Facile, green and affordable strategy for structuring natural graphite/polymer composite with efficient electromagnetic interference shielding

Abstract

An electromagnetic interference (EMI) shielding composite based on natural, economical graphite and ultrahigh molecular weight polyethylene (UHMWPE) with a typical segregated structure was first fabricated by a facile and green method, i.e., mechanical mixing plus hot compaction, without the use of intensive dispersion and any organic solvents. Superior shielding effectiveness of 51.6 dB was achieved at a low graphite loading of only 7.05 vol%, which was comparable to or even superior to the expensive carbon nanofillers (e.g., carbon nanotube and graphene) based polymer composites owning to the successful creation of the segregated structure in which the graphite particles were selectively located at the interfaces of UHMWPE polyhedrons. Our work suggests a new way of effectively utilizing economical graphite in conductive polymer composites, especially for EMI shielding applications.

---

Introduction

With the extensive applications of sensitive electronic devices, such as laptops, cell phones, TV picture transmitters, and the like, electromagnetic interference (EMI) imposes a serious problem to human society.^1,2 The past decades have witnessed the revolutionary development of conductive polymer composites (CPCs) as promising advanced materials for EMI protection.^3–5 Compared to the traditional metal-based EMI shielding materials, CPCs desirably offer unique strengths in enabling the achievement of light weight, easy processability, chemical resistance, and tunable electronic conductivity over a wide range.^6–10 Recently, much attention has been paid to the development of novel EMI shielding CPCs based on various carbon nanofillers, such as carbon nanofiber (CNF),¹¹ carbon nanotube (CNT),^12,13 and graphene nanosheet (GNS).¹⁴ Such CPCs present very low percolation threshold and superior electrical properties. Nevertheless, the applications of such nanofillers are limited due to their ultra-high cost, aggregation, and processing difficulties. Micro-scale graphite is well known to be a naturally abundant and economical material, owning layered structure in which carbon atoms bonded with each other by van der Waals forces to form layers, with high electrical conductivity of 10³ S cm⁻¹ at room temperature.¹⁵ Many approaches have been developed to prepare graphite based polymer composites, however, fairly poor electrical conductivity always appears.^16,17 For example, though a very high content of graphite (up to 25 vol%) was applied to nylon 6,6, relatively low EMI shielding effectiveness (EMI SE) of 12 dB is achieved.¹⁸ Thus, it is an attractive goal to advance the electrical and EMI shielding properties with low loadings of incorporated fillers, without significantly increasing the cost of the CPCs.¹⁹ To this end, elaborate structural design is normally required. The formation of a segregated structure in CPCs offers the tremendous opportunity to achieve high electrical conductivity and EMI SE even at low conductive filler loadings,²⁰ due to the formation of effective conductive paths through the distribution of major fillers at the interfaces among polymer matrix domains,²¹ which has been summarized systematically in our recent review.²² For example, Pham et al. fabricated a graphene/poly(methyl methacrylate) segregated composite, presenting a percolation threshold as low as 0.16 vol% and an electrical conductivity of 64 S m⁻¹ at only 2.7 vol%.²³ Maiti et al. achieved an EMI SE of 23.1 dB in 2 wt% CNT/polycarbonate composite with through selective localization of carbon nanotubes.²⁴ Very recently, Yan et al. reported an graphene/ultrahigh molecular weight polyethylene (UHMWPE) composite with EMI SE of 28.3–32.4 dB at an ultralow graphene loading of 0.660 vol%.⁵ It should be noted that the available CPCs with segregated structure are mainly based on nanofillers with high aspect ratio, and the agglomeration of nanofillers invariably exists, especially at relatively high loading for EMI shielding application.²⁴ Then what will happen in electrical and EMI shielding performance if micro-scale and economical graphite is introduced to the segregated CPCs? In case of high electrical conductivity and EMI SE in such CPCs, a major breakthrough can be achieved in developing affordable and accessible EMI shielding materials. Stimulated by the interesting but rarely reported issue, we attempt to launch a comprehensive study for the segregated graphite/UHMWPE composites, where UHMWPE was selected as the polymer matrix for its high melt viscosity, in great need for the generation of a segregated structure during conventional compression molding. The segregated composite containing graphite loading of only 7.05 vol% exhibited high electrical conductivity of 3.9 S m⁻¹ and satisfactory EMI SE of 51.6 dB. The obtained EMI SE is much higher than the results for graphite randomly distributed CPCs,^18,25 and even comparable to the results for CPCs containing CNF,^26,27 CNT^28,29 or GNS.^4,4,5,30 It is worth mentioning that the fabrication of the segregated composite in this work is involved in mechanical mixing plus hot compaction method, without the use of any organic solvent, showing a facile, green and affordable strategy for developing efficient EMI shielding materials.

