When charge and density fluctuations critically couple Jean-Nol - - PowerPoint PPT Presentation

When charge and density fluctuations critically couple

Jean-Noël Aqua INSP, Univ Paris 6

Analytical results in Statistical Physics, In memory of Bernard Jancovici,

nov 2015

Soluble models as cartoons for the ‘real’ world

• 2D Coulomb fluid : screening of an external electrostaticfield
• Coulomb sphericalmodel :

universalityclass, screening effect, ionicity

Soluble models as cartoons for the ‘real’ world

• 2D Coulomb fluid : screening of an external electrostaticfield
• Coulomb sphericalmodel :

universalityclass, screening effect, ionicity

Experiments in 2D (1980’s) : Kim, Chan good comparison experiments/theory

Critical point

Onsager (1944) : Exact solution of the 2D Ising model Divergence of the specific heat at the critical point

Liquid-gas critical point

ü Universality class : Ising ü Singularities : ü Scaling laws with given critical exponents (MF)

Experimental controversy

ü Singh and Pitzer (1988-90) ü Japas and Levelt-Sengers (1990)

What is the universality class of charged fluids ?

Critical charged fluids

What is the influence of the long range of Coulomb interactions ? Critical phase separation ü Short-range interactions : Ising ü Power-law interactions : universality class function of ü Coulomb interaction : ?? what role for the screening effect ?

Critical charged fluids

What is the universality class of Coulomb fluids ? ü Simulations : Ising Caillol, Levesque, Weis (1997) Luijten, Fisher, Panagiotopoulos, Orkoulas (2002) … ü Cross-over temperature why should ?

Influence of asymmetry

ü Stell (1995) : the fluid asymmetry (ex: +2e,-e, different hard-cores … ) could lead to a change in the universality class NO in Monte-Carlo simulations of asymmetric +e,-e electrolytes What influence of the short-range asymmetry on the critical properties ? ü Universality class of charge asymmetric electrolytes : Ising for +2e,-e Not clear for +3e,-e Critical parameters , hardly reproduced

Critical phase separation

When , density correlations at large distances, behave as For common fluids, Ex : 2 components fluid (+,-)

Classical Coulomb fluids

Charge correlations are screened when Debye screening length Ex : 2 components fluid (+,-) Conducting Coulomb system : Stillinger-Lovett sum rule where Quid for and when at the critical point ?

Spherical model (Berlin, Kac, 1952)

… Need of exact results to elucidate the physics at work guide the theoretical investigations ü Ising model discrete spins ü Spherical model constrained continuum spins Exact solution for a model of spins of dimension n when

Coulomb spherical model

ü In a ionic+short-range interaction fluid, the universality class is not changed by the Coulomb interactions ü For a symmetric fluid, even at the critical point : ü For a size-asymmetric fluid : The density correlations infect the charge correlations through a generalmechanism when non-conducting at

2 species system : a general decomposition

2 species : interaction matrix for the 2 scalar fields 2 eigenmodes General decomposition : ü Symmetric system : Charge and density correlations are decoupled ü Asymmetric system : Charge and density fluctuations mix !!

Symmetric system

Singularities arise when the determinant of the interaction matrix vanishes Electroneutrality : ü is associated with the critical behavior of the density correlations ü is linked to the screening effect

Asymmetricsystem

ü ü at small k

• i. at

the Stillinger-Lovett sum-rule is violated non-conducting at

• ii. when not at the critical point,

iii. Charge correlations get infected by the density fluctuations Screening effect is impacted by the symmetry of the short-range interactions when when

Asymmetricsystem

ü evolution of the critical parameters : the critical temperature decreases when size asymmetry increases OK with simulations / not OK with MSA …

Critical parameters of a simple fluid with added salt

A single-component, nonionic fluid with a standard gas-liquid critical point + salt concentration … need for a 3 body spherical model (n,+,-) … Experiments : singular behavior Mean-field Debye-Hückel theory

Soluble models as cartoons for the ‘real’ world

• 2D Coulomb fluid : screening of an external electrostaticfield
• Coulomb sphericalmodel :

universalityclass, screening effect, ionicity