Penetrant molecules transport

Diffusion of small molecular penetrants in polymers often assumes Fickian characteristics at temperatures above Tg of the system. As such, classical diffusion theory is sufficient for describing the mass transport, and a mutual diffusion coefficient can be determined unambiguously by sorption and permeation methods. For a penetrant molecule of a size comparable to that of the monomeric unit of a polymer, diffusion requires cooperative movement of several monomeric units. The mobility of the polymer chains thus controls the rate of diffusion, and factors affecting the chain mobility will also influence the diffusion coefficient. The key factors here are temperature and concentration. Increasing temperature enhances the Brownian motion of the polymer segments the effect is to weaken the interaction between chains and thus increase the interchain distance. A similar effect can be expected upon the addition of a small molecular penetrant. 

While to some extent the boundary between light and heavy penetrant molecules in polymers appears arbitrary, theoretical explanations of the transport behavior of the latter tend to be more complex. 

Somewhat closer to the designation of a microscopic model are those diffusion theories which model the transport processes by stochastic rate equations. In the most simple of these models an unique transition rate of penetrant molecules between smaller cells of the same energy is determined as function of gross thermodynamic properties and molecular structure characteristics of the penetrant polymer system. Unfortunately, until now the diffusion models developed on this basis also require a number of adjustable parameters without precise physical meaning. Moreover, the problem of these later models is that in order to predict the absolute value of the diffusion coefficient at least a most probable average length of the elementary diffusion jump must be known. But in the framework of this type of microscopic model, it is not possible to determine this parameter from first principles . 

Another model for the sorption and transport of gases in glassy polymers at super atmospheric pressures is the gas-polymer-matrix model, proposed by Raucher and Sefcik (1983). The premise of this model is that the penetrant molecules exist in the glassy polymer as a single population and that the observed pressure dependence of the mobility is completely due to gas-polymer interactions. In the mathematical representation of this model the following expression for sorption and transport is used ... 

The models most frequently used to describe the concentration dependence of diffusion and permeability coefficients of gases and vapors, including hydrocarbons, are transport model of dual-mode sorption (which is usually used to describe diffusion and permeation in polymer glasses) as well as its various modifications molecular models analyzing the relation of diffusion coefficients to the movement of penetrant molecules and the effect of intermolecular forces on these processes and free volume models describing the relation of diffusion coefficients and fractional free volume of the system. Molecular models and free volume models are commonly used to describe diffusion in rubbery polymers. However, some versions of these models that fall into both classification groups have been used for both mbbery and glassy polymers. These are the models by Pace-Datyner and Duda-Vrentas [7,29,30]. 

The barrier performance [4] of a polymer can be defined as its resistance to the transport of penetrant molecules, i.e., as the inverse of its permeability. A lower value of P therefore indicates better performance as a barrier material. 

The differences in the transport and solution behavior of gases in rubbery and glassy polymers are due to the fact that, as mentioned previously, the latter are not in a state of true thermodynamic equilibrium (1,3-8). Rubbery polymers have very short relaxation times and respond very rapidly to stresses that tend to change their physical conditions. Thus, a change in a temperature causes an immediate adjustment to a new equilibrium state (e.g., a new volume). A similar adjustment occurs when small penetrant molecules are absorbed by a rubbery polymer at constant temperature and pressure absorption (solution) equilibrium is very rapidly established. Furthermore, there appears to exist a unique mode of penetrant absorption and diffusion in rubbery polymers (2) ... 

A substantial number and variety of models of gas transport in polymers have been proposed during the last 20-30 years, in view of the great practical and scientific importance of this process. Molecular-type models are potentially most useful, since they relate diffusion coefficients to fundamental physicochemical properties of the polymers and penetrant molecules, in conjunction with the pertinent molecular interactions. However, the molecular models proposed up to now are overly simplified and contain one or more adjustable parameters. Phenomenological models, such as the dual-mode sorption model and some free-volume models, are very useful for the correlation and comparison of experimental data. 

Transport of Penetrant Molecules Through Copolymers of Vinylidene Chloride and... 

The study of the transport of penetrant molecules through polymers [1,2] is important in many areas of technology. There are two types of industrially important polymeric systems for which such transport phenomena are crucial ... 

Figure 1. Schematic illustration of how the results of three different types of calculations, each one providing a perspective at a different scale, can be combined synergistically, to construct a unified physical model for the transport of penetrant molecules in plastics.

A study is in progress on the transport of penetrant molecules in barrier plastics, utilizing a synergistic combination of techniques. 

The diffusant molecule from a topically applied formulation has three potential routes of entry to the subepidermal tissue (1) the transappenda-geal route, (2) the transcellular route and (3) the intercellular route (Fig. 2) [ ] Percutaneous absorption refers to the overall process of mass transport of substances applied topically and includes their transport across each layer of the skin and finally their uptake by the microcirculation of the skin. The process of percutaneous absorption can be described by a series of individual transport events occurring in sequence. First, deposition of a penetrant molecule onto the stratum corneum, then the diffusion through it and through the viable epidermis, the passage through the upper part of the papillary dermis, and finally uptake into the microcirculation for subsequent systemic distribution [1,3,4]. The viable tissue layers and the capillaries are relatively permeable, and the peripheral circulation is sufficiently rapid,... 

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