Diffusion coefficients polymers

The meaning of this term is shown by Figure 2.5 and it is essentially the time required to attain steady state flux across a barrier. When the resistance in the boundary layer is negligible, the lag-time equation provides a convenient means of calculating membrane or polymer-diffusion coefficients. 

A theoretical expression for the concentration dependence of the polymer diffusion coefficient is derived. The final result is shown to describe experimental results for polystyrene at theta conditions within experimental errors without adjustable parameters. The basic theoretical expression is applied to theta solvents and good solvents and to polymer gels and polyelectrolytes. 

Combining the above descriptions leads to a picture that describes the experimentally observed concentration dependence of the polymer diffusion coefficient. At low concentrations the decrease of the translational diffusion coefficient is due to hydrodynamic interactions that increase the friction coefficient and thereby slow down the motion of the polymer chain. At high concentrations the system becomes an entangled network. The cooperative diffusion of the chains becomes a cooperative process, and the diffusion of the chains increases with increasing polymer concentration. This description requires two different expressions in the two concentration regimes. A microscopic, hydrodynamic theory should be capable of explaining the observed behavior at all concentrations. 

We have shown that the microscopic expression for the polymer diffusion coefficient. Equation 2, is the starting point for a discussion of diffusion in a wide range of polymer systems. For the example worked out, polymer diffusion at theta conditions, the resulting expresssion describes the experimental data without adjustable parameters. It should be possible to derive expressions for diffusion... 

In their investigation of polydimethylsiloxane and polyethylene oxide) in solution with various solvents, Tanner, Liu, and Anderson40 extrapolated the observed polymer diffusion coefficients to zero polymer concentration c. They applied Flory s theory of dilute solutions 45) to the case of diffusion ... 

Figure 4.6 Hydrodynamic radius for globular proteins, dextran and DNA polymers. Diffusion coefficients were obtained as described in Table 4.2. The hydrodynamic radius was calculated for proteins (squares), DNA (circles), and dextran (triangles).

Here, Dp is the polymer diffusion coefficient. The above equation is valid in a... 

As indicated above, the permeability coefficient P combines two more fundamental parameters the diffusion and solubility coefficients. When the polymer diffusion coefficient D is independent of the permeant concentration, and the penetrant dissolves in the polymer according to Henry s law of solubility, Eqs. 11.8 and 11.7 yield the well known relationship... 

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