P. Bowen, EPFL. 31/10/2017 1

LTPÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE

Powder Technology

From Landslides and Avalanches to Concrete and Chocolate

Prof. P. Bowen (EPFL), Dr. P. Derlet (PSI)

WEEK 7

Particle – Particle Interactions (2)

P. Bowen, EPFL. 31/10/2017 2

Course Contents - Plan

Boehmite

4 semaines

3 semaines

2 semaines

2 semaines

1 semaine1. Introduction – general introduction to course– example transparent ceramics

2. Particle Packing and Powder Compaction - Theoretical and empirical models (PB)- Powder compaction (PD)

3 Particle-Particle Interactions (PB)- Colloidal Dispersions- DLVO –theory and limitations- non-DLVO and steric forces

4. Introduction to Atomistic Scale Simulations (PD)- introduction to modeling of surfaces and interfaces at the atomic scale - defects in metals – towards sintering

5. Sintering mechanisms (PD)- metals, ceramics- influence of microstructure- simulation

6. New Powder Processing Technologies (PB)- rapid prototyping- laser sintering, Spark Plasma Sintering

2 semaines

P. Bowen, EPFL. 31/10/2017 3

Teaching plan 2017

• Files of lectures and notes to be found on LTP website : http://ltp.epfl.ch/Teaching

Week-DATE File.

no.

Powder Technology – Wednesday 10.15-12.00 – MXG 110

1- sept 20 1 Introduction - PB

2 – sept 27 2 Powder packing and compaction - 1- PB -

3 – oct 4 3 Powder packing and compaction - 2-PB- and guest lecturer - MS

4 – oct 11 4 Powder packing and compaction -3- PD

5 – oct 18 4 Powder packing and compaction - 4 – PD

6 – oct 25 5 Particle – Particle Interactions 1 - PB

7 – nov1 6 Particle – Particle Interactions 2- PB

8 – nov 8 7 Particle – Particle Interactions - 3-PB

9 – nov -15 8 Introduction to atomistic scale simulations PD

10 – nov 22 9 Compaction, Sintering & Defects in metals at atomistic scale - PD

11 -nov-29 10 Sintering Mechanisms& New Technologies - 1 – PB

12 - dec 6 11 Sintering Mechanisms & New Technologies - 2 - PD

13 – dec 13 11 Sintering Mechanisms &New Technologies -3 PD

14 – dec 20 10 Sintering Mechanisms & New Technologies- and exam 4 – PB

PB – Prof. Paul Bowen (EPFL), PD – Dr. Peter Derlet (PSI)

MS- Dr. Mark Sawley (EPFL)

P. Bowen, EPFL. 31/10/2017 4

Last week’s Course (objectives)

Aggregation/agglomeration effect – rheology – effective volume – maximum

packing – hence ceramic microstructures – dispersion important – how to assure

particles do not aggregate……

Introduction – Forces and colloidal stability, snow a sinterable material (slides 5-12)

Attractive forces – van der Waals – brief summary (treated in detail 3rd yr*) (13-16)

Repulsive forces – electrostatic (17-42)

– Poisson-Boltzmann Equation

– Surface Potentials

– Composition of double layer (double couche)

Zeta potential measurement (43-47)

Examples (48 -61)

Real size of nanosized spherical silica particles

Atomistic modelling of water-inorganic solid interface – particle size of nanosized

iron oxides

*Chp. 5 – The Colloidal Domain–D. F. Evans & H. Wennerström, Wiley, 1999

P. Bowen, EPFL. 31/10/2017 5

Today’s Course (objectives)

Interparticle forces – continued – limitations of Mean Field Approaches

Repulsive forces – electrostatic (slides 5-20)

– Poisson-Boltzmann Equation – limitations - atomistic approach

– Forces between charged surfaces

– Close approach – limit of mean field approach

– Ion correlation forces and others......

What is the coherent force in concrete and cement? (20-34)

– CSH - Calcium Silicate Hydrates

Other non-DLVO forces (35-45)

Capillary forces – colloidal crystals from nanosized particles

Examples- Electrophoretic deposition - nanoparticle coatings on surfaces– drying

P. Bowen, EPFL. 31/10/2017 6

Ionic concentration and surface potential

*J. Israelachvili – Intermolecular & Surface Forces

2nd edition, Academic Press, London, 1992

Limitations of mean field theory on close

approach 2-5 nm (Stern layer)

– Ion-correlation effects due to highly

polarisable layers – attractive

– Finite ion size – excluded volume

effect – repulsive

– Image forces – "reflected" charge by

surface gives "image in surface"-

repulsive

– Surface charges discreet – not

averaged as above – attractive

– Solvation forces -

displacement/ordering of solvent –

attractive, repulsive, oscillatory

P. Bowen, EPFL. 31/10/2017 7

Finite Ion Size – Solvent Interactions – Molecular Dynamics

Goethite Surface in Contact with Electrolyte Solution*

0

1

2

3

4

5

6

0 5 10 15 20 25 30 35 40

Distance from Surface (A)

De

ns

ity

Re

lati

ve

to

Bu

lk

So

luti

on

SODIUM

CHLORINE

WATER

NaCl – 0.5 M

*Kerisit S, Cooke DJ, Marmier A, Parker SC “CHEMICAL COMMUNICATIONS(24): 3027-3029 (2005)

•Charge neutral surface, 1st water in valleys of surface corrugation, 2nd attached to surface hydroxyls

• Little change in water structure with NaCl, potential determined by ionic distribution -

• Very similar results for -ve, +ve and neutral surfaces!!

