solid liquid interface -
TRANSCRIPT
MBMB--JASS 2006JASS 2006 ZelenogradZelenograd, , MoscowMoscow
NanobiotechnologyNanobiotechnology and Biosensorsand Biosensors
SolidSolidLiquidLiquid
InterfaceInterface
Alexander Mehlich
Content
I. Motivation
II. Introduction
III. Theoretical Approach
IV. Experiment
V. Simulation
VI. Application
VII. Review
Motivation
Understanding of Solid/Liquid-Interface is inevitable for applicationsin the field of Nanobiotechnology and Biosensors
• Biosensors – metal/electrolyte-contacte.g. ISFET:
• Nanotubes – solid tubes with liquid inside
• Electrokinetics & microfluidics
Introduction
• Structure: crystalline grid
• Smallest unit: unit cell → immobile • Structure: no particular order
• Smallest unit: atoms and molecules → mobile
Solid Liquid
• Dominant forces: covalent bonding
Conductance: electronicConductance: ionic
• Dominant forces: ionic and hydrogen bonds
• special: hydration, surface tension
Theoretical Approach Helmholtz layer
Concept of the „Electric double layer“
• The Helmholtz layer:charged surface
→ electric field→ attraction of counterions
→ arrangement of plate-capacitor with molecular size
Capacitance per unit area:
dC A
H0εε ⋅
= d - half diameter of solvated ionε - dielectric constant of water
Potential - Poisson equation (PE):
0
2
εερψ −=∇ linear potential drop
0=ρ
Theoretical Approach Gouy Chapman –Poisson-Boltzmann
• Gouy-Chapman Theory (GCT):
thermal fluctuations of charge carriers→ „diffuse electric double layer“
Boltzmann equation (BE):
⎟⎟⎠
⎞⎜⎜⎝
⎛ −⋅=
TkWccB
iii exp0 ( ) ( )
⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛−⋅=−= −+
Tkzyxe
Tkzyxeeccce
BB
,,exp,,exp)( 0ψψρ
use for local charge density
Poisson-Boltzmann equation (PBE = PB + BE):
⎟⎟⎠
⎞⎜⎜⎝
⎛−⋅=∇
−Tk
eTk
e
BB eeec ψψ
εεψ
0
02assumptions made:
• 1:1 salt; otherwise:• only electric work done
eze i ⋅→
Theoretical Approach Gouy Chapman – planar surface
Applying PBE to a planar surface:
→ series expansion
xzyx →,,
0→⇒<<Tk
eTke
BB
ψψ
•
•
simplifications:
ψεε
ψ⋅=
Tkec
dxd
B0
02
2 2result: → linearized PBE orDebye-Hückel approximation
boundary conditions
with:
∑=≡i
iiBB
zcTk
eTk
ec 20
0
2
0
202
εεεεκ
general casexe κψψ −⋅= 0
Theoretical Approach Gouy Chapman –planar surface II
xe κψψ −⋅= 0 Dλκ =−1 → decay length calledDebye length
• exponential drop of potential• increase of salt concentration→ steeper drop, shorter Dλ
reason: better screening of surface charge with more ions
Theoretical Approach Gouy Chapman –linear and full solution
Comparing linear and full solution of PBE:
⎟⎟⎠
⎞⎜⎜⎝
⎛−⋅=∇
−Tk
eTk
e
BB eeec ψψ
εεψ
0
02
xe κψψ −⋅= 0
xy
y
y
y
eee
ee κ−
ΥΥ
⋅+−
=+−
434213210
0
0
11
11
2/
2/
2/
2/
⎟⎟⎠
⎞⎜⎜⎝
⎛=
Tkey
B
ψ
20 mM monovalent salt
• small surface potential:good linear fit
• higher potentials:full solution has lower potentials+ steeper decay for x < λ/2
Theoretical Approach Gouy Chapman – capacity
Capacity of the diffuse electric double layer:
→ relation between surface charge and surface potential ?σ 0ψ
Grahame equation:
DBB Tk
eTkcdxλψεεψεερσ 000
000 2
sinh8... ≈⎟⎟⎠
⎞⎜⎜⎝
⎛⋅==⋅−= ∫
∞
Capacitance:
• low potentials: linear behaviour• high salt concentration:→ more surface charge required
for same potentialDBD
AGC Tk
eddC
λεεψ
λεε
ψσ 000
0 2cosh ≈⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅==
⎟⎠⎞
⎜⎝⎛ =
dUdQC electric double layer like plate capacitor with d = !Dλ
Theoretical Approach Gouy Chapman – discussion
Discussion – limitations of GCT:
• finite size of ions neglected
• continuous charge distribution considered
• non-Coulombic interactions disregarded
• continuous solvent with constant permittivity ε
• flat surface assumed
• …
BUT - good predictions for symmetric electrolytes at: salt concentrations < 0.2 Mpotentials < 50-80 mV
Theoretical Approach Stern‘s Modification
Tuning GCT:
0ψ
βψ
dψ
βσ
dσ
0σ
IHP OHP
diffuse layer
Stern layer
potential characteristics:
capacitance:( )Tke
dCCC B
DA
GCAH
Atot 2/cosh
111
000 ψεελ
εε ⋅+=+=
- - - - - - - - - - - - - - - - - - - - - - - solid surface - - - - - - - - - - - - - - - - - - - - - - -
Stern layer – bound layer of adsorbed ions, immobile: IHP – specific adsorbtionOHP – nonspecific adsorb.
