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Electrostatic effects in soft matter Electrostatic effects in soft matter (after a long introduction to colloidal systems) (after a long introduction to colloidal systems)
Emmanuel TrizacLPTMS / University of Orsay October 2004
BibliographyBibliography
D. Frenkel Introduction to colloidal systems, in Soft and Fragile Matter, proceedings of the 53rd SUSSP, edited by M. Cates and M. Evans
W. Russel, D. Saville and W. Schowalter Colloidal dispersions, Cambridge University Press 1989
J.L. Barrat and J.P. Hansen, Basic concepts for simple and complex liquids, Cambridge University Press 2003
L. Belloni Colloidal interactions, J. Phys.: Condens. Matt. 12, R549 (2000)
What are colloidal systems ?What are colloidal systems ?
Definition : size from 109 to 106 m Dispersed entity, in a suspending medium mesoscopic species / microscopic species dust in fog, pigments, physiological DNA...
Involved in the vast majority of industrial processes food industry, cosmetics, pharmaceutical industry...
Why such a definition (size criterion) ?
T. Graham
Different types of colloidal dispersionsDifferent types of colloidal dispersions
emulsion aerosol foam
Another type of colloid : opalsAnother type of colloid : opals
Hydrated silicon dioxide (amorphous)Bell laboratories snapshot
Elise Beynon gallery...Elise Beynon gallery...
L'Eglise d'Auvers, van GoghColumnar phase of Gibbsite platelets (polarization microscope)
The Scream, MunchPMMA spheres of 400 nm (electronic microscope)
Elise Beynon gallery IIElise Beynon gallery II
EM snaphot Gibbsite platelets / EM snaphots
Silica colloids / confocal microscopeSilicium rods / EM snaphots
Properties of colloidal systems :Properties of colloidal systems :Thixotropy...Thixotropy...
... and the blood of St Januarius (Napoli)
For a LennardJones fluidFor a LennardJones fluid
From Barrat/Hansen, Basic concepts for simple and complex fluids (2003)
Gas
Liquid
Solid
Au menu yesterday :Au menu yesterday :
IA What are colloids ?
IB Properties of colloidal systems
IC Forces between colloidspair potential of mean force
Nc body potential of mean force...
... no effective potentials so far
Henderson theorem is nice...Henderson theorem is nice...... but in practice, g(r) ... but in practice, g(r) pair potential is (very) difficult pair potential is (very) difficult
A. Louis (2002)
Does not violate Henderson theorem...`̀same'' means `̀close''
The physicochemistry of The physicochemistry of LE PASTISLE PASTIS
Sambuca (Italy) Raki (Turquey)
I. Grillo, small angle neutron scattering study, Colloids and Surfaces A: Physicochem. Eng. Aspects 225, 153 (2004)
Generic phenomenon:Generic phenomenon:The Ouzo effectThe Ouzo effect
S. Vitale and J. Katz, Langmuir 19, 4105 (2003)
Insoluble in water
Solu
ble
in w
ater
meta
binodal: miscibility limit / spinodal: stability limit
The electric doublelayerThe electric doublelayer Charged colloids Ze ; microions ±ze ; ∣Z∣ ≫ ∣z∣≈ 1
Electrostatic ↔ Entropic condensation Ze / +ze Smears out the profiles ?
conterion, charge +zecoion, charge ze
ZeGlobaly neutral system
The electric doublelayerThe electric doublelayer
Compromise Boltzmann / Coulomb : diffuse and inhomogeneous clouds around mesoscopic ions the electric doublelayer (central object for dispersions)
⇒ Screening effect (caracteristic length 1/)
renormalization of charge screening length
Zr
Zr
e− r Zr
e− r
Last week...Last week...
IA What are colloids ?
IB Properties of colloidal systems
IC Forces between colloidspotentials of mean force versus effective potential
dominant forces between colloids hard core, dispersion, Coulomb
↳ today: Focus on depletion forces
Depletion forces: Depletion forces: an exactly solvable lattice modelan exactly solvable lattice model
Frenkel and Louis, Phys. Rev. Lett. 68, 3363 (1992)
Spheresphere depletion potentialSpheresphere depletion potential
Colloidpolymer mixture
Mechanical and entropicinterpretations fully coincide
Polymer induced flocculationPolymer induced flocculation
expected mechanism
PMMA spheres (70 nm) + polystyrene
The dark hand of entropyThe dark hand of entropy
Entropic phase transition for hard spheres (NASA experiment)
Entropic phase transition for Entropic phase transition for binary mixtures...binary mixtures...
