Engineering:Conductivity of transparency
In physics the conductivity of transparency describes the combination of the sheet resistance and the transparency and utilizes the properties of graphene as the reference.
Description
The properties of electroconductive and transparent materials can be described by the sheet resistance and the transparency (at 550 nm). The conductivity of transparency was introduced on the basis of graphene to compare different materials without the use of two independent parameters.[1]
Conductivity of Transparency
- [math]\displaystyle{ \sigma_{gt}=\frac{\epsilon_{graphene}} {-\lg\left( \frac{I} {I_0}\right) \rho_{sample}} }[/math]
- [math]\displaystyle{ \sigma_{gt} }[/math]
- conductivity of transparency based on graphene;
- [math]\displaystyle{ \epsilon_{graphene} }[/math]
- absorption coefficient of graphene;
- [math]\displaystyle{ \rho_{sample} }[/math]
- sheet resistance of the sample;
- I
- intensity of light after absorption;
- [math]\displaystyle{ I_0 }[/math]
- intensity of light before absorption.
Derivation
The absorption of a single graphene layer was published in 2008. So graphene absorbs 2.3% of white light.[2] Hence, assuming that the ideal inter-layer distance of two graphene sheets is [math]\displaystyle{ d_{graphite}=0.335\ \mathrm{nm} }[/math], as in graphite, one can calculate the absorption coefficient of graphene according to the Bouguer-Lambert law to [math]\displaystyle{ 301655\ \mathrm{cm}^{-1} }[/math].
Applied Bouguer-Lambert law:
- [math]\displaystyle{ -\lg\left( \frac{I} {I_0}\right) =\epsilon^*cd; \epsilon^*c=\epsilon_{graphene} }[/math]
- [math]\displaystyle{ \epsilon_{graphene}= \frac {-\lg\left( \frac{I} {I_0}\right)} {d_{graphite}} = \frac {-\lg\left( \frac{97.7\%} {100\%}\right)} {3.35 \times 10^{-8}\ \mathrm{cm}}=301655\ \mathrm{cm}^{-1} }[/math]
The outcome of this is the general formula to determine the conductivity of transparency of arbitrary electroconductive and transparent materials, utilizing graphene as the reference:
Formula to determine the Conductivity of Transparency
- [math]\displaystyle{ \sigma_{gt}=\frac{301655\ \mathrm{cm}^{-1}} {-\lg\left( \frac{I} {100\%}\right) \rho_{sample}} }[/math]
So, to determine the conductivity of transparency it is necessary to measure the transmission (at 550 nm) and the sheet resistance of the sample. The sheet resistance can be obtained by four-point probe measurement (Sheet resistance, Van der Pauw method). Contrary to the electrical conductivity it is not necessary to determine the thickness of the sample, because graphene is utilized as the reference by using the transparency.
Examples
| Materials | I (%) | ρ (Ω) | [math]\displaystyle{ \sigma_{gt} }[/math] (S/cm) | references |
|---|---|---|---|---|
| graphene | 97.7 | 6000 | 4975 | Blake et al.[3] |
| graphene oxide | 96 | 3.0×1011 | 5.7×10−5 | Becerril et al.[4] |
| reduced graphene oxide | 87 | 1×105 | 50 | Eda et al.[5] |
| nanographene (1100 °C) | 56 | 1600 | 749 | Wang et al.[6] |
| graphene (CVD) | 90 | 350 | 1.8×104 | Li et al.[7] |
| SWCNTs | 70 | 30 | 6.5×104 | Wu et al.[8] |
| ITO | 77 | 100 | 2.7×104 | Sigma–Aldrich catalog no. 639281 [9] |
References
- ↑ S. Eigler (2009). "A new parameter based on graphene for characterizing transparent, conductive materials". Carbon 47 (12): 2936–2939. doi:10.1016/j.carbon.2009.06.047.
- ↑ R. R. Nair; P. Blake; A. N. Grigorenko; K. S. Novoselov; T. J. Booth; T. Stauber; N. M. R. Peres; A. K. Geim (2008). "Fine Structure Constant Defines Visual Transparency of Graphene". Science 320 (5881): 1308. doi:10.1126/science.1156965. PMID 18388259. Bibcode: 2008Sci...320.1308N.
- ↑ P. Blake; P. D. Brimicombe; R. R. Nair; T. J. Booth; D. Jiang; F. Schedin; L. A. Ponomarenko; S. V. Morozov et al. (2008). "Graphene-Based Liquid Crystal Device". Nano Letters 8 (6): 1704–1708. doi:10.1021/nl080649i. PMID 18444691. Bibcode: 2008NanoL...8.1704B.
- ↑ H. A. Becerril; J. Mao; Z. Liu; R. M. Stoltenberg; Z. Bao; Y. Chen (2008). "Evaluation of Solution-Processed Reduced Graphene Oxide Films as Transparent Conductors". ACS Nano 2 (3): 463–470. doi:10.1021/nn700375n. PMID 19206571.
- ↑ G. Eda; G. Fanchini; M. Chhowalla (2008). "Large-area ultrathin films of reduced graphene oxide as a transparent and flexible electronic material". Nature Nanotechnology 3 (5): 270–274. doi:10.1038/nnano.2008.83. PMID 18654522.
- ↑ X. Wang; L. Zhi; N. Tsao; Z. Tomovic; J. Li; K. Müllen (2008). "Transparent Carbon Films as Electrodes in Organic Solar Cells". Angewandte Chemie International Edition 47 (16): 2990–2992. doi:10.1002/anie.200704909. PMID 18330884.
- ↑ X. Li; Y. Zhu; W. Cai; M. Borysiak; B. Han; D. Chen; R. D. Piner; L. Colombo et al. (2009). "Transfer of Large-Area Graphene Films for High-Performance Transparent Conductive Electrodes". Nano Letters 9 (12): 4359–4363. doi:10.1021/nl902623y. PMID 19845330. Bibcode: 2009NanoL...9.4359L.
- ↑ Z. Wu; Z. Chen; X. Du; J. M. Logan; J. Sippel; M. Nikolou; K. Kamaras; J. R. Reynolds et al. (2004). "Transparent, Conductive Carbon Nanotube Films". Science 305 (5688): 1273–1276. doi:10.1126/science.1101243. PMID 15333836. Bibcode: 2004Sci...305.1273W.
- ↑ Sigma–Aldrich catalog no. 639281|
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