Capillary surface instability

FIGURE 1.8. (a) Schematic representation of the device used to study capillary surface instabilities. A polymer-air bilayer of thicknesses /ip and /ia, respectively, is formed by two planar silicon wafer held at a separation d by spacers. A capillary instability with wavelength k = 27t/q is observed upon applying a voltage U or a temperature difference AT. (b) Dispersion relation (prediction of Eq. (1.6)). While all modes are damped (r < 0) in the absence of an interfacial pressure pei, the application of an interfacial force gradient leads to the amplification of a range of k-values, with /.m the maximally amplified mode. 

A second approach makes use of capillary surface instabilities that occur in the presence of a destabilizing surface force. Since such a instability mirrors the details of the destabilizing force field, it can be employed as a sensitive tool to study and explore forces that act at the... 

It should be noted that glass, which is often used as a substrate in inkjet printing experiments, is an insulator. Similarly, although thermo-capillary surface instabilities have been seen to develop in the spreading and evaporation of volatile drops on conductive substrates (silicon and brass), no surface oscillations were observed for those droplets placed on glass. ... 

In addition, patterns created by surface instabilities can be used to pattern polymer films with a lateral resolution down to 100 nm [7]. Here, I summarize various possible approaches that show how instabilities that may take place during the manufacture of thin films can be harnessed to replicate surface patterns in a controlled fashion. Two different approaches are reviewed, together with possible applications (a) patterns that are formed by the demixing of a multi-component blend and (b) pattern formation by capillary instabilities. 

The theoretical framework, within which the existence of surface instabilities created by capillary waves can be predicted is the linear stability analysis [23, 24]. This model assumes a spectrum of capillary waves with wave vectors q and time constant r (Fig. 1.8a). 

Current instability Fouled capillary surface V Capillary-Associated Problems ... 

In applications in the semiconductor industry, polymer structures are required on length scales down to individual molecules. A bottom-up approach is better than a top-down approach in order to achieve this. A lateral resolution less than 100 nm can be created by surface instabilities and pattern formation in polymer films. Steiner [6] discussed demixing of polymer blends and pattern formation by capillary instabilities for nanostructure formation. 

Different phase separated morphologies can be found in different polymer solvent systems. The pattern formation consists of several stages. In the initial stage, phase separation results in a layered morphology of the two solvent swollen phases. As more solvent evaporates, this double layer is destabilized in two ways (1) capillary instability of the interface, and (2) surface instability. Each of the mechanisms results in different morphological length scales. Core shell spherical domains in phase-separated ternary systems have also been found. The shell thickness can be a few nanometers. 

For solid surfaces interacting in air, the adhesion forces mainly result from van der Waals interaction and capillary force, but the effects of electrostatic forces due to the formation of an electrical double-layer have to be included for analyzing adhesion in solutions. Besides, adhesion has to be studied as a dynamic process in which the approach and separation of two surfaces are always accompanied by unstable motions, jump in and out, attributing to the instability of sliding system. 

The simplest approach to minimizing protein-wall interaction is to use a buffer pH at which interactions do not occur. At acidic pH the silanols on the surface of the capillary are protonated, and the net charge of the proteins is positive. At high pH, the wall is negatively charged, and so are the sample components. Both conditions result in electrostatic repulsion. Problems associated with operation at pH extremes include the potential instability of proteins (denaturation, degradation, and precipitation) and the limited pH range in which to achieve resolution. Additionally, operation at extreme pH does not eliminate all nonspecific interactions. 

This occurs by an instability of one of the free interfaces the polymer-polymer interface, the film surface, or a combination of the two, each of which gives rise to a distinct lateral length scale. Which of the two capillary instabilities is selected is a complex issue. It depends on various parameters, such as polymer-polymer and polymer-solvent compatibility, solvent volatility, substrate properties, etc. in a way which is not understood. Despite this lack of knowledge, playing with these parameters permits the selection of one of the two distinct length scales associated with these two mechanisms, or a combination thereof. 

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