- - - - - - - - - - - - - - - - - - - - - - - - ζ-potential - - - - - - - - - - - - - - - - - - - - - - - -
Gouy-Chapman layer – diffuse layer, mobile
- - - - - - - - - - - - - - - - - - - - - - - - bulk water - - - - - - - - - - - - - - - - - - - - - - - - x
Content
I. Motivation
II. Introduction
III. Theoretical Approach
IV. Experiment
V. Simulation
VI. Application
VII. Review
Experiment Adsorption – mercury drop
Adsorbtion at the Interface:
→ experiment: mercury drop in electrolytecharge density at interface?
AG∂∂
=γ • p, T - const• formation of surface unfavourable
special: surface tension -
Gibbs Adsorption Equation:
0,
1
0,
1
1
0
=+++− ∑∑−=
=
−=
=kj
Kk
kkj
Jj
jS dndQdAdpVdTS µεγ σσσσ
σ – surface related, ε – overall potential diff.n – # of charge carriers on surface, µ- chem. potential
∑=−i
ii dA
nd µγσ
→ p, T const: - Gibbs Adsorption isotherm
dEd Mσγ =−AnF eM −=σ
- electrocapillary equation
- excess charge
Experiment Adsorption – mercury drop II
⎟⎠⎞
⎜⎝⎛−=
dEdM γσ
repelling excess charge carriers → lowering of γ- excess charge
Def.: point of zero charge (pzc) ≡ no charge within the metal
expectation for γ over potential?
pzc
asymmetric! → coulombic + specific adsorption
here anions specifically adsorb, cations not
Experiment Specific Adsorption – parameters
Parameters influencing specific adsorption:
• Charge density on solid surface
specific adsorption of ion ↑↔ opposite charge within solid ↑
note:anions can be adsorbed at negative charge (see graph)
• Ion Size Effectsize of ion ↑→ specific adsorption ↑
( hydration weaker…)
• IonTypeanions have greater tendencyto spec. adsorb than cations
(for metals observed…)
Experiment Specific Adsorption – parameters II
• Hydration
strong primary hydration sheath → little specific adsorption
Anion F(-) Cl(-) Br(-) I(-)Ion-Solvent Interaction [kcal/mol] -20.6 -13.6 -12.2 -10.7
• Concentration Changehigher concentration → higher specific adsorption
• Temperature
increase of temperature→ decrease of
specific adsorption
Experiment (Specific) Adsorption – general parameters
of general importance is:
• type of the solid→ type of “docking stations” for adsorbates (surface texture)
• solvent-solid interaction→ solvation of surface + desorption for creating vacancies
• solvent-adsorbate interaction→ hydration sheath
…
Experiment Limits of Observation
Problem:• many influences can be measured directly, others cannot
• there are experimental results striking the so far developed theory
• complexity of parameters to be considered is rising
→ no “all-describing”-theory found yet!
Way out:developing models for simulation +
comparing results with real experiment
Simulation Four State Model - idea
special property of water:DIPOLE
Four state model (1975):experimental data –capacity over excess charge:
explanation?
