(97i) Estimation of Critical Exponents Using Asymptotic Approximants

The virial equation of state is a power series in number density that incorporates attractive and repulsive interactions between molecules, which gives it the ability to be one of the best tools for modeling fluid behavior. Unfortunately, the virial series is expressed in terms of bulk fluid properties, so, although the virial series is theoretically infinite, coefficients are expensive to compute. Additionally, if there is a thermodynamic critical point, this sets the series’ radius of convergence, which can make it difficult to predict critical properties using the virial series.

This project primarily analyzes the effectiveness of asymptotic approximants, which incorporate the virial series and known critical scaling laws. This method will be used to estimate the critical exponent along the critical isotherm. A case study is also conducted in estimating the critical exponent for the high temperature susceptibility expansion of the Ising model and comparing the estimates between the asymptotic approximant and more traditional methods. The aim of this work is to provide a methodology for constructing equations of state and predicting fluid properties over a broad range of fluids and conditions.