AB2 superstructurealso observed in gem opals
AB13 superstructurealso observed in gem opals
System : sterically stabilized PMMA spheres P. Bartlett, R. Ottewill, P. Pusey, Phys. Rev. Lett. 68, 3801 (1992)
Endless first chapter...Endless first chapter......still not over !...still not over !
IA What are colloids ?
IB Properties of colloidal systems
IC Forces between colloidspotentials of mean force versus effective potential
dominant forces between colloids hard core, dispersion, Coulomb, depletion
colloidal phase behaviour entropic phase transitions
↳ today: back to colloidpolymer mixtures
A surprising statementA surprising statement
The existence and general properties of solids and gases are relativelyeasy to understand once it is realized that atoms or molecules have certaintypical properties and interactions that follow from quantum mechanics.Liquids are harder to understand. Assume that a group of intelligent
theoretical physicists had lived in closed buildings from birth such that they never had occasion to see any natural structure [...] They probablywould predict the existence of atoms, of molecules, of solid crystals,
both metals and insulators, of gases, but most likely not the existence of liquids
V. Weisskopf, Trans. N.Y. Acad. Sci II, 38, 202 (1977)
Standard phase diagramStandard phase diagramfor a molecular systemfor a molecular system
van der Waals
Keep in mind:c*= 3 close to 0.3
Tc*=kT/ close to 1↳ no small parameter
Phase diagram changing Phase diagram changing the range of attractionthe range of attraction
Liquid/vapor becomes metastable, then unstable
The capillary lengthThe capillary lengthand the leaking tapand the leaking tap
Snapshot N. Garnier, Ens Lyon
Water striders Water striders could also inspire artists !could also inspire artists !
D. Lu, B. Chan, J.W. Bush, Nature 424, 663 (2003)
Thermal capillary waves...Thermal capillary waves...
Aarts, Schmidt and Lekkerkerker, Science 304, 847 (2004)PMMA spheres (70 nm) + polystyrene
...and imaging coalescence events...and imaging coalescence events
Aarts, Schmidt and Lek(ker)3, Science 304, 847 (2004)PMMA spheres (70 nm) + polystyrene
Tunable colloidal crystalsTunable colloidal crystals
Yethiraj and van Blaaderen, Nature 421, 513 (2003)
body cent. tetragonalsp. filling tetragonal
b. c. orthorombic
Colloids as big atoms ?Colloids as big atoms ?
To some, the word colloidal conjures up visions of things indefinite in shape, indefinite in chemical composition and physical properties, fickle in chemical deportment, things generally unmanageable.
Hedges, Colloids, 1931
Interest for the physicist ?Interest for the physicist ?
Experimentalist : comparare with ordinary molecular systems
Size ~ λvisible
Low density → fragile → soft matter Relaxation time → 101 rather than 1012 second
Theoretician micro/meso scale separation (length + time)
→ eliminate microscopic degrees of freedom → develop effective approaches (for mesoscopic degrees of freedom)
Fine tuning of effective potentials from short to long range (adding polymers, electrolyte...) impossible with molecular systems !
Model systems described by few parameters ideal to test and refine statistical mechanics tools
In short... why study colloids ?In short... why study colloids ?
Soft
Slow
Seeable(W. Poon)
large + small dressed large
Scope of the (remaining) lecturesScope of the (remaining) lecturesconcentrate on fundamental Coulombic effectsconcentrate on fundamental Coulombic effects
Symmetric electrolytes
PoissonBoltzmann theory
DLVO and the stability of colloids
Strange electrostatics
Introduction to electrokinetic effects
Spectacular Coulombic effectsSpectacular Coulombic effects
Like charge attraction (beyond meanfield)
Overcharging
Anomalous electrophoresis (includes meanfield or (xor) non meanfield effects)
DNA ejection from bacteriophages...
...
Statistical mechanics of charged Statistical mechanics of charged systems: The pionneerssystems: The pionneers
Michael Faraday (1830)
Swante Arrhenius (1884) bad PhD but...