idea: dipoles cause extra potential drop → influence on capacitance
assumption: no specific adsorption→ first adsorbed layer only water→ four states to be differed
Simulation Four State Model - model
Monolayer of water with single molecules + clusters of molecules – 2 dipole directions
cN +
cN −
N +
N −
cµ
µ → 4 statesN – # molecules of certain state in monolayerµ – dipole moment
Energies:
solvent molecule in cluster -
monolayer permittivity
}/c cµ σ ε+ = −U
{/c cµ σ ε− =U
charge on metal
/ bUµσ ε += − ++U
{/ bUµσ ε −= +-U
due to different bonding
free solvent molecule -
Potential drop across inner layer:}
{0
free charge
dipoles Cσφ ψ χ∆ = + = + χ / / / /c c c cN N N Nχ µ ε µ ε µ ε µ ε+ − + −= − + − +→
idea: Boltzmann for N + varying parameters
Simulation Four State Model - results
Total capacitance:
0
1 1
i
d dC d C d
φ χσ σ∆
= = +
achieved plots:simulation
experiment
Simulation Four State Model - results II
results from adapting the parameters:
10 0 -10 -20 -30 -40
0.0
0.2
0.4
0.6
0.8
1.0
NC+
NC_
N+
N_
mol
ecul
es /
NT
charge density (µC/cm2)
• asymmetry, because of different stability of 2 orientations of free molecules
• 3 water molecules per cluster
• total dipole moment of cluster approxsame as dipole moment of free molecule→ ring groupings of water possible:
• maxima + minima are deduced ashigh or low switching-possibilitiesof the dipole orientation:
0, , , ,c b bU U Cε µ + −
Simulation Diffuse Layer Capacitance
Diffuse Layer Capacitance:
Influence of diffuse layer around pzcstrong for low concentrations:More experimental capacitance-data:
DBD
AGC Tk
eddC
λεεψ
λεε
ψσ 000
0 2cosh ≈⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅==
Huge minimum at very low concentrations
Simulation Adsorption Capacitance
Adsorption Capacitance:
• Assume absorbed charged moleculesRTFzRTGb
iii eea //0
1φ
θθ −∆−=−
→ Adsorption isotherm – here: Langmuir isotherm:
• Surface charge:
-10 -5 0 5 10
0.0
0.5
1.0
Surfa
ce c
over
age,
θ
∆G/kT-10 -5 0 5 10
0.00
0.05
0.10
0.15
0.20
0.25
dθ/d∆G
= C
apac
itanc
e
∆G/kT
θ⋅= iSadsp qQ
→ Capacitance due to adsorbed molecules = ( ) ( )θθφθ
φ−== 1RTFzq
ddq
ddQ
iiiSadsp
(θ – surface coverage)
Simulation Molecular Dynamics Simulations –model, results
Molecular Dynamics Simulations (MDS) of water at hydrophobic substrates:(2004)
• Aim: water density depending on - curvature (spherical, planar)- temperature- pressure
• Model: for interactions used models
simulation cell: cubic box filled with ~ 1000 – 3000 water moleculesperiodic boundary conditions
- Lennard-Jones + Coulomb potential- Buckingham potential
I: spherical solute in box• Results
- increased density for small solute- water depletion for large solute
- Temperature increase causesdecrease of density
- Same pressure dependenceas at Results II
Simulation Molecular Dynamics Simulations – results II
• Results II: planar surface in box
64 alkane molecules + 2781 water molecules
- water depletion at interface→ layer thickness ~ 2.5 A
- high pressure reduces depletion layer
- layerthickness rises with Temperature
- potential drop at interface→ caused by dipoles→ top water layer oriented
Simulation Molecular Dynamics Simulations –facing reality
Experiments on depletion (2003):Experimental data also gives reason to a depletion layer of water onhydrophobic substrates:
Neutron Reflectivity Measurements&
Atomic Force Microscopy
• Layer thickness:2-5nm
20nm
• Oberserved interface:
on ahydrophobic plane
OD2
• memory-effect observed
3D-plot
AFM: tapping mode topology image of„nanobubbles“
NRM: Kiessig oszillations due to gas layer
Content
I. Motivation
II. Introduction
III. Theoretical Approach
IV. Experiment
V. Simulation
VI. Application
VII. Review
Application Electrokinetics – zeta potential
Electrokinetics:
• due to strong electrostatic forcesions in the inner layer are immobile• under pressure driven flow (pdf)
ions of the diffuse layer are able tomove → shear plane is formed
zeta-potential:
( ) ( )bulkshear xx ψψζ −=
Application Electrokinetics –stream current & potential
fluid in a (micro)tube:
• zeta-potential ≠ 0 grants movablenet charges in diffuse layer
• pdf induces a stream of chargesin a capillary:
DσDν
( ) ( ) { DDA
Dstream rdArrI νρπρν 2== ∫ - drift velocitiy in diffuse layer- charge densitiy in diffuse layer
capillary radius
• depletion and accumulation of charges at ends of capillary respectively:
krl
CiU DD
stream ⋅==
