Field-Induced Water Bridge Formation in a Nonplanar Interface

4 Field-Induced Water Bridge Formation in a Nonplanar Interface 

Numerical simulations that include the geometry for a nonplanar interface as well as the shape of the water protrusion give a more detailed picture of the different regimes involved in the formation of a field-induced nanoscale water bridge.  

The electric field generated by applying a voltage V is approximated bythe one produced by a sphere of radius R. Furthermore, the field has a radial symmetry, as shown in Fig. 13.3, and is calculated by using a spherical capacitor with the tip placed at its center. The above geometry has special relevance because it contains the main elements that characterize an AFM interface. The simulations show the existence of three main regimes. Two of them are 

The above discussion has been focused on describing the field-induced formation of water bridges however, the same equations and methodology can be used to describe the formation of other liquid bridges. The only requirement is to use the values of the dielectric constant, the surface energy, the molar volume, and the Hamaker constant that characterize the liquid. 

The electric fields associated with the formation of a water bridge in a force microscope interface are extremely high ( 1 V nm = 10 V/m). The electric field at the solid-liquid interface fora droplet just before the formation of a water bridge is about one to two orders of magnitude smaller than the one inside the bridge. The dependence of the maximum electric field at the silicon interface is depicted in the insets of Fig. 13.5. Two fields are calculated, the electric field at the solid-liquid interface underneath the tip s axis for a bias just below (solid line) and the field for a voltage just above (discontinuous line). 

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