Supposition of graphene stacks to estimate the contact resistance and conductivity of nanocomposites

doi:10.1007/s10483-024-3102-7

摘要/Abstract

Abstract:

In this study, the effects of stacked nanosheets and the surrounding interphase zone on the resistance of the contact region between nanosheets and the tunneling conductivity of samples are evaluated with developed equations superior to those previously reported. The contact resistance and nanocomposite conductivity are modeled by several influencing factors, including stack properties, interphase depth, tunneling size, and contact diameter. The developed model's accuracy is verified through numerous experimental measurements. To further validate the models and establish correlations between parameters, the effects of all the variables on contact resistance and nanocomposite conductivity are analyzed. Notably, the contact resistance is primarily dependent on the polymer tunnel resistivity, contact area, and tunneling size. The dimensions of the graphene nanosheets significantly influence the conductivity, which ranges from 0 S/m to 90 S/m. An increased number of nanosheets in stacks and a larger gap between them enhance the nanocomposite's conductivity. Furthermore, the thicker interphase and smaller tunneling size can lead to higher sample conductivity due to their optimistic effects on the percolation threshold and network efficacy.

Key words: graphene polymer composite, stacked nanosheet, tunneling conductivity, contact resistance, interphase

中图分类号:

00A72

. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(4): 663-676.

Y. ZARE, M. T. MUNIR, G. J. WENG, K. Y. RHEE. Supposition of graphene stacks to estimate the contact resistance and conductivity of nanocomposites[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(4): 663-676.

