Film thickness rheological properties

Another remarkable feature of thin film rheology to be discussed here is the quantized" property of molecularly thin films. It has been reported [8,24] that measured normal forces between two mica surfaces across molecularly thin films exhibit oscillations between attraction and repulsion with an amplitude in exponential growth and a periodicity approximately equal to the dimension of the confined molecules. Thus, the normal force is quantized, depending on the thickness of the confined films. The quantized property in normal force results from an ordering structure of the confined liquid, known as the layering, that molecules are packed in thin films layer by layer, as revealed by computer simulations (see Fig. 12 in Section 3.4). The quantized property appears also in friction measurements. Friction forces between smooth mica surfaces separated by three layers of the liquid octamethylcyclotetrasiloxane (OMCTS), for example, were measured as a function of time [24]. Results show that friction increased to higher values in a quantized way when the number of layers falls from n = 3 to n = 2 and then to M = 1. 

Unlike traditional textbooks of tribology, in this book we regard boundary lubrication as a limit state of hydrodynamic lubrication when film thickness is down to molecular dimension and independent of the velocity of relative motion. The discussions are based on the existing results, some from literatures but mostly from the authors own work. The topics are mainly focused on the mechanical properties of boundary films, including rheology transitions, molecular ordering, and shear responses. Ordered molecule films, such as L-B films and SAM, are discussed, with emphasis on the frictional performance, energy dissipation and the effects from structural features. Boundary films can be modeled either as a confined substance, or an adsorbed/reacted layer on the... 

An effective viscosity rp has been introduced in the Reynolds equation to describe the non-Newtonian lubricant properties. Ignoring the variation of viscosity across the film thickness, one may evaluate the effective viscosity via the following rheological model that considers a possible shearthinning effect [19],... 

TABLE 12.2. Common Material Rheological Properties and Resulting Film Thickness for Printing Technologies... 

Thin solid films of polymeric materials used in various microelectronic applications are usually commercially produced the spin coating deposition (SCD) process. This paper reports on a comprehensive theoretical study of the fundamental physical mechanisms of polymer thin film formation onto substrates by the SCD process. A mathematical model was used to predict the film thickness and film thickness uniformity as well as the effects of rheological properties, solvent evaporation, substrate surface topography and planarization phenomena. A theoretical expression is shown to provide a universal dimensionless correlation of dry film thickness data in terms of initial viscosity, angular speed, initial volume dispensed, time and two solvent evaporation parameters. 

In the evaluation of viscosity by tilting the container, panel members indicated that their judgments were based on the rate at which each sample flowed down the side of the beaker, that is, viscosity was judged from the behavior of the apex of the film which flowed down the side of the container when it was first tilted. The major variable was the thickness of the film flowing down the side and its rate of flow, that is, viscosity evaluation by tilting the container depends on the shear rate of (10 —100 s ) developed at a shear stress (6-60 Pa) (Figure 7-4) which varies with the rheological properties of the sample. 

The coalescence process can be described by two steps. At first, there is a mutual approach of the drops which is controlled by the rheological properties of the continuous (organic) phase (see Figure 4a). Secondly, a flattening of the droplets appears by the formation of a so called "dimple" (see Figure 4b). The decrease in distance d is determined by the rate of flow out of the continuous phase between the droplets (14,15). A thin film is formed which decreases to a certain critical film thickness, dcrit at which point approach stops (16). 

Coalescence of the droplets can only happen if it is possible to break up the thin film. This occurs if surface waves are formed or if external forces are applied. At a certain point, the thickness will fall below the critical value and coalescence occurs (17, 18). The influence of this step is given by the interfacial and surface rheological properties such as interface elasticity, interface viscosity, type of surfactant, etc. (19-25). 

Five key variables influence the drum dryer performance. They are (1) steam pressure or heating medium temperature (2) speed of rotation (3) thickness of film (4) feed properties (e.g., solids concentration, rheology, temperature, etc.) and (5) method of removing dust flakes by scraper or knife. Because they allow control of the temperature, drum dryers may be used to produce a precise hydrate of a chemical compound rather than a mixture of hydrates. 

Adsorbed protein film properties thickness, rheology (viscosity, cohesiveness, elasticity), net charge and its distribution, degree of hydration... 

The surface forces apparatus (SFA) measures forces between atomically flat surfaces of mica. Mica is the only material that can be prepared with surfaces that are atomically flat across square-millimetre areas. The SFA confines liquid films of a few molecular layers thickness between two mica surfaces and then measures shear and normal forces between them (figure C2.9.3)b)). In essence, it measures the rheological properties of confined, ultra-thin fluid films. The SFA is limited to the use of mica or modified mica surfaces but can be used to study the properties of a wide range of fluids. It has provided experimental evidence for the formation oflayered structures in fluids confined between surfaces and evidence for shear-induced freezing of confined liquids at temperatures far higher than their bulk freezing temperatures [14. 15]. 

Flack and co-workers developed a complex model that included the effects of evaporation on the rheological properties of the viscous fluid. Their work established the idea that only fluid viscosity, angular speed, and evaporative effects are important in determining the final film thickness. Dispense volume, dispense rate, and other factors seem not to be particularly critical in determining the final film thickness as long as the wafer is spun for a sufficiently long time. Yet, in spite of evaporative effects, the final thickness /if of the fluid can be fairly well predicted with an inverse power law relationship [Eq. (11.13)], where C is a constant depending on the viscosity and contains the effects of viscous forces. 

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