Experimental

Raw materials

The ultrahigh molecular weight polyethylene (UHMWPE) powder was a commercial product from Beijing no. 2 Auxiliary Agent Factory, and was featured by the following physical properties: average diameter of 150 μm, density ρ = 0.945 g cm⁻³, melting temperature T_m = 137 °C, viscosity average molecular weight M_v = 5.5–6.0 × 10⁶ g mol⁻¹. High density polyethylene (HDPE, Grade 5000S) was supplied by Da Qing Petroleum Chemical Co. (Daqing, China), with a melt flow rate of 0.9 g/10 min at 190 °C, under a load of 21.6 N. The graphite powder was provided by Beishu Graphite Co. Shangdong, China, with density of 2.2 g cm⁻³ and lateral dimension of 20 μm.

Fabrication of polymer composites

Sample preparation. The fabrication process of the graphite/UHMWPE composite is shown schematically in Fig. 1. First, mechanical mixing was utilized to obtain UHMWPE complex granules embedded by various graphite contents (from 0.043 to 7.046 vol%). The complex granules were homogenized thorough in a porcelain mortar to the visually homogeneous state. Subsequently, the resultant graphite coated UHMWPE complex granules were placed into a hot mold heated to 200 °C and subsequently hot compressed for 5 min at 10 MPa followed by the quenching to room temperature. Finally, the samples of the molded composites for performance measurements were machined into discs with a thickness of 2.5 mm.

Fig. 1 Schematic for fabrication of graphite/UHMWPE segregated composite.

Characterization

Optical microscopy (OM) observation. OM observation was carried out to clarify the morphological structure and the conductive networks in the composites. Microtomy was applied to obtain thin sections (∼20 μm) at room temperature using an ultramicrotome (Leica EM UC6, Germany) equipped with a glass knife. The sections were then squeezed between two glass slides. An Olympus BX51 OM (Olympus Co., Tokyo, Japan) equipped with a MicroPublisher 3.3 RTV CCD was applied to observe the morphology.

Scanning electron microscopy (SEM) observation. A field-emission SEM (Inspect F, FEI, Finland) was used for SEM observations, with the accelerated voltage of 20 kV. The graphite coated UHMWPE complex particles were directly used for SEM observation, while the composite discs were cryogenically fractured after frozen in liquid nitrogen for 0.5 h. Prior to SEM observation, the fracture surfaces were sputter-coated with gold.

Electrical conductivity. For the determination of electrical performance, the conductive UHMWPE composites were cut into rectangular sheets with a dimension of 20 × 5 × 2.5 mm³. Silver paste was coated onto the sides of the sheets to insure the close electrical contact with the electrodes, and thus to provide reliable values of electrical resistance. The volume conductivities of graphite/UHMWPE composite samples higher than 10⁻⁶ S m⁻¹ were carried out using a four-probe method using a SDY-6 resistivity measurement system and the volume electrical conductivities below 10⁻⁶ S m⁻¹ were measured using a Keithley electrometer Model 4200-SCS.

EMI SE. EMI shielding characteristics of the composite reported here were conducted by a coaxial test cell (APC-7 connector) in conjunction with an Agilent N5230 vector network analyzer, according to ASTM ES7-83 (Schematic of measurement setup was shown in Fig. S1.†). The APC-7 connector is a precision coaxial connector that was used on laboratory microwave test equipment and can be utilized at frequencies up to 18 GHz. The Agilent N5230 vector network analyzer was calibrated using the standard APC-7 connector open, short, and 50 Ω loads. The intermediate frequency bandwidth was set as 1 kHz during the measurement and 201 points were collected for each specimen. All the samples with 10 mm diameter and 2.5 mm thickness were placed in the specimen holder, which were connected through Agilent 85132F coaxial line to separate VNA ports.

The scattering parameters (S₁₁ and S₂₁) of the graphite/UHMWPE composites in the frequency range of 8.2–12.4 GHz (X-Band) were gained to calculate the EMI SE. EMI SE (SE_Total) is the summation of the reflection from the material surface (SE_R), the absorption of electromagnetic energy (SE_A), and the multiple internal reflections (SE_M) of electromagnetic radiation. SE_R is related to the impedance mismatch between air and absorber; SE_A can be regarded as the energy dissipation of the electromagnetic microwave in the absorber; and SE_M is considered as the scattering effect of the inhomogeneity within the materials which can be negligible when SE_Total ≥ 15 dB.

Results and discussion

Optical observation concerning the distribution of graphite particles in the UHMWPE matrix was carried out to examine the preferred formation of segregated structure.³¹ Fig. 2 shows the evolution of typical segregated structure with the graphite concentrations The selective distribution of graphite in the composites can be easily identified due to the light transmittance difference between graphite and UHMWPE, in which the black pathways indicate the assembly of graphite and the light gray zones suggest the existence of UHMWPE matrix. The high melt viscosity of UHMWPE granules could prevent the penetration of graphite into their interior, which is beneficial to the selective distribution of graphite. When the graphite loading is only 0.043 vol%, an incompleted conductive network is detected (Fig. 2a). Increasing graphite contents to 0.129 and 0.215 vol% desirably permit the construction of conductive pathways that feature higher density and larger thickness, showing well defined graphite conductive networks (Fig. 2b and c). Such architecture reveals the formation of segregated structure with graphite fillers selectively located at the interfaces of UHMWPE polyhedrons.

Fig. 2 Optical micrographs of compression-molded UHMWPE composites containing (a) 0.043 vol%, (b) 0.129 vol%, and (c) 0.215 vol% graphite powders.

Fig. 3a compares the SEM micrographs of 0.215 vol% graphite coated UHMWPE complex granules and the hot compressed composite, tracing the origin of the segregated network. Fig. 3a manifests that graphite is uniformly covered onto UHMWPE granule surfaces. Under the pressure during molding, because of the gel state of UHMWPE induced by the molecular weight entanglement and the lack of shear, the graphite coated UHMWPE granules are almost not broken up. However, these complex granules showed plastic deformation under pressure to form irregular polyhedrons (Fig. 3b). Additionally, the graphite particles are difficult to penetrate into the interior of UHMWPE granules also due to their gel state, thus, resulting in a microstructure with an ordered segregated network of graphite wrapped UHMWPE polyhedrons. The subsequent polymer crystallization upon cooling led to the preservation of these polyhedrons. Specifically, the conductive fillers are preferably distributed onto the surfaces of these matrix polyhedrons rather uniform dispersion in the matrix, distinctly revealing a microstructure with an ordered segregated network of graphite. Given the establishment of perfect conductive networks in the composites, one may expect their high performances in electrical conductivity and EMI SE.

Fig. 3 SEM images of (a) graphite coated UHMWPE complex grannules and (b) compression-molded UHMWPE composite containing 0.215 vol% graphite. The inset of (a) shows a smooth surface for the raw polymer particles, while the inset of (b) demonstrates that conductive fillers are preferably distributed on the surfaces of graphite.

Fig. 4 plots the electrical conductivity of the graphite/UHMWPE segregated composites as a function of the volume fraction of graphite. A percolation behavior appears in the segregated composites, with a drastic increase of nearly 12 orders of magnitude in electrical conductivity observed in a very narrow graphite content range from 0 to 0.129 vol%. The construction of the conductive network was rationalized with regard to the critical concentration of conductive fillers using the following scaling law.³² According to classical percolation theory, electrical conductivity of a composite can be described as: σ = σ₀(φ − φ_C)^t, where σ represents the electrical conductivity of composites, σ₀ stands for a constant related to the intrinsic conductivity of graphite, φ indicates the volume fraction of graphite, φ_C is the percolation concentration, and t suggests the critical exponent. The fitted φ_C is 0.115 vol%, a very low value for graphite based composites compared to the available values reported in the existing literature. For example, Zheng et al.¹⁷ found graphite/poly(methyl methacrylate) showed a high percolation threshold of 1.845 vol%, fifteen times more of this work. With respect to the high-density polyethylene composites studied by Balik et al., the composites were conductive only after over 34.53 vol% graphite were incorporated.¹⁶ The preferred distribution of graphite in our graphite/UHMWPE composites with a segregated structure can significantly improve the effective graphite concentration and the probability of creating more conducting pathways, thus permitting the unprecedented low percolation threshold. The obtained critical exponent t, related to the dimensionality of the conductive network in a CPC, is 1.76. For a single percolation system, the critical exponent depends only on the dimensionality of the composites and follows a power-law dependence of approximately 2 (1.6–2) in a three-dimensional system, and 1–1.3 in a two-dimensional one.³³ Thus, an ideal three-dimensional conductive network present in the graphite/UHMWPE segregated composites, which is well in line with the morphological observation of the three dimensional networks.

