical micro combustor, Energy Convers. Manage. 155, 276 (2018)

    Google Scholar 

  111. Y. Cui, H. Gong, Y. Wang, D. Li, and H. Bai, A thermally insulating textile inspired by polar bear hair, Adv. Mater. 30(14), 1706807 (2018)

    Google Scholar 

  112. Y. N. Song, Y. Li, D. X. Yan, J. Lei, and Z. M. Li, Novel passive cooling composite textile for both outdoor and indoor personal thermal management, Compos. Part A Appl. Sci. Manuf. 130, 105738 (2020)

    Google Scholar 

  113. R. Hu, Y. Liu, S. Shin, S. Huang, X. Ren, W. Shu, J. Cheng, G. Tao, W. Xu, R. Chen, and X. Luo, Emerging materials and strategies for personal thermal management, Adv. Energy Mater. 10(17), 1903921 (2020)

    Google Scholar 

  114. Y. Guo, C. Dun, J. Xu, J. Mu, P. Li, L. Gu, C. Hou, C. A. Hewitt, Q. Zhang, Y. Li, D. L. Carroll, and H. Wang, Ultrathin, washable, and large-area graphene papers for personal thermal management, Small 13(44), 1702645 (2017)

    Google Scholar 

  115. G. Dai, Designing nonlinear thermal devices and metamaterials under the Fourier law: A route to nonlinear thermotics, Front. Phys. 16, 1 (2021)

    Google Scholar 

  116. L. Qiu, N. Zhu, Y. Feng, E. E. Michaelides, G. Żyła, D. Jing, X. Zhang, P. M. Norris, C. N. Markides, and O. Mahian, A review of recent advances in thermophysical properties at the nanoscale: From solid state to colloids, Phys. Rep. 843, 1 (2020)

    Google Scholar 

  117. G. Xu, K. Dong, Y. Li, H. Li, K. Liu, L. Li, J. Wu, and C. Qiu, Tunable analog thermal material, Nat. Commun. 11, 1 (2020)

    Google Scholar 

  118. M. Chen, D. Pang, J. Mandal, X. Chen, H. Yan, Y. He, N. Yu, and Y. Yang, Designing mesoporous photonic structures for high-performance passive daytime radiative cooling, Nano Lett. 21(3), 1412 (2021)

    Google Scholar 

  119. T. Wang, M. C. Long, H. B. Zhao, B. W. Liu, H. G. Shi, W. L. An, S. L. Li, S. M. Xu, and Y. Z. Wang, An ultralow-temperature superelastic polymer aerogel with high strength as a great thermal insulator under extreme conditions, J. Mater. Chem. A Mater. Energy Sustain. 8(36), 18698 (2020)

    Google Scholar 

  120. F. Hu, S. Wu, and Y. Sun, Hollow-structured materials for thermal insulation, Adv. Mater. 31(38), 1801001 (2019)

    Google Scholar 

  121. Y. Guo, Z. Zhang, M. Bescond, S. Xiong, M. Nomura, and S. Volz, Anharmonic phonon-phonon scattering at the interface between two solids by nonequilibrium Green’s function formalism, Phys. Rev. B 103(17), 174306 (2021)

    Google Scholar 

  122. G. Wang, C. Wang, J. Zhao, G. Wang, C. B. Park, and G. Zhao, Modelling of thermal transport through a nanocellular polymer foam: toward the generation of a new superinsulating material, Nanoscale 9(18), 5996 (2017)

    Google Scholar 

  123. G. Wang, C. Wang, J. Zhao, G. Wang, C. B. Park, G. Zhao, W. Van De Walle, and H. Janssen, Correction: Modelling of thermal transport through a nanocellular polymer foam: Toward the generation of a new superin-sulating material, Nanoscale 10(43), 20469 (2018)

    Google Scholar 

  124. E. Cuce, C. H. Young, and S. B. Riffat, Performance investigation of heat insulation solar glass for low-carbon buildings, Energy Convers. Manage. 88, 834 (2014)