• Finite size of ions and solvent interactions (discreet charges, surface polarisation)

Na – purple

Cl - green

Fe - yellow

H -white

O - red/blue

P. Bowen, EPFL. 31/10/2017 8

Interparticle forces – continued -

Ch. 5 Colloidal Domain

The force F between two surfaces or particles separated by a distance h, is determined

the Gibbs change of free energy with h:

(5.1.1)

The repulsive force is positive.

F (G

h)T (

H

h)T T(

S

h)T

The force caused by osmotic pressure is the force measured when the bulk is expelled

by bringing the two surfaces together.

In the following calculations the authors try to always link directly the intermolecular

forces with the thermodynamic quantities.

(G

h)T

d

h

a1a2h

P. Bowen, EPFL. 31/10/2017 9

Interparticle forces – continued-

For plane and parallel surfaces by dividing the force by the surface we have:

For an incompressible solvant:

Since (1.5.5b)

It is possible to write, using the equation 1.5.11 (V Posm = -m):

The solvant osmotic pressure between two plates

ns number of moles of the solvant, Vs molar volume of the solvant

F

surf

1

surf(G

h)T (

G

V)T

1

Vs

(G

ns

)T

(G

ns

)T ms

F

surf

1

surf(G

ns

)T ms

Vs

osmxh

P. Bowen, EPFL. 31/10/2017 10

The case of two surfaces identically charged

♦ Superposition of the charge distribution

(approximation) : rr1 r2Because of PB linearity: FF1 F2

♦ The above approach (neutral surface) is also valid but in relation to the mid-plane from which we have:

♦ Electric neutrality,

♦ Ionic concentration and

♦ Free energy are identical

♦ Therefore we can write:

(5.1.24)

♦ This equation can be applied directly to the swelling of

laminar anisotropic liquid crystals and of some clays.

0 hz

+

-- +

+

+

+

+

+

+-

-+

+ er

s

-

-

-

-

-

-

s

-

-

-

-

-

-

+

+

++

+

+

h/2

0

F

F1

F

F2

F

z1 z2zmilieu

osm kT ci

*(planmilieu )

i

P. Bowen, EPFL. 31/10/2017 11

The bulk often gives a good reference for the potential (5.1.4)

Solvants and ions between the colloidal particle surfaces in a medium in contact with a

solution (bulk )

The ions are attracted and the solvant is expelled from the space between them.

The resulting force between the surfaces is :

(5.1.26)

F

surf osm(plan milieu )osm(bulk)

kT[ c i

*(planmilieu ) c i0

*]

i

i

The bulk imposes the chemical potential of the ionique species and is used as a

natural reference for the electric potential.

This explains why F(h/2)=Fd≠0

According to the Bolzmann distribution, it is possible to write:

(5.1.27)

(5.1.28)

ci

*(plan milieu) ci0

*exp(

zieFd

kT)

F

surf kT c i0

*

i

[exp(zieFd

kT1)

P. Bowen, EPFL. 31/10/2017 12

Force between 2 planes

The equation 5.1.28 is central to describe the force between 2 similar surfaces charged in

equilibrium with a solution (bulk).

The force is the free energy derivative and it is composed of an electrostatic interaction and

of one entropic part due to the counter ion distribution.

To use the equation 5.1.28 with known quantities, the PB equation has to be solved first. In

general this is done numerically.

When 2 double-layers are superimposed, they undergo a repulsive force:

(5.1.31)

is the electrolyte concentration of the bulk solution and = tanh(zeF0/4kT)

Fsurf

64Tc0*0

2 exp(h)

c0*

The important points are:

At long distances, the double layer force decreases exponentially with and linearly with .

The influence of the divalent ions is much more important on .

When F0 tends towards tends towards 1

An upper limit to the force therefore exists.

c0*

12

0

2 *

0

1

( )

r

i

i

i

kT

e cz

e e

P. Bowen, EPFL. 31/10/2017 13

Sum of Forces - DLVO

Derjaguin-Landau-Verwey-Overbeek (DLVO) Theory

Net force is algebraic sum of

– electrostatic repulsion VR and

– attractive dispersion* forces VA

Good to ~2nm, for infinite plates

T A RV V V

*Hamaker approach depends on individual Hamaker constants (p 253 Colloidal

Domain, polymers and minerals).

• Lifshitz’s theory, based on the electrodynamics of a continuous medium gives a

different, more general solution to calculate the attractive interactions.

