# Elastic Properties of Symmetric Liquid-Liquid Interfaces

## TL;DR

This study uses self-consistent field theory to accurately calculate the elastic bending rigidities of symmetric liquid-liquid interfaces, revealing their signs and scaling behavior near criticality and at strong segregation.

## Contribution

It provides high-precision, mean-field results for the bending rigidities of symmetric liquid-liquid interfaces using a specific SCF model, clarifying their signs and dependence on system parameters.

## Key findings

- Both moduli are positive near criticality, scaling with interfacial tension.
- At strong segregation, Gaussian rigidity becomes negative.
- Chain length influences the length scale  significantly at small N.

## Abstract

The mean ($\kappa$) and Gaussian ($\bar{\kappa}$) bending rigidities of liquid-liquid interfaces, of importance for shape fluctuations and topology of interfaces, respectively, are not yet established: even their signs are debated. Using the Scheutjens Fleer variant of the self-consistent field theory, we implemented a model for a symmetric L/L interface and obtained high precision (mean field) results in the grand canonical $(\mu, V, T)$-ensemble. We report positive values for both moduli when the system is close to critical where the rigidities show the same scaling behavior as the interfacial tension $\gamma$. At strong segregation, when the interfacial width becomes of the order of the segment size, $\bar{\kappa}$ turns negative. The length scale $\lambda \equiv \sqrt{\kappa/\gamma}$ is of order the segment size for all strengths of interaction; yet the $1/\sqrt{N}$ chain length correction reduces $\lambda$ significantly when the chain length $N$ is small.