Implications of a non-analytic small-k asymptotics of the direct correlation function in the liquid-vapor interface

✍ Scribed by M. Requardt; H.J. Wagner

• Book ID: 103894820
• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 533 KB
• Volume: 196
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(93)90082-f

✦ Synopsis

We analyze the large-s respectively small-k asymptotics of the correlation functions H(s), C(s) and their Fourier transforms H(k), C(k) in the, say, liquid-vapor interfacial layer. We show that their behavior may differ appreciably from the expected one if (~(k) develops a sufficiently strong non-analyticity at k = 0. This possibility has also been considered recently by Robert.

In such a scenario we find that, typically, the zero eigenvalue of C(k = 0) may be degenerated. As a consequence, the sometimes used "one-eigenfunction assumption" then leads to incorrect results. Furthermore, t~(k) displays a rather complex low-k behavior and there is no simple relation between the leading orders of/:/(k) and (~(k) -t~(0) in the small-k regime.

To illustrate these considerations, we introduce and explicitly solve a class of both viable and nontrivial interface models which display all these unexpected properties.

• 1 There recently appeared a paper [15] in which the authors, while seemingly being unaware of our findings, arrived at similar results.