• Bergström# characterises most materials by 4 parameters, two of which are measured

in the I.R and two in the U.V. (Spectroscopic ellipsometry – polished surfaces)•# Adv. Colloid Interface Sci. 70 (1997) 125-169

P. Bowen, EPFL. 31/10/2017 14

Comparison - measured and calculated force between 2 mica

surfaces

Continuous calculated curves (DLVO)

with constant charge and potential

Repulsive forces measured with the atomic force device for two charged mica surfaces; The

dots are the experimental data and the lines are DLVO theory predictions. (Israelachvili, 1992)

Constant potential

- Higher line

• Recent work at Geneva University – suggests charge regulation model needed for accurate DLVO predictions

(depends on adsorption equilibria of pdi’s)

• F. Javier Montes Ruiz-Cabello, Plinio Maroni, and Michal Borkovec. J.CHEM.PHYS. 138, 234705 (2013)

P. Bowen, EPFL. 31/10/2017 15

)

) )

2

2

0 22

1

e

e

h L

ES h L

eF a

e

ee

Electrostatic force – Spherical particles

Depends on surface charge density – either dissociated groups,

adsorbed ions or adsorbed polyelectrolytes – polyacrylic acid (PAA)

Electrical double layer – Poisson-Boltzmann and Debye-Huckel

theory to describe ion distribution in solution near a charged interface

– simple ionic medium (e.g Na Cl)

Electrostatic potential

- can derive from measured zeta potential

-Electrical double layer –

Le – surface charge plane – particle surface

(with polymer e.g. PAA not so obvious)

Harmonic

average radius

-1

1 2

1 2

2

a a

a aa

hak

al

r = ( h + 2a )

P. Bowen, EPFL. 31/10/2017 16

5.3 Electrostatic Interactions – attraction by correlation

PB approach – mean field approach

Surfaces often inhomogeneous

– incomplete adsorption layer

– adsorbed or surface dipole-dipole interactions

– variations in double layer concentrations

– real size of ions-molecules - not point charges – steric effects

– discreetness of surface charges not ”smeared” out

Lead to additional attractive forces other than van der Waals

– can sometimes dominate

Teng, Geochim Cosmochim Acta, 68(2), 2004

Surface of growing calcite crystal

Calcium - green

Carbon – grey

Oxygen - redAschauer et al JCIS.

346 (2010) 226–231

P. Bowen, EPFL. 31/10/2017 17

5.3.1 – Ion correlations in Double Layer

Charges at the solid surface are localised (Fig 5.12)

Gauss's law for mean field gave us zero field at mid-point between two charged planes

However possible fluctuations giving rise to non-zero fields

Possible minimisation of energy

attractive contribution to force between planes

particulary important for divalent counterions eg Ca2+

P. Bowen, EPFL. 31/10/2017 18

Force between 2 plates – divalent counterions

Simulation – Monte Carlo considers instantaneous ion-ion interactions

surface charge densities s > 0.03 C/m2 attractive forces from ion-ion interactions become important

at s .23 C/m2 balances repulsion from double layer overlap (1mM = 2500 N/m2)

-di-valent

-10-3 M

-water

-h= 2.1 nms > 0.03 C/m2

s 0.23 C/m2

Figure 5.1.3

d

h

P. Bowen, EPFL. 31/10/2017 19

Ion correlation forces and divalent ions (1)

Looked at monovalent and divalent ions - Take into account

Ionic correlations all electrostatic interactions

Osmotic pressure from confinement of ions

Real size of ions instead of point charges

Monte-Carlo simulations

by Pellenq et al (J.Phys

Chem. 1997, 101, 8584)

Symmetrical

distribution – PB OK

Non-symmetrical

distribution –

PB fails for high

charge density

Introduction: Cement

Cement: Most used material in the world -

Buildings, dams, bridges and many other structures…..

Portland cement is in use for over 100 years

Why study cement ???

CO2 emission in the clinker phase production - video

Limestone (CaCO3), clay, gypsum 5-8 % of man made

CO2 emission

Production expected to double in next 30 years

Limestone reserves are limited….Need alternatives for cost and environment

Use of supplementary cementitious materials to replace limestone– lower CO2 production

Calcined clay, slag, fly ash, silica fume

Affects the reactivity – modify early age strength – speed and cost of construction

Better understanding of the mechanisms needed

Ongoing research in LMC - Pure phases studied – clarify mechanisms …

01/07/15

20/26

C –CaO, S- SiO2, A- Al2O3, F- Fe2O3, H -H2O, $- SO3

http://www.youtube.com/watch?v=woaUs5XnjUo

Introduction: C-S-H

Cement is complex 4-5 anhydrous phases – 4-5 hydrated phases

Any time 8-10 phases…..very complex.. Need to use model system…

To get growth mechanism of main phase, calcium silicate hydrate – C-S-H

Use well controlled precipitation method – synthetic C-S-H, study kinetics

C-S-H

Atomic structure unknown- poorly crystalline – XRD amorphous

Variable stoichiometry – Ca/Si ratio varies from ~1.2 to 2.1…

Difficult to characterize experimentally

SEM - Ca3SiO5 hydration stopped at 6h

C-S- H particles (Ca/Si ~1.7)C-S-H

01/07/15

21/26

XRD

Introduction – C-S-H structure• Closet analogue natural layered calcium silicate minerals (jennite, tobermorite)

• Dreierketten- linear three-unit repetition silicon chains

• Planar Ca-O sheets (red dots (CaMP) flanked by infinite silicate chains

• 14 Å tobermorite considered as good model structure

• 29Si NMR has been the most relevant method to study Si arrangement in C-S-H

• Qn – n number of Si nieghbours

22

Q1 The end of Si chain

Q2p The middle of Si chain, which are

coordinated by calcium planes

Q2b The third silicate are not coordinated by

calcium planes, bridging 2 Q2p sites

Q3 The tetrahedra linking two silicate chains

in the interlayer space (IL) Q2p

Q1

Q3

Q2b

IL

IL

14 Å tobermorite

14 Å Tobermorite to C-S-H

( Ca/Si)tobermorite = 0.83

( Ca/Si)C-S-H ~1.7 (varies from ~1.2 to 2.1)

Different ways of modifying structure to modify Ca/Si – crystal chemistry rules and NMR…

Semi-empirical:

Removal of bridging silica tetrahedra (SiO2)

Replacement by Ca(OH)2

Deprotonation of silanol groups charge compensated by Ca ions or CaOH+ in the interlayer (IL)

01/07/15

23/26

Q2p

Q1

Q3

Q2b

IL

IL

*Sandra Galmarini, EPFL thesis 5754 (2013)

Conclusion

C-S-H represented by a defective tobermorite with required Ca/Si ratio

But are these defects stable?

