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Calculation of capillary forces between silica nanoparticles,

using MD simulations University of Natural Resources and Applied Life Sciences

Vienna Austria

S. Leroch

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Contents

Introduction Model Silica particles Structure, surface Contact between wetted silica particles Encountered problems Wetted silica plates Outlook

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Introduction For product quality and process

performance it is necessary to predict particle flow.

It depends on surface roughness surface chemistry and the amount of adsorbed molecules from the surrounding atmosphere.

At contact distances or particle sizes of a few nanometers most continuum theories fail to describe particle interactions properly which are dominantly of vdW and Coulomb type.

Study of physical/chemical processes

on atomistic scale

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Introduction

Depending on relative humidity of the air water bridges are formed between roughnesses on the contacting surfaces of larger particles, which cannot be account for in macroscopic models.

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Model Nano particles with adsorbed water layers

in contact with another nano particle or a wall.

At the moment, small particles are in

atomistic resolution. Basic atomistic interactions are

parametrised potentials and force fields from biochemistry

Adsorbed amount of water depends on the relative humidity H

V/Vm = 1/(1-H) For H of 40% -70% 3 ML are typically

adsorped, for 20% and less usually portions of ML

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Force calculation Basic atomistic interactions are parametrised potentials and

force fields from biochemistry.

F = FLJ + FCoul + Finternal

FLJ = Σij 24πε/σ[2(σ/r)13 − (σ/r)7]

FCoul = - Σij Cqiqj/r2

with i,j the sum over all atoms in the system.

Finternal accounts for vibrations and bending motions of the

atoms in the nanoparticles which can be of Morse type for silica particles

Finternal = Σij D2α[e-α(r-r0)-e-2α(r-r0)]

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Forces

In vacuum: Silica forces are of Morse type plus Coulomb interaction.

In water:Water-Water interaction: TIP3P, SPCWater-Silica interface and Silica-Silica interaction: 1) CHARMM-like forcefield parametrised by Schulten et al to

reproduce experimental water contact angles 2) ClayFF

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Force profile and binding energy Forces are calculated for different particle distances r and/or

orientations -> force profile Total particle/particle interactions origin from atomic forces on the

particles itself and from adsorbed deformable layers The binding energy of the particles, also called potential of mean

force (PMF), can be deduced from A(r) =

where n(r) stands for the radial distribution function.

n(r) gives information about the particle arrangement (the structure) in the collection.

The global minimum of the binding energy defines the contact distance of the particles, the corresponding minimum in the force profile the pull-off force.

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Preparation of silica particles Amorphous silica particles are

prepared by melting β−cristobalith applying the Morse potential.

Sample is heated up to 7000 K and slowly cooled down with rates

of 4K/ps to deduce amorphous bulk silica, cooling rate dictates the number of dangling bonds in the sample.

Finally sphere is cut out with the

constraint that portion Si:O is 1:2 Multiple annealing cycles are

necessary to reduce DA on the surface

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Structure of annealed Silica Particles

Tetrahedral geometry around Si, connecting O are free to rotate

g(r) and angle distributions are similar to those in the bulk

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Coordination numbers

Problem with high number of dangling bonds 4/nm2

Usual number between 1 and 4/nm2

Perfect surface hydrophopic, our surface mimics fully hydroxilated one

0.010.920.07O-Si

0.010.880.11Si-O

5.821.933.873.79

6.072.003.99 3.78

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Wetted particles Particles are covered

with 3 ML of water and brought into contact till bridges are formed, and finally water is squeezed out between particles.

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Silica Plate silanol density 1/nm2

Further annealing of the surface leads to a number of dangling bonds of 1/nm2

DA Si and O are saturated with OH and H to give silanols

Empirical contact angle in dependence of silanol density a

cos γ = 0.257 a +0.743

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Water droplet on silica surface (charmm)

Microscopic contact angle is extrapolated to to get macroscopic one, which is related to the surface tension via Youngs equation.

γ = 5 5 degrees

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Water droplet on silica surface (ClayFF)

Density close to the surface hardly increased.

Strong hydrophobic γ = 75 degrees

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Liquid bridge ClayFF Example of an

asymmetric liquid bridge between silica plates, in red are the silanol groups.

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Next steps Calculation of Adhesion forces using ClayFF

and charmm are in progress Next step hydroxilation of the surface,

typical densities 2.6 – 4.6/nm2

Repeat calculations for different amounts of water coverage in dependence of relative humidity (2ML and below).

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Thank you for your attention !