Fig. 4 Dependency of graphite content on the electrical conductivity. The inset presents a log–log plot of the conductivity as a function of φ − φ_C for graphite/UHMWPE composites, in which the line manifests the least square fitting of the experimental data.

The graphite based composites represent an important category of conductive composites, however, their possibility in EMI shielding has rarely examined.^34–37 Here we show the effective EMI shielding performance for pure UHMWPE and the graphite/UHMWPE composites as a function of graphite (0.43–7.05 vol%) over the frequency range (8.2–12.4 GHz), as demonstrated in Fig. 5a. It is evidently pure UHMWPE shows an average EMI SE of only 2.7 dB, revealing very weak ability to the shield of electromagnetic wave. With the addition of graphite, all the composites present weak frequency-dependent EMI SE performance, but show dramatically increased EMI SE upon addition of graphite. For instance, the segregated composite containing only 0.87 vol% graphite exhibited an average EMI SE of 19.3 dB, already close to the target value of EMI SE required for practical application (20 dB). As the graphite loading rises to 7.05 vol%, very high EMI SE of 51.6 dB was obtained, indicating only 0.0007% electromagnetic wave transmission through the shielding material. The EMI SE of a composite is closely associated with its electrical conductivity, normally showing a positive correlation.^12,38,39 On microscale, a higher graphite content results in a thicker conductive interface between UHMWPE polyhedrons, which presents stronger interaction with incoming electromagnetic waves, and thus improving the EMI SE.

Fig. 5 EMI SE curves plotted as a function of frequency in the X band for pure UHMWPE and the graphite/UHMWPE segregated composite with various graphite contents.

The EMI SE of the graphite/UHMWPE segregated composites is outstanding compared to previously reported graphite-based CPC materials, and even comparable to other materials using the nanofillers like CNF, CNT, and GNS, as listed in Table 1. The exceptional EMI SE must lie in the highly conducting interconnected graphite networks, mainly attributed to the formation of the segregated structure that significantly increasing the effective graphite concentration and the probability of forming more conducting pathways. Additionally, the comparable EMI SE in our shielding material containing micro-scale graphite to that of nanofillers reveals tremendous economical superiority. More importantly, the construction of segregated network in the graphite/UHMWPE composite is accessible using mechanical mixing and hot compaction method, which is significantly different from the use of ultrasonic dispersion and many organic solvents in preparing CPCs containing nanofillers, demonstrating a facile, green and affordable strategy for developing efficient EMI shielding materials. This effort shows enormous promise of structuring filler distribution and conductive pathways in optimizing the EMI shielding performance, thereby holding great potential for extending the applications of graphite based composites that are quite economic and fit industrial manufacturing.^{13,31,32,36,37}

Table 1 Average EMI SE for the graphite/UHMWPE segregated composites in this work and several CPCs based on graphite, CNF, CNT, or GNS reported in literature

CPC materials	Filler content (vol%)	Sample thickness (mm)	EMI SE (dB)	References
a PMMA is poly(methyl methacrylate).
Graphite/UHMWPE	1.76	2.5	27.4	Present work
Graphite/UHMWPE	3.60	2.5	36.6	Present work
Graphite/UHMWPE	7.05	2.5	51.6	Present work
Graphite/polyethylene	18.7	3.0	33	25
Graphite/nylon 6,6	25	3.2	12	18
CNF/polyethylene	7.5	2.0	22.5	27
CNF/polystyrene	7.5	2.0	24	26
CNT/polystyrene	2.78	2.0	17.2	29
CNT/polycarbonate	2.77	1.85	25	28
GNS/Epoxy	8.8	2.0	21.0	30
GNS/PMMA^a	2.67	3.4	25.0	30
GNS/polystyrene	3.47	2.5	45.1	40

