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# Conductivity of transparency

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

$\sigma_{gt}=\frac{\epsilon_{graphene}} {-lg( \frac{I} {I_0}) \rho_{sample}}$

σgt : conductivity of transparency based on graphene; $\epsilon_{graphene}$ : absorption coefficient of graphene; ρsample : sheet resistance of the sample; I : intensity of light after absorption; I0 : 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 dgraphite = 0.335nm, as in graphite, one can calculate the absorption coefficient of graphene according to the Bouguer-Lambert law to 301655cm − 1.

Applied Bouguer-Lambert law:

$-lg( \frac{I} {I_0}) =\epsilon^*cd; \epsilon^*c=\epsilon_{graphene}$

$\epsilon_{graphene}= \frac {-lg( \frac{I} {I_0})} {d_{graphite}} = \frac {-lg( \frac{97.7%} {100%})} {3.35 \times 10^{-8}cm}=301655cm^{-1}$

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

$\sigma_{gt}=\frac{301655cm^{-1}} {-lg( \frac{I} {100%}) \rho_{sample}}$

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) σgt (S/cm) references
graphene 97.7 6000 4975 Blake et al.[3]
graphene oxide 96 3.0x1011 5.7x10 − 5 Becerril et al.[4]
reduced graphene oxide 87 1x105 50 Eda et al.[5]
nanographene (1100°C) 56 1600 749 Wang et al.[6]
graphene (CVD) 90 350 1.8x104 Li et al.[7]
SWCNTs 70 30 6.5x104 Wu et al.[8]
ITO 77 100 2.7x104 Sigma–Aldrich catalog no. 639281 [9]

## References

1. ^ 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.
2. ^ 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. Bibcode 2008Sci...320.1308N. doi:10.1126/science.1156965. PMID 18388259.
3. ^ P. Blake, P. D. Brimicombe, R. R. Nair, T. J. Booth, D. Jiang, F. Schedin, L. A. Ponomarenko, S. V. Morozov, H. F. Gleeson, E. W. Hill, A. K. Geim, K. S. Novoselov (2008). "Graphene-Based Liquid Crystal Device". Nano Letters 8 (6): 1704–1708. Bibcode 2008NanoL...8.1704B. doi:10.1021/nl080649i. PMID 18444691.
4. ^ 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.
5. ^ 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.
6. ^ X. Wang, L. Zhi, N. Tsao, Z. Tomovic, J. Li, K. (2008). "Transparent Carbon Films as Electrodes in Organic Solar Cells". Angewandte Chemie International Edition 47 (16): 2990–2992. doi:10.1002/anie.200704909.
7. ^ X. Li, Y. Zhu, W. Cai, M. Borysiak, B. Han, D. Chen, R. D. Piner, L. Colombo, R. S. Ruoff (2009). "Transfer of Large-Area Graphene Films for High-Performance Transparent Conductive Electrodes". Nano Letters 9 (12): 4359–4363. Bibcode 2009NanoL...9.4359L. doi:10.1021/nl902623y. PMID 19845330.
8. ^ Z. Wu, Z. Chen, X. Du, J. M. Logan, J. Sippel, M. Nikolou, K. Kamaras, J. R. Reynolds, D. B. Tanner, A. F. Hebard, A. G. Rinzler (2004). "Transparent, Conductive Carbon Nanotube Films". Science 305 (5688): 1273–1276. Bibcode 2004Sci...305.1273W. doi:10.1126/science.1101243. PMID 15333836.
9. ^ Sigma–Aldrich catalog no. 639281|

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