Atomistic simulations - Molecular Dynamics *

Identified series of energetically stable defects with Ca/Si from 1 to 2.5

P. Bowen, EPFL. 31/10/2017 24

Ion correlation forces and divalent ions

Na+ - always repulsive – ion correlation forces negligible and PB approach gives a reasonable approximation of reality and cohesive forces

Ca2+ - attractive – at high charge densities - CSH attractive well of -60 MPa at 0.7nm separation

From Monte Carlo atomistic scale simulations*

100 x greater than van der Waals forces at same distance!!

Strong contribution to cohesion of cement – interlayer Ca thought to be strongly ionic-covalent*

But atomistic structure of C-S-H still under debate….

Clays – similar attractive forces with Ca2+

Attractive well much smaller - 0.6 MPa but thought to be important in dispersion of 2% swelling clays for alpine debris flow!!!

CSHClay

*Pellenq&Van Damme, MRS

Bulletin, 319-323, May (2004)

P. Bowen, EPFL. 31/10/2017 25

C-S-H and cement strength ion-ion correlation*

a) Sketch illustrating the role

played by C-S-H nanoplatelets

around C3S grains. At early stages

grains are connected only at a few

points - weak network. Further

hydration - increases contact area

- strengthening the network.

[Jonsson, et al Langmuir 2005, 21,

9211]

b) Force as a function of distance

between C-S-H surfaces by AFM

- > 1 mM Ca(OH)2, the force

switches from repulsive to

attractive due to ion–ion

correlation effects. [Plassard et al,

Langmuir 2005, 21, 7263

c) C-S-H nanoparticles

precipitated onto a cement surface

and visualized by AFM.[A.

Nonat, Cem. Concr. Res. 2004,

34, 1521]* Rieger et al, Angew. Chem. Int. Ed. 2014, 53, 12380 – 12396

P. Bowen, EPFL. 31/10/2017 26

14 Å Tobermorite – Structures - Reaction Enthalpies

26

• LTP approach - estimated “precipitation” enthalpies for formation of tobermorite (& defects)

4·[CaSiO2(OH)2]aq + 3.5H2O →

[Ca2.5Si3O8(OH)·3.5H2O]tob + 1.5·[Ca2+]aq + 3·[OH-]aq + [Si(OH)4]aq

Hexp : -8.3±0.8 eV3) ∆HDFT : -7.7±0.5 eV ∆HMD : - 6.6±0.7 eV

1) Bonaccorsi et al. 2005, 2) Partially minimized MD snapshot, 3) Lothenbach et al. 2006

XRD 1) DFT (by Steve Parker) Classical MD 2)

Purple – water, Red – Oxygen, Green - Calcium, White – Hydrogen, Grey - Silicon

• 14 Å Tobermorite Polymorph b11m – similar enthalpies and

• Structures from Experiment, DFT and Molecular dynamics –

• Main differences in water position and orientation….

*Sandra Galmarini, EPFL thesis 5754 (2013)

P. Bowen, EPFL. 31/10/2017 27

Low Energy Defects* – 14 Å Tobermorite (H b11m)

Ca/Si: 0.83 Ca/Si: 1.00 Ca/Si: 1.50 Ca/Si: 2.00

Red – Oxygen, Green - Calcium, White – Hydrogen, Grey - Silicon

-3.48 eV -2.83 eV -0.14 eV -0.36 eV

*Sandra Galmarini, EPFL thesis 5754 (2013)

Precipitation method

Precipitation by mixing 2 – solutions

Calcium nitrate & sodium silicate

Controlled atmosphere (N2)

Kinetics by in-situ monitoring, pH, Ca 2+,

Thermodynamic modelling (GEMS)*

Predict precipitation conditions for

5 Ca/Si Ratios

1, 1.25, 1.5, 1.75, 2.0

Precipitate collected, washed, dried

Characterised by

XRD, ICP,XRF, SEM,

TEM-EDX, FTIR, Raman

29Si NMR – DNP, 2D…..

28/26

01/07/15

* Gibbs Energy Minimisation Software, D. Kulik,

CCR, 41 (2011) 477–495

A B

Precipitation results - stoichiometry

29/26

01/07/15

Thermodynamics modelled Synthesis! Chemical system - Ca(NO3)2.4H2O [0.2 mol/l], Na2SiO3.5H2O [0.1 mol/l] & NaOH (pH control).

! Operating Conditions - Room temperature, pH range 13.3

Initial Ca/SiFinal Ca/Si

(GEMS)NaOH (GEMS) pH (GEMS) pH (Exp.)