    Google Scholar 

  125. Y. Xu, L. Lin, M. Xiao, S. Wang, A. T. Smith, L. Sun, and Y. Meng, Synthesis and properties of CO2-based plastics: Environmentally-friendly, energy-saving and biomedical polymeric materials, Prog. Polym. Sci. 80, 163 (2018)

    Google Scholar 

  126. J. Weng, D. Ouyang, X. Yang, M. Chen, G. Zhang, and J. Wang, Alleviation of thermal runaway propagation in thermal management modules using aerogel felt coupled with flame-retarded phase change material, Energy Convers. Manage. 200, 112071 (2019)

    Google Scholar 

  127. I. Oropeza-Perez and P. A. Østergaard, Active and passive cooling methods for dwellings: A review, Renew. Sustain. Energy Rev. 82, 531 (2018)

    Google Scholar 

  128. S. Kashyap, S. Kabra, and B. Kandasubramanian, Graphene aerogel-based phase changing composites for thermal energy storage systems, J. Mater. Sci. 55(10), 4127 (2020)

    Google Scholar 

  129. https://spinoff.nasa.gov/spinoff2001/ch5.html

  130. P. R. Ferrer, A. Mace, S. N. Thomas, and J. W. Jeon, Nanostructured porous graphene and its composites for energy storage applications, Nano Converg. 4, 1 (2017)

    Google Scholar 

  131. E. Pakdel, M. Naebe, L. Sun, and X. Wang, Advanced functional fibrous materials for enhanced thermoregulating performance, ACS Appl. Mater. Interfaces 11(14), 13039 (2019)

    Google Scholar 

  132. A. Yang, L. Cai, R. Zhang, J. Wang, P. C. Hsu, H. Wang, G. Zhou, J. Xu, and Y. Cui, Thermal management in nanofiber-based face mask, Nano Lett. 17(6), 3506 (2017)

    Google Scholar 

  133. Y. Yang and Y. Zhang, Passive daytime radiative cooling: Principle, application, and economic analysis, MRS Energy Sustain. 7, 18 (2020)

    Google Scholar 

  134. M. Alvarez-Lainez, M. A. Rodriguez-Perez, and J. A. DE Saja, Thermal conductivity of open-cell polyolefin foams, J. Polym. Sci. B Polym. Phys. 46(2), 212 (2008)

    Google Scholar 

  135. L. R. Glicksman, in: Low Density Cellular Plastics, Springer Netherlands, 1994, pp 104–152

    Google Scholar 

  136. P. Buahom, C. Wang, M. Alshrah, G. Wang, P. Gong, M. P. Tran, and C. B. Park, Wrong expectation of superinsulation behavior from largely-expanded nanocellular foams, Nanoscale 12(24), 13064 (2020)

    Google Scholar 

  137. L. R. Glicksman, M. Torpey, and A. Marge, Means to improve the thermal conductivity of foam insulation, J. Cell. Plast. 28(6), 571 (1992)

    Google Scholar 

  138. A. G. Leach, The thermal conductivity of foams (I): Models for heat conduction, J. Phys. D Appl. Phys. 26(5), 733 (1993)

    Google Scholar 

  139. M. A. Schuetz and L. R. Glicksman, A basic study of heat transfer through foam insulation, J. Cell. Plast. 20(2), 114 (1984)

    Google Scholar 

  140. Z. M. Zhang, Nano/Microscale Heat Transfer, New York: McGraw-Hill, 2007

    MATH  Google Scholar 

  141. Y. L. He and T. Xie, Advances of thermal conductivity models of nanoscale silica aerogel insulation material, Appl. Therm. Eng. 81, 28 (2015)

    Google Scholar 

  142. T. Xie, Y. L. He, and Z. J. Hu, Theoretical study on thermal conductivities of silica aerogel composite insulating material, Int. J. Heat Mass Transf. 58(1–2), 540 (2013)

    Google Scholar 

  143. B. Notario, J. Pinto, E. Solorzano, J. A. De Saja, M. Dumon, and M. A. Rodríguez-Pérez, Experimental validation of the Knudsen effect in nanocellular polymeric foams, Polymer (Guildf.) 56, 57 (2015)

    Google Scholar 

  144. V. Bernardo, J. Martin-de Leon, J. Pinto, R. Verdejo, and M. A. Rodriguez-Perez, Modeling the heat transfer by conduction of nanocellular polymers with bimodal cellular structures, Polymer (Guildf.) 160, 126 (2019)

    Google Scholar 

  145. L. Wu, A slip model for rarefied gas flows at arbitrary Knudsen number, Appl. Phys. Lett. 93(25), 253103 (2008)

    Google Scholar 

  146. T. Inamuro, M. Yoshino, and F. Ogino, Accuracy of the lattice Boltzmann method for small Knudsen number with finite Reynolds number, Phys. Fluids 9(11), 3535 (1997)

    MathSciNet  MATH  Google Scholar 

  147. S. Fukui and R. Kaneko, A database for interpolation of Poiseuille flow rates for high Knudsen number Lubrication problems, J. Tribol. 112(1), 78 (1990)

    Google Scholar 

  148. F. Tao and L. Nguyen, Interactions of gaseous molecules with X-ray photons and photoelectrons in AP-XPS study of solid surface in gas phase, Phys. Chem. Chem. Phys. 20(15), 9812 (2018)

    Google Scholar 

  149. D. R. Snelling, F. Liu, G. J. Smallwood, and Ö. L. Gülder, Determination of the soot absorption function and thermal accommodation coefficient using low-fluence LII in a laminar coflow ethylene diffusion flame, Combust. Flame 136(1–2), 180 (2004)

    Google Scholar 

  150. K. J. Daun, Thermal accommodation coefficients between polyatomic gas molecules and soot in laser-induced incandescence experiments, Int. J. Heat Mass Transf. 52(21–22), 5081 (2009)

    MATH  Google Scholar 

  151. G. Torzo, G. Delfitto, B. Pecori, and P. Scatturin, A new microcomputer-based laboratory version of the Rüchardt experiment for measuring the ratio γ = Cp/Cv in air, Am. J. Phys. 69(11), 1205 (2001)

    Google Scholar 

  152. M. Pyda and B. Wunderlich, Computation of heat capacities of liquid polymers, Macromolecules 32(6), 2044 (1999)

    Google Scholar 

  153. G. Reichenauer, U. Heinemann, and H. P. Ebert, Relationship between pore size and the gas pressure dependence of the gaseous thermal conductivity, Colloids Surf. A Physicochem. Eng. Asp. 300(1–2), 204 (2007)

    Google Scholar 

  154. S. Q. Zeng, A. Hunt, and R. Greif, Mean free path and apparent thermal conductivity of a gas in a porous medium, J. Heat Transfer 117(3), 758 (1995)

    Google Scholar 

  155. G. Lu, X. D. Wang, Y. Y. Duan, and X. W. Li, Effects of non-ideal structures and high temperatures on the insulation properties of aerogel-based composite materials, J. Non-Cryst. Solids 357(22–23), 3822 (2011)

    Google Scholar 

  156. S. Q. Zeng, A. J. Hunt, W. Cao, and R. Greif, Pore size distribution and apparent gas thermal conductivity of silica aerogel, J. Heat Transfer 116(3), 756 (1994)

    Google Scholar 

  157. C. Bi, G. H. Tang, and W. Q. Tao, Prediction of the gaseous thermal conductivity in aerogels with nonuniform pore-size distribution, J. Non-Cryst. Solids 358(23), 3124 (2012)

    Google Scholar 

  158. J. Fricke, X. Lu, P. Wang, D. Büttner, and U. Heinemann, Optimization of monolithic silica aerogel insulants, Int. J. Heat Mass Transf. 35(9), 2305 (1992)

    Google Scholar 

  159. J. Lee, J. Lim, and P. Yang, Ballistic phonon transport in holey silicon, Nano Lett. 15(5), 3273 (2015)

    Google Scholar 

  160. G. Chen, Nonlocal and nonequilibrium heat conduction in the vicinity of nanoparticles, J. Heat Transfer 118(3), 539 (1996)

    Google Scholar 

  161. M. Alshrah, L. H. Mark, C. Zhao, H. E. Naguib, and C. B. Park, Nanostructure to thermal property relationship of resorcinol formaldehyde aerogels using the fractal technique, Nanoscale 10(22), 10564 (2018)

    Google Scholar 

  162. O. J. Lee, K. H. Lee, T. Jin Yim, S. Young Kim, and K. P. Yoo, Determination of mesopore size of aerogels from thermal conductivity measurements, J. Non-Cryst. Solids 298(2–3), 287 (2002)

    Google Scholar 

  163. Z. Deng, J. Wang, A. Wu, J. Shen, and B. Zhou, High strength SiO2 aerogel insulation, J. Non-Cryst. Solids 225, 101 (1998)

    Google Scholar 

  164. S. Spagnol, B. Lartigue, A. Trombe, and V. Gibiat, Thermal modeling of two-dimensional periodic fractal patterns, an application to nanoporous media, Europhysics Letters (EPL) 78(4), 46005 (2007)

    MathSciNet  MATH  Google Scholar 

  165. K. Swimm, G. Reichenauer, S. Vidi, and H. P. Ebert, Gas pressure dependence of the heat transport in porous solids with pores smaller than 10 µm, Int. J. Thermophys. 30(4), 1329 (2009)

    Google Scholar 

  166. S. Yang, J. Wang, G. Dai, F. Yang, and J. Huang, Controlling macroscopic heat transfer with thermal metamaterials: Theory, experiment and application, Phys. Rep. 908, 1 (2021)

    MathSciNet  Google Scholar 

  167. J. Huang, Theoretical Thermotics: Transformation Thermotics and Extended Theories for Thermal Metamaterials, Springer, 2021

  168. G. Wei, Y. Liu, X. Zhang, F. Yu, and X. Du, Thermal conductivities study on silica aerogel and its composite insulation materials, Int. J. Heat Mass Transf. 54(11–12), 2355 (2011)

    MATH  Google Scholar 

  169. J. J. Zhao, Y. Y. Duan, X. D. Wang, and B. X. Wang, An analytical model for combined radiative and conductive heat transfer in fiber-loaded silica aerogels, J. Non-Cryst. Solids 358(10), 1303 (2012)

    Google Scholar 

  170. W. L. Power and T. E. Tullis, Euclidean and fractal models for the description of rock surface roughness, J. Geophys. Res. 96(B1), 415 (1991)

    Google Scholar 

  171. R. Vacher, T. Woignier, J. Pelous, and E. Courtens, Structure and self-similarity of silica aerogels, Phys. Rev. B 37(11), 6500 (1988)

    Google Scholar 

  172. G. Edgar, Measure, Topology, and Fractal Geometry, Springer New York, 2008

    MATH  Google Scholar 

  173. B. B. Mandelbrot, The Fractal Geometry of Nature, New York: WH Freeman, 1982

    MATH  Google Scholar 

  174. G. Pia and U. Sanna, Intermingled fractal units model and electrical equivalence fractal approach for prediction of thermal conductivity of porous materials, Appl. Therm. Eng. 61(2), 186 (2013)

    Google Scholar 

  175. G. Pia and U. Sanna, An intermingled fractal units model to evaluate pore size distribution influence on thermal conductivity values in porous materials, Appl. Therm. Eng. 65(1–2), 330 (2014)

    Google Scholar 

  176. X. Huai, W. Wang, and Z. Li, Analysis of the effective thermal conductivity of fractal porous media, Appl. Therm. Eng. 27(17–18), 2815 (2007)

    Google Scholar 

  177. Y. Hayase and T. Ohta, Sierpinski gasket in a reaction-diffusion system, Phys. Rev. Lett. 81(8), 1726 (1998)

    Google Scholar 

  178. Y. Ma, B. Yu, D. Zhang, and M. Zou, A self-similarity model for effective thermal conductivity of porous media, J. Phys. D Appl. Phys. 36(17), 2157 (2003)

