Raman Shift Versus Youngs Modulus

As discussed in Chap. 15, the solution to the Hamiltonian of a vibration system is a Fourier series with multiple terms of frequencies being fold of that of the primary mode [36]. Any perturbation to the Hamiltonian causes the Raman frequencies to shift from the initially ideal values. Therefore, applied strain, pressure, temperature, or the atomic CN variation can modulate the length and energy of the involved bonds, or their representative, and hence the phonon frequencies in terms of bond relaxation and vibration. 

From the dimensional analysis, the vibration frequency is proportional to the square root of the bond stiffness. Equaling the vibration energy of an ideal harmonic oscillator to the corresponding term in the Taylor series of the interatomic potential around its equilibrium, one can find. 

The elastic modulus correlates thus with the Raman shift of the specimen. 

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More recently, Liu et al. (47), compared OH- covalently functionalized SWNTs to SDS stabilized SWNTs. The authors used Raman spectroscopy to understand why the improvements of the Young s modulus and strength are greater for covalently functionalized nanotubes. The Raman shift was plotted versus the tensile strain in the two composites PVA/OH-SWNTs and PVA/ SDS dispersed SWNTs, in the elastic regime (for strain values below 1.2%). The shift is linear in this regime, and a larger slope is measured... 

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