2 1.0 50.00 μL 10.87 11.10

2 1.25 05.16 mL 11.47 12.50

2 1.5 10.58 mL 12.05 12.58

2 1.75 16.62 mL 12.55 12.67

2 2 20.00 mL 12.81 12.75

9

Precipitation results – morphology -uniformity

30/26

01/07/15

Thin Foils , 4-6 nm thick, 200-400nm diameter, for all Ca/Si ratios with pH > 13

Morphology typical of real cement systems with high alkali content…

STEM-EDX – 40-60 points measured on each sample – 3nm resolution – very verynarrow composition range – very very uniform in Ca/ Si ratio…

Ca/Si : 1.25

1.23 ± 0.01

Ca/Si : 2.00

1.85 ± 0.01STEM-EDX

Kumar et al, J.Phys.Chem.C 121(32) 17188–17196

(2017). DOI: 10.1021/acs.jpcc.7b02439

NMR fitted spectra

31/26

01/07/15

DNP – loss of resolution fitting needed but good coherent results with atomisticmodels – quantity of Q1, Q2p and Q2b Si sites, no Q3 sites observed…

Q1

Q2b

Q2p

Kumar et al, J.Phys.Chem.C 121(32) 17188–17196 (2017).

NMR DNP results – Si distribution

32/26

01/07/15

Ca/Si Q1 Q2p Q2b Q2p/Q2b

1.0 0.29 0.52 0.17 3.1

1.25 0.57 0.27 0.16 1.7

1.5 0.73 0.20 0.08 2.6

1.75 0.78 0.14 0.08 1.6

2.0 0.83 0.11 0.06 2.0

Atomistic simulation – possible structures…depends on Si connectivity and degreeof deprotonation of silanol groups -charge compensated with Ca2+ in interlayer

e.g possible model structure for Ca/Si…1.5 good agreement with experiment

Sample P(Q(1)) P(Q(2b)) P(Q(2p))

Ca:Si = 1.00 0.290 ± 0.027 0.237 ± 0.009 0.473 ± 0.018

Ca:Si = 1.25 0.597 ± 0.107 0.134 ± 0.036 0.269 ± 0.071

Ca:Si = 1.50 0.700 ± 0.051 0.100 ± 0.017 0.200 ± 0.034

Ca:Si = 1.75 0.783 ± 0.053 0.072 ± 0.018 0.145 ± 0.035

Ca:Si = 2.00 0.830 ± 0.036 0.057 ± 0.012 0.113 ± 0.024

Q(1) Q(2p) Q(2b) MCL

29Si NMR 0.700 ± 0.051 0.200 ± 0.034 0.100 ± 0.017 2.85

Model 0.707 0.195 0.098 2.83

NMR DNP– 1H-29Si HETCOR – interlayer Ca

33/26

01/07/15

Bridging calcium holds

the silicate chains

together.

Strong

hydrogen

bonding – but

with what

DFT

Bulk C-S-H structures…Ca/Si 1.25 to 2

34/26

01/07/15

Q species

Ca/Si = 1.25

Ca/Si = 1.5

Ca/Si = 1.75

Ca/Si = 2.0

• Possible structures – stable after 2ns MD runs….

• Expect many defect configurations of similar energies

• Constructed by hand…next step…

• Mutations of these structures….

• Family of stable structures….

• Then surfaces……

Kumar et al, J.Phys.Chem.C 121(32) 17188–17196 (2017).

Conclusions – Next steps….

Synthetic C-S-H synthesised with controlled stoichiometry

Ca/Si >1.5 for the first time…can control and tailor Ca/Si…

Homogeneous down to 3nm!!

DNP-NMR – identified Si environment – consistent with 14 Å tobermorite 3n+2 model

1H-29Si NMR – and DFT strong hydrogen bonding onlyseen if Ca in bridging site…

Atomistic structures – consistent with NMR results and

Proposed Structures stable in MD simulations….

Next steps

From kinetic data - investigate growth mechanism using thermodynamic and population balance modelling…get nucleation and growth ….formation pathway…

Introduce surfaces into C-S-H atomistic modelling…..

Start approaching complexity of real system…adding heterogeneous substrates and minor elements….

35/26

01/07/15

P. Bowen, EPFL. 31/10/2017 36

5.3.2 Surface dipole correlation – parallel forces

Eq. 5.3.1

m dipole moment

r surface density of dipoles

1/h5 dependence same as derived

from the full Lifshitz theory

22

0

5

4 r

m

F

A kTh

r

e e

Surface may have dipolar components – eg zwitterionic head groups*

Parallel to plane & randomly oriented - no net dipole moment

But as second surface approaches dipole on one surface may interact

with a dipole on the other surface - attractive force results

using a the Hamaker approach – sum of all dipole interactions at

surface we get Eq. 5.3.1

* e.g glycine (amino acid) – CH2NH2COOH → CH2NH3+COO-

Other NON-DLVO Forces

P. Bowen, EPFL. 31/10/2017 37

5.3.2 Surface dipole correlation – normal forces

Figure 5.14 – attractive or repulsive as fn of angle

Uniform distribution – cancels – no net force when epitaxial

Strong attraction at short range for dipole lattice shifted by a/2 important contribution to