    Google Scholar 

  179. C. Jiang, K. Davey, and R. Prosser, A tessellated continuum approach to thermal analysis: Discontinuity networks., Contin. Mech. Thermodyn. 29(1), 145 (2017)

    MathSciNet  MATH  Google Scholar 

  180. G. P. Saracco, G. Gonnella, D. Marenduzzo, and E. Orlandini, Equilibrium and dynamical behavior in the Vicsek model for self-propelled particles under shear, Cent. Eur. J. Phys. 10, 1109 (2012)

    Google Scholar 

  181. M. van den Berg, Heat equation on the arithmetic von Koch snowflake, Probab. Theory Relat. Fields 118(1), 17 (2000)

    MathSciNet  MATH  Google Scholar 

  182. B. Yu and P. Cheng, Fractal models for the effective thermal conductivity of bidispersed porous media, J. Thermophys. Heat Trans. 16(1), 22 (2002)

    Google Scholar 

  183. T. Xie, Y. L. He, and Z. J. Hu, Theoretical study on thermal conductivities of silica aerogel composite insulating material, Int. J. Heat Mass Transf. 58(1–2), 540 (2013)

    Google Scholar 

  184. S. S. Sundarram and W. Li, On thermal conductivity of micro- and nanocellular polymer foams, Polym. Eng. Sci. 53(9), 1901 (2013)

    Google Scholar 

  185. Y. Amani, A. Takahashi, P. Chantrenne, S. Maruyama, S. Dancette, and E. Maire, Thermal conductivity of highly porous metal foams: Experimental and image based finite element analysis, Int. J. Heat Mass Transf. 122, 1 (2018)

    Google Scholar 

  186. Y. Amani and A. Öchsner, Finite element simulation of arrays of hollow sphere structures, Materialwiss. Werkstofftech. 46(4–5), 462 (2015)

    Google Scholar 

  187. H. Zhong and J. R. Lukes, Interfacial thermal resistance between carbon nanotubes: Molecular dynamics simulations and analytical thermal modeling, Phys. Rev. B 74(12), 125403 (2006)

    Google Scholar 

  188. S. G. Volz and G. Chen, Molecular dynamics simulation of thermal conductivity of silicon nanowires, Appl. Phys. Lett. 75(14), 2056 (1999)

    Google Scholar 

  189. W. Zhu, G. Zheng, S. Cao, and H. He, Thermal conductivity of amorphous SiO2 thin film: A molecular dynamics study, Sci. Rep. 8, 1 (2018)

    Google Scholar 

  190. A. Henry and G. Chen, High thermal conductivity of single polyethylene chains using molecular dynamics simulations, Phys. Rev. Lett. 101(23), 235502 (2008)

    Google Scholar 

  191. Z. Y. Ong and E. Pop, Molecular dynamics simulation of thermal boundary conductance between carbon nanotubes and SiO2, Phys. Rev. B 81(15), 155408 (2010)

    Google Scholar 

  192. P. K. Schelling, S. R. Phillpot, and P. Keblinski, Comparison of atomic-level simulation methods for computing thermal conductivity, Phys. Rev. B 65(14), 144306 (2002)

    Google Scholar 

  193. J. Che, T. Çagin, and W. A. IIIGoddard, Thermal conductivity of carbon nanotubes, Nanotechnology 11(2), 65 (2000)

    Google Scholar 

  194. A. J. H. McGaughey, and M. Kaviany, Thermal conductivity decomposition and analysis using molecular dynamics simulations, Int. J. Heat Mass Transf. 47(8–9), 1799 (2004)

    MATH  Google Scholar 

  195. Y. G. Yoon, R. Car, D. J. Srolovitz, and S. Scandolo, Thermal conductivity of crystalline quartz from classical simulations, Phys. Rev. B 70(1), 012302 (2004)

    Google Scholar 

  196. D. P. Sellan, E. S. Landry, J. E. Turney, A. J. H. McGaughey, and C. H. Amon, Size effects in molecular dynamics thermal conductivity predictions, Phys. Rev. B 81(21), 214305 (2010)

