Diffusion in Polymeric Materials

For polymeric materials, our interest is often in the diffusive motion of small foreign molecules (e.g., O2, H2O, CO2, CH4) between the molecular chains rather than in the diffusive motion of chain atoms within the polymer structure. A polymer s permeability and absorption characteristics relate to the degree to which foreign substances diffuse into the material. Penetration of these foreign substances can lead to swelling and/or chemical reactions with the polymer molecules and often a degradation of the material s mechanical and physical properties (Section 17.11). 

Foreign molecule size also affects the diffusion rate smaller molecules diffuse faster than larger ones. Fmthermore, diffusion is more rapid for foreign molecules that are chemically inert than for those that interact with the polymer. 

One step in diffusion throngh a polymer membrane is the dissolution of the molecn-lar species in the membrane material. This dissolntion is a time-dependent process, and, if slower than the diffusive motion, may limit the overall rate of diffusion. Consequently, the diffusion properties of polymers are often characterized in terms of a permeability coefficient (denoted by P /), where for the case of steady-state diffnsion through a polymer membrane, Fick s first law (Equation 5.2), is modified as 

In this expression, / is the diffusion flux of gas through the membrane [(cm STP)/ (cm -s)]. Pm is the permeability coefficient. Ax is the membrane thickness, and AP is the difference in pressure of the gas across the membrane. For small molecules in nonglassy polymers the permeability coefficient can be approximated as the product of the diffusion coefficient (D) and solubility of the diffusing species in the polymer (5 ) —that is, 

For some applications, low permeability rates through polymeric materials are desirable, as with food and beverage packaging and automobile tires and inner tubes. 

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Gibson, C., Matthews, I. and Samuel, A., Microwave enhanced diffusion in polymeric materials, /. Microwave Power Electromagn. Energy, 1998, 23, 17. 

For diffusion in polymeric materials, a can be related to the polymer diffusivity of the sorbate... 

The physics of sorption and diffusion through polymeric materials in the rigid and rubbery states is discussed thoroughly in several outstanding reviews [14-18],... 

The kinetic aspects of immobilized enzymes are rather complicated. A typical situation is when the enzyme is immobilized within some polymeric material, which may be cut into slices and immersed in a suitably buffered solution of the substrate. This is the type of situation that occurs in a biological system, an example being a muscle (in which the enzyme myosin is immobilized) surrounded by a solution of the substrate ATP. For reaction to occur, the substrate has to diffuse through the polymeric material in order to reach the enzyme. Reaction then occurs and the products must diffuse out into the free solution. Since diffusion in polymeric materia occurs more slowly than in water, there is now a greater possibility of diffusion control (see p. 403) the overall rate of reaction may depend to some extent on the rates with which these diffusion processes occur. 

Let us consider a particular example of the effect of RS substances on the water resistance of adhesive-bonded joints. Adhesives based on imsaturated polyester resins, such as PN-1, are distinguished by low water resistance. The influence of water on a steel joint cemented by such an adhesive actually results in some initial increase of the specific electrical resistance along the adhesive-steel interface and then in an abrupt drop (Fig. 5.5). The increase is explained by more complete consumption of the monomer in the system. When ATG is added to the adhesive (which decreases the interphase tension) the specific electrical resistance stabilizes after a drop. The decrease seems to be related to the processes of relaxation of the internal stresses in the adhesive interlayer. The stresses facilitate the diffusion of liquids in polymeric materials, in particular the stress concentration at the polymer-metal interface. 

Diffusion of small molecules in polymeric materials is too diverse to be described by a simple relationship applicable to all of the above eases. There are several types of diffusion ... 

In order to model the transport phenomena in polymeric materials, Lefebvre et derived a nonlinear diffusion coefficient based on the concept of free volume. According to this theory, the diffusion coefficient D for a polymeric material above its glass transition temperature is given by... 

NMR imaging techniques have been used for the study of sorption, diffusion and chemical reactions as well as the desorption of chemical substances in polymeric materials [23]. NMR imaging can directly provide the diffusion coefficient as a characteristic quantity of the fluidity of a component in a sample, making it possible to map molecular migration on a microscopic scale. 

During the last decades interest in membrane separation processes and in solutions for packaging problems has given a substantial boost to research on sorption and mass transport in polymeric materials. Several interpretative models for the solubility and diffusivity in rubbery polymers are now available which, at least in principle, allow for the prediction of the permeability of low molecular weight species in polymeric films above their glass transition temperature. 

The main factors affecting small penetrants permeability in polymeric material include free volume and its distribution, " density, tanperature and pressure, crystallinity," polymer chain length, mobility and packing, solute size, and affinity for the material. In addition, computational parameters used in the simulations such as the type of force field employed and the size of the model also affect the permeability value computed. An increase in tanperature generally leads to a decrease in the solubility and conversely for the diffusion. For all three physical quantities P, S, and D, the tanperature dependence can be described by a Van t Hoff-Arrhenius equation. In particular, for the solubility... 

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