Planar soft surface

2 PLANAR SOFT SURFACE 4.2.1 Poisson-Boltzmann Equation 

The charge density Pei(x) resulting from the mobile charged ionic species is related to the electric potential i/ (x) by the Poisson equation 

Biophysical Chemistry of Biointerfaces By Hiroyuki Ohshima Copyright 2010 by John Wiley Sons, Inc. 

FIGURE 4.1 Ion and potential distribution around a hard surface (a) and a soft surface (b). When the surface layer is thick, the potential deep inside the surface layer becomes the Donnan potential. 

FIGURE 4.2 The scaled potential y x) as a function of the scaled distance kx across an ion-penetrahle surface charge layer of the scaled thickness Kcl for several values of kcI kcI = 0.5, 1, and 2) at NIn = 5, Z= — 1, and z = 1. The vertical dotted line stands for the position of the surface of the particle core for the respective cases. The dashed curve corresponds to the hntiting case of Kd — oo. From Ref [4]. 

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Consider an ion-penetrable planar soft surface consisting of two sublayers 1 and 2 (Fig. 4.7). The surface is in equilibrium with a monovalent electrolyte solution of bulk concentration n. Note here that n represents the total concentration of monovalent cations including ions and that of monovalent anions including OH ions. Let h be the concentration in the bulk solution phase. Sublayer 2 is... 

Expressions for the Double-Layer Free Energy for a Planar Soft Surface... 

FIGURE 5.3 Planar soft surface of thickness li in an electrolyte solution. 

The sign reversal takes place also in the electrophoretic mobility of a non-uniformly charged soft particles, as shown in this section. We treat a large soft particle. The x-axis is taken to be perpendicular to the soft surface with its origin at the front edge of the surface layer (Fig. 21.8). The soft surface consists of the outer layer —d < x < 0) and the inner layer (x < —d), where the inner layer is sufficiently thick so that the inner layer can be considered practically to be infinitely thick. The liquid flow m(x) and equilibrium electric potential i//(x) satisfy the following planar Navier-Stokes equations and the Poisson-Boltzmann equations [39] ... 

At its simplest, an onlap trap may be a blanket sand that pinches out up-dip (Fig. 8D). It is sealed by impermeable rocks beneath and by an onlapping shale (generally the source rock, as well as the cap). Many unconformities are old land surfaces, however, and sands may be deposited in old topographic lows. Alternating hard and soft sediments may have been weathered and eroded to form scarps, dip slopes, and strike valleys. Fluvial or shallow marine sands may have been deposited along the old valleys and sealed by marine muds. Stratigraphic traps of this type are known as the Mississippian Pennsylvanian imconformity of Oklahoma. Alternatively, the unconformity may have been a planar land surface that was locally incised by alluvial valleys. These may have been sand filled and drowned by... 

In the JKR experiments, a macroscopic spherical cap of a soft, elastic material is in contact with a planar surface. In these experiments, the contact radius is measured as a function of the applied load (a versus P) using an optical microscope, and the interfacial adhesion (W) is determined using Eqs. 11 and 16. In their original work, Johnson et al. [6] measured a versus P between a rubber-rubber interface, and the interface between crosslinked silicone rubber sphere and poly(methyl methacrylate) flat. The apparatus used for these measurements was fairly simple. The contact radius was measured using a simple optical microscope. This type of measurement is particularly suitable for soft elastic materials. 

The surface stress free (SSF) approach for removal of the Cu layer and planarization without polishing is critical for manufacturing a new generation of IC wafer composed of soft low-k materials [54]. 

In the JKR theory it is assumed that surface forces are active only in the contact area. In reality, surface forces are active also outside of direct contact. This is, for instance, the case for van der Waals forces. Derjaguin, Muller, and Toporov took this effect into account and developed the so-called DMT theory [206], A consequence is that a kind of neck or meniscus forms at the contact line. As one example, the case of a hard sphere on a soft planar surface, is shown in Fig. 6.19. 

Soft Lithography Lithography is essentially a process for printing features on a planar surface. Nanolithography tools, commonly referred to as soft lithography, allow precisely defined nanoscale features to be produced on a substrate, which can be removed from the substrate as free-standing 3D nano-objects. A number of techniques fall within the field of soft lithography, primarily for construction of micrometer-sized objects ... 

Multilayer or stacked pads are commonly used in the CMP processes for better polishing performance such as uniform material removal and good planarization across the wafer surface. A multilayer or stacked pad usually consists of a stiff, hard top layer and a soft, flexible subpad, and possibly some medium layer(s), as shown in Fig. 5.3. 

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