Heat capacity and thermodynamic functions of nano-TiO sub(2) anatase in relation to bulk-TiO sub(2) anatase

Several conflicting reports have suggested that heat capacities and the thermodynamic properties of materials change as their particle size decreases into the nanoscale. To further investigate this, we have measured the constant pressure heat capacities of three 7 nm TiO sub(2) anatase 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 fit to a sum of theoretical functions in the low temperature (T < 15 K) range, orthogonal polynomials in the mid temperature range (10 > T > 75 K), and a combination of Debye and Einstein functions in the high temperature range (T > 35 K). These fits were used to generate C sub(p,m) degree Cp,m degree , Delta 0TSm degree , Delta 0THm degree , and phi sub(m) degree phi m degree values at smoothed temperatures between (0.5 and 300) K for all hydrated samples. Standard molar entropies at T = 298.15 K were calculated to be 73.868, 66.072, and 63.845 J . K super(-1) . mol super(-1) all with a standard uncertainty of 0.002. Delta 0TSm degree for samples TiO sub(2) . 0.677H sub(2)O, TiO sub(2) . 0.532H sub(2)O, and TiO sub(2) . 0.379H sub(2)O, respectively. These and other thermodynamic values were then corrected for water content to yield bare nano-TiO sub(2) thermodynamic properties at T = 298.15 K, and we show that the resultant thermodynamic properties of anhydrous TiO sub(2) anatase nanoparticles equal those of bulk TiO sub(2) anatase within experimental uncertainty. Thus we show quantitatively that the difference in thermodynamic properties between bulk and nano-TiO sub(2) must be attributed to surface adsorbed water.