Adhesion and Wetting of Soft Nanoparticles on Textured Surfaces: Transition between Wenzel and Cassie-Baxter States

We use a combination of the molecular dynamics simulations and scaling analysis to study interactions between gel-like nanoparticles and substrates covered with rectangular shape posts. Nanoparticle in contact with a substrate undergo a first order transition between Wenzel and Cassie-Baxter states depending on nanoparticle shear modulus, the strength of nanoparticle-substrate interactions, height of the substrate posts and nanoparticle size, $R_{\mathrm{p}}$. There is a range of system parameters where these two states coexist such that the average indentation $\delta $ produced by substrate posts changes monotonically with nanoparticle shear modulus. We have developed a model that describes deformation of nanoparticle in contact with patterned substrate. The effect of the patterned substrate can be taken into account by introducing an effective work of adhesion, $W_{\mathrm{eff}}$, which describes the first order transition between Wenzel and Cassie-Baxter states. There are two different shape deformation regimes for nanoparticles with shear modulus $G_{\mathrm{p}}$ and surface tension $\gamma_{\mathrm{p}}$. Shape of small nanoparticles with size $R_{p} <\gamma_{p}^{3/2} G_{p}^{-1} W_{eff}^{-1/2} $ is controlled by capillary forces while deformation of large nanoparticles, $R_{p} >\gamma_{p}^{3/2} G_{p}^{-1} W_{eff}^{-1/2} $, is determined by nanoparticle elastic and contact free energies.