Diffusion friction coefficient

Reference 115 gives the diffusion coefficient of DTAB (dodecyltrimethylammo-nium bromide) as 1.07 x 10" cm /sec. Estimate the micelle radius (use the Einstein equation relating diffusion coefficient and friction factor and the Stokes equation for the friction factor of a sphere) and compare with the value given in the reference. Estimate also the number of monomer units in the micelle. Assume 25°C. 

Silver coatings may blister above 200°C because of oxygen diffusion. A nickel undercoat stops interdiffusion with a copper substrate above 150°C. Alloying with antimony, selenium, sulphur or rhenium increases hardness—the coefficient of friction is also much reduced in the last case. ... 

Titanium Nitride. TiN is chemically stable. TiN forms an excellent diffusion barrier and has a low coefficient of friction. As such, it is well suited for reducing corrosion, erosion, and galling. It is used extensively as a coating for gear components and tube- and wire-drawing dies. 

Frictional Welding Two pieces of PMMA are to be welded frictionally. Estimate the normal pressure that has to be applied in order to raise the interface temperature from 25°C to 120°C in 1 s. The relative velocity between the sheets is 10 cm/s. The thermal conductivity of PMMA is 4.8 x 10-4 cal/cm s, the thermal diffusivity is 9 x 10 4cm2/s, and the coefficient of friction is 0.5. 

For non-spherical particles the friction coefficient, B, depends on both particle size and shape, for which reason the use of any one, either diffusional or sedimentation, method yield only some conditional particle radius corresponding to that of a spherical particle with the same sedimentation or diffusion coefficient. The values of such equivalent radii may differ, depending on which experimental method was used for their assessment. To determine the true particle size or mass, m, of non-spherical particles, and to obtain the information regarding particle shape, one must perform an independent determination of the sedimentation coefficient and friction factor... 

The planning of experiments on three-component diffusion for the determination of diffusion coefficients and frictions, in a way which makes full use of the available instrumental accuracy, is a question of considerable complexity. There are three main t5rpes of experiment to consider, viz., two components are dilute (e.g. 1 and 3), one is dilute (e.g. 2), or none is dilute. The latter requires the full equations reported above. The first case is of interest as it enables us to determine the special flow interaction between two components which arises at low concentrations of the components, and which is therefore simplest to interpret... 

Sedimentation coefficients, diffusion coefficients, and frictional ratios for polyisoprene in solution ... 

When a chain moves in a dense system (like a polymer melt), the frictional forces acting on each monomer are totally independent. Hence, the total frictional force experienced by the moving chain is simply the sum of the frictional forces on each individual monomer. How can we find these frictional forces on the monomers Let s focus on one monomer suppose it has a velocity v. This is the velocity of diffusion, so it is not too high. (To be more precise, it is of the same order as the thermal velocity of the monomer.) This gives us the right to take the force f of viscous friction to be proportional to the velocity f = —pv. Here p is the coefficient of friction for a single monomer. Since the total friction is the sum over all the monomers, the same must be true for the coefficients of friction. The... 

It is just because the motion is Brownian that (x ) is proportional to t cf. (6.2).) How does friction come into this picture Evidently, the greater the coefficient of friction /i for some particle, the lower will be the diffusion coefficient D, and vice versa. The exact relationship between the two was found in 1905 by Albert Einstein, and is called the Einstein relation. It states that... 

The diffusion coefficient D is also related to the frictional coefficient /. The frictional force increases with the velocity dr/dt of the particles the proportionality constant is the frictional coefficient fj) ... 

The Rouse model is formulated in terms of three parameters the number of beads A, the length of the Kuhn segment b, and the monomeric friction coefficient The friction coefficient can be calculated directly from the diffusion coefficient D through... 

Flow Field-Flow Fractionation This method is similar to dialysis or ultrafiltration, with the solvent acting uniformly on all the solutes. The field is generated by the flow of the solvent. The separation is mainly determined by the diffusion coefficient or frictional coefficient. The value of X is calculated using... 

Here f is the frictional coefficient and v is the velocity. The diffusion coefficient and frictional coefficient are related to kinetic energy via... 

Diffusion coefficients for cellodextrin alditols (d.p. 1—5) were found to be 22% less in 0.32M sodium hydroxide than in water. The alditols had slightly lower rates of diffusion and higher coefficients of friction and Einstein-Stokes hydrodynamic radii in water than the corresponding cellodextrins. 

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