    Google Scholar 

  197. Y. F. Han, X. L. Xia, H. P. Tan, and H. D. Liu, Modeling of phonon heat transfer in spherical segment of silica aerogel grains, Physica B 420, 58 (2013)

    Google Scholar 

  198. T. Zeng and W. Liu, Phonon heat conduction in micro- and nano-core-shell structures with cylindrical and spherical geometries, J. Appl. Phys. 93(7), 4163 (2003)

    Google Scholar 

  199. A. Fakhari and T. Lee, Numerics of the lattice boltzmann method on nonuniform grids: Standard LBM and finitedifference LBM, Comput. Fluids 107, 205 (2015)

    MathSciNet  MATH  Google Scholar 

  200. S. Chen and G. D. Doolen, Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech. 30(1), 329 (1998)

    MathSciNet  MATH  Google Scholar 

  201. G. H. Tang, W. Q. Tao, and Y. L. He, Gas slippage effect on microscale porous flow using the lattice Boltzmann method, Phys. Rev. E 97, 104918 (2005)

    Google Scholar 

  202. Y. Peng, Y. T. Chew, and C. Shu, Numerical simulation of natural convection in a concentric annulus between a square outer cylinder and a circular inner cylinder using the Taylor-series-expansion and least-squares-based lattice Boltzmann method, Phys. Rev. E 67(2), 026701 (2003)

    Google Scholar 

  203. C. Y. Zhao, L. N. Dai, G. H. Tang, Z. G. Qu, and Z. Y. Li, Numerical study of natural convection in porous media (metals) using lattice Boltzmann method (LBM), Int. J. Heat Fluid Flow 31(5), 925 (2010)

    Google Scholar 

  204. H. Yu, H. Zhang, P. Buahom, J. Liu, X. Xia, and C. B. Park, Prediction of thermal conductivity of micro/nano porous dielectric materials: Theoretical model and impact factors, Energy 233, 121140 (2021)

    Google Scholar 

  205. S. Wang, Y. Huang, E. Chang, C. Zhao, A. Ameli, H. E. Naguib, and C. B. Park, Evaluation and modeling of electrical conductivity in conductive polymer nanocomposite foams with multiwalled carbon nanotube networks, Chem. Eng. J. 411, 128382 (2021)

    Google Scholar 

  206. A. Rizvi, R. K. M. Chu, and C. B. Park, Scalable fabrication of thermally insulating mechanically resilient hierarchically porous polymer foams, ACS Appl. Mater. Interfaces 10(44), 38410 (2018)

    Google Scholar 

  207. P. Gong, S. Zhai, R. Lee, C. Zhao, P. Buahom, G. Li, and C. B. Park, Environmentally Friendly Polylactic Acid-Based Thermal Insulation Foams Blown with Supercritical CO2, Ind. Eng. Chem. Res. 57(15), 5464 (2018)

    Google Scholar 

  208. G. Wang, J. Zhao, G. Wang, L. H. Mark, C. B. Park, and G. Zhao, Low-density and structure-tunable micro-cellular PMMA foams with improved thermal-insulation and compressive mechanical properties, Eur. Polym. J. 95, 382 (2017)

    Google Scholar 

  209. J. R. Howell, R. Siegel, and M. P. Mengüç, Thermal Radiation Heat Transfer, 5th Ed., CRC Press, Taylor & Francis Group, 2010

  210. Y. Feng and C. Wang, Discontinuous finite element method applied to transient pure and coupled radiative heat transfer, Int. Commun. Heat Mass Transf. 122, 105156 (2021)

    Google Scholar 

  211. T. Xie and Y. L. He, Heat transfer characteristics of silica aerogel composite materials: Structure reconstruction and numerical modeling, Int. J. Heat Mass Transf. 95, 621 (2016)

    Google Scholar 

  212. A. V. Gusarov, E. Poloni, V. Shklover, A. Sologubenko, J. Leuthold, S. White, and J. Lawson, Radiative transfer in porous carbon-fiber materials for thermal protection systems, Int. J. Heat Mass Transf. 144, 118582 (2019)

