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2π· Chapter 3 β Raman Spectroscopy of Graphene and Graphene-based Strain Sensors In case of uniaxial strain the Gruneisen parameters for G (πΎπΊπ’ππππ₯πππ) and 2D (πΎππππ₯πππ) band are given by following equations as determined by Mohiuddin et al.256 π’ππππ₯πππ βππΊ++βππΊβ πΎπΊ = β 2ππΊ0 (1βπ)π Equation 3.1 Equation 3.2 πΎπ’ππππ₯πππ = β βπ2π· 2π· π0 (1βπ)π 2π· Where, ΞππΊ+βπ, ΞππΊββπ and Ξπ2π·βπ are the uniaxial strain shift rates of G+ mode, G- mode and 2D band, respectively, π0 and π0 are initial position (frequency) of πΊ 2π· G and 2D band before straining, respectively, and π is the Poissonβs ratio of the substrate. It is clear from the Equation 3-1 and Equation 3-2 that the Poisson ratio plays an important role in determining the strain in the system. It should be noted when analysing the strain in a system in which the graphene is adhered well to a substrate, the Poisson ratio of the substrate should be used rather than the in-plane Poisson ratio of graphite. Whereas in case of biaxial graphene, the Gruneisen parameter of G and 2D (or D) band is given by,256, 267 πΎππππ₯πππ = β βππ Equation 3.3 π 2 π π0 π Where π being G or 2D band, Ξππβπ is the biaxial strain shift rate of G or 2D band and ππ0 is the initial frequency of G or 2D band before straining. Biaxial strains are more suitable for calculating the πΎ since it does not depend on the Poisson ratio. Several groups have studied the effect of strain on Raman bands of graphene and have calculated various values for πΎ, and it is still a matter of debate. The uniaxial or biaxial strain can be applied to graphene via various ways including; inducing strain by utilising the difference in thermal expansion coefficient of substrate and graphene268, piezoelectric substrates266, and the most common method by stretching or bending the graphene deposited on a flexible substrates such as PMMA32, 269-274, PET256, 263, 264 and PDMS.265, 275-277 The Table 3-1 reports the various literature values of shift rates of Raman bands of graphene (mainly G and 2D band are presented). It also includes calculated or experimentally derived Gruneisen parameter values. 81PDF Image | PRODUCTION AND APPLICATIONS OF GRAPHENE AND ITS COMPOSITES
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