Diffusion and Barrier Properties

The (Fickian) diffusion coefficient of a chemical within a polymer is governed by two sets of properties. The first comes from the polymer itself its free volume and its ability to undergo main-chain segmental motion. The second comes from the chemical its molecular size, its degree of branching, and its general stiffness. The compatibilities of polymer/ chemical are not, surprisingly, reflected directly in the diffusion constant. 

So for PLA, the single largest factor governing the rate of diffusion should be the degree of crystallinity the higher it is, the slower the diffusion. The should be is there because there is evident surprise in a number of papers that the degree of crystallinity seems to make little or no difference in diffusivity of chemical compounds [41]. 

A chemist can evaluate two molecules and make estimates of their relative diffusion constants. The linear 1-hexanone, for example, will diffuse relatively quickly, whereas the relatively rigid chair conformation of cyclohexanone makes it notoriously slow to diffuse out of the many polymers for which it is a good solvent. Similarly, 1-butanol will diffuse 

But we aU know that chemical compatibility plays a significant role in diffusion and barrier properties. Although the above analysis is correct about diffusion constants, diffusion requires a concentration gradient to drive it. If the chemical and PLA are not compatible, then the concentration of the chemical in the surface layer of the polymer will be low and so will be the rate of diffusion. So, solubility (and therefore solubility parameters) is very important. For the packaging industry in particular, the permeabiUty is the most used measure and this neatly combines both issues because permeability = diffiisivity x solubility in the large number of cases where Fickian diffusion is the governing phenomenon. 

The other key factor is that when a compatible chemical is present, it plasticizes the polymer and allows more main-chain segmental motion. So, there can be a large (orders of magnitude) increase in diffusion coefficient as the chemical diffuses into the polymer. If the chemical is sufficiently compatible to disrupt the crystalline (essentially impenetrable) domains, then the increase in rate of diffusion can be dramatic. 

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The aim of this section is to give a broad overview of the polymers that have been commonly used in controlled delivery by the oral route but not to develop the rationale underlying the formulation of these types of systems. The development of matrix or reservoir systems is based on the properties of the materials themselves, e.g. their swelling, diffusion and barrier properties, and suitable polymers must be chosen for the specific properties of the materials they form, e.g. tablets, microgranules and films, in the presence of physiological fluids. Commonly used polymers in this area are presented according to this classification. 

Skin. The skin s unique molecular transport and barrier properties pose a challenge for transdermal dmg dehvery. Diffusion of dmgs through the stratum corneum, the outer layer primarily responsible for the skin s limited permeabUity, varies by dmg, by skin site, and among individuals. Until recently, virtuaUy aU dmgs appHed to skin were topical treatments. 

Figure 9 displays the probability distribution function (p r) and the effectiveness factor r] k), which have been calculated via Eqs. 36 and 34 from the tracer exchange curves in the limiting cases of single-hle diffusion, normal diffusion and barrier confinement. The fact that in all cases the residence time distribution function is found to decrease monotonically may be easily rationalized as a quite general property. Due to the assumed stationarity of the residence time distribution function, the number of molecules with a residence time r is clearly the same at any instant of time. The number of molecules with a residence time r + At may therefore be considered as the number of molecules with a residence time r minus the number of molecules which will leave the system in the subsequent time interval At. Therefore, (p x) must quite generally be a monotonically decaying function. 

In practice, intercalation is relatively easy to achieve, while something close to true exfoliation is much more difficult. It is worth noting that enhancement of properties may be seen in both cases. While mechanical properties are most improved through exfoliation, improved thermal, fire, and barrier properties and decreased thermal expansion coefficients may be expected without complete exfoliation based solely on arguments of silicate layer properties and increased tortuosity with respect to the path of diffusing species. 

To prevent or reduce diffusion, a barrier is placed between the two materials. The ideal barrier material must not react with the materials it separates and have suitable electrical and thermal properties. Many designs call for the barrier to be deposited with constant thickness inside very narrow (0.35 im) and deep holes (aspect ratio of 2 to 1 or more). 

One of the key parameters for correlating molecular structure and chemical properties with bioavailability has been transcorneal flux or, alternatively, the corneal permeability coefficient. The epithelium has been modeled as a lipid barrier (possibly with a limited number of aqueous pores that, for this physical model, serve as the equivalent of the extracellular space in a more physiological description) and the stroma as an aqueous barrier (Fig. 11). The endothelium is very thin and porous compared with the epithelium [189] and often has been ignored in the analysis, although mathematically it can be included as part of the lipid barrier. Diffusion through bilayer membranes of various structures has been modeled for some time [202] and adapted to ophthalmic applications more recently [203,204]. For a series of molecules of similar size, it was shown that the permeability increases with octa-nol/water distribution (or partition) coefficient until a plateau is reached. Modeling of this type of data has led to the earlier statement that drugs need to be both... 

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