Scale effects in the latent heat of melting in nanopores

Abstract

The curvature of a liquid vapor interface has long been known to change the equilibrium vapor pressure. It has also been shown that a capillary structure will affect the temperature at which both freezing and vaporization of a substance will occur. However, describing interfacial effects on the latent heat of a phase change has proven more difficult. Here, we present a classical thermodynamic model for how the latent heat of melting changes as the size of the particles undergoing the transition decreases. The scale dependence for the surface tension is taken into consideration using a Tolman length correction. The resulting model is tested by fitting to published experimental data for the latent heat of melting for benzene, heptane, naphthalene, and water contained in nano-porous glass. In all cases the model fits the data with a R(2) ≥ 0.94.

Understanding and Analyzing Freezing-Point Transitions of Confined Fluids within Nanopores

“…Several researchers have employed the Tolman length correction 13,14,21 to predict diameter-dependent γ SL (eq 2)…”

“…Recent theoretical work by Deinert and co-workers 14 attempts to explain the changes in the enthalpy of fusion at small pore radii for the same data set used here. 10,19 Their model (eq 4) assumes a spherical particle in equilibrium with its own melt and uses a simplified Tolman length (eq 2) to describe γ SL (r).…”

“…Several researchers have employed the Tolman length correction ,, to predict diameter-dependent γ SL (eq )­ where γ SL,∞ denotes the planar solid–liquid surface tension and δ denotes the Tolman length and is equal to ( R e – R s ). Here R e is the radius of the equimolar dividing surface (a dividing surface such that the system on the either side of the surface would contain an equal number of molecules, while the density changes discontinuously at the surface itself).…”

“…Although the Tolman length described by eq is commonly used, it is a first-order approximation of eq (by expanding around 2δ/ r = 0, a planar surface), originally derived by Tolman Recent theoretical work by Deinert and co-workers attempts to explain the changes in the enthalpy of fusion at small pore radii for the same data set used here. , Their model (eq ) assumes a spherical particle in equilibrium with its own melt and uses a simplified Tolman length (eq ) to describe γ SL ( r ). They fitted the data set of Δ H m as a function of pore radii using δ as a fitting parameter and demonstrated an excellent correlation with the experimental data. Here, we used this analysis and obtained δ and the diameter-dependent γ SL ( r ).…”

“…Although many researchers use the GT equation assuming a constant values of Δ H m and γ SL , thermocalorimetry data and theoretical models − show that these two parameters can change by almost an order of magnitude with the size of the nanopores. However, as we show here, even after accounting for the dependence of Δ H m and γ SL on the pore diameter, the GT equation fails to accurately predict Δ T f for most fluids (water, chlorobenzene, trans -decalin, cis -decalin, benzene, heptane, naphthalene, and cyclohexane).…”