cohesion energy for polar solids

Seen in atomistic simulations for uncharged 1 nm MgO cubes -Spagnoli - Parker –

J.Phys.Chem C 112 (38) 2008 …maybe…

a

h/tan 54°

P. Bowen, EPFL. 31/10/2017 38

Oriented attachment – Simualtions S. Parker group

P. Bowen, EPFL. 31/10/2017 39

5.3.3 – Surface charge inhomogeneities

Inhomogeneities on colloidal scale

– domains from lateral phase separation – fig 2.15 p.84

– adsorption of polyelectrolyte lateral domain interactions Fig. 5.15

Correlations similar to zwitterionic example above but much larger

distances 10–100 nm

Large entities electrolyte screening important -1 or R (domain dipolar

radius) determines range of such interactions – fig 5.16

P. Bowen, EPFL. 31/10/2017 40

Fig 5.16 – surface domain dipolar interactions

-1 = 10 screening dominates domain size

-1 = 50 domain size dominates

Always larger than van der Waals & long range

Force between two planar surfaces

– eg -1 = 10 or 50 nm

– R = 50 or 500 nm

P. Bowen, EPFL. 31/10/2017 41

5.4 Density inhomogeneities at surfaces

Surfaces rarely molecularly flat –

– mica and graphite model exceptions

Hamaker and Lifshitz theories assume liquid and solid media have

homogeneous density right up to interface

4 examples in book (The Colloidal Domain)

– solvent at smooth surfaces

– capillary induced phase separations

– Non-adsorbing solutes – depletion

– adsorbing solutes – kinetics for desorption (see constant charge –

constant potential Chp. 3)

P. Bowen, EPFL. 31/10/2017 42

5.4.1 Solvent molecule packing near surface

Density of liquid shows variations

molecular scale

Pronounced effects for smooth surfaces –

graphite ( e.g. High Surface Area Graphite)

Hard sphere - hard wall model describes

density variation

Described by damped oscillation

Characteristic length l1 s molecular

diameter

P. Bowen, EPFL. 31/10/2017 43

Solvent molecule packing surfaces approach

Two planar surfaces approach

density profiles interfere

Optimum arrangement for h = nl1

– showing free energy minimum

Packing hindered for h = (n+1/2)l1

– local free energy maximum

Giving rise to an oscillatory force

P. Bowen, EPFL. 31/10/2017 44

Oscillatory force as surfaces approach

Fig 5.19 two mica surfaces –

atomistically smooth

Atomic force apparatus

with octa methyl cyclo tetrasiloxane

spherical molecule around 1nm

diameter

Measure 10 oscillations

for cylindrical molecules independent

of length but a function of diameter

Inset is peak to peak amplitude of the

oscillations as a function of D

Gets more and more difficult to push

solvent out of its attractive minimum

as we get closer to surface

P. Bowen, EPFL. 31/10/2017 45

Non-adsorbing solute or polymer

attractive force

osmotic pressure as no solute or polymer

in depletion zone when h < h dep

Attractive force – depending on

concentration profile

solute

depletion

zone

Fig 5.24 – possible concentration profiles

Non-adsorbing solutes – depletion

A - Monotonic conc. decay

C- Solute conc. oscillation

B - Conc. Peak at h>hdep

Example: gum arabic for oil in water emulsion stabilisation

P. Bowen, EPFL. 31/10/2017 46

Depletion flocculation example

Gum arabic used to stabilise oil in water

emulsion (amphiphilic polysacharide)

For citrus and cola flavour oils in soft drinks

Not a very high surfactant activity

Need high concentration but

Too much can lead to depletion flocculation…

Loss of emulsion properties ..coalescence and

creaming – phase separation of products

Depletion zone

Chanamai&McClements –

J.Food Science 66(3) 457 (2001)

Ghosh&Bandyopadhyay -"The

Complex World of Polysaccharides",

DOI: 10.5772/50561, 2012

P. Bowen, EPFL. 31/10/2017 47

3D structure – colloidal crystal:

SiO2 75nm particles – capillary forces

Teflon

ring

Substrate

Colloidal

suspension

Teflon Ring Cell Better control of

the drying front than simple droplet Cabinet

•Contolled T and RH

•Balance & microscope

•Follow drying in-situ

rP lv

c

cos2

lv surface tension - liquid-vapour, Qis the wetting

angle (s/l), r cylindrical pore radius –depends on the

particle size and packing

Stress Proportional to capillary pressure

P. Bowen, EPFL. 31/10/2017 48

Film’s TOP surface

BOTTOM -Substrate/film InterfaceEDGE - Film profiles (crack)

3D structure – colloidal crystal:

SiO2 75nm particles (pH 2-10, 19%v)

500nm

1mm

1mm

1mm

1mm

SEM Micrographs: B. Senior, EPFL

Dry silica film

AFM

Fourier transform

P. Bowen, EPFL. 31/10/2017 49

3D structure – colloidal crystal:

drying mechanism$

3.5

4

4.5

5

5.5

6

6.5

7

7.5

8

3000 3500 4000 4500 5000 5500 6000

time [s]

weig

ht

w [

mg

]-2.5E-03

-2.0E-03

-1.5E-03

-1.0E-03

-5.0E-04

0.0E+00

5.0E-04

dw

/dt

[mg

/s]

dw/dt

w

weight loss vs. of time at constant temperature

and relative humidity.

Theory of drying – 3 rates*

Constant

Rate period

1st falling rate

period

2nd falling

rate period

*G.W. Scherer, J. Non-Cryst. Sol. 1989, 109, 171-182

2) Critical point: network max.

compacted (max. stress) -

in-situ film – drying – cracks

appear at exactly –this point

3) Falling rate

periods:

evacuation of

water from the

network

1) Constant

rate period:

water constant

evaporation

1.520.31090

6.94.32050

17.51.73010

smax [MPa]t [h]T [°C]R.H. [%]

max stress smax, at critical point

$F. Juillerat, et al, "Formation and drying of colloidal crystals using nanosized silica particles" Langmuir, 22, 2249-2257 (2006).

