Self-diffusion coefficient, polymer interdiffusion

Diffusion of Water in poly[PFSA] Membranes To describe diffusion of water through the membrane in the presence of a water activity gradient, an appropriate interdiffusion coefficient must be determined. Experimental methods used to study diffusion of water in these polymers, such as radiotracer and pulsed gradient spin-echo NMR techniques, probe intrad-iffusion coefficients, often referred to as tracer or self-diffusion coefficients, determined in the absence of a chemical potential gradient. Intra- and interdiffusion coefficients are related for the case of diffusion of a small molecule in a polymeric matrix as follows [28] ... 

We conclude this section with a discussion of possible relations between interdiffusion in polymer blends and the self-diffusion coefficients of the polymer chains, which have been proposed to interpret the Gnsager coefficient A(0) in Eqs. (78), (79) or (85), respectively. According to the slow mode theory [9, 78, 191-192] the slowly diffusing component controls interdiffusion in a blend,... 

If Dp depends significantly on Cp, extrapolation to Cp 0 must be performed. The initial slope of the dependence of Dp on probe concentration, and the slope s dependence on matrix concentration, have been measured in some systems and should be accessible to theoretical analysis. In this review If the probe and matrix polymers differ appreciably in molecular weight or chemical nature, the phrase probe diffusion coefficient is applied. If the probe and matrix polymers differ primarily in that the probes are labelled, the phrase self diffusion coefficient is applied. The tracer diffusion coefficient is a single-particle diffusion coefficient, including both the self cind probe diffusion coefficients as special cases. The interdiffusion and cooperative diffusion coefficients characterize the relaxation times in a ternary system in which neither m lcrocomponent is dilute. 

De Gennes (1979) has empha.sized that, depending on the performance of an experiment, two different diffusion coefficients are observed in polymer systems, namely, the self-diffusion coefficient (Dj) and the interdiffusion one (D), the latter also called by him the cooperative diffusion coefficient (cf. subsections 2.4.3 and 3.2.1). 

The interdiffusion coefficient D is mea,sured when polymer is redistributed under a gradient of its concentration. Theoretical consideration of this process is ba.sed on the laws of unequilibriiim thermodynamics (sec subsections 2.4.3 and 3.3.1). If a labelled macro-molecule is present among their ensemble (see subsection 3.6.2) its motion is characterized by the self-diffusion coefficient (D2). Roth those quantities coincide in dilute solutions D D i Do, but the coefficient D rises with polymer concentration while D decreases significantly. 

Radioactive tracers were utilized by Bueche (1962) to measure self diSusion coefficients for polymer systems above their glass-transition temperature, Tg. Price et al. (1978) described a novel approach that used scanning electron microscopy (SEM) and dispersive energy X-ray fluorescence analysis to measure the interdiffusion (D Kh cmVsec) of compatible polymer/polymer systems. Quasi-elastic light scattering (QELS) is an unusual technique due to its ability to measure both the mutual and self diffusion coefficients. Patterson et al. (1981) and Amis s. (1983) have demonstrated the apphcahon of this technique to polymeric gels. 

The kinetics of phase separation is controlled by A/B interdiffusion. Polymer/polymer interdiffusion is an important field which has remained poorly understood for many years, and is indeed rather complicated. For the above binary mixture system, three distinct diffusion coefficients can be defined. The self-diffusion coefficients of A or B, and the mutual diffusion coefficient which all strongly depend on the respective A... 

It should be noted that the radiotracer and pulsed field gradient NMR techniques measure the self-diffusion coefficient of water, Ds, rather than the Fickian or interdiffusion coefficient of water through the polymer membrane, D, and some correction is required, because it is the Fickian water diffusion coefficient that is the proper transport property to use in macroscopic studies of water diffusion [17]. The relationship is ... 

The diffusion coefficient appearing in Eq. (20.4-3) b a true measure of the molecular mobiitty of the penetrant in question. Intuitively, the free-volume theory proponents argue that a penetram can execute a diffitsive jump when a free-volume element greater than or equal to a critical size presorts itself to a penetrant. The native poiymer, totally devoid of penetrant, still possesses a certain amount of free-volume packets of distributed size which wander spontaneously and randomly through the rubbery matrix. In fact, when a packet of sufficient size presents itself to a polymer segment, the polymer may execute a self-diffiisive motion, and this is the action that causes slow interdiffusion of polymer chains. 

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