Pressure of active system under the electric double layer interaction

Abstract

Self-driven particle systems consist of particles that can extract energy from the environment and transform into active motion, and thus are significantly different from the classical passive particle systems. For such an active system, the question of whether there is a classical equation of state (EOS) has caused spreading concern. Recent studies analyzed the validity of the EOS of an active system under the harmonic potential (Solon et. al, 2015 <i>Nature Physics</i>, <b>11</b> 673). In contrast, this paper explores the conditions for and the specific forms of the EOS of an active system under electric double-layer interaction between the wall and the particles. The results show that the wall pressure is related to the shape of the active particles. When a wall exerts a moment on the active particles, the particles orientation turns to the equilibrium state parallel to the wall surface under the action of the moment, and the increase of the wall-particle interaction strength enhances the parallel-orientation trend, which reduces the system pressure. The association of pressure and wall means that the active system does not have a general equation of state. In the case where the wall-particle interaction intensity is extremely small or extremely large, by defining the effective temperature, the active system has an equation of state similar to that of the ideal gas. In addition, it is found that the extent of the shape of particles deviating from the rotational symmetry is a key factor affecting the pressure of active particles. The research results provide a reference for the study of the current active system equilibrium properties, and provide a basis for studying the thermodynamic properties of active systems under more complex interaction potentials.