---

To clarify the EMI shielding mechanism in the graphite/UHMWPE segregated composites, the total EMI shielding effectiveness (SE_Total), microwave absorption (SE_A), and microwave reflection (SE_R) were calculated from the measured scattering parameters (detailed calculations could be found in the our previously reported work^4,5), and plots of SE_Total, SE_A, and SE_R as a function of graphite loading at the frequency of 8.2 GHz are presented in Fig. 6. It is clear that increasing graphite loading increases both SE_A and SE_R. The increase of SE_Total with graphite loading is mainly attributed to the contribution of SE_A, while the contribution of SE_R is negligible over all the graphite loading. For instance, the SE_Total, SE_A, SE_R of the composite with 3.60 vol% graphite are 35.8, 32.5, and 3.3 dB, respectively, which indicates that the contribution of absorption to the total EMI SE (91%) is much larger than that from reflection (9%), suggesting an absorption dominated shielding mechanism rather than reflection in the graphite/UHMWPE segregated composite. This is a little similar with the shielding mechanism in the previously reported graphene/polymer foam.^1,4

Fig. 6 Comparison of the total EMI shielding effectiveness (SE_Total), microwave absorption (SE_A), and microwave reflection (SE_R) at the frequency of 8.2 GHz for the graphite/UHMWPE segregated composites with various graphite loadings.

Conclusions

This effort discloses a facile and environmentally friendly approach to fabricate graphite/UHMWPE segregated composites penetrated a three-dimensional conductive network, in which an impressive EMI SE performance of 51.6 dB at a fairly low graphite concentration of 7.05 vol%. It is primarily appraised from the selective distribution of graphite particles at the interfaces among UHMWPE domains. Showing a unique set of multifunctional performances, the graphite based composites are evident beneficiary of the segregated structure which favors potential application in the future.

Acknowledgements

The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (Grant nos 51421061, U1162131, 51273131, 51473102), the Innovation Team Program of Science and Technology Department of Sichuan Province (Grant no. 2014TD0002).

