Small Molecules in Polymers

Whereas equations 3 and 32 together are essentially equivalent to writing 

Fujita has proposed for diffusion a relation essentially equivalent to 

From measurements of the diffusion of radioactively tagged n-hexadecane through various polymers (above Tg) and polymer solutions, values of 

BdjB ranging from 0.6 to 1.0 have been obtained. From a more complicated analysis involving dependence on concentration as well as temperature, Fujita and Kishi-moto have found values of BdjB for many systems to be generally somewhat less than unity these studies will be described in Chapter 17. With this provision, the free-volume interpretation of temperature dependence of diffusion appears to be quite satisfactory and offers an alternative method for analyzing the rates of molecular motions. 

EXAMPLES OF MORE UMITED APPLICABILITY OF THE METHOD OF REDUCED VARIABLES 

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The diffusion of small molecules in polymers can be described using Pick s first and second laws. In a onedimensional situation, the flux J(c, x) as a function of the concentration c and the position x is given by... 

Several ideas have been put forward to calculate tire diffusion coefficient of small molecules in polymers. Glasstone et al [M] proposed an expression based on transition-state tlieory... 

Otlier expressions for tire diffusion coefficient are based on tire concept of free volume [57], i.e. tire amount of volume in tire sample tliat is not occupied by tire polymer molecules. Computer simulations have also been used to quantify tire mobility of small molecules in polymers [58]. In a first approach, tire partition functions of tire ground... 

Frisch FI L and Stern S A 1983 Diffusion of small molecules in polymers Crit. Rev. Solid State Mater. Sc/. 11 123... 

Of particular interest in the usage of polymers is the permeability of a gas, vapour or liquid through a film. Permeation is a three-part process and involves solution of small molecules in polymer, migration or diffusion through the polymer according to the concentration gradient, and emergence of the small particle at the outer surface. Hence permeability is the product of solubility and diffusion and it is possible to write, where the solubility obeys Henry s law,... 

Sax, J.E. "Transport of Small Molecules in Polymer Blends Transport-Morphology Relationships" University Microfilms Inter-national Ann Arbor, 1985. 

Another semi-empirical diffusion model has been developed (Limm and Hollifield, 1995b) which is based on the simplification of existing diffusion theories by Pace and Datyner (1979) and the generalized trend found by Berens and Hopfenberg (1982) for the diffusion of small molecules in polymers (Chapter 5). From these studies it is possible to arrive at the following relationship ... 

Wilkens, J. B., and F. A. Long A free-volume model for diffusion of small molecules in polymers. Trans. Faraday Soc. 53, 1146 (1957). 

These equations describe the coupled phenomena between diffusion and viscous stresses, existing, for example, in diffusion of small molecules in polymer matrix. Other possible couplings occur in shear-induced diffusion and shear-induced separation. 

Gusev, A.A. and Suter, U.W. Dynamics of small molecules in polymers subject to thermal motion, /. Chem. Phys., 99, 2228, 1993. 

Pace and Datyner ( 5, 5) have also proposed a model for the absorption (solution) of small molecules in polymers applicable at temperatures above and below Tg, which incorporates the dual-mode sorption model for the glassy region. The presence of microvoids is assumed for rubbery polymers as well as for polymer glasses. "Hole filling" is suggested as an important sorption mode above as well as below Tg, with one crucial difference between the sorption mechanism in the rubbery and glassy regions hole saturation does not occur in the rubbery state because new microvoids are formed to replace those filled with penetrant molecules. 

The purpose of this chapter is to outline some of the basic Issues and principles that pertain to the transport of small molecules in polymers and to introduce a few examples in which transport properties of polymers may be important or lead to new uses for polymers. 

Mechanical Release of Small Molecules in Polymer Matrices. 228... 

The factors, which influence the permeability or mass transport, are the following chemical composition of the polymer matrix and its free volume. In fact, crystallinity, molecular orientation, and physical aging in turn influence the free volume of a polymer matrix. In addition, porosity and voids, like free volume, offer sites into which molecules can absorb and are far less of a barrier to transport than solid polymer. Temperature also affects permeability and diffusion properties of small molecules in polymers. With increased temperature, the mobility of molecular chains (in polymer) increases and thermal expansion leads to reduced density therefore, the free volume in the system will increase. External tensile stress applied is expected to increase free volume and open up internal voids or crazes, providing additional sites into which molecules can absorb. Of course, there may be unquantified internal residual stresses, arising from processing, present in the polymers. It is well established that the properties of materials... 

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