图/表 7

参考文献 46

1	ABD, EL-KADER M., AWWAD, N. S., IBRAHIUM, H. A., and AHMED, M. Graphene oxide fillers through polymeric blends of PVC/PVDF using laser ablation technique: electrical behavior, cell viability, and thermal stability. Journal of Materials Research and Technology, 13, 1878- 1886 (2021)
2	ALIYA, M., ZARE, E. N., FARIDNOURI, H., GHOMI, M., and MAKVANDI, P. Sulfonated starch-graft-polyaniline@graphene electrically conductive nanocomposite: application for tyrosinase immobilization. Biosensors, 12, 939 (2022)
3	FAROUQ, R. Functionalized graphene/polystyrene composite, green synthesis and characterization. Scientific Reports, 12, 21757 (2022)
4	WANG, S., MAO, J., ZHANG, W., and LU, H. Nonlocal thermal buckling and postbuckling of functionally graded graphene nanoplatelet reinforced piezoelectric micro-plate. Applied Mathematics and Mechanics (English Edition), 43 (3), 341- 354 (2022) doi: 10.1007/s10483-022-2821-8
5	HU, B., LIU, J., WANG, Y., ZHANG, B., WANG, J., and SHEN, H. Study on wave dispersion characteristics of piezoelectric sandwich nanoplates considering surface effects. Applied Mathematics and Mechanics (English Edition), 43 (9), 1339- 1354 (2022) doi: 10.1007/s10483-022-2897-9
6	ZARE, Y., and RHEE, K. The roles of polymer-graphene interface and contact resistance among nanosheets in the effective conductivity of nanocomposites. Applied Mathematics and Mechanics (English Edition), 44 (11), 1941- 1956 (2023) doi: 10.1007/s10483-023-3046-9
7	ZARE, Y., GHARIB, N., and RHEE, K. Y. Influences of graphene morphology and contact distance between nanosheets on the effective conductivity of polymer nanocomposites. Journal of Materials Research and Technology, 25, 3588- 3597 (2023)
8	ZHOU, Y., BAO, Q., TANG, L. A. L., ZHONG, Y., and LOH, K. P. Hydrothermal dehydration for the "green" reduction of exfoliated graphene oxide to graphene and demonstration of tunable optical limiting properties. Chemistry of Materials, 21, 2950- 2956 (2009)
9	COMPTON, O. C., and NGUYEN, S. T. Graphene oxide, highly reduced graphene oxide, and graphene: versatile building blocks for carbon-based materials. Small, 6, 711- 723 (2010)
10	CHIPARA, D., TREVINO, A., MARTIROSYAN, K. S., and CHIPARA, M. Interphase in polymer-based nanocomposites: polyoctenamer-single-walled carbon nanotubes. Surfaces and Interfaces, 40, 103011 (2023)
11	CHIPARA, M., BAIBARAC, M., COMPAGNINI, G., and GAO, J. From interface to interphase. Surfaces and Interfaces, 42, 103435 (2023)
12	CREMONEZZI, J. M. D., PINTO, G. M., MINCHEVA, R., ANDRADE, R. J. E., RAQUEZ, J. M., and FECHINE, G. J. M. The micromechanics of graphene oxide and molybdenum disulfide in thermoplastic nanocomposites and the impact to the polymer-filler interphase. Composites Science and Technology, 243, 110236 (2023)
13	FALLAHI, H., KAYNAN, O., and ASADI, A. Insights into the effect of fiber-matrix interphase physiochemical-mechanical properties on delamination resistance and fracture toughness of hybrid composites. Composites Part A: Applied Science and Manufacturing, 166, 107390 (2023)
14	KAMAE, T., and DRZAL, L. T. Carbon fiber/epoxy composite property enhancement through incorporation of carbon nanotubes at the fiber-matrix interphase, part Ⅱ: mechanical and electrical properties of carbon nanotube coated carbon fiber composites. Composites Part A: Applied Science and Manufacturing, 160, 107023 (2022)
15	BAEK, K., SHIN, H., and CHO, M. Multiscale modeling of mechanical behaviors of nano-SiC/epoxy nanocomposites with modified interphase model: effect of nanoparticle clustering. Composites Science and Technology, 203, 108572 (2021)
16	QIAO, R., and BRINSON, L. C. Simulation of interphase percolation and gradients in polymer nanocomposites. Composites Science and Technology, 69, 491- 499 (2009)
17	BAXTER, S. C., and ROBINSON, C. T. Pseudo-percolation: critical volume fractions and mechanical percolation in polymer nanocomposites. Composites Science and Technology, 71, 1273- 1279 (2011)
18	ZARE, Y., and RHEE, K. Y. A simple methodology to predict the tunneling conductivity of polymer/CNT nanocomposites by the roles of tunneling distance, interphase and CNT waviness. RSC Advances, 7, 34912- 34921 (2017)
19	DU, F., SCOGNA, R. C., ZHOU, W., BRAND, S., FISCHER, J. E., and WINEY, K. I. Nanotube networks in polymer nanocomposites: rheology and electrical conductivity. Macromolecules, 37, 9048- 9055 (2004)
20	RYVKINA, N., TCHMUTIN, I., VILČÁKOVÁ, J., PELÍŠKOVÁ, M., and SÁHA, P. The deformation behavior of conductivity in composites where charge carrier transport is by tunneling: theoretical modeling and experimental results. Synthetic Metals, 148, 141- 146 (2005)
21	AMBROSETTI, G., GRIMALDI, C., BALBERG, I., MAEDER, T., DANANI, A., and RYSER, P. Solution of the tunneling-percolation problem in the nanocomposite regime. Physical Review B, 81, 155434 (2010)
22	HU, N., KARUBE, Y., YAN, C., MASUDA, Z., and FUKUNAGA, H. Tunneling effect in a polymer/carbon nanotube nanocomposite strain sensor. Acta Materialia, 56, 2929- 2936 (2008)
23	KAZEMI, F., MOHAMMADPOUR, Z., NAGHIB, S. M., ZARE, Y., and RHEE, K. Y. Percolation onset and electrical conductivity for a multiphase system containing carbon nanotubes and nanoclay. Journal of Materials Research and Technology, 15, 1777- 1788 (2021)