Peter Debye (1923)
Critical behaviourCritical behaviour
Charge asymmetric but equisizedprimitive model ( z=e+ / e_)Field theory results divided by 6after S. Banergee and M. Fisher
First five lecturesFirst five lecturesI Introduction
IA What are colloids ?
IB Properties of colloidal systems
IC Forces between colloids and phase behaviour
II Symmetric electrolytes
IIA Background
IIB Ionized gases ans screening
IIC Critical behaviour within DebyeHuckel theory
III PoissonBoltzmann theory
IIIA Formal derivation
IIIB Solutions known
IIIC Properties
The WignerSeitz cell approachThe WignerSeitz cell approach
Validity of the modelization...
P = kT density RWS
Equation of state (P in Pascal)bromopolystyrene dispersionspherical colloids a ⋲51nm(Reus et al. 1997)
(packing fraction)
PB+WS
Comparison with Monte Carlo (Linse, 2000)Charged hard spheres (Z = 40)+ point counterions (z = 1)
predict critical point
(« low » density) (« high » density)
Relevance of the WignerSeitz cell Relevance of the WignerSeitz cell approach for liquid stateapproach for liquid state
Refined estimation of PBRefined estimation of PBvalidity domainvalidity domain
R. R. Netz,EPJE 5, 557 (2001)
couplingparameter
²
=z/(Gouy length)
Summary of relevant length scalesSummary of relevant length scales At least 5 independent and relevant scales
a
a+b1
: repulsion ~ kBT
e e
b : Gouy
: Bjerrum
1 : Debye
: density
a : size
= e2 / (kBT)
Charge renormalisationCharge renormalisation
Multiple scale expansion, (a)1 small parameterSpherical and cylindrical macroions
SPHERES
Aubouy, Trizac, Bocquet, J. Phys. A 36, 5835 (2003)
Colloidal molecular crystalsColloidal molecular crystals
M. Brunner and C. Bechinger, Phys. Rev. Lett. 88, 248302 (2002)
CMC on triangular latticesCMC on triangular lattices
C. Reichhardt and C. Olson, Phys. Rev. Lett. 88, 248301 (2002)
CMC on square latticesCMC on square lattices
C. Reichhardt and C. Olson, Phys. Rev. Lett. 88, 248301 (2002)
R. Agra, F. van Wijland and E. Trizac, Phys. Rev. Lett. 93, 018304 (2004)
Likecharge attraction, a simple argumentLikecharge attraction, a simple argument2 charged planes 2 charged planes <0, no electrolyte (counterions <0, no electrolyte (counterions ⊕ ⊕ only)only)
When h < a⊥, profile (r) uniform contact mean 2h
P (1h/b) attraction if h > b
Argument requires b < a⊥, min
and h < hseuil = Å in water
Field theory (Netz/high couplings) exact result !
P = Pcin Pél
Pcin = k B T ϱcontact , repulsive
Pél = −2 2/ , attractive
a⊥e b
b 1/
0 b a⊥
hrepulsion attraction ?
= e2 / (kT)
Come back to failure of meanfield Come back to failure of meanfield at short distancesat short distances
When h < a⊥, profile (r) uniform P (1h/b) attraction when h > b, ALWAYS TRUE
Within meanfield, discrete nature of microions neglected, only local density matters a⊥ = 0 when do profiles become uniform ? h < b and thus P (1h/b) > 0 ! meanfield correct for b > a⊥ a⊥ / b defines the coupling parameter
In any case, meanfield valid for colloidal dispersions
P = Pcin Pél
a⊥e b
b 1/
0 b a⊥
hrepulsion attraction ?
A surprisingly attractive coupleA surprisingly attractive couple
Importance of confinement
Attraction beyond any « reasonable » length scale
ORIGIN ?
Larsen, GrierNature, 1997
Pitfalls in confined geometry...Pitfalls in confined geometry...
↳ repulsion
↳ spurious attraction !
Conclusion : do not mix up effective potentials and potentials of mean force
Interpretation of experimental results ?Interpretation of experimental results ?
Attraction seems impossible at large distances (meanfield valid)
Electrohydrodynamic effect (Squires & Brenner, PRL 2000)
mechanism with an adjustable parameter...
© T. Squires, PR Focus 2000