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Single particle contact versus particle packing behavior: model based analysis of chemically modified glass particles

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Abstract

Smooth spherical micro glass particles are the reference particle system to demonstrate the correlation between single contacts and the particle packing properties. To investigate the influence of the van der Waals attraction force, the particles will be functionalized to obtain hydrophilic and hydrophobic surfaces. To remove the impurities and hydrophilize the particle surfaces a very strong oxidizing agent is used—the peroxymonosulfuric acid. In order to generate a hydrophobic glass surface, the process of silanization is applied. The comprehensive force displacement model of elastic-plastic and adhesive contacts are discussed. Therefore the model ‘stiff particles with soft contacts’ is used to quantify and compare the elastic-plastic contact properties. In this work, the particle contacts are experimentally investigated by means of atomic force microscopy (AFM), nanoindentation and shear tests. While the AFM and nanoindenter measurements are aimed to analyse single particle contacts, shear tests are used for particle packing studies. The fundamental challenge and question is addressed and answered: How do the micro mechanical material properties change when the glass surfaces are functionalized? Do we obtain the same behavior for the used micro glass particles when we compare the different methods?

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Abbreviations

\(\hbox {a}_{0}\) :

Minimum molecular surface distance (nm)

\(\hbox {C}_\mathrm{H}\) :

Hamaker constant (J)

\(\upgamma \) :

Surface energy \((\hbox {mJ/m}^{2})\)

\(\upgamma _\mathrm{D}\) :

Surface energy dispersive fraction \((\hbox {mJ/m}^{2})\)

\(\upgamma _\mathrm{P}\) :

Surface energy polar fraction \((\hbox {mJ/m}^{2})\)

d:

Particle diameter \((\upmu \hbox {m})\)

E:

Effective modulus of elasticity \((\hbox {kN/mm}^{2})\)

\(\hbox {ff}_\mathrm{c }\) :

Flow function (\(-\))

\(\hbox {F}_\mathrm{G}\) :

Gravitational force (nN)

\(\hbox {F}_\mathrm{H}\) :

Adhesion force (in general) \((\upmu \hbox {N})\)

\(\hbox {F}_\mathrm{H0}\) :

Adhesion force of contact point (nN)

\(\hbox {F}_\mathrm{N}\) :

Normal force \((\upmu \hbox {N})\)

\(\hbox {F}_\mathrm{N,Y}\) :

Normal force at yield point (nN)

\(\hbox {h}_\mathrm{K}\) :

Displacement (nm)

\(\hbox {h}_\mathrm{K,Y}\) :

Displacement at yield point (nm)

\(\hbox {k}_\mathrm{N,el-pl}\) :

Elastic-plastic contact stiffness (N/m)

\({\upkappa }\) :

Contact consolidation coefficient (\(-\))

\({\upkappa }_\mathrm{A}\) :

Elastic-plastic contact surface ratio (\(-\))

\({\upkappa }_\mathrm{p}\) :

Plastic repulsion coefficient (\(-\))

\(\hbox {p}_\mathrm{f}\) :

Micro-yield strength (MPa)

\(\hbox {p}_\mathrm{VdW}\) :

van der Waals bond stress (MPa)

\(\hbox {r}_{1,2}\) :

Effective particle radius (nm)

\(\hbox {r}_\mathrm{K,el}\) :

Elastic contact radius (nm)

\(\hbox {W}_\mathrm{diss}\) :

Energy absorption or dissipation (Nm)

\(\uprho \) :

Density \((\hbox {g/cm}^{3})\)

\(\uprho _\mathrm{b }\) :

Bulk density \((\hbox {g/cm}^{3})\)

\(\upsigma \) :

Normal stress (Pa)

\(\upsigma _\mathrm{c}\) :

Uniaxial compressive strength (Pa)

\(\upsigma _{0}\) :

Isostatic tensile strength (Pa)

\(\upsigma _{1}\) :

Major principal stress (Pa)

\(\upsigma _\mathrm{pre}\) :

Preshear stress (Pa)

\(\uptau \) :

Shear stress (Pa)

\(\upvarphi _\mathrm{i}\) :

Angle of internal friction \((^\circ )\)

\(\upvarphi _\mathrm{e}\) :

Effective angle of internal friction \((^\circ )\)

\(\upvarphi _\mathrm{st}\) :

Stationary angle of internal friction \((^\circ )\)

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Acknowledgments

We would like to acknowledge the financial support of the German Research Foundation (DFG) through the priority program ‘PiKo – Particles in Contact’.

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Authors and Affiliations

  1. Institute for Process Engineering, Mechanical Process Engineering, Otto von Guericke University Magdeburg, Universitätsplatz 2, 39106 , Magdeburg, Germany

    Katja Mader-Arndt, Zinaida Kutelova, Werner Hintz & Jürgen Tomas

  2. Institute of Materials Engineering, Surface and Materials Technology, University of Siegen, Paul-Bonatz-Straße 9-11, 57076 , Siegen, Germany

    Regina Fuchs, Jan Meyer & Thorsten Staedler

Authors
  1. Katja Mader-Arndt
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  2. Zinaida Kutelova
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  3. Regina Fuchs
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  4. Jan Meyer
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  6. Werner Hintz
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  7. Jürgen Tomas
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Correspondence to Katja Mader-Arndt.

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Mader-Arndt, K., Kutelova, Z., Fuchs, R. et al. Single particle contact versus particle packing behavior: model based analysis of chemically modified glass particles. Granular Matter 16, 359–375 (2014). https://doi.org/10.1007/s10035-013-0478-9

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