Particle film thickness

FIG. 21 Cross section of sample subjected to 10-fold alternating dipping into dispersions of lb (5X) and 2 (5X). The bar indicates the average particle film thickness of 1.2 p,m. (From Ref. 93, with permission from Elsevier, Amsterdam.)... 

An important mixing operation involves bringing different molecular species together to obtain a chemical reaction. The components may be miscible liquids, immiscible liquids, solid particles and a liquid, a gas and a liquid, a gas and solid particles, or two gases. In some cases, temperature differences exist between an equipment surface and the bulk fluid, or between the suspended particles and the continuous phase fluid. The same mechanisms that enhance mass transfer by reducing the film thickness are used to promote heat transfer by increasing the temperature gradient in the film. These mechanisms are bulk flow, eddy diffusion, and molecular diffusion. The performance of equipment in which heat transfer occurs is expressed in terms of forced convective heat transfer coefficients. 

Figure 12.7 Cliromatograms of a polycarbonate sample (a) microcolumn SEC ti ace (b) capillary GC ti ace of inti oduced fractions. SEC conditions fused-silica (30 cm X 250 mm i.d.) packed with PL-GEL (50 A pore size, 5 mm particle diameter) eluent, THE at aElow rate of 2.0ml/min injection size, 200 NL UV detection at 254 nm x represents the polymer additive fraction ti ansfeired to EC system (ca. 6 p-L). GC conditions DB-1 column (15m X 0.25 mm i.d., 0.25 pm film thickness) deactivated fused-silica uncoated inlet (5 m X 0.32 mm i.d.) temperature program, 100 °C for 8 min, rising to 350 °C at a rate of 12°C/min flame ionization detection. Peak identification is as follows 1, 2,4-rert-butylphenol 2, nonylphenol isomers 3, di(4-tert-butylphenyl) carbonate 4, Tinuvin 329 5, solvent impurity 6, Ii gaphos 168 (oxidized). Reprinted with permission from Ref. (14).

Now assuming that (k ) is a constant (which, for a given solute, will be true in SEC) and a given column is considered, then the particle diameter and the film thickness are also constants. Furthermore, as the mobile phase and stationary phases are the same liquids (the stationary phase consists of the mobile phase held in the pores), then Dm = Ds. 

Typically, the arguments considered for a continuum depend on molecules being very small relative to the problem scale (i.e., the film thickness), as shown in Fig. 2(a), which implies a spatial averaging. One must choose a small region of space (the point), which contains many particles, but is still much smaller than the problem scale. If certain ratios remain constant as the region of space is reduced in size, i.e., if a limit exists, a smoothly varying continuum spatial averaged property (e.g., density) can be defined ... 

The effective viscosity is also affected by the microrotation of the rigid particles. If the gap is much larger than the molecular dimensions, the boundary walls will have little influence on the microrotation motion. This means that if the gap between the solid walls is sufficiently large, the micropolarity can be reasonably taken out of consideration without losing precision. The microrotation in thin film lubrication will result in viscosity-enhancements and consequently higher film thicknesses, which contribute to a better performance of lubrication. 

Sundararajan et al. [131] in 1999 calculated the slurry film thickness and hydrodynamic pressure in CMP by solving the Re5molds equation. The abrasive particles undergo rotational and linear motion in the shear flow. This motion of the abrasive particles enhances the dissolution rate of the surface by facilitating the liquid phase convective mass transfer of the dissolved copper species away from the wafer surface. It is proposed that the enhancement in the polish rate is directly proportional to the product of abrasive concentration and the shear stress on the wafer surface. Hence, the ratio of the polish rate with abrasive to the polish rate without abrasive can be written as... 

Metrology - The goal of most metrology machine efforts is to keep the process under control, whether it involves making measurements of physical size of individual features and film thickness, or making electriccd measurements of parametric test structures. Defects are also measured and estimated, including excess particles and misplaced features in the composite. 

Since the nuclear and electronic scattering cross sections for alpha particles are well known, the relative concentrations of the elements and their depth profiles can be easily obtained. The relative element concentrations are determined by the relative scattering intensities. The depth profile is obtained from the energy spread of the scattered particles, which lose energy before and after the nuclear collision, by inelastic scattering with electrons. The knowledge of the elements areal density and of the film thickness allows the determination of film density. 

As diffusion to the surface of a polymer is one of the limiting steps in extraction, the particle size or film thickness of a sample is also important [278,333,337-340]. With the typical diffusion coefficients of additives in polymers a particle diameter of about 0.3 mm is required for an extraction time of about 1000 s at 40 °C. An exception to this is the extraction of thin films and foams, for which the shortest dimension is small. It is not surprising that no more than 50 % of antioxidants could be extracted from PP pellets as opposed to 90 % recoveries from the same polymer extruded into film [341]. Grinding of the polymer is usually an essential step before extraction. Care should be taken to avoid loss of volatile additives owing to the heat generated in such processes. Therefore, cryogrind-ing is preferred. 

On-line SFE-SFC method development for validated quantitative analysis of PP/(Irganox 1010/1076, Tinuvin 327) has been reported [93]. SFE conditions required optimisation of extraction time and pressure, matrix type (particle or film) and matrix parameters (particle size, film thickness, sample weight). About 30% of extracts were lost during collection. Very poor recoveries (20-25 %) were reported from ground samples (particle size 100 p,m dependent recoveries of 45-70% for 30-p.m-thick films. Biicherl... 

Lateral structures were observed after 40 min of annealing, when typical spinodally decomposed structures were apparent. After 315 min the mean diameter of the dPS particles has reached the film thickness, and for larger times, two-dimensional domain growth takes place. 

It is possible to derive a simple particle dissolution model where diffu-sional film thickness is not explicitly required. However, the boundary layer concentration profile derived from this model will extend for distances which cover an order of magnitude of the initial particle radius. 

The second approach assigns thermal resistance to a gaseous boundary layer at the heat transfer surface. The enhancement of heat transfer found in fluidized beds is then attributed to the scouring action of solid particles on the gas film, decreasing the effective film thickness. The early works of Leva et al. (1949), Dow and Jacob (1951), and Levenspiel and Walton (1954) utilized this approach. Models following this approach generally attempt to correlate a heat transfer Nusselt number in terms of the fluid Prandtl number and a modified Reynolds number with either the particle diameter or the tube diameter as the characteristic length scale. Examples are ... 

In studies of steric stabilizers too little attention is generally paid to the dispersion force attractions between particles and the critical separation distance (H ) needed to keep particles from flocculating. Adsorbed steric stabilizers can provide a certain film thickness on each particle but if the separation distance between colliding particles is less than H the particles will flocculate. The calculation of H is not cr difficult and measurements to prove or disprove such calculations are not difficult either. For equal-sized spheres of substance 1 with radius or in medium 2 the Hamaker equation for the dispersion force attractive energy (Uj2i) at close approach is (7) ... 

Particle size of the micelle was determined by light scattering. Distance between the copper electrodes was maintained at 1 cm. After electrochemical deposition the electrode was removed from the cell and dried at 100° C for 10 min to remove water. Electrochemical deposition was done initially under galvanostatic conditions with the applied current density of 30 - 60 A per square foot, and then changed to potentiostatic conditions after achieving a required film thickness. 

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