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

1955-1962: Graduate student at University of Amsterdam

Time of expectations in NONEQUILIBRIUM STATISTICAL PHYSICS:

1872: Boltzmann

1922: Enskog

1946: Bogoliubov

1958: Uhlenbeck

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

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

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)

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

Isobutyric acid + water

J.G. ShanksPh.D. Thesis (1986)

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).

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)

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

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)

Gutkowski, Anisimov, Sengers, J. Chem. Phys. 114, 3133 (2001)

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)]

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

Anisimov, Kostko, Sengers, Yudin, J. Chem. Phys. 123, 164901 (2005)

Acknowledgments

• Mikhail A. Anisimov • Andrei F. Kostko

Thanks, Joel,for shepherdingour statistical-physicscommunity for 50 years

And last but not least: