Adhesion and Wetting in Soft Polymeric Systems

We have developed a generalized model of particle/surface interactions describing adhesion and wetting phenomena. We show that for an elastic nanoparticle with radius $R_{\mathrm{p}}$ and shear modulus $G_{\mathrm{p}}$ interacting with an elastic substrate having shear modulus $G_{\mathrm{s}}$ the crossover between adhesion and wetting-like behavior is determined by a dimensionless parameter $\beta \propto \gamma^{\ast }(G^{\ast }R_{p} )^{-2/3}W^{-1/3}$. In the limit of small values of the parameter $\beta $\textit{ \textless }\textless 1, our model reproduces JKR model for particle adhesion on elastic substrates (adhesion regime). However, in the opposite limit, $\beta $\textgreater \textgreater 1, the capillary forces play a dominant role and determine particle/substrate interactions (wetting regime). We extended our approach to describe the detachment of rigid nanoparticles from elastic surfaces. Simulation results confirm that the detachment force, $f$*, depends on a dimensionless parameter $\delta \propto \gamma_{s} (G_{s} R_{p} )^{-1/3}W^{-2/3}$, which corresponds to the ratio of the surface energy of the neck and the substrate elastic energy. In the case when $\delta $\textit{ \textless }\textless 1, the critical detachment force approaches a critical value calculated in the framework of the JKR model, $f\ast =1.5\pi WR_{p} $ (JKR regime). However, in the opposite limit, the critical detachment force scales as$f\ast \propto \gamma_{s}^{3/2} R_{p}^{1/2} G_{s} ^{-1/2}$ (necking regime). All simulation data can be described by a crossover function $f\ast \propto \gamma_{s}^{3/2} R_{p}^{1/2} G_{s} ^{-1/2}\delta^{-1.89}$.