νσ2l
krC2π
=
(k = specific conductivity of solution)
- conductanceOhm‘s law
Application Electrokinetic Measurements on Adsorption -idea
Analysing charge density of the inner layer using electrokinetic measurements:(2001)
ζ-potential separates immobile and mobile layer
basic idea:sign of ζ-potential reveals sign of totalcharge within the inner layer
electrokinetic values measured:streaming potential & current
correlation with ζ-potential:
( )dpdI
bhLI S
rS εε
ηζ0
=( )dp
dUKU S
r
BS εε
ηζ0
= experimental setup
Application Electrokinetic Measurements on Adsorption -plots
Obtained data:
conclusions:
• HCl:
• pure water: +− +↔ OHOHOH 322→ negative ζ-potential
• KOH:
• KCl:
- first H-ions preferred → sign reversal- then: double layer compression
- first OH-ions preferred, afterwards:- compression of the double layer→ increasing surface charge compensation
already within inner layer (screening…)- only double layer compression
Application Electrokinetic Measurements on Adsorption -results
Conclusions:+−+− =>>> KClOHOH 3preferential adsorption:
IEP
• pH-dependence:→ low IEP proves result above
important factors for adsorption:
• structure of hydration shell important(OH-ion known to have less stable hydrationstructures → escapes more easily and buildsup hydrogen bonds with interfacial water)
• capability to bind interfacial water via hydrogen bonds
• another experiment using pH-Dependant Force Spectroscopy leads to conclusion:
- immobilized interfacial water acting as template for hydroxyl adsorption- density of molecular units of water building networks on the surface crucial
Application Electroosmosis – what it is
Electroosmosis:
• Applying electric field along capillary→ movement of liquid relative to stationary charged surface
• electric field induces force on net chargein diffuse layer
• diffuse layer displacement leads todragging of bulk fluid
drift velocity of fluid:
xEηεςνς = - Helmholtz-Smoluchowski
cµ - osmotic mobility
Application Electroosmosis – properties
the way to have laminar flow in microfluidicsat low Reynold‘s numbers
• advantage of electroosmosis:
- ζ-potential = -100mV- electric field = 2.5 x 10³V/m
• example:
time development after switching on the e-field → dragging → laminar flow
sm /200µνς =
Review
44444 344444 21
?1.
2.3.
4.Theory
HelmholtzGouy-ChapmanStern
ExperimentAdsorption &its parameters,AFM, NRM…
ApplicationElectrokinetics, microfluidics…
Simulation4 state model, MDS…
References
•! Hans Juergen Butt, Karlheinz Graf, Michael Kappl, Physics and Chemistry ofInterfaces, Wiley-VCH Verlag & Co. KGaA, 2003• S. Roy Morrison, Electrochemistry at Semiconductor and Oxidized Metal Electrodes,Plenum Press, New York 1980• Horst Kuchling, Taschenbuch der Physik, 17. Auflage, Fachbuchverlag Leipzig imCarl Hanser Verlag, München Wien 2001• J. O‘M. Bockris, Brian E. Conway, Ernest Yeager, Comprehensive Treatise ofElectrochemistry - Volume 1: The Double Layer, Plenum Press, New York and London1975+• Roger Parsons, A Primitive Four State Model for Solvent at the Electrode-SolutionInterface, printed in Electroanalytical Chemistry and Interfacial Electrochemistry, 59,229-237, Elsevier Sequoia S.A., Lausanne - printed in Netherlands 1975•! Rolando Guidelli, Wolfgang Schmickler, Recent Developments in Models for theInterface between a Metal and an Aqueous Solution, printed in Electrochimica Acta, 45,2317-2338, Elsevier Science Ltd., 2000
References
• Ralf Zimmermann, Stanislav Dukhin, Carsten Werner, Electrokinetic MeasurementsReveal Interfacial Charge at Polymer Films Caused by Simple Electrolyte Ions, printedin J. Phys. Chem., 105, 8544-8549, American Chemical Society, on web 2001• Christian Dicke, Georg Haehner, pH-Dependent Force Spectroscopy ofTri(ethylene Glycol)- and Methyl-Terminated Self-Assembled Monolayers Adsorbedon Gold, JACS articles, 124, 12619-12625, American Chemical Society, on web 2002• Roland Steitz, …, Nanobubbles and Their Precursor Layer at the Interface of WaterAgainst a Hydrophobic Substrate, Langmuir, 19, 2409- 2418, American ChemicalSociety, on web 2003• Roland R. Netz, Shavkat I. Mamatkulov, Pulat K. Khabibullaev, Water at HydrophobicSubstrates: Curvature, Pressure and Temperature Effects, Langmuir, 20 , 4756-4763, American Chemical Society, on web 2004
0 20
30
14 2
5.315 /
0.31
0.28 1.4 10
7 10c
tot
C F cmd nm d
Cm
N cm
ε ε ε µ
µ µ −
−
= ⋅ ⎫= ≈⎬= ⎭
= ⋅ = ⋅
= ⋅
Qualitative: