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The relative permittivity of dipolar fluids is important in many industrial and scientific applications, e.g. whenever electrolytes or electromagnetic fields are present. For non-polarizable model molecules, it is directly linked to the mutual molecular orientation and thereby usually not accessible by equations of state. However, the recently developed Co-Oriented Fluid Functional Equation for Electrostatic interactions (COFFEE) allows for calculating the orientation distribution function of simple polar molecules and thereby establishes a connection between the thermodynamic behavior and the relative permittivity. In this article, we develop an expression to calculate the relative permittivity from the orientation distribution known from COFFEE. Furthermore, we calculate the relative permittivity of simple polar fluids using molecular simulations. We study the original Stockmayer fluid and the shifted Stockmayer fluid, in which the dipole is shifted away from the Lennard-Jones center along the dipole axis. For both fluids, different dipole strengths are investigated. The results from the theoretical expression from COFFEE are compared to the simulation data. Thereby, a possible link between polar equations of state and electric fields or electrolytes is developed.
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