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^{1}UPIITA-IPN, Mexico

^{2}CICATA-IPN, Mexico

^{3}CINVESTAV-IPN, Mexico

**Keywords:** nanoparticles normal modes**property:** specific heat**material:** TiO_{2}

The normal modes of nanometric particles involve the collective movement of a very large number of atoms, in such a way it is possible calculate them using the elasticity theory. The spherical case can be used successfully in the calculation of the normal modes frequencies of nanoparticles. In a sphere with free boundaries, these normal modes frequencies are inversely proportional to its radius. Theoretically, it is also possible calculate the modes of embedded spheres in a matrix. In this work, we calculate the normal modes of TiO_{2} nanoparticles in a colloidal solution in order to obtain the specific heat of the system. In agreement with this model, the specific heat must be a function of the nanoparticle's size. Our results are compared with experimental data obtained from phototermal techniques and/or specific heat measurements at room temperature.

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