Elastic Properties of Symmetric Liquid-Liquid Interfaces
The mean ($κ$) and Gaussian ($\barκ$) 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 $(μ, V, T)$-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 $γ$. At strong segregation, when the interfacial width becomes of the order of the segment size, $\barκ$ turns negative. The length scale $λ\equiv \sqrt{κ/γ}$ is of order the segment size for all strengths of interaction; yet the $1/\sqrt{N}$ chain length correction reduces $λ$ significantly when the chain length $N$ is small.