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Understanding and Manipulation of Nanoparticle Contact Forces by Capillary Bridges

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Abstract

Since, in the presence of humidity the inter-particle processes are dominated by capillary forces, a fundamental understanding of the water adsorption and the capillary bridge formation is very important. However, the adsorbed water structure and thus the capillary bridge formation is influenced by various parameters like the particle morphology (e.g. particle size, roughness) as well as the surface chemistry (surface energy, adsorbate structure) and therefore needs to be analyzed on a submicroscopic or even molecular basis. A multi-scale approach ranging from experiments on an individual particle level (AFM and liquid bridge simulation) and investigations on small particle ensembles (combined QCM-D/FTIR) up to macroscopic description of bulk behavior is presented in this chapter. In this context, the combined in situ QCM-D/FTIR experiments are bridging the gap between experiments on an individual particle level and macroscopic bulk behavior. Variation of surface chemistry by means of adsorption of functional organic molecules allows for the correlation of macroscopic particle behavior to nanoscopic effects like the presence and structure of adsorbate layers as well as the formation of capillary bridges while keeping the disperse properties constant. Besides extensive experimental work, simulations of capillary bridges formed by condensation from humid air are presented. It is clearly shown that well known approximations which have been introduced for micron-sized particles are not valid any more for nano-scaled particles. The forces between nanoparticles by static liquid bridges and their dependency on particle size, contact angle, humidity and interparticle distance are discussed in detail. Furthermore, capillary forces during separation of particles are studied thoroughly and a constitutive law based on a contact stiffness allows the transfer to DEM simulations of wet powders. Finally, it is demonstrated by comparison to Molecular Dynamics simulations, that the used continuum approach to simulate capillary bridges might even be used down to particle sizes of a few nanometers, if some additional effects are considered correctly.

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Abbreviations

ffc:

Flowability index (–)

D:

Particle diameter (m)

d:

Distance between particle surfaces (m)

f:

Frequency (Hz)

F:

Force (N)

h:

Size of capillary bridge (m)

k:

Stiffness of capillary bridge contact (m−1)

n:

Overtone number

p:

Pressure (Pa)

r:

Radius of curvature (m)

R:

Universal gas constant (8,314 J mol−1 K−1)

T:

Temperature (K)

VM:

Molar volume (m3 mol−1)

V:

Volume (m3)

β:

Filling angle of capillary bridge (°)

γ:

Surface tension (N m−1)

ΔΓ:

Dissipation in (Hz)

φ:

Relative humidity (–)

λ:

Surface enhancement factor (–)

Θ:

Contact angle (°)

ρ:

Density (kg m−3)

σ:

Stress (Pa)

C:

Capillary

eff:

Effective

K:

Kelvin

max:

Maximum

min:

Minimum

mod:

Modified

P:

Pressure related

Pl:

Plate

S:

Saturation

S:

Surface tension related

Sp:

Sphere

BET:

Determination of specific surface area according to Brunauer, Emmett, and Teller

FE-SEM:

Field emission scanning electron microscopy

FTIR:

Fourier transform infrared (spectroscopy)

MD:

Molecular dynamics

ODS:

Octadecyltriethoxysiloxane

ODT:

1-octadecanthiol

PE-CVD:

Plasma enhanced chemical vapour deposition

PM-IRRAS:

Photoelastic-modulated Fourier transform infrared absorption spectroscopy

QCM:

Quartz crystal microbalance

QCM-D:

QCM with dissipation monitoring

RH:

Relative humidity

SEM:

Scanning electron microscopy

DEM:

Discrete Element Modeling

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Acknowledgements

We would like to thank the Deutsche Forschungsgemeinschaft (DFG) for supporting this work by the projects SCHM1429/7 and GR1709/12.

We thank Prof. Anjana Devi and her co-workers at the Ruhr University in Bochum for the atomic layer deposition of ultra-thin TiO2 films.

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Authors and Affiliations

  1. Particle Technology Group, University of Paderborn, Paderborn, Germany

    Hans-Joachim Schmid & Michael Dörmann

  2. Technical and Macromolecular Chemistry Group, University of Paderborn, Paderborn, Germany

    Guido Grundmeier, Alejandro González Orive, Teresa de los Arcos & Boray Torun

Authors
  1. Hans-Joachim Schmid
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  2. Guido Grundmeier
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  3. Michael Dörmann
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  4. Alejandro González Orive
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  5. Teresa de los Arcos
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  6. Boray Torun
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Correspondence to Hans-Joachim Schmid .

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  1. Institute of Particle Process Engineering, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Sergiy Antonyuk

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Schmid, HJ., Grundmeier, G., Dörmann, M., Orive, A.G., de los Arcos, T., Torun, B. (2019). Understanding and Manipulation of Nanoparticle Contact Forces by Capillary Bridges. In: Antonyuk, S. (eds) Particles in Contact. Springer, Cham. https://doi.org/10.1007/978-3-030-15899-6_2

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