Heat capacity and thermodynamic functions of nano-TiO2 rutile in relation to bulk-TiO2 rutile

Several conflicting reports have suggested that the thermodynamic properties of materials change with respect to particle size. To investigate this, we have measured the constant pressure heat capacities of three 7 nm TiO₂ rutile samples containing varying amounts of surface-adsorbed water using a combination of adiabatic and semi-adiabatic calorimetric methods. These samples have a high degree of chemical, phase, and size purity determined by rigorous characterization. Molar heat capacities were measured from T = (0.5 to 320) K, and data were fitted to a sum of theoretical functions in the low temperature (T < 15 K) range, orthogonal polynomials in the mid temperature range (10 > T/K > 75), and a combination of Debye and Einstein functions in the high temperature range (T > 35 K). These fits were used to generate $\mathit{Cp}\text{,}{\text{m}}^{°}$, ${\mathrm{\Delta }}_0^{\text{T}}{S}_{\text{m}}^{°}$, ${\mathrm{\Delta }}_0^{\text{T}}{H}_{\text{m}}^{°}$, and ${\phi }_{\text{m}}^{°}$ values at selected temperatures between (0.5 and 300) K for all samples. Standard molar entropies at T = 298.15 K were calculated to be (62.066, 59.422, and 58.035) J · K^?1 · mol^?1 all with a standard uncertainty of 0.002·${\mathrm{\Delta }}_0^{\text{T}}{S}_{\text{m}}^{°}$ for samples TiO₂·0.361H₂O, TiO₂·0.296H₂O, and TiO₂·0.244H₂O, respectively. These and other thermodynamic values were then corrected for water content to yield bare nano-TiO₂ thermodynamic properties at T = 298.15 K, and we show that the resultant thermodynamic properties of anhydrous TiO₂ rutile nanoparticles equal those of bulk TiO₂ rutile within experimental uncertainty. Thus we show quantitatively that the difference in thermodynamic properties between bulk and nano-TiO₂ must be attributed to surface adsorbed water.