Mechanics of nanoparticle adhesion â A continuum approach

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26J. TomasFigure 4. Characteristic particle contact deformation. (e) Contact detachment [148]. Again, if oneapplies a certain pull-off force F N,Z = –F H,A as given in Eq. (67) but here negative, the adhesionboundary line at failure point A is reached and the contact plates fail and detach with the increasingdistance a= aF = 0+ hK,A−h K. This actual particle separation is considered for the calculation by a3hyperbolic adhesion force curve F N,Z = –F ∝ a − of the plate–plate model Eq. (68).HA ,
Mechanics of nanoparticle adhesion — A continuum approach 27Figure 5. Characteristic particle contact deformation. The complete survey of loading, unloading,reloading, dissipation and detachment behaviors of titania [148]. This hysteresis behavior could beshifted along the elastic–plastic boundary and depends on the pre-loading, or in other words, preconsolidationlevel. Thus, the variation in adhesion forces between particles depends directly on thisfrozen irreversible deformation, the so-called contact pre-consolidation history.FF + π ⋅r ⋅p ⋅hH0 1,2 VdW K,AN,Z( hK ) =−3 hK,Ah 1K + −aF= 0aF=0(68)These generalized functions in Fig. 3 for the combination of elastic-plastic, adhesionand dissipative force–displacement behaviors of a spherical particle contactwere derived on the basis of the theories of Krupp [49], Molerus [13], Maugis
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Mechanics of nanoparticle adhesion â A continuum approach