Case II transport

The rate and type of release can be analyzed by the expression Mt/Moo=ktn (76). In the case of pure Fickian diffusion n = 0.5, whereas n > 0.5 indicates anomalous transport, i.e., in addition to diffusion another process (or processes) also occurs. If n = 1 (zero order release), transport is controlled by polymer relaxation ("Case II transport") (76). The ln(Mt/Mco) versus In t plots, shown in Figure 4, give n = 0.47 and 0.67 for samples A-9.5-49 and A-4-56, respectively. Evidently theophylline release is controlled by Fickian diffusion in the former network whereas the release is... 

IV. TRANSPORT IN SWELLABLE POLYMERS A. Swelling and Case II Transport... 

HB Hopfenberg, L Nicolais, E Drioli. Relaxation controlled (case II) transport of lower alcohols in poly(methyl methacrylate). Polymer 17 195-198, 1976. 

Case n transport is an interesting special case of sorption because the linear time dependence of the relaxation process means that a constant swelling rate could be observed [119,121,128,129,132-135], Mechanistically, case II transport... 

Kinetic effects were determined by measurements of dissolution and penetration rates. A constant penetration velocity was observed for almost all compositions for both binary solvent mixtures. In all studies, case II transport assumptions provided good agreement with experimental results. For MEK-IPA, penetration rates increased with increasing MEK concentration. For MIBK-methanol, however, a maximum penetration rate was observed at a 60 40 MIBK/methanol ratio. 

From the values of A listed in Table 4.1, only the two extreme values 0.5 and 1.0 for thin films (or slabs) have a physical meaning. When A = 0.5, pure Fickian diffusion operates and results in diffusion-controlled drug release. It should be recalled here that the derivation of the relevant (4.3) relies on short-time approximations and therefore the Fickian release is not maintained throughout the release process. When A = 1.0, zero-order kinetics (Case II transport) are justified in accord with (4.4). Finally, the intermediate values of A (cf. the inequalities in Table 4.1) indicate a combination of Fickian diffusion and Case II transport, which is usually called anomalous transport. 

Figure 4.3 Fractional drug release q(t) /qoo vs. time (arbitrary units) for Case II transport with axial and radial release from a cylinder. Comparison of the solutions presented by (4.10) with k0 = 0.01, cq = 0.5, p = 1, L = 2.5 (dashed line) and (4.12) with k = 0.052 (solid line).

When Fickian diffusion in normal Euclidean space is justified, further verification can be obtained from the analysis of 60% of the release data using the power law in accord with the values of the exponent quoted in Table 4.1. Special attention is given below for the values of b in the range 0.75-1.0, which indicate a combined release mechanism. Simulated pseudodata were used to substantiate this argument assuming that the release obeys exclusively Fickian diffusion up to time t = 90 (arbitrary units), while for I, > 90 a Case II transport starts to operate too this scenario can be modeled using... 

Also, the following equation was used to simulate concurrent release mechanisms of Fickian diffusion and Case II transport throughout the release process ... 

The nice fittings of the previous functions to the release data generated from (4.16) and (4.17), respectively, verify the argument that the power law can describe the entire set of release data following combined release mechanisms. In this context, the experimental data reported in Figures 4.8 to 4.10 and the nice fittings of the power-law equation to the entire set of these data can be reinterpreted as a combined release mechanism, i.e., Fickian diffusion and a Case II transport. 

Between these two extremes there are a series of transitions. The so-called "Case II" transport (Alfrey et al., 1966) or "partial penetrant stress controlled transport" is characterised by an activation energy, which increases with the penetrant activity. It is a highly activated process (80-200 kj/mol) and is confined to temperatures in the vicinity of and below the effective Tg of the system (dashed line in Fig. 18.13). 

In general, tte diffusivities of penetrants that swell glassy and rubbery polymers increase with concentratioiu The sorption i tterms are normally well-described by the Flory-Hug ns equaticm. Clustering of penetrant can also occur and cause deviations from this behavior In the case of as prdymers and strong swelling solvents, so-called Case II transport can occur . As drown in Fig. 6 an initial linear increase in samjde weight with time characterizes II uptake in film samples. 

Sarti, G. C. Solvent Osmotic Stresses and the Prediction of Case II Transport Kinetics, Polymer, in press... 

Case II transport occurs when the sorption is entirely controlled by stress-induced relaxations taking place at a sharp boundary separating an outer swollen shell, essentially at equihbrium penetrant concentration, from an unpenetrated glassy core. Ideally, this sharp boundary moves through the polymer at a constant velocity during case II transport. Super-case II transport occurs when the velocity of the case II sorption boundary is sufficiently slow so that a Fickian tail may develop ahead of the sorption discontinuity [63]. 

A second limiting transport process finds the weight gain of penetrant a linear function of time over the entire sorption range. This process has been termed Case II Transport, and is mechanistically quite different from Fickian diffusion. The rate controlling phenomena are penetrant induced polymeric relaxations. A combination of Case I and Case II processes has been... 

Classic Case II transport behavior finds weight gain a linear function of time (18). A constant rate of absorption will be the result of a constant rate relax-ation process if diffusion of penetrant to the relaxing boundary is rapid when compared to penetrant induced relaxations. A relation describing penetrant uptake as a function of time has been given (26) ... 

Quite interestingly, an anomalous water transport was observed for the gels which were the most highly crosslinked with the dialdehydes. Case II transport seemed even to be operating for the 25 mPa s MC gel crosslinked with glyoxal and for the 4000 mPa s MC gel crosslinked with glutaraldehyde. 

Case II Transport. At temperatures well below Tg and at penetrant activities near unity, the initial weight gain is proportional to time rather than to This is termed case II transport (9, JO). A boundary exists between swollen gel and glassy polymer, which advances at constant velocity, independent of the sample thickness. The anomaly is believed to arise because diffusion proceeds more rapidly behind the advancing boundary in the gel phase than the polymer relaxations at the boundary itself (JO). If the penetrant has a sufficiently high activity, the stresses developed at the advancing boundary may be sufficient to cause fracture or crazing of the material. 

In contrast, at temperatures below Tg, we have the so-called Case II and Super Case II transport, the other extreme, in which diffusion is very rapid compared with simultaneous relaxation processes. Sorption processes may be complicated by a strong dependence on swelling kinetics. Finally we have anomalous diffusion, which occurs when the diffusion and relaxation rates are comparable. 

Recent theoretical and experimental work has significantly advanced the understanding of Case II transport however, because of the general complexity of this work, a review of it is beyond the scope of this article. The interested reader is directed to the work of Petropoulos and co-workers (151), Wu and Peppas (152), Huang and Burning (153), and the references therein. 

Pick s first and second laws were developed to describe the diffusion process in polymers. Fickian or case I transport is obtained when the local rate of change in the concentration of a diffusing species is controlled by the rate of diffusion of the penetrant. For most purposes, diffusion in rubbery polymers typically follows Fickian law. This is because these rubbery polymers adjust very rapidly to the presence of a penetrant. Polymer segments in their glassy states are relatively immobile, and do not respond rapidly to changes in their conditions. These glassy polymers often exhibit anomalous or non-Fickian transport. When the anomalies are due to an extremely slow diffusion rate as compared to the rate of polymer relaxation, the non-Fickian behaviour is called case II transport. Case II sorption is characterized by a discontinuous boundary between the outer layers of the polymer that are at sorption equilibrium with the penetrant, and the inner layers which are unrelaxed and unswollen. 

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