P. Bowen, EPFL. 31/10/2017 50

a: Particle radius (80 nm)

D: Interparticle separation

: Surface potential

: Debye-Hückel parameter

AH: Hamaker constant

: Wetting angle

: Surface tension of the suspending fluid

h: Emersion parameter

rk – dry diameter of submerged particle

2D Ordered Films – Potentials*

DBLSA e

aD

a

ze

TkV

ee 2

22

02

4

)1ln(2 2

0

D

HHF eaV ee

Re

pu

lsiv

e

2

2

2

222

0

2

2

2

2

2

2

)2(

41ln

4

241

2

212.1

)2(

41ln

)2(

2

4

201.1

6

aD

a

a

aaDD

aD

a

aD

a

aD

a

aDD

a

AV H

Vincent

l

Att

rac

tiv

e

aD

aarhahV k

C2

))/(arcsin(sin)2(2~

2

Ca

pil

lary

* Juillerat et al Langmuir, 22(5) 2249-2257 (2006)

P. Bowen, EPFL. 31/10/2017 51

• Derivative of these potentials with respect to interparticle separation Forces

• Capillary Forces dominate for 80 nm particles at all separations

• Pores = hexagonal close packed - 0.225-0.29 particle diameter – 18-24 nm….

• Impossible to avoid cracking without addition of binders

2D ordered films – Forces

Interparticle

separation

[nm]

Electrostatic Repulsion Forces [N]Attraction

Force

(Vincent)

[N]

Capillary

Force [N]Particle-ParticleParticle-

Substrate

HHF LSA LSA

1 2.15 10-11 4.52 10-11 1.28 10-12 1.59 10-11 2.99 10-7

10 1.19 10-11 1.58 10-11 5.03 10-13 8.62 10-14 2.99 10-8

100 1.39 10-15 6.53 10-16 4.37 10-17 6.46 10-17 2.99 10-9

P. Bowen, EPFL. 31/10/2017 52

52

Gas Turbine Engines - power and aircraft

P. Bowen, EPFL. 31/10/2017 53

Role of Airfoil Materials

53

P. Bowen, EPFL. 31/10/2017 54

Electrophoretic Deposition – Nanosized powders

♦ Top Nano 21 project - Alstom (T.Kaiser, M.Konter) ETHZ (V. Shklover) LTP

(K.Belaroui)

♦ Nanostructured ceramic coating for turbine blade applications

♦ Reduce thermal conductivity - phonon scattering by nanostructure

♦ Diffusion barrier – prevent spallation of Thermal Barrier Coating (TBC) due to

interdiffusion of metals and oxide formation

Transition oxides (mixed

Al2O3 and other oxides,

detrimental for TBC)

Superalloy

TBC

O2

Bond coat

Interdiffusion

Nanostructured layer

Gamma Al2O3

P. Bowen, EPFL. 31/10/2017 55

Electrophoretic Deposition – Nanosized powders

Drying

EP Deposition

Substrate

Dip coating

Substrate

Suspension

♦ Possible Coating processes for complex shapes

♦ Industrial scale: - Dip coating, - EPD

♦ Lab scale : - Tape casting, - Slip casting

P. Bowen, EPFL. 31/10/2017 56

EPD Coatings

Non-aqueous (ethanol) dispersion pHeff = 3 zeta +50 mV

wet 30 sec

5 min • - Al2O3 powder - dv50 = 22 nm

• Small particles Large capillary forces

(5-9 MPa) catastrophic cracking

• Even with cellusose binders – only

when films 1 mm crack free films

P. Bowen, EPFL. 31/10/2017 57

EPD Coatings – –Al2O3

AKP-50 -Al2O3, dv50 = 165 nm

♦ Larger particles

lower capillary forces

1MPa

no cracking

Critical pore diamter

for these alumina

systems around

100nm

rP lv

c

cos2

lv surface tension - liquid-vapour,

Qis the wetting angle (s/l)

r cylindrical pore radius –depends on

the particle size and packing

Stress Proportional to capillary pressure

P. Bowen, EPFL. 31/10/2017 58

Tape Cast - coatings

Tape casting – aqueous dispersion (PAA, binder PVA)

Milled Deg C -Al2O3 powder, dv50 = 22 nm

• Slow drying >7 days – no macrocracks

• Thickness = 17 4 µm• Roughness = 1.3 0.03 µm

200 mm 100 mm

P. Bowen, EPFL. 31/10/2017 59

Spallation of coating due to metals interdiffusion and

oxides formation

Transition oxides

(detrimental for TBC)

Superalloy

TBC

O2

Bond coat

20 µm

(a)

20 µm

Sans nano-couche – 500hrs

LTP-ETHZ-ABB

Projet – dépostion d’une couche

de nanoparticules de

– Al2O3 – modifie interface

Avec nano-couche – 500hrs

Current practice grow alpha alumina at interface by thermal treatment, easier than depositing NP

P. Bowen, EPFL. 31/10/2017 60

Next week

Adsorbed molecules & polymers – steric forces (slides 5-27)

