Thermodynamic expressions for the Tolman length.

Area of Science:

• Thermodynamics
• Physical Chemistry
• Interfacial Science

Background:

• The Tolman length quantifies the deviation of surface tension in small liquid drops from the planar value.
• Debate persists regarding the sign of the Tolman length for simple liquids, despite theoretical interest.
• Recent work proposed a thermodynamic relation between Tolman length and isothermal compressibility at two-phase coexistence.

Purpose of the Study:

• To review the derivation of the proposed thermodynamic relation for Tolman length.
• To connect this relation to earlier thermodynamic expressions.
• To assess the applicability of the relation using the squared-gradient model for liquid-vapor interfaces.

Main Methods:

• Review of existing thermodynamic derivations.
• Analysis of the relation within the framework of the squared-gradient model.
• Comparison with theoretical predictions and experimental data (implicitly).

Main Results:

• The derivation of the delta approximately -kappa([script-l])sigma relation is reviewed.
• The relation is shown to be connected to prior thermodynamic formulations.
• The squared-gradient model confirms the relation's semiquantitative correctness, with deviations near the critical point.

Conclusions:

• The reviewed thermodynamic relation for Tolman length is validated within the squared-gradient model.
• The model's limitations near the critical point are highlighted.
• This work contributes to understanding interfacial thermodynamics and the Tolman length.