A time lag method is described for use with a membrane-covered, rotated disc electrode that allows determination of the partitioning and diffusivity of small molecules in hydrophilic gel membranes Polymeric membranes have found many applications in biomedical and industrial technology. Many separation processes such as reverse osmosis, hemodialysis, filtration, and blood oxygenation are based on membranes. There is a need to accurately characterize the transport of solutes in these membranes as a basis for design of more effective processes. If the membrane can be approximated as a homogeneous phase containing a linear distribution of solute, a parameter that describes diffusive transport of the solute within the membrane is membrane permeability, P,, given by:where a is the partition coefficient, D,, is the diffusion coefficient for the solute within the membrane, and 6, is the membrane thickness.In this formulation, membrane permeability depends on the product of two physical parameters, a and D,, which must be measured independently and represent different mechanisms of transport control by the membrane. Thc partition cocfficicnt is the equilibrium ratio of solute concentration in the membrane to that in the external phase, and can have an effect even in the absence of net transport through the membrane. The partitioning effect can be dominant where processes occur in the membrane that are a function of the local concentration, such as absorption or chemical reaction of the solute in immobilized enzyme systems (Filippusson and Hornby, 1970;Engasser and Horvath, 1976). Conversely, the diffusion coefficient is a measure of the resistance to transport through the membrane once the solute has already entered and exited the membrane phase. If instantaneous equilibria across the membrane-solution interface can be assumed, D , alone is the important transport parameter in the decay of transient phenomena in the membrane. Therefore, complete characterization, that could facilitate the design of new membranes, requires direct measurement of either Lyor
CUD,6, P, = -D, in addition to P, and 6,.Accurate meaurement of the diffusion coefficient of small molecules within the membrane is complicated by transport in the layers of solution on either side of the membrane. In early studies, attempts were made to eliminate these concentration boundary layers by intensive stirring. However, it is now thought that complete elimination is impossible and that the effects of the solution layers must be taken into account (Smith et al., 1968; M a h e and Anderson, 1977). A quantitative measure of the significance of the solution boundary layer effects in the measurement of membrane permeability is the mass transfer Biot number (Eckert and Drake, 1972): Bi = P,/P, where P, is the permeability o r mass transfer coefficient for the solution layer. For a membrane with gas phases on either side the Biot number is very large and hence boundary layer effects are negligible. However, for membranes in contact with liquid phases, the Biot num...