Notes and references

1. H. B. Zhang, Q. Yan, W. G. Zheng, Z. He and Z. Z. Yu, ACS Appl. Mater. Interfaces, 2011, 3, 918–924.
2. M. H. Al-Saleh, W. H. Saadeh and U. Sundararaj, Carbon, 2013, 60, 146–156.
3. G. A. Gelves, M. H. Al-Saleh and U. Sundararaj, J. Mater. Chem., 2011, 21, 829.
4. D. X. Yan, P. G. Ren, H. Pang, Q. Fu, M. B. Yang and Z. M. Li, J. Mater. Chem., 2012, 22, 18772.
5. D. X. Yan, H. Pang, L. Xu, Y. Bao, P. G. Ren, J. Lei and Z. M. Li, Nanotechnology, 2014, 25, 145705.
6. Q. Liu, J. Tu, X. Wang, W. Yu, W. Zheng and Z. Zhao, Carbon, 2012, 50, 339–341.
7. N. Joseph and M. Thomas Sebastian, Mater. Lett., 2013, 90, 64–67.
8. Q. Y. Chen, J. Gao, K. Dai, H. Pang, J. Z. Xu, J. H. Tang and Z. M. Li, Chin. J. Polym. Sci., 2013, 31, 211–217.
9. B. Li, X. B. Xu, Z. M. Li and Y. C. Song, J. Appl. Polym. Sci., 2008, 110, 3073–3079.
10. B. Li, Y. C. Zhang, Z. M. Li, S. N. Li and X. N. Zhang, J. Phys. Chem. B, 2010, 114, 689–696.
11. M. S. Cao, W. L. Song, Z. L. Hou, B. Wen and J. Yuan, Carbon, 2010, 48, 788–796.
12. Y. Huang, N. Li, Y. Ma, F. Du, F. Li, X. He, X. Lin, H. Gao and Y. Chen, Carbon, 2007, 45, 1614–1621.
13. H. Pang, C. Chen, Y. C. Zhang, P. G. Ren, D. X. Yan and Z. M. Li, Carbon, 2011, 49, 1980–1988.
14. Z. Chen, C. Xu, C. Ma, W. Ren and H. M. Cheng, Adv. Mater., 2013, 25, 1296–1300.
15. J. Wu and D. D. L. Chung, Carbon, 2003, 41, 1313–1315.
16. W. Thongruang, R. J. Spontak and C. M. Balik, Polymer, 2002, 43, 2279–2286.
17. W. Zheng and S. C. Wong, Compos. Sci. Technol., 2003, 63, 225–235.
18. Q. J. Krueger and J. A. King, Adv. Polym. Technol., 2003, 22, 96–111.
19. X. Hao, G. Gai, Y. Yang, Y. Zhang and C. W. Nan, Mater. Chem. Phys., 2008, 109, 15–19.
20. H. Hu, G. Zhang, L. Xiao, H. Wang, Q. Zhang and Z. Zhao, Carbon, 2012, 50, 4596–4599.
21. J. Du, L. Zhao, Y. Zeng, L. Zhang, F. Li, P. Liu and C. Liu, Carbon, 2011, 49, 1094–1100.
22. H. Pang, L. Xu, D. X. Yan and Z. M. Li, Prog. Polym. Sci., 2014, 39(11), 1908–1933.
23. V. H. Pham, T. T. Dang, S. H. Hur, E. J. Kim and J. S. Chung, ACS Appl. Mater. Interfaces, 2012, 4, 2630–2636.
24. S. Maiti, S. Suin, N. K. Shrivastava and B. B. Khatua, RSC Adv., 2014, 4, 7979.
25. V. Panwar and R. Mehra, Polym. Eng. Sci., 2008, 48, 2178–2187.
26. M. H. Al-Saleh and U. Sundararaj, Polym. Int., 2013, 62, 601–607.
27. M. H. Al-Saleh and U. Sundararaj, Polymer, 2010, 51, 2740–2747.
28. M. Arjmand, M. Mahmoodi, G. A. Gelves, S. Park and U. Sundararaj, Carbon, 2011, 49, 3430–3440.
29. M. Arjmand, T. Apperley, M. Okoniewski and U. Sundararaj, Carbon, 2012, 50, 5126–5134.
30. J. J. Liang, Y. Wang, Y. Huang, Y. F. Ma, Z. F. Liu, J. M. Cai, C. D. Zhang, H. J. Gao and Y. S. Chen, Carbon, 2009, 47, 922–925.
31. H. Pang, C. Chen, Y. Bao, J. Chen, X. Ji, J. Lei and Z. M. Li, Mater. Lett., 2012, 79, 96–99.
32. H. Pang, D. X. Yan, Y. Bao, J. B. Chen, C. Chen and Z. M. Li, J. Mater. Chem., 2012, 22, 23568–23575.
33. K. Levon, A. Margolina and A. Z. Patashinsky, Macromolecules, 1993, 26, 4061–4063.
34. A. Yu, P. Ramesh, M. E. Itkis, E. Bekyarova and R. C. Haddon, J. Phys. Chem. C, 2007, 111, 7565–7569.
35. Z. Antar, J. F. Feller, H. Noel, P. Glouannec and K. Elleuch, Mater. Lett., 2012, 67, 210–214.
36. M. T. Pettes, H. Ji, R. S. Ruoff and L. Shi, Nano Lett., 2012, 12, 2959–2964.
37. V. Panwar, R. M. Mehra, J. O. Park and S. H. Park, J. Appl. Polym. Sci., 2012, 125, E610–E619.
38. H. Kim, K. Kim, C. Lee, J. Joo, S. Cho, H. Yoon, D. Pejaković, J. Yoo and A. Epstein, Appl. Phys. Lett., 2004, 84, 589–591.
39. N. Li, Y. Huang, F. Du, X. He, X. Lin, H. Gao, Y. Ma, F. Li, Y. Chen and P. C. Eklund, Nano Lett., 2006, 6, 1141–1145.
40. D. X. Yan, H. Pang, B. Li, R. Vajtai, L. Xu, P. G. Ren, J. H. Wang and Z. M. Li, Adv. Funct. Mater., 2015, 25, 559–566.

---

Footnote

† Electronic supplementary information (ESI) available: Detailed experimental methods and supporting figures. See DOI: 10.1039/c4ra11332b

---