Phase transition of a colloidal suspension in the vicinity of a fluctuating membrane using the lattice gas model

Abstract

This investigation aims to study the phase transition of colloidal particles near a fluctuating membrane using the lattice gas model. The first step is to derive a new Ising-like Hamiltonian. We addressed this problem in the continuous limit by applying the Hubbard–Stratonovich transformation. The values predicted by the mean-field approximation, or its generalization namely, the Landau approximation are ${\alpha }^{\prime +}={\alpha }^{\prime -}=0$, ${\beta }^{{}^{\prime }}=1/2$, ${\gamma }_{+}={\gamma }_{-}=1$, $\delta =3$, $\eta =0$ and $\nu =1/2$. We have also established scaling relations between these critical exponents. The gas-on-network model was employed to demonstrate the hysteresis phenomenon, providing a quantitative description at the microscopic scale of the phase transition in the colloidal suspension, from the ordered phase to the disordered phase. In comparison with recent studies, the lattice gas model remains a valuable tool and promising for describing the organization of colloidal particles near a soft interface.