Self-and tracer diffusion

Comparison is primarily made with a stretched-exponential concentration dependence 

Some studies report the effect on the concentration dependence of varying M or P. In these systems, Ds for multiple matrix and probe molecular weights was also compared with 

Section 8.2 presents an analysis of measurements of the true self-diffusion coefficient, which refers to systems in which the molecular weights and chemical compositions of the probe and matrix chains are the same. Section 8.3 presents the more complex analysis required for systems in which the probe and matrix chains are chemically distinct in composition or molecular weight. Section 8.4 discusses significant experiments that do not match the foci of the prior sections. Finally, Section 8.5 considers some unifying features of single-chain diffusion. 

This section presents measurements of the self-diffusion coefficient, which describes the motion of a labeled chain through a solution of otherwise identical albeit unlabeled chains. This section emphasizes the concentration dependence of Ds observed at fixed polymer M. Forms unifying the c and M dependences of Ds, e.g., Eq. 8.2, are tested later. 

Values of Ds c) of polystyrenes in CCI4 and CeDe were obtained by Callaghan and Pinder(4, 5, 6). Results extend deep into the dilute regime in CCI4 but not CeDg solutions. Polymer molecular weight distributions were narrow  

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Theory for the self- and tracer-diffusion of a diblock copolymer in a weakly ordered lamellar phase was developed by Fredrickson and Milner (1990). They modelled the interactions between the matrix chains and a labelled tracer molecule as a static, sinusoidal, chemical potential field and considered the Brownian dynamics of the tracer for small-amplitude fields. For a macroscopically-oriented lamellar phase, they were able to account for the anisotropy of the tracer diffusion observed experimentally. The diffusion parallel and perpendicular to the lamellae was found to be sensitive to the mechanism assumed for the Brownian dynamics of the tracer. If the tracer has sufficiently low molecular weight to be unentangled with the matrix, then its motion can be described by a Rouse model, with an added term representing the periodic potential (Fredrickson and Bates 1996) (see Fig. 2.50). In this case, motion parallel to the lamellae does not change the potential on the chains, and Dy is unaffected by... 

G. Szamel and K. S. Schweizer, Reptation as a dynamic mean field theory -self and tracer diffusion in a simple model of rodlike polymers, J. Chem. Phys., 100 (1994) 3127-3141. 

Dynamical aspects of Q2D suspensions of spherical colloids and asymmetric colloid mixtures with long-range repulsive forces have been investigated by Brownian dynamics simulations [193-195]. These works emphasize dynamic scaling and the importance of hydrodynamic interactions on self- and tracer diffusion. 

Figure 8.30 Nemoto, et al. s measurements of self- and tracer diffusion of photo-labeled polystyrene through unlabeled 40 wt% polystyrene dibutylphthalate(48). Systems with ( ) F M are connected by a dashed line. Dg for systems with (O) M/P > 5 and ( ) self-diffusion measurements follow the solid lines.

The objective here is to identify features characteristic of single-chain diffusion by an ideal polymer in solution, following which it becomes possible to identify specific chemical effects in particular series of measurements. As discussed below first, the functional forms of the concentration and molecular weight dependences of the self- and tracer diffusion coefficients are found. Second, having found that Ds almost always follows a particular functional form, correlations of the function s phenomenological parameters with other polymer properties are examined. Third, for papers in which diffusion coefficients were reported for a series of homologous polymers, a joint function of matrix concentration and matrix and probe molecular weights is found to describe Ds. Fourth, a few exceptional cases are considered. These cases show that power-law behavior can be identified when it is actually present. Finally, correlations between Ds, rj, and Cp are noted. In more detail ... 

This chapter examines the diffusion of mesoscopic rigid probe particles through polymer solutions. These measurements form a valuable complement to studies of polymer self- and tracer diffusion, and to studies of self- and tracer diffusion in colloid suspensions. Any properties that are common to probe diffusion and polymer self-diffusion cannot arise from the flexibility of the polymer probes or from their ability to be interpenetrated by neighboring matrix chains. Any properties that are common to probe diffusion and to colloid diffusion cannot arise from the flexibility of the matrix polymers or from the ability of matrix chains to interpenetrate each other. Conversely, phenomena that require that the probe and matrix macromolecules be able to change shape or to interpenetrate each other will reveal themselves in the differences between probe diffusion, single-chain diffusion, and colloid single-particle diffusion. 

Chapter 2 introduced an experimental motif to be seen repeatedly in later chapters, notably those on dielectric relaxation, self- and tracer diffusion, colloidal properties, and probe diffusion. Given that one has a molecule whose position or... 

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