Polymer diffusion coefficient coefficients

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... 

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... 

Assuming that Eq. (2.67) applies to small molecules in the limit as n 1, calculate To, using D = 3 X 10" m sec" for a typical low molecular weight molecule. Use this value of Tq to estimate t for a polymer with n = 10. Based on Eq. (2.63), evaluate diffusion coefficient for bulk... 

Note that the diffusion coefficient for a polymer through an environment of low molecular weight molecules is typically on the order of magnitude of 10"" m" sec". If the first subscript indicates the diffusing species, and the second the surrounding molecules, and P stands for polymer and S for small molecules, we see that the order of diffusion coefficients is Ds g > Dp g > Dp P sequence which makes sense in terms of relative frictional resistance. 

At first glance, the contents of Chap. 9 read like a catchall for unrelated topics. In it we examine the intrinsic viscosity of polymer solutions, the diffusion coefficient, the sedimentation coefficient, sedimentation equilibrium, and gel permeation chromatography. While all of these techniques can be related in one way or another to the molecular weight of the polymer, the more fundamental unifying principle which connects these topics is their common dependence on the spatial extension of the molecules. The radius of gyration is the parameter of interest in this context, and the intrinsic viscosity in particular can be interpreted to give a value for this important quantity. The experimental techniques discussed in Chap. 9 have been used extensively in the study of biopolymers. 

The effect of copolymer composition on gas permeability is shown in Table 9. The inherent barrier in VDC copolymers can best be exploited by using films containing Htde or no plasticizers and as much VDC as possible. However, the permeabiUty of even completely amorphous copolymers, for example, 60% VDC—40% AN or 50% VDC—50% VC, is low compared to that of other polymers. The primary reason is that diffusion coefficients of molecules in VDC copolymers are very low. This factor, together with the low solubiUty of many gases in VDC copolymers and the high crystallinity, results in very low permeabiUty. PermeabiUty is affected by the kind and amounts of comonomer as well as crystallinity. A change from PVDC to 50 wt °/ VC or 40 wt % AN increases permeabiUty 10-fold, but has Httle effect on the solubiUty coefficient. 

Table 11. Diffusion Coefficients and Solubility Coefficients of Selected Penetrants in Polymers at 25°C ...

Humidity does not affect the permeabihty, diffusion coefficient, or solubihty coefficient of flavor/aroma compounds in vinyhdene chloride copolymer films. Studies based on /n j -2-hexenal and D-limonene from 0 to 100% rh showed no difference in these transport properties (97,98). The permeabihties and diffusion coefficients of /n j -2-hexenal in two barrier polymers are compared in Table 12. Humidity does not affect the vinyhdene chloride copolymer. In contrast, transport in an EVOH film is strongly plasticized by humidity. 

The diffusion coefficient, sometimes called the diffusivity, is the kinetic term that describes the speed of movement. The solubiHty coefficient, which should not be called the solubiHty, is the thermodynamic term that describes the amount of permeant that will dissolve ia the polymer. The solubiHty coefficient is a reciprocal Henry s Law coefficient as shown ia equation 3. 

The permeation of flavor, aroma, and solvent molecules in polymers follows the same physics as the permeation of small molecules. However, there are two significant differences. For these larger molecules, the diffusion coefficients are much lower and the solubihty coefficients are much higher. This means... 

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