Isobaric Critical Exponents: Test of Analyticity against NIST Reference Data

TL;DR

This study tests the analyticity-based prediction of universal isobaric critical exponents using NIST data for various molecules, finding consistency within a specific temperature range and revealing a characteristic natural number for each molecule.

Contribution

It provides empirical validation for the analyticity prediction of critical exponents in finite systems under isobaric conditions, linking them to a characteristic natural number.

Findings

Critical exponents match predictions within a specific temperature range.

Each molecule exhibits a characteristic natural number determining its critical exponents.

Universal value of n=2 observed for temperatures above critical temperature.

Abstract

Finite systems may undergo first or second order phase transitions under not isovolumetric but isobaric condition. The `analyticity' of a finite-system partition function has been argued to imply universal values for isobaric critical exponents, $\alpha_{{\scriptscriptstyle{P}}}$, $\beta_{{\scriptscriptstyle{P}}}$ and $\gamma_{{\scriptscriptstyle{P}}}$. Here we test this prediction by analyzing NIST REFPROP data for twenty major molecules, including $\mathrm{H_{2}O, CO_{2}, O_{2}}$, etc. We report they are consistent with the prediction for temperature range, $10^{-5} <|T/T_{c}-1|<10^{-3}$. For each molecule, there appears to exist a characteristic natural number, $n=2,3,4,5,6$, which determines all the critical exponents for $T<T_{c}$ as $\alpha_{{\scriptscriptstyle{P}}}=\gamma_{{\scriptscriptstyle{P}}}=\frac{n}{n+1}$ and $\beta_{{\scriptscriptstyle{P}}}=\delta^{-1}=\frac{1}{n+1}$. For the opposite $T>T_{c}$, all the fluids seem to indicate the universal value of ${n=2}$.