Polymer self-diffusion coefficient

Previously, the assumption has been made that the polymer self-diffusion coefficient is proportional to l/f21. The assumptions involved in the derivation of this relationship have been shown experimentally to be invalid 8). 

The power law exponent, n, is unity for a Newtonian fluid and less than unity for a shear-thinning fluid. One of the central questions of polymer physics concerns the molecular basis for the constitutive equations. Because NMR is so sensitive to molecular dynamical parameters, the simultaneous mapping of velocity profiles and molecular properties such as the polymer self-diffusion coefficient by means of the dynamic NMR microscopy technique offers an effective test of much molecular models. 

Combination of equations 18 and 19 and use of the definition of mobility leads to the following expression for the polymer self-diffusion coefficient, when... 

Figures 8 and 9 show applications of NMR microscopy in the rheological investigation of complex viscoelastic fluids. In Figure 8 comparative velocity and diffusion profiles are shown across the diameter of a 700 p,m diameter capillary though which is pumped a solution of high-molecular-mass polymer undergoing laminar flow. The velocity profile is distinctly non-Poiseuille, consistent with shear thinning, while the polymer self-diffusion coefficients exhibit a dramatic enhancement once the shear rate (the velocity gradient) exceeds a characteristic value. This value corresponds to the slowest relaxation rate of the molecule where rj is the so-...

Hydrodynamic scaling model for self-diffusion and viscosity As shown in Chapter 8 on polymer self-diffusion, the concentration dependence of the polymer self-diffusion coefficient Ds is uniformly given by... 

S. C. Merriam and G. D. J. Phillies. Fourth-order hydrodynamic contribution to the polymer self-diffusion coefficient. J. Polym. Sci. B, 42 (2004), 1663-1670. 

Table 5, Average polymer chain concentration (ape), polymer swellability (S), rotational correlation times of TEMPONE (r) and self-diffusion coefficient of methanol (Zf) in the swollen 2,2% Pd catalysts.

In general, mass transfer processes involving polymer-penetrant mixtures are generally analyzed by using a mutual diffusion coefficient. Therefore, a relationship between the mutual diffusion coefficient, D, and self-diffusion coefficients, ZVs is needed. Vrentas et al. [30] proposed an equation relating D to D, for polymer-penetrant systems in which Dx is much larger than Dr. 

Here ZT is calculated from the self-diffusion coefficients of the polymer-penetrant pair, i.e.,... 

CW Paul. A model for predicting solvent self-diffusion coefficients in nonglassy polymer/solvent solutions. J Polym Sci, Polym Phys Ed 21 425-439, 1983. 

Water self-diffusion coefficients (Dh o) have been determined by pulse field gradient NMR for Nation (Nil/) , BPSH, and SPEEKK and have been shown to increase with increasing acid and water content. At high water contents, the values for PEMs approach the corresponding value for pure water. This is due to the increase in volume fraction of free water. At low water content, however. Nation exhibits greater Dnp values than either BPSH or SPEEKK. In corranon with the observations for EOD, this has been attributed to the smaller channels in aromatic-based polymers, leading to a considerably lower dielectric constant for the water in the channels. 

For comparison purposes, the proton mobility. Do (for Nafion solvated with water), which is closely related to the self-diffusion coefficient of water, is also plotted. At low degrees of hydration, where only hydrated protons (e.g., H3O+) are mobile, it has a tendency to fall below the water diffusion coefficient (this effect is even more pronounced in other polymers), which may be due to the stiffening of the water structure within the regions that contain excess protons, as discussed in Section 3.1.1. . Interestingly, the proton mobility in Nafion solvated with methanol (Da(MeOH) in Figure 14a) is even lower than the methanol self-diffusion (Z ieon). This may... 

The dynamic behavior of liquid-crystalline polymers in concentrated solution is strongly affected by the collision of polymer chains. We treat the interchain collision effect by modelling the stiff polymer chain by what we refer to as the fuzzy cylinder [19]. This model allows the translational and rotational (self-)diffusion coefficients as well as the stress of the solution to be formulated without resort to the hypothetical tube model (Sect. 6). The results of formulation are compared with experimental data in Sects. 7-9. 

Bueche et al. (33) determined chain dimensions indirectly, through measurements of the diffusion coefficient of C1 Magged polymers in concentrated solutions and melts.The self-diffusion coefficient is related to the molar frictional coefficient JVa 0 through the Einstein equation ... 

To dearly distinguish between these two modes of solvent penetration of the gel, we immersed poly(acrylamide-co-sodium methacrylate) gels swollen with water and equilibrated with either pH 4.0 HQ or pH 9.2 NaOH solution into limited volumes of solutions of 10 wt % deuterium oxide (DzO) in water at the same pHs. By measuring the decline in density of the solution with time using a densitometer, we extracted the diffusion coefficient of D20 into the gel using a least squares curve fit of the exact solution for this diffusion problem to the data [121,149]. The curve fit in each case was excellent, and the diffusion coefficients obtained were 2.3 x 10 5cm2/s into the ionized pH 9.2 gel and 2.4 x 10 5 cm2/s into the nonionized pH 4.0 gel. These compare favorably with the self diffusion coefficient of D20, which is 2.6 x 10 5 cm2/s, since the presence of the polymer can be expected to reduce the diffusion coefficient about 10% in these cases [150], In short, these experiments show that individual solvent molecules can rapidly redistribute between the solution and the gel by a Fickian diffusion process with diffusion coefficients slightly less than in the free solution. 

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