(208c) Critical Properties Extracted From Virial Series Using Approximants Consistent With Universal Scaling-Laws

Barlow, N. S., University at Buffalo, The State University of New York
Schultz, A. J., University at Buffalo, The State University of New York
Kofke, D. A., University at Buffalo, The State University of New York
Weinstein, S. J., Rochester Institute of Technology

We report on our work towards establishing the necessary and sufficient conditions for an asymptotically consistent approximant used to predict critical fluid properties based solely on the virial equation of state (virial series) and knowledge of the established universal critical behavior at the critical point. Given enough coefficients, accurate estimates of the critical temperature Tc and pressure Pc of a fluid can be extracted from the virial series. However, using this approach, the critical density ρc is consistently predicted as being too low. We provide evidence that this is a result of the non-singular nature of the virial series. In an effort to explore techniques that would allow one to capture a more accurate estimate of ρc, we draw from known critical scaling-laws and cast the critical density as a branch-point singularity, using an approximant method to analytically continue the series. As a result, critical isotherms are constructed that capture the non-classical (singular) behavior at the critical point, while still retaining the low density behavior of the virial series. The approach to the critical region (from above, T >Tc) is also explored, using approximants that are asymptotically consistent with universal scaling laws.