    Google Scholar 

  213. T. J. Hendricks and J. R. Howell, Absorption/scattering coefficients and scattering phase functions in reticulated porous ceramics, J. Heat Transfer 118(1), 79 (1996)

    Google Scholar 

  214. B. Quistián-Vázquez, B. Morales-Cruzado, E. Sarmiento-Gómez, and F. G. Pérez-Gutiérrez, Retrieval of absorption or scattering coefficient spectrum (RASCS) program: A tool to monitor optical properties in real time, Lasers Surg. Med. 52(6), 552 (2020)

    Google Scholar 

  215. F. Vaudelle, J. P. L’Huillier, and M. L. Askoura, Light source distribution and scattering phase function influence light transport in diffuse multi-layered media, Opt. Commun. 392, 268 (2017)

    Google Scholar 

  216. J. E. Sipe, New Green-function formalism for surface optics, J. Opt. Soc. Am. B 4(4), 481 (1987)

    Google Scholar 

  217. L. Dombrovsky, J. Randrianalisoa, and D. Baillis, Modified two-flux approximation for identification of radiative properties of absorbing and scattering media from directional-hemispherical measurements, J. Opt. Soc. Am. A 23(1), 91 (2006)

    MathSciNet  Google Scholar 

  218. L. Dombrovsky, A. Leonid, G. Krithiga, and L. Wojciech, Combined two-flux approximation and Monte Carlo model for identification of radiative properties of highly scattering dispersed materials, Comput. Therm. Sci.: Int. J. 4, 4 (2012)

    Google Scholar 

  219. S. Chandrasekhar, The stability of non-dissipative Couette flow in hydromagnetics, Proc. Natl. Acad. Sci. USA 46(2), 253 (1960)

    MathSciNet  MATH  Google Scholar 

  220. T. K. Kim, J. A. Menart, and H. S. Lee, Nongray radiative gas analyses using the S-N discrete ordinates method, J. Heat Transfer 113(4), 946 (1991)

    Google Scholar 

  221. R. Eymard, T. Gallouët, and R. Herbin, Finite volume methods, Handbook Numer. Anal. 7, 713 (2000)

    MathSciNet  MATH  Google Scholar 

  222. A. Cohen, Wavelet methods in numerical analysis, Handbook Numer. Anal. 7, 417 (2000)

    MathSciNet  MATH  Google Scholar 

  223. H. Yu, H. Zhang, Y. Guo, H. Tan, Y. Li, and G. Xie, Thermodynamic analysis of shark skin texture surfaces for microchannel flow, Contin. Mech. Thermodyn. 28(5), 1361 (2016)

    MathSciNet  MATH  Google Scholar 

  224. H. Yu, H. Zhang, and X. Xia, A fractal-skeleton model of high porosity macroporous aluminum and its heat transfer characterizes, J. Therm. Anal. Calorim. 1, 1 (2020)

    Google Scholar 

  225. H. Yu, H. Zhang, C. Su, K. Wang, and L. Jin, The spectral radiative effect of Si/SiO2 substrate on monolayer aluminum porous microstructure, Therm. Sci. 22(Suppl. 2), 629 (2018)

    Google Scholar 

  226. P. S. Cumber, Improvements to the discrete transfer method of calculating radiative heat transfer, Int. J. Heat Mass Transf. 38(12), 2251 (1995)

    MATH  Google Scholar 

  227. M. Fairweather, W. P. Jones, and R. P. Lindstedt, Predictions of radiative transfer from a turbulent reacting jet in a cross-wind, Combust. Flame 89(1), 45 (1992)

    Google Scholar 

  228. E. Solórzano, M. A. Rodriguez-Perez, J. Lázaro, and J. A. de Saja, Influence of solid phase conductivity and cellular structure on the heat transfer mechanisms of cellular materials: Diverse case studies, Adv. Eng. Mater. 11(10), 818 (2009)

    Google Scholar 

  229. L. R. Glicksman, T. Yule, and A. Dyrness, Prediction of the expansion of fluidized beds containing tubes, Chem. Eng. Sci. 46(7), 1561 (1991)

