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Critical crossover phenomenain fluids
Jan V. SengersInstitute for Physical Science & Technology
University of Maryland, College Park, Md 20742
A celebration of 50 years Statistical PhysicsRutgers 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
2-, ,0 e aq tS q t S q
pa c
-1 0 as finite
pp
ca c
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J.V. Sengers and A. Michels (1962)
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
M.R. Moldover, W.A. Little (1965):
CV of He3 and He4 diverges at critical point
Coexistence curves are not parabolic
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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.)
Mode-coupling theory(Fixman,Kadanoff, Swift, Kawasaki)
Renormalization-group theory(K.G. Wilson, M.E. Fisher)
Scaling in fluids (B. Widom)
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Critical power laws and universality
ξ is correlation length
χ = (M/H)T is susceptibility
τ = (T Tc)/T
ξ = ξ0τν χ = χ0γ
Ising like Classical ν 0.63 ν = 0.50 γ 1.24 γ = 1.00
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Isobutyric acid + water
J.G. ShanksPh.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*: eff
log
log
d
d
Ising limit: γeff = 1.24
Mean-field limit: γeff = 1.00
*Kouvel and Fisher (1964)
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Anisimov, Povodyrev, Kulikov, Sengers, Phys. Rev. Lett. 75, 3146 (1995)
3-methylpentane+nitroethane
tetra-n-butyl ammonium picrate+ 1,4-butanediol/ 1-dodecanol
xenon
isobutyric acid+ water
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Crossover theory
( , , )u TWO crossover parameters:
is coupling constant u
Λ is dimensionless cutoff wave number related to a length ξD = v0
1/3/πΛ
Ginzburg number NG 2( )u
First nonasymptotic correction 1 u
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)
Tc(N)
phase separation boundaries
-point
T
N -1
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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
Thanks, Joel,for shepherdingour statistical-physicscommunity for 50 years
And last but not least: