Interfacial tensions near critical endpoints: experimental checks of EdGF theory

Abstract

Predictions of the extended de Gennes–Fisher local-functional theory for the universal scaling functions of interfacial tensions near critical endpoints are compared with experimental data. Various observations of the binary mixture isobutyric acid + water are correlated to facilitate an analysis of the experiments of Nagarajan, Webb and Widom who observed the vapour–liquid interfacial tension as a function of both temperature and density. Antonow's rule is confirmed and, with the aid of previously studied universal amplitude ratios, the crucial analytic ‘background’ contribution to the surface tension near the endpoint is estimated. The residual singular behaviour thus uncovered is consistent with the theoretical scaling predictions and confirms the expected lack of symmetry in (T−T_c ). A searching test of theory, however, demands more precise and extensive experiments; furthermore, the analysis highlights a previously noted but surprising, threefold discrepancy in the magnitude of the surface tension of isobutyric acid + water relative to other systems.

Acknowledgement

We appreciate the keen interest of B. Widom and comments from J. Indekeu and M. R. Moldover. We are indebted to C. M. Knobler and I. L. Pegg for informative discussions regarding their surface tension measurements. The support of the National Science Foundation through grants CHE 99-81772 and CHE 03-01101 is gratefully acknowledged.

Especially on this occasion, it is a pleasure for MEF to acknowledge the inspiration provided over more than four decades by the limpidly insightful researches of Benjamin Widom.

Notes

†In contrast to the NWW data, the coexistence curve measured by Greer [16] is somewhat less symmetric: on the basis of her data, the diameter can be represented by

.

†NWW supposed the volume fraction ϕ _w of water in the mixture to be related to the mass fraction m_w via ϕ _w = m_w /[m_w + (1−m_w )/c], where c=0.970 is a constant that represents the ratio of the density of pure isobutyric acid to that of pure water at

. (B. Widom, private communication.).

†Moldover in his review of experiments on many systems [33], quotes

from HWK; but as we discuss further in the Appendix, Moldover also reports the value

on the basis of a private communication from I.L. Pegg and C.M. Knobler: unfortunately, these two values are drastically inconsistent. However, since the first accords well with our analysis of both the HWK and NWW data, we proceed, at this point, with the estimate (25).

†Fenzl [35] has discussed the NWW data and challenged the validity of Antonow's rule for their experiments. However, as pointed out in the article by Fenzl himself (B. Widom, private communication), the direction in which it is argued that the rule is violated actually contradicts thermodynamic interfacial stability. In figure 2 the tendency for the high-density surface tension data to rise up (relative to the parallelogram) and vice versa for the low-density data, indicates a trend (violating stability) that Fenzl may have noticed. Otherwise, Fenzl also argues that, contrary to our approach and the theoretical analysis of NWW, the critical behaviour they observed corresponds to a very small surface field h₁ (and, correspondingly, small M₁ ). In light of the observations just made concerning Antonow's rule and the successful fits we achieve here, Fenzl's proposal does not seem sustainable.

†We are indebted to B. Widom for drawing our attention to [36, 37].

†See the footnote attached to the text following equation (25).

†This point has been reconfirmed by C.M. Knobler who has kindly re-examined the original records of the HWK experiments and sees no reasonable sources of larger errors.