Widom line

2011-11-28T11:10:59Z

161.116.80.7: /* References */

{{stub-general}}
The '''Widom line'''<ref>[http://dx.doi.org/10.1073/pnas.0507870102 Limei Xu, Pradeep Kumar, S. V. Buldyrev, S.-H. Chen, P. H. Poole, F. Sciortino, and H. E. Stanley "Relation between the Widom line and the dynamic crossover in systems with a liquid–liquid phase transition", PNAS '''102''' pp. 16558-16562 (2005)]</ref> (not to be confused with the [[Fisher-Widom line]]) is defined as the line in the [[Phase diagrams: Pressure-temperature plane | pressure-temperature plane]] where the [[Critical exponents#Correlation length |correlation length]] has its maximum <ref>[http://dx.doi.org/10.1140/epjst/e2008-00746-3 H. E. Stanley, P. Kumar, G. Franzese, L. Xu, Z. Yan, M. G. Mazza, S. V. Buldyrev, S.-H. Chen and F. Mallamace "Liquid polyamorphism: Possible relation to the anomalous behaviour of water", European Physical Journal - Special Topics '''161''' pp. 1-17 (2008)]</ref> , and emanates from the hypothesized
[[Liquid-liquid phase transitions |liquid–liquid]] [[critical points | critical point]] of [[water]] . It was named the Widom line by [[H. Eugene Stanley]]<ref>[http://www.bu.edu/phpbin/researchbriefs/display.php?id=659 Sergey V. Buldyrev "Water wisdom and Widom", Boston University Research Briefs '''December 6''' (2005)]</ref> in honour of [[Benjamin Widom]].
==References==
<references/>
;Related reading
*[http://dx.doi.org/10.1038/nphys1683 G. G. Simeoni, T. Bryk, F. A. Gorelli, M. Krisch, G. Ruocco, M. Santoro, and T. Scopigno "The Widom line as the crossover between liquid-like and gas-like behaviour in supercritical fluids", Nature Physics '''6''' pp. 503-507 (2010)]

*[http://iopscience.iop.org/0953-8984/19/20/205126 Giancarlo Franzese and H. Eugene Stanley "The Widom line of supercooled water", Journal of Physics: Condensed Matter '''19''' 205126 (2007)]

[[category: statistical mechanics]]

Square shoulder + square well model

2011-04-06T08:09:49Z

161.116.80.7: References have been corrected

{{Stub-general}}
The '''Square shoulder + square well''' model consists, as its name suggests, of a combination of the [[square shoulder model]] and the [[square well model]]. The model is given by

:<math>
\Phi_{12}\left( r \right) =
\left\{ \begin{array}{ccc}
\infty & ; & r < \sigma \\
\epsilon_1 & ; &\sigma \le r < \lambda_1 \sigma \\
- \epsilon_2 & ; &\lambda_1\sigma \le r < \lambda_2 \sigma \\
0 & ; & r \ge \lambda_2 \sigma \end{array} \right.
</math>

where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>\epsilon_1</math> and <math>\epsilon_2</math> are the well ''depths'', <math>r</math> is the distance between site 1 and site 2 where <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>, σ is the hard core diameter
and <math>\lambda_1,\lambda_2>1</math>
==Critical points==
See Ref.s 1-5.
==Liquid-liquid transition==
For certain parameter sets the square shoulder + square well model has a [[Polyamorphic systems | liquid-liquid transition]]. See Ref.s 1-4.
==References==
#[http://www.nature.com/nature/journal/v409/n6821/full/409692a0.html Giancarlo Franzese, Gianpietro Malescio, Anna Skibinsky, Sergey V. Buldyrev, and H. Eugene Stanley "Generic mechanism for generating a liquid-liquid phase transition", Nature '''409''', pp. 692-695 (2001)]
#[http://pre.aps.org/abstract/PRE/v66/i5/e051206 Giancarlo Franzese, Gianpietro Malescio, Anna Skibinsky, Sergey V. Buldyrev, and H. Eugene Stanley, "Metstable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly", Physical Review E '''66''', 051206 (2002)]
#[http://pre.aps.org/abstract/PRE/v69/i6/e061206 Anna Skibinsky, Sergey V. Buldyrev, Giancarlo Franzese, Gianpietro Malescio, and H. Eugene Stanley, "Liquid-liquid phase transitions for soft-core attractive potentials", Physical Review E '''69''', 061206 (2004)]
#[http://pre.aps.org/abstract/PRE/v71/i6/e061504 Gianpietro Malescio, Giancarlo Franzese, Anna Skibinsky, Sergey V. Buldyrev, and H. Eugene Stanley, "Liquid-liquid phase transition for an attractive isotropic potential with wide repulsive range", Physical Review E '''71''', 061504 (2005)]
#[http://dx.doi.org/10.1063/1.2970884 W. Rzysko, O. Pizio, A. Patrykiejew, and S. Sokolowski "Phase diagram of a square-shoulder, square-well fluid revisited", Journal of Chemical Physics '''129''' 124502 (2008)]
#[http://dx.doi.org/10.1063/1.2982162 Shiqi Zhou, A. Lajovic, and A. Jamnik "Local structures of fluid with discrete spherical potential: Theory and grand canonical ensemble Monte Carlo simulation", Journal of Chemical Physics '''129''' 124503 (2008)]
[[Category: Models]]
[[category: Polyamorphic systems]]

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Widom line

Square shoulder + square well model