Diffusion, rate

The simulation of molecules in solution can be broken down into two categories. The first is a list of elfects that are not defined for a single molecule, such as diffusion rates. These types of effects require modeling the bulk liquid as discussed in Chapters 7 and 39. The other type of effect is a solvation effect, which is a change in the molecular behavior due to the presence of a solvent. This chapter addresses this second type of effect. 

Amberlite IRA-402 1.3 1.07 Lower cross-linkage than IRA-400 better diffusion rate with large organic molecules. 

Column Si. Size-exclusion chromatography columns are generally the largest column on a process scale. Separation is based strictly on diffusion rates of the molecules inside the gel particles. No proteins or other solutes are adsorbed or otherwise retained owing to adsorption, thus, significant dilution of the sample of volume can occur, particularly for small sample volumes. The volumetric capacity of this type of chromatography is determined by the concentration of the proteins for a given volume of the feed placed on the column. 

Rate equations 28 and 30 combine the advantages of concentration-independent mass transfer coefficients, even in situations of multicomponent diffusion, and a familiar mathematical form involving concentration driving forces. The main inconvenience is the use of an effective diffusivity which may itself depend somewhat on the mixture composition and in certain cases even on the diffusion rates. This advantage can be eliminated by working with a different form of the MaxweU-Stefan equation (30—32). One thus obtains a set of rate equations of an unconventional form having concentration-independent mass transfer coefficients that are defined for each binary pair directiy based on the MaxweU-Stefan diffusivities. 

Crimp. The tow is usually relaxed at this point. Relaxation is essential because it gready reduces the tendency for fibrillation and increases the dimensional stabiUty of the fiber. Relaxation also increases fiber elongation and improves dye diffusion rates. This relaxation can be done in-line on Superba equipment or in batches in an autoclave. Generally saturated steam is used because the moisture reduces the process temperatures required. Fiber shrinkage during relaxation ranges from 10 to 40% depending on the temperature used, the polymer composition used for the fiber, and the amount of prior orientation and relaxation. The amount of relaxation is also tailored to the intended apphcation of the fiber product. 

The result is the formation of a dense and uniform metal oxide layer in which the deposition rate is controlled by the diffusion rate of ionic species and the concentration of electronic charge carriers. This procedure is used to fabricate the thin layer of soHd electrolyte (yttria-stabilized 2irconia) and the interconnection (Mg-doped lanthanum chromite). 

Adsorption systems employing molecular sieves are available for feed gases having low acid gas concentrations. Another option is based on the use of polymeric, semipermeable membranes which rely on the higher solubiHties and diffusion rates of carbon dioxide and hydrogen sulfide in the polymeric material relative to methane for membrane selectivity and separation of the various constituents. Membrane units have been designed that are effective at small and medium flow rates for the bulk removal of carbon dioxide. 

The only metals having good or excellent resistance to corrosion by amalgamation with mercury are vanadium, iron, niobium, molybdenum, cesium, tantalum, and tungsten (8). The diffusion rates of some metals in mercury are given in Table 5. 

Metal CAS Registry Number Diffusion rate, cm /s X 10 Metal CAS Registry Number Diffusion rate, cm /s X 10 ... 

Bulk Polymerization. This is the method of choice for the manufacture of poly(methyl methacrylate) sheets, rods, and tubes, and molding and extmsion compounds. In methyl methacrylate bulk polymerization, an auto acceleration is observed beginning at 20—50% conversion. At this point, there is also a corresponding increase in the molecular weight of the polymer formed. This acceleration, which continues up to high conversion, is known as the Trommsdorff effect, and is attributed to the increase in viscosity of the mixture to such an extent that the diffusion rate, and therefore the termination reaction of the growing radicals, is reduced. This reduced termination rate ultimately results in a polymerization rate that is limited only by the diffusion rate of the monomer. Detailed kinetic data on the bulk polymerization of methyl methacrylate can be found in Reference 42. 

Cementation coatings rely on diffusion to develop the desired surface aUoy layer. Not only does the coating continue to diffuse into the substrate during service, thereby depleting the surface coating, but often the substrate material diffuses into the surface where it can be oxidized. Because the diffusion rate is temperature dependent, this may occur slowly at lower service temperatures. 

Wire cords are particularly subject to degradation of their adhesion values by moisture. To combat this, halogenated butyl (HIIR) is used in tire innerliners because of its property of low air and water vapor diffusion rates. Moisture is present in most air pumps and many tires are mounted with water left in the tire on mounting. For these reasons tires and tire compounds are tested extensively at simulated aging conditions in the laboratory and on test vehicles before they are sold to the customer. 

Processing variables that affect the properties of the thermal CVD material include the precursor vapors being used, substrate temperature, precursor vapor temperature gradient above substrate, gas flow pattern and velocity, gas composition and pressure, vapor saturation above substrate, diffusion rate through the boundary layer, substrate material, and impurities in the gases. Eor PECVD, plasma uniformity, plasma properties such as ion and electron temperature and densities, and concurrent energetic particle bombardment during deposition are also important. 

The degree to which inhaled gases, vapors, and particulates are absorbed, and hence their potential to produce systemic toxicity, depends on their solubihty in tissue fluids, any metaboHsm by lung tissue, diffusion rates, and equiUbrium state. 

Drying of the poly(vinyl alcohol) is critical to both the color and solubiHty of the final product. Excessive drying temperatures result in high product color and an increase in the crystallinity, which in turn reduces the solubiHty of the product. Drying is initially subjected to a flash regime, where the solvent not contained within the particles is flashed off. This first phase is foUowed by a period where the rate is controUed by the diffusion rate of solvent from the poly(vinyl alcohol) particles. Because the diffusion rate falls as the material dries, complete drying is not practical. The polymer is therefore generally sold at a specification of 95% soHds. 

In plasticized PVC, Hquid plasticizers first fill the voids or pores in the PVC grains fairly rapidly during powder mixing. If a large amount of plasticizer is added, the excess plasticizer beyond the capacity of the pores initially remains on the surface of the grains, making the powder somewhat wet and sticky. Continued heating increases the diffusion rate of plasticizer into the PVC mass where the excess Hquid is eventually absorbed and the powder dries. 

Film thickness is an important factor iu solvent loss and film formation. In the first stage of solvent evaporation, the rate of solvent loss depends on the first power of film thickness. However, iu the second stage when the solvent loss is diffusion rate controlled, it depends on the square of the film thickness. Although thin films lose solvent more rapidly than thick films, if the T of the dryiug film iucreases to ambient temperature duriug the evaporation of the solvent, then, even iu thin films, solvent loss is extremely slow. Models have been developed that predict the rate of solvent loss from films as functions of the evaporation rate, thickness, temperature, and concentration of solvent iu the film (9). 

However, this difference would not seem to be large enough to account for the very large differences in solvent losses that have been reported. Another factor may be that high solids coatings may reach a stage where solvent loss is controUed by diffusion rate much eadier than is the case in low solids coatings (8,43). 

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