Diffusion coefficient, fixative penetration

Here (DJp is the polymer-fixed diffusion coefficient of the penetrant component (see section 1.1) and at is the activity of the penetrant in the given polymer-diluent mixture. Combining Eqs. (2) and (31) and noticing that the product c, , is equal to the volume fraction vt of the penetrant component in the mixture, one obtains... 

In the aq/polymer/org situation, the organic solvent typically penetrates the polymer causing it to swell considerably, and the situation is very similar to that of MMLLE. With a fixed composition of the membrane, the possibilities for chemical tuning (such as application of carriers) of the separation process are greatly reduced compared to SLM extraction or MMLLE. Also, as diffusion coefficients in polymers are lower than in liquids, the mass transfer is slower, leading to slower extractions. On the other hand, as the membrane is virtually insoluble, any combination of aqueous and organic liquids can be used, and the entire system becomes very stable. 

For molecular interpretation, D (also called the mutual diffusion coefficient, or diffusion coeflBcient of the penetrant and polymer relative to the local enter of volume) has to be modified to take into account the bulk flow of the penetrant. Accordingly, a new coefficient, referred to as intrinsic diffusion coefficient, has been defined in terms of the rate of mass transfer relative to the center of mass. Crank (1968) shows that for negligible polymer mobility, the intrinsic diffusivity of the penetrant (designated as Z j, which is also the diffusivity of the penetrant based on the polymer frame of reference) is related to the volume-fixed mutual diffusion coefficient, D, by... 

In principle, each of the coefficients in equation 22 can be evaluated independently by observing the effects on Da over a sufficiently wide range of temperatures, external hydrostatic pressures, and sorbed penetrant concentrations. Hydrostatic effects on p can be decoupled from penetrant sorptive effects on y by using a very low sorbing penetrant, such as helium in the presence of a fixed partial pressure of the penetrant of interest. On the one hand, hydrostatic pressure is expected to have a rather small effect on Da since solid pol5uners are only slightly compressible. On the other, increases in temperature and sorbed penetrant concentration cause large increases in the free-volume fraction Vf and in the self-diffusion coefficient Da. ... 

Membrane and Barrier Implications. In the case of typical rubbers, crankshaft and other related rotational motions of the repeat units are so large that little difference in diffusion coefficients exists for simple gaseous penetrants, the sizes of which differ by less than a few hundredths of a nanometer. Of course, since permeation is a solution-diffusion process, membranes or selective barriers do not operate strictly on the basis of size selection. Under a fixed partial pressure driving force for component i, the flux through a material of given thickness i is determined by the permeability, as can be seen by rearrangement of equation 24. 

In the original Gusev Suter TST method a frozen polymer method has been used. All polymer chains are considered fixed in place, and TST-based rate constants are calculated from the energy barriers found for a penetrant to pass from one local potential energy minimum to another. This method is the most straightforward however, in polymers it yields rate constants that lead to diffusion coefficients much lower (by factors of 10 10 ) than experimental values, because neglecting chain fluctuation contributions is physically... 

At short diffusion duration and low temperature, at which polymerization rate is low, deep permeation of the penetrating agent into the matrix and decrease of RI at the mask surface and the area below it are observed. The authors associate this fact with an increase of the diffusion coefficient with temperature up to the fixing point. As a result, the penetrating agent does not actively diffuse deep into the matrix until the sample is polymerized completely. 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

In its simplest form, the penetration ihcoty assumes that a fluid of initial composition is brought into contact with en juteiface at a fixed composition xA, for a time i. For short contact rimes the composition far from the interface (j - ) remains at Jtj. If bulk How is neglected (dilute solution or low transfer runs), solution of the unsteady-stale diffusion equation provides an expression for the average mass transfer flux and coefficient for a contact time 6. 

Although Gruber and Verboven (1999) find a significant negative correlation between mainline penetration and speed of diffusion of mobile telephone in Europe, the penetration rates with mobile and fixed-line telephones correlate within the OECD witli a correlation coefficient of r =0.55 between 1987 and 1995. 

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