Critical crossover phenomena in fluids

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Critical crossover phenomenain fluids

• Jan V. Sengers
• Institute for Physical Science Technology
• University of Maryland, College Park, Md 20742

A celebration of 50 years Statistical
Physics Rutgers University, December 2008
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1955-1962 Graduate student at University of
Amsterdam Time of expectations in NONEQUILIBRIUM
STATISTICAL PHYSICS
1872 Boltzmann 1922 Enskog 1946
Bogoliubov 1958 Uhlenbeck
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CRITICAL SLOWING DOWN OF FLUCTUATIONS Classical
Van Hove theory

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M.I. Bagatskii, A.V. Voronel, V.G. Gusak
(1962) CV of argon diverges at critical point
W.M. Fairbank, M.J. Buckingham, C.F.
Kellers (1960) CV of liquid helium diverges at
lambda line
Coexistence curves are not parabolic
M.R. Moldover, W.A. Little (1965) CV of He3 and
He4 diverges at critical point
J.V. Sengers and A. Michels (1962)
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Universality of critical phenomena? (M.S. Green,
L.P. Kadanoff)
Critical exponents (M.E. Fisher)
Lattice models (C. Domb et al.)
Scaling in fluids (B. Widom)
Renormalization-group theory (K.G. Wilson, M.E.
Fisher)
Mode-coupling theory (Fixman,Kadanoff, Swift,
Kawasaki)
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Critical power laws and universality
? is correlation length ? (?M/?H)T is
susceptibility t (T ? Tc)/T ? ?0t?? ?
?0??
Ising like
Classical ? ? 0.63 ?
0.50 ? ? 1.24
? 1.00
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Isobutyric acid water
J.G. Shanks Ph.D. Thesis (1986)
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All fluids, simple and complex, are
asymptotically Ising
CONSENSUS
Peter Debye at first conference on critical
phenomena in 1965 in Washington DC I would like
that the theoretical people tell me when I am so
and so far away from the critical point, then my
curve should look so and so. (p. 129).
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• Crossover critical behavior
• Effective critical exponent

Ising limit ?eff 1.24 Mean-field
limit ?eff 1.00
Kouvel and Fisher (1964)
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3-methylpentane nitroethane
xenon
isobutyric acid water
tetra-n-butyl ammonium picrate
1,4-butanediol/ 1-dodecanol
Anisimov, Povodyrev, Kulikov, Sengers, Phys. Rev.
Lett. 75, 3146 (1995)
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Crossover theory
TWO crossover parameters
? is dimensionless cutoff wave number related to
a length ?D v01/3/p?
Ginzburg number NG ?
First nonasymptotic correction ?
Z.Y Chen, P.C. Albright, J.V. Sengers, Phys. Rev.
A 41, 3161 (1990) M.A. Anisimov, S.B. Kiselev,
J.V. Sengers, S. Tang, Physica A 188, 487 (1992)
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Gutkowski, Anisimov, Sengers, J. Chem. Phys. 114,
3133 (2001)
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Y.C. Kim, M.A. Anisimov, J.V. Sengers, E.
Luijten, J. Stat. Phys. 109, 591 (2003)
Computer simulations E. Luijten and K. Binder,
Phys. Rev. E (1999)
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Phase diagram for polymer solutions
Theta-point limiting point for line of critical
points
tricritical point ? (almost) mean-field
  Critical point of demixing ?
fluctuations induced behavior (Ising)
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Anisimov, Kostko, Sengers, Yudin, J. Chem. Phys.
123, 164901 (2005)
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Acknowledgments

• Mikhail A. Anisimov
• Andrei F. Kostko

And last but not least
Thanks, Joel, for shepherding our
statistical-physics community for 50 years