    Google Scholar 

  230. H. P. Tan, L. H. Liu, H. L. Yi, J. M. Zhao, H. Qi, and J. Y. Tan, Recent progress in computational thermal radiative transfer, Chin. Sci. Bull. 54(22), 4135 (2009)

    Google Scholar 

  231. S. Basu and Z. M. Zhang, Maximum energy transfer in near-field thermal radiation at nanometer distances, J. Appl. Phys. 105(9), 093535 (2009)

    Google Scholar 

  232. V. Bernardo, J. Martin-de Leon, J. Pinto, U. Schade, and M. A. Rodriguez-Perez, On the interaction of infrared radiation and nanocellular polymers: First experimental determination of the extinction coefficient, Colloids Surf. A 600, 124937 (2020)

    Google Scholar 

  233. J. Martín-de León, J. L. Pura, V. Bernardo, and M. Á. Rodríguez-Pérez, Transparent nanocellular PMMA: Characterization and modeling of the optical properties, Polymer (Guildf.) 170, 16 (2019)

    Google Scholar 

  234. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles, Wiley, Hoboken, 2004

    Google Scholar 

  235. M. Nieto-Vesperinas, Fundamentals of Mie scattering, Woodhead Publishing, 2020

  236. S. Shen, A. Narayanaswamy, and G. Chen, Surface phonon polaritons mediated energy transfer between nanoscale gaps, Nano Lett. 9(8), 2909 (2009)

    Google Scholar 

  237. S. Shen, A. Henry, J. Tong, R. Zheng, and G. Chen, Polyethylene nanofibres with very high thermal conductivities, Nat. Nanotechnol. 5(4), 251 (2010)

    Google Scholar 

  238. X. Liu, L. Wang, and Z. M. Zhang, Near-field thermal radiation: Recent progress and outlook, Nanoscale Microscale Thermophys. Eng. 19(2), 98 (2015)

    Google Scholar 

  239. H. Yu, H. Zhang, H. Wang, and D. Zhang, The equivalent thermal conductivity of the micro/nano scaled periodic cubic frame silver and its thermal radiation mechanism analysis, Energies 14, 1 (2021)

    Google Scholar 

  240. B. Liu, F. Sun, X. Chen, and X. Xia, Prediction of radiation spectra of composite with periodic micron porous structure, Numer. Heat Transf. B 78(1), 54 (2020)

    Google Scholar 

  241. S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarski, Principles of Statistical Radiophysics, Springer-Verlag, 1987

  242. H. Yu, H. Zhang, Z. Dai, and X. Xia, Design and analysis of low emissivity radiative cooling multilayer films based on effective medium theory, ES Energy & Environment 6, 69 (2019)

    Google Scholar 

  243. L. X. Ma, C. C. Wang, and J. Y. Tan, Light scattering by densely packed optically soft particle systems, with consideration of the particle agglomeration and dependent scattering, Appl. Opt. 58(27), 7336 (2019)

    Google Scholar 

  244. S. Basu, Z. Zhang, and C. Fu, Review of near-field thermal radiation and its application to energy conversion, Int. J. Energy Res. 33(13), 1203 (2009)

    Google Scholar 

  245. X. Wu, C. Fu, and Z. M. Zhang, Effect of orientation on the directional and hemispherical emissivity of hyperbolic metamaterials, Int. J. Heat Mass Transf. 135, 1207 (2019)

    Google Scholar 

  246. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, Elsevier, 2013

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Acknowledgements

The authors are grateful to the National Natural Science Foundation of China (Nos. 51776050 and 51536001).

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Correspondence to Haochun Zhang.

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arXiv: 2108.02445. This article can also be found at http://journal.hep.com.cn/fop/EN/10.1007/s11467-021-1107-4.

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Yu, H., Zhang, H., Zhao, J. et al. Thermal conductivity of micro/nano-porous polymers: Prediction models and applications. Front. Phys. 17, 23202 (2022). https://doi.org/10.1007/s11467-021-1107-4

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  • DOI: https://doi.org/10.1007/s11467-021-1107-4

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