Heat of Fusion and Surface Tension of Solids Confined in Porous Materials Derived from a Combined Use of NMR and Calorimetry

Assuming the heat of fusion (Δ h f ) of a material confined in a porous material to be approximated by a function Δ h f = Δ h 0 (1 + a 0 (10 3 / T ) + a 1 (10 3 / T ) 2 ), where T is the absolute temperature, a theoretical model is derived that enables the coefficients a i to be determined from a combined use of NMR and calorimetric measurements. The model has been applied on solid ice confined in cement pastes resulting in a 0 = −0.136 K and a 1 = −0.00413 K 2 in the temperature range 273 K > T > 210 K. Δ h 0 was determined from the known value of Δ h f of bulk water at 273 K, giving Δ h 0 = 749 J/g. Likewise, assuming the surface tension (γ) of the ice−water interface to be approximated by a corresponding second-order polynomial in 1/ T, i.e., γ = γ 0 (1 + b 0 (10 3 / T ) + b 1 (10 3 / T ) 2 ), the coefficients b i were determined from the Gibbs−Thomson equation: Δ T = K f (γ/ρΔ h f )(1/ R ), where K f is a constant, ρ the density, and Δ T the lowering of the melting point of ice confined in pores with radius R . The model fit revealed a best fit to a linear function in 1/ T, with b 1 = 0 and b 0 = −(0.114 ± 0.033) K . The γ 0 was determined from the known value of γ at 273 K, resulting in γ 0 = 130 erg/cm.