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|S ε | / cm -1 . -11311975ARTICLE IN PRESS+ MODEL44 G. Gouadec, Ph. Colomban / Progress in Crystal Growth and Characterization of Materialsxx (2007) 1e56AramidKevlarCarbon - PANFT700 - pitchPBZTP75 - pitchTyrannoNLM3130 60 90 120 1501000 E -1/2 / GPa -1/2Fig. 26. Absolute value of the Raman Mechanical Coefficient (RMC) of the carbon G band plotted versus the inverse ofYoung’s modulus square root. Reprinted from Ref. [38, pp. 1249e1259] with permission from Elsevier.in the literature but these results were based on a narrower exploration of Young’s Modulus,limited to aramid [447,467,491], polyethylene [492] or carbon [453] fibres. Deviations fromthe linear trend in Fig. 26 can be explained with the following arguments:(i) A few of the S 3 values appearing in Fig. 26 were measured under compression and theyare not necessarily comparable with those obtained through tensile straining. Indeed, theS 3 coefficients suppose a linear dependence of the Raman wavenumbers on the macroscopicdeformation but a general relationship would rather be quadratic [450]:Dn ¼ a D3 þ bðD3Þ 2ð60ÞS 3 is thus subject to change when passing from tensile to compressive stress. There is almostno effect (b w 0) for isotropic structures like SiC fibres with strong covalent bonds in all directionsbut Melanitis et al. [451] found a/b w 5 (only!) in ‘‘PAN-based’’ carbon fibres.(ii) Not all S 3 values in Fig. 26 were obtained with the same laser line. Yet, carbon is a resonantspecies and both the spectrum and the penetration depth therefore depend on theactual wavelength. Most papers on Raman extensometry of carbon have neglected thisaspect of the problem.(iii) The reasoning that drove to Fig. 26 neglected the k b and kb 0 distributions in the material. Thissimplification is probably acceptable for carbon fibres but certainly not for SiC fibres (Tyrannoand NLM grades), where CeC and CeSiC bonds coexist. For that matter, the secondand third generation SiC fibres have such a specific behaviour that they were not even includedin Fig. 26. In such fibres with small amorphous or crystalline particles, CeC bondsare largely outnumbered by SieC and inter-particles bonds. The E fibre (macroscopic scale)can no longer be considered as the counterpart of S 3=sparticles(bond scale) [375].Fig. 27 shows that the variations of Young’s Modulus (the slope on the strainestress curve)in a semi-crystalline polymer such as PET can be correlated with the Raman shifts of the lowfrequency contributions corresponding to the amorphous and crystalline substructures (seePlease cite this article in press as: G. Gouadec, Ph. Colomban, Prog. Cryst. Growth Charact. Mater. (2007),doi:10.1016/j.pcrysgrow.2007.01.001
ARTICLE IN PRESS+ MODELG. Gouadec, Ph. Colomban / Progress in Crystal Growth and Characterization of Materialsxx (2007) 1e562crystalline contribution120045Δν / cm -10-2-4-6-8-10-121 22'3-14-2 0 2 4 6 8 10 12 14Strain /amorphouscontribution10008006004002000σ/ MPaFig. 27. Comparison of the strain dependency of the crystalline and amorphous low frequency Raman contributions (lefthand scale) with the stressestrain tensile curve (right hand scale) for PET fibres. Reprinted from Ref. [172, pp. 2463e2475] with permission from Elsevier.Fig. 5). In PET fibres, most of the stress is obviously transferred to the amorphous matrix,whereas nano-crystallites are only slightly compressed by a Poisson’s effect. In polyamide fibres,both the amorphous and crystalline moieties accommodate the stress because the nanostructureputs them ‘‘in series’’. Wavenumberestrain curves then start with a plateau thatcorresponds to the disentanglement of the polymer chains (visco-elastic regime) and wavenumbersstart downshifting as soon as ‘‘knots’’ block this process (elastic regime) [169e172].5.5. CNTs used as nanometric stress gaugesOn account of their very small dimension, the direct determination of CNTs Young’s modulusis difficult. Most experimental values were obtained through manipulations with an AFMtip (see Table 4 in Ref. [493]) but Lourie and Wagner [494] demonstrated that an indirect measurementwas possible using RS on ‘‘quenched’’ matrix-embedded nanotubes. Using a ‘‘concentriccylinders’’ modelling of each CNT and the surrounding matrix, they calculated the axialtube stress due to cooling by DT degrees and established an expression for nanotubes Young’smodulus E NT :E NT ¼ Da DT3 NT1 ð1fNT Þf NTE m ð61Þwhere Da is the difference in thermal expansion, f NT is the volume fraction of nanotubes, E mthe Young’s modulus of the matrix and 3 NT is the compressive strain. The latter was measuredby the strain dependency of the D* Raman band of SWCNTs, which allowed Young’s modulusdetermination. Conversely, some authors filled composites matrices with nanotubes and usedthem to sense fibre stress in polymers [471,495,496].References[1] Ph. Colomban, Ceramics Int. 15 (1989) 23.[2] Ph. Colomban, G. Sagon, X. Faurel, J. Raman Spectrosc. 32 (2001) 351.Please cite this article in press as: G. Gouadec, Ph. Colomban, Prog. Cryst. Growth Charact. Mater. (2007),doi:10.1016/j.pcrysgrow.2007.01.001
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