Related Experiment Video
Updated: Jun 6, 2026
08:05
Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces
Published on: September 9, 2022
Fluctuation-dissipation framework for size-dependent surface tension
Sergii Burian1, Yevhenii Shportun1, Liudmyla Klochko2
1Faculty of Physics, Taras Shevchenko National University of Kyiv, 64/13 Volodymyrska Street, Kyiv 01601, Ukraine.
The Journal of Chemical Physics
|June 5, 2026
Summary
Researchers developed a new framework to calculate the Tolman length, a key factor in nanoscale liquid-vapor surface tension. This method relates the Tolman length to bulk liquid properties, simplifying its determination for various fluids like water.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Physical Chemistry
Background:
- Surface tension's size dependence is crucial for nanoscale phenomena like wetting and phase change.
- The Tolman length, representing the first curvature correction to surface tension, is challenging to measure experimentally and theoretically.
- Existing models often struggle to accurately predict the Tolman length for diverse liquid systems.
Purpose of the Study:
- To establish a thermodynamic and statistical-mechanical framework for calculating the Tolman length.
- To connect the Tolman length to measurable bulk response properties of one-component liquids.
- To provide a practical method for determining the Tolman length, especially for weakly compressible liquids.
Main Methods:
- Developed a theoretical framework linking Tolman length to bulk liquid properties near liquid-vapor coexistence.
- Analyzed capillary-chemical balance using two local formulations: excess pressures and relative density deviations.
- Employed homogeneous (N, P, T) simulations for water using the extended simple point charge (SPC) and TIP4P/2005 models.
Main Results:
- The planar-limit Tolman length for a liquid is shown to be a combination of its isothermal compressibility and pressure derivative.
- For water at 300 K, simulations yield Tolman length estimates around -0.7 Å.
- Independent evaluation using the IAPWS-IF97 formulation confirms values near -0.713 Å for water, predicting weak temperature dependence.
Conclusions:
- The developed framework successfully relates the Tolman length to bulk liquid properties, simplifying its calculation.
- The method is applicable to other one-component liquids with known equations of state or bulk volume statistics.
- This work offers a more accessible route to determining a critical parameter for understanding nanoscale interfacial phenomena.
Related Concept Videos
01:22Surface Tension of Fluid
Surface tension is a fundamental property of fluids, occurring at the boundary between a liquid and a gas or between two immiscible liquids. This phenomenon arises from the cohesive forces between molecules at the fluid's surface, creating an effect similar to a stretched elastic membrane. Inside each fluid, molecules are equally attracted in all directions by neighboring molecules, but surface molecules experience a net inward force, resulting in surface tension.
Surface tension varies with...
Surface tension varies with...
01:24Surface Tension
Surface tension is defined as the force per unit length (γ) acting along the surface of a liquid. It arises due to strong intermolecular forces of attraction. A molecule located inside the bulk of the liquid is surrounded by other molecules and experiences equal forces in all directions. However, a molecule at the surface experiences unbalanced forces because there are more neighboring molecules below than above. This creates a net inward force that pulls surface molecules toward the interior,...
01:16Surface Tension and Surface Energy
When a paint brush is immersed in water, the bristles wave freely inside the water. When it is taken out, the bristles stick together. The reason behind this effect is surface tension.
Consider a beaker filled with liquid. The bulk molecules in the liquid experience equal attractive forces on all sides with the surrounding molecules. However, the surface molecules experience a net attractive force downward due to the bulk molecules. The surface of the liquid behaves like a stretched membrane,...
Consider a beaker filled with liquid. The bulk molecules in the liquid experience equal attractive forces on all sides with the surrounding molecules. However, the surface molecules experience a net attractive force downward due to the bulk molecules. The surface of the liquid behaves like a stretched membrane,...
02:57Surface Tension, Capillary Action, and Viscosity
Surface Tension
The various IMFs between identical molecules of a substance are examples of cohesive forces. The molecules within a liquid are surrounded by other molecules and are attracted equally in all directions by the cohesive forces within the liquid. However, the molecules on the surface of a liquid are attracted only by about one-half as many molecules. Because of the unbalanced molecular attractions on the surface molecules, liquids contract to form a shape that minimizes the number...
The various IMFs between identical molecules of a substance are examples of cohesive forces. The molecules within a liquid are surrounded by other molecules and are attracted equally in all directions by the cohesive forces within the liquid. However, the molecules on the surface of a liquid are attracted only by about one-half as many molecules. Because of the unbalanced molecular attractions on the surface molecules, liquids contract to form a shape that minimizes the number...
01:09Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model
Various dissolution theories provide insight into the factors that influence the dissolution rate. Danckwerts' Model suggests that turbulence, rather than a stagnant layer, characterizes the dissolution medium at the solid-liquid interface. In this model, the agitated solvent contains macroscopic packets that move to the interface via eddy currents, facilitating the absorption and delivery of the drug to the bulk solution. The regular replenishment of solvent packets maintains the concentration...
01:13Excess Pressure Inside a Drop and a Bubble
The shape of a small drop of liquid can be considered spherical, neglecting the effect of gravity. This drop can further be considered as two equal hemispherical drops put together due to surface tension. The forces acting on the spherical drop are due to the pressure of the liquid inside the drop, the pressure due to air outside the drop, and the force due to the surface tension acting on the two hemispherical drops.