24	RAZAVI, R., ZARE, Y., and RHEE, K. Y. A two-step model for the tunneling conductivity of polymer carbon nanotube nanocomposites assuming the conduction of interphase regions. RSC Advances, 7, 50225- 50233 (2017)
25	ARJMANDI, S. K., YEGANEH, J. K., ZARE, Y., and RHEE, K. Y. Development of Kovacs model for electrical conductivity of carbon nanofiber-polymer systems. Scientific Reports, 13, 7 (2023)
26	MOHAMMADPOUR-HARATBAR, A., ZARE, Y., and RHEE, K. Y. Simulation of electrical conductivity for polymer silver nanowires systems. Scientific Reports, 13, 5 (2023)
27	CLINGERMAN, M. L., KING, J. A., SCHULZ, K. H., and MEYERS, J. D. Evaluation of electrical conductivity models for conductive polymer composites. Journal of Applied Polymer Science, 83, 1341- 1356 (2002)
28	CHANG, L., FRIEDRICH, K., YE, L., and TORO, P. Evaluation and visualization of the percolating networks in multi-wall carbon nanotube/epoxy composites. Journal of Materials Science, 44, 4003- 4012 (2009)
29	KARA, S., ARDA, E., DOLASTIR, F., and PEKCAN, Ö. Electrical and optical percolations of polystyrene latex-multiwalled carbon nanotube composites. Journal of Colloid and Interface Science, 344, 395- 401 (2010)
30	ZARE, Y., and RHEE, K. Y. An innovative model for conductivity of graphene-based system by networked nano-sheets, interphase and tunneling zone. Scientific Reports, 12, 15179 (2022)
31	ZARE, Y., and RHEE, K. Y. Effect of contact resistance on the electrical conductivity of polymer graphene nanocomposites to optimize the biosensors detecting breast cancer cells. Scientific Reports, 12, 5406 (2022)
32	KIM, H., ABDALA, A. A., and MACOSKO, C. W. Graphene/polymer nanocomposites. Macromolecules, 43, 6515- 6530 (2010)
33	MITTAL, G., DHAND, V., RHEE, K. Y., PARK, S. J., and LEE, W. R. A review on carbon nanotubes and graphene as fillers in reinforced polymer nanocomposites. Journal of Industrial and Engineering Chemistry, 21, 11- 25 (2015)
34	BRUNE, D. A., and BICERANO, J. Micromechanics of nanocomposites: comparison of tensile and compressive elastic moduli, and prediction of effects of incomplete exfoliation and imperfect alignment on modulus. Polymer, 43, 369- 387 (2002)
35	LI, J., and KIM, J. K. Percolation threshold of conducting polymer composites containing 3D randomly distributed graphite nanoplatelets. Composites Science and Technology, 67, 2114- 2120 (2007)
36	YANOVSKY, Y. G., KOZLOV, G., and KARNET, Y. N. Fractal description of significant nano-effects in polymer composites with nanosized fillers, aggregation, phase interaction, and reinforcement. Physical Mesomechanics, 16, 9- 22 (2013)
37	MESSINA, E., LEONE, N., FOTI, A., DI MARCO, G., RICCUCCI, C., DI CARLO, G., DI MAGGIO, F., CASSATA, A., GARGANO, L., and D'ANDREA, C. Double-wall nanotubes and graphene nanoplatelets for hybrid conductive adhesives with enhanced thermal and electrical conductivity. ACS Applied Materials & Interfaces, 8, 23244- 23259 (2016)
38	MOHIUDDIN, M., and HOA, S. V. Estimation of contact resistance and its effect on electrical conductivity of CNT/PEEK composites. Composites Science and Technology, 79, 42- 48 (2013)
39	KOVACS, J. Z., VELAGALA, B. S., SCHULTE, K., and BAUHOFER, W. Two percolation thresholds in carbon nanotube epoxy composites. Composites Science and Technology, 67, 922- 928 (2007)
40	TU, Z., WANG, J., YU, C., XIAO, H., JIANG, T., YANG, Y., SHI, D., MAI, Y. W., and LI, R. K. A facile approach for preparation of polystyrene/graphene nanocomposites with ultra-low percolation threshold through an electrostatic assembly process. Composites Science and Technology, 134, 49- 56 (2016)
41	GAO, C., ZHANG, S., WANG, F., WEN, B., HAN, C., DING, Y., and YANG, M. Graphene networks with low percolation threshold in ABS nanocomposites: selective localization and electrical and rheological properties. ACS Applied Materials & Interfaces, 6, 12252- 12260 (2014)
42	ZHANG, H. B., ZHENG, W. G., YAN, Q., YANG, Y., WANG, J. W., LU, Z. H., JI, G. Y., and YU, Z. Z. Electrically conductive polyethylene terephthalate/graphene nanocomposites prepared by melt compounding. Polymer, 51, 1191- 1196 (2010)
43	XU, L., CHEN, G., WANG, W., LI, L., and FANG, X. A facile assembly of polyimide/graphene core-shell structured nanocomposites with both high electrical and thermal conductivities. Composites Part A: Applied Science and Manufacturing, 84, 472- 481 (2016)
44	AL-SALEH, M. H. Influence of conductive network structure on the EMI shielding and electrical percolation of carbon nanotube/polymer nanocomposites. Synthetic Metals, 205, 78- 84 (2015)
45	LI, Y., ZHANG, H., PORWAL, H., HUANG, Z., BILOTTI, E., and PEIJS, T. Mechanical, electrical and thermal properties of in-situ exfoliated graphene/epoxy nanocomposites. Composites Part A: Applied Science and Manufacturing, 95, 229- 236 (2017)
46	KIM, H., and MACOSKO, C. W. Morphology and properties of polyester/exfoliated graphite nanocomposites. Macromolecules, 41, 3317- 3327 (2008)

[1]	徐玉秀;胡海岩;闻邦椿. 1/3 PURE SUB-HARMONIC SOLUTION AND FRACTAL CHARACTERISTIC OF TRANSIENT PROCESS FOR DUFFING'S EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(9): 1171-1176 .
[2]	Y. ZARE, K. Y. RHEE. The roles of polymer-graphene interface and contact resistance among nanosheets in the effective conductivity of nanocomposites[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(11): 1941-1956.