Unswollen region

The above case of dual-sorption model can be considered a special case of what has been termed anomalous diffusion in polymers. Because organic vapors or liquids can interact strongly with a polymer and cause it to swell, an extreme case of anomalous diffusion occurs when the mass uptake (time-integrated flux) into the polymer is totally controlled by the stress gradient between the swollen and unswollen regions rather than by the concentration gradient. This was first characterized by Alfrey and coworkers [31] and referred to as case II diffusion. Fickian diffusion leads to an initial mass uptake of a polymer film or sheet exposed to a swelling solvent that follows the expression [32] ... 

Fig. 2 Left . Simulated monomer density profile (distribution of intrastar density around the center of mass) for a melt of stars of varying arm number f (from left star to right open square . 2 (linear chain), 4, 8, 16, 24, 36, 48, 64) [41]. The low intrastar density at low functionalities indicates penetrability by other stars (to satisfy incompressibility condition), whereas at high functionality the star core is formed with constant density. Inset . Cartoon illustration of a multiarm star with the three areas in different colors melt-like inner black core, theta-like intermediate blue unswollen and excluded-volume outer red swollen region. Right . The predicted Daoud-Cotton [28] monomer density distribution. The horizontal dashed line indicates the average solution concentration...

The velocity of the advancing penetrant front characterizes ease II transport. Here, the unswollen polymer lies ahead of the front, while the equilibrium swollen material exists in the region behind the front position. 

Figure 7.1.11 illustrates that both equations ([7.1.5] and [7.1.6]) apply only to the steady state diEfusion but they do not describe sorption which is the initial stage of difiu-sioa DiEfusion in unswollen and swollen regions are characteristic for two different stages, namely sorption and permeation, with the last characterized by a steady state diEfu-... 

In this model the star polymer is divided into three regions. The segment density is constant of order unity near the center further out there is a region with unswollen polymer [Eq. (9b)] and the corona is characterized by swollen arms [Eq. (7b)]. 

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