Polystyrene diffusion coefficient

Figure 2.20 Permeant diffusion coefficient as a function of permeant molecular weight in water, natural rubber, silicone rubber and polystyrene. Diffusion coefficients of solutes in polymers usually lie between the value in natural rubber, an extremely permeable polymer, and the value in polystyrene, an extremely impermeable material [28]...

TABLE 16-8 Self Diffusion Coefficients in Polystyrene-divinylbenzene Ion Exchangers... 

The non-bonded interaction energy, the van-der-Waals and electrostatic part of the interaction Hamiltonian are best determined by parametrizing a molecular liquid that contains the same chemical groups as the polymers against the experimentally measured thermodynamical and dynamical data, e.g., enthalpy of vaporization, diffusion coefficient, or viscosity. The parameters can then be transferred to polymers, as was done in our case, for instance in polystyrene (from benzene) [19] or poly (vinyl alcohol) (from ethanol) [20,21]. 

FIQ. 3 Diffusion coefficient of benzene molecules in benzene-polystyrene mixtures normalized by the diffusion coefficient of neat benzene molecular dynamics results, NMR measurements and prediction by the Mackie-Meares model [26]. 

The resolution of infra-red densitometry (IR-D) is on the other hand more in the region of some micrometers even with the use of IR-microscopes. The interface is also viewed from the side (Fig. 4d) and the density profile is obtained mostly between deuterated and protonated polymers. The strength of specific IR-bands is monitored during a scan across the interface to yield a concentration profile of species. While in the initial experiments on polyethylene diffusion the resolution was of the order of 60 pm [69] it has been improved e.g. in polystyrene diffusion experiments [70] to 10 pm by the application of a Fourier transform-IR-microscope. This technique is nicely suited to measure profiles on a micrometer scale as well as interdiffusion coefficients of polymers but it is far from reaching molecular resolution. 

In a number of experimental studies of polymer diffusion, molar mass exponents close to 2 have been found, though always with some deviations. For example, using radio-labelled molecules, the diffusion coefficient of polystyrene in dibutyl phthalate was found to follow the relationship... 

The diffusion coefficient (D) of ferf-butyloxycarbonyl-L-phenylalanine (Boc-Phe) was determined in a Merrifield network of polystyrene (PS) gels used as a solid phase reaction field.108 When probe molecules have multicomponents in diffusion on the measurement time scale, the total echo attenuation is given by a superposition of contributions from the individual components ... 

In a study in which styrene was stripped from polystyrene, Latinen (1962) concluded that his theory correctly described the dependence of mass transfer rates on screw speed and flow rate. This conclusion was based on the agreement obtained between the measured and predicted exit concentration of styrene over a broad range of screw speeds and flow rates (Fig. 8). But, agreement between the theoretical expression and the experimental data was obtained using a diffusion coefficient of the order of 3 X 10 m sec , at 2(X)°C a value which is unrealistically high for this system. If the system ethylbenzene-polystyrene—which has a diffusion... 

Biesenberger and Kessidis were able to correlate their experimental data at atmospheric pressure in terms of N in accordance with Eq. (36) [their Eqs. (4)-(9)], but the diffusion coefficient which they computed using Eq. (36) along with the experimental data was found to be roughly D = 10 m sec" at 177°C. Again, if the ethylbenzene-polystyrene system is used as a basis for comparison, Duda et al. (1982) report a value of 3 x 10"" m /sec at 178°C, which is considerably smaller than the value obtained by Biesenberger and Kessidis (1982). In the experiments con-... 

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. 

Figure 2. Concentration dependence of the diffusion coefficient for polystyrene in two solvents at the theta point for various molecular weights. The line is the theoretical curve. (Reproduced from Ref. 12. Copyright 1983 American Chemical Society.)...

We compare our theoretical expression with the experimental ly measured values for the diffusion coefficient of polystyrene. The... 

The crossover concentration calculated for polystyrene with this expression is in the range of the reported values(12,13) Finally, the above discussion points out that c is not a sharp dividing line It is therefore not physically meaningful to scale the concentration axis in a plot of D/Dq versus concentration divided by the crossover concentration Equation 13 demonstrates that it is better to plot the relative diffusion coefficient vs the weight concentration of the polymer, as was done by Munch et al (12) ... 

The solvent mobility in atactic polystyrene-toluene solutions has been studied as a function of temperature using NMR. The local reorientation of the solvent was studied using deuterium NMR relaxation times on the deuterated solvent. Longer range motions were also probed using the pulsed-gradient spin-echo NMR method for the measurement of diffusion coefficients on the protonated solvent. The measurements were taken above and below the gel transition temperatures reported by Tan et al. (Macromolecules, 1983. 16, 28). It was found that both the relaxation time measurements and the diffusion coefficients of the solvent varied smoothly through the reported transition temperature. Consequently, it appears that in this system, the solvent dynamics are unaffected by gel formation. This result is similar to that found in other chemically crossed-linked systems. 

Lastly, Callaghan and Pinder believed to have detected cooperative diffusion in their experiment48). Their polystyrene specimen of M = 2x 10 displayed a two-component echo attenuation, interpreted in terms of two time-dependent diffusion coefficients. The more rapid component was not observable at long diffusion times, and at short diffusion time (t = 16 ms) scaled with polymer concentration (2, 4, and 8 %) in the manner... 

Calculate the diffusion coefficient K for the polystyrene standard whose relative molecular mass is 3 250 daltons. 

Homologous Polymers. As the size of a molecule increases, it is expected that its diffusion coefficient will decrease. Figure 5 shows a plot of D° vs. M for solutions of polystyrene in 2-butanone (methyl ethyl ketone) where the relationship between D° and M may be expressed by the semiempirical formula... 

Figure 5. Graph of the diffusion coefficient extrapolated to infinite dilution (D°) vs. molecular weight of polystyrene (31).

Fig. 16. Translational diffusion coefficient distributions G(D) of a simulated polymer mixture at two scattering angles ( , 17° and O , 14°). The mixture contains two polystyrene standards of distinctly different weight average molar masses (3.0 x 105 and 5.9 x 106 g/mol) and a high mass polystyrene...

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