Example – porous films for ink-jet media – slides (5-12)

Measurement techniques (28-32)

– Atomic force microscopy – adsorbed layer thickness

Hamaker Programme – LTP-Website – interparticle interaction

potentials (33-35)

InterParticle Forces & Suspension Rheology -YODEL model (36-

47)

Examples

– Dispersion of cement and concrete

Conclusions on Dispersion – (85)

Typical questions on interparticle forces (87)

P. Bowen, EPFL. 31/10/2017 61

Porous Films for Ink-Jet Applications – steric repulsion

♦ For high quality images paper coated with polymer

♦ General Drawbacks

– Slow ink absorption (secs), slow drying (mins)

– Not water-fast

– Blurring of image - diffusion over time

♦ Why and how with ceramics

– Need to be nanosized for transparent coating – colour quality

– Sufficient loadings of nano-sized powders in suspensions stable for 24hrs

– Nanosized pores rapid ink absorption (msecs) and instantly dry to touch

– Waterfast - strong dye adsorption

Paper

Polymer

61

P. Bowen, EPFL. 31/10/2017 62

Colloidal Stability Calculations and Rheology - 1

♦ Studied Gamma alumina

♦ with C1-C4 carboxlic acidsAcetic Acid

Formic Acid

Propionic AcidButyric Acid

Real relative size

62

♦ Industrial project with ILFORD SA, Marly, Switzerland♦ Initial dispersion of alumina 40 nm Dv50 with HNO3

♦ Zeta potential of 64 mV♦ Max volume fraction dispersion 10% volume too low♦ Looked at carboxylic acids formic, acetic, propionic, butyric♦ With acetic 19% volume fraction possible♦ Interparticle interaction energy calculations to understand why

P. Bowen, EPFL. 31/10/2017 63

Colloidal Stability Calculations and Rheology*

Formic Acid

Acetic Acid

Propionic

Acid

Butyric Acid

♦ PSD Horiba Capa 700 - roughly spherical primary

particles still agglomerates*

0

10

20

30

0 20 40 60 80 100

Fre

qu

ency

[V

ol.

%]

E.S. Diameter [nm] Acid dV50

[nm]

sV50

nmF

AGFN dh

Formic 44.8 37.3 2.33 5 37.6

Acetic 41.6 32.8 2.16 4 25.4

Propanoic 38.0 27.8 1.63 3 23.3

Butyric 37.4 44.1 1.94 3 26.7

♦ Degussa C ,

(Germany >

99.6 Al2O3)

D e g C

% 2.8

S S A (m 2 /g ) 107

d B E T ( nm ) 16.5

d v50 ( nm ) 41.6

s v50 ( nm ) 32.8

F a g 2.2

F N 10

P o r e dia ( n m ) 13.3

25 nm

*M. Staiger, et al, Ceramic

Processing Science VI., pp.

173-178, The American

Ceramic Society, 2001

tail

P. Bowen, EPFL. 31/10/2017 64

Colloidal stability calculations and rheology

Acid

(2%wt

aq. sol.)

Zeta

Pot.

mV

Ionic

Conc

(M)

Thick-

ness

[nm]

Nitric 64 0.16 0.0

Formic 56 0.032 0.27

Acetic 49 0.0083 0.5

Acid Macroscopic

Properties

Nitric Gelation

Formic Gelation

Acetic No gelation

-40

-30

-20

-10

0

10

20

30

40

0 1 10 100

h [nm]

P. Bowen, EPFL. 31/10/2017 65

Volume fraction - rheology

Maximum volume fraction

easily dispersed = 0.195

If double layer felt at 12.5 nm

this is an effective volume

fraction

Veff = 0.655

Acetic Acid dispersions

-40

-30

-20

-10

0

10

20

30

40

0 1 10 100

h [nm] Close packing from model log-

normal powders = 0.68

(Nolan & Kavanagh – NOL93)

P. Bowen, EPFL. 31/10/2017 66

Limitations with Interparticle Interaction calculations

Particle packing – choice for touching particles delicate changes particle coordination number drastically

Shape - Spherical particles assumed Adsorbed layer thickness and conformation – OK for simple acids

not so easy for polyelectrolytes cf PAA (polyacrylic acid) Position of charge plane for polyelectrolyte

Particle surface, polymer surface or intermediate? Hamaker constant for porous gamma alumina ? Hydrodynamic forces ignored

R. J. Flatt, P. Bowen, "YODEL: a Yield stress mODEL for suspensions"

J.Amer.Ceram.Soc., 89(4) 1244-56, (2006) .

P. Bowen, EPFL. 31/10/2017 67

Final Film Surface Microstructure

♦ Finally Degussa C too many particles >80nm

– haze

♦ Commercial Films produced using

– rare-earth doped Aluminium Oxide Hydroxide®

♦ Steric stabilisation – small molecules – electrostatic

insufficient

♦ Excellent quality

– high gloss, high transparency

– waterfast at 70°C

– sufficient pore volume

– rapid printing

♦ Production running for several years

– 100 m/min range – multilayer photographic

coater (cascade)

– Commercially Available – Instant Dry

Dispersing Media

Av. PoreSize (nm)

Pore Vol.[cm3/g]

Nitric Acid

Formic Acid Acetic Acid

14.1 0.32

27.2 0.78

21 0.70

P. Bowen, EPFL. 31/10/2017 68

Nanoparticle Porous Films - Commercial products