Polystyrene self-diffusion coefficient

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

The (idealized) radius of a polystyrene styrene sulfonate may be several hundred angstroms. Were you to measure the self-diffusion coefficient, what equation would you use to obtain a measure of the ion s size Explain the principles (showing appropriate equations) of obtaining an individual ionic entropy and an individual ionic entropy of hydration. 

Figure 10. Logarithm of self-diffusion coefficient vs. polymer-fraction function for 1200-EW perfluorosulfonate polymer, at 25°C. Na and Cs" lines without data points polystyrene sulfonate behavior. (Refs. 163 and 207 reprinted by permission of the publisher. The Electrochemical Society, Inc.)...

It is possible that the lower than required values of D2 reflect a problem with incorrect values of Q, which if too large would result in smaller values of D2. In an interferometric study of the diffusion of toluene in an uncrosslinked natural rubber sample, Mozisek (15) reported results for the mutual diffusion coefficient which were similar to the results of Hayes and Park. In the absence of thermodynamic data from Mozisek s work, correction factors calculated for the present work were applied to his data. The results are shown in Figure 7, which reproduces Mozisek s data along with the values for D2. The extrapolated value at 1, would exceed the self diffusion coefficient for toluene by about two orders of magnitude, similar to the discrepancy seen with Hayes and Park s data. This indicates that the fault with the results in the present case is not due to overly high values of the correction factors. Moreover, the method of calculating D from D12 has been confirmed experimentally by Duda and Vrentas (16) in a comparison of vapor sorption results for toluene diffusion in molten polystyrene with the values of D1 obtained directly using radio-labeled toluene. 

The self-diffusion coefficients of toluene in polystyrene gels are approximately the same as in solutions of the same volume fraction lymer, according to pulsed field gradient NMR experiments (2fl). Toluene in a 10% cross-linked polystyrene swollen to 0.55 volume fraction polymer has a self-diffusion coefficient about 0.08 times that of bulk liquid toluene. Rates of rotational diffusion (molecular Brownian motion) determined from NMR spin-lattice relaxation times of toluene in 2% cross-linked ((polystytyl)methyl)tri-/t-butylphosphonium ion phase transfer catalysts arc reduced by factors of 3 to 20 compai with bulk liquid toluene (21). Rates of rotational diffusion of a soluble nitroxide in polystyrene gels, determined from ESR linewidths, decrease as the degree of swelling of the polymer decreases (321. 

Figure 7.1.4. Mutual and self-diffusion coefficients for polystyrene/toluene system at 110 C. [Adapted, by permission, from F D Blum, S Pickup, R A Waggoner, Polym. Prep., 31 (1), 125-6 (1990).]...

Figure 7.1.4 shows the effect of concentration of polystyrene on mutual and self-diffusion coefficients measured by pulsed-gradient spin-echo NMR. The data show that the two coefficients approach each other at high concentrations of polymer as predicted by theory. ... 

Figure 7.1.9. Self-diffusion coefficient vs. polystyrene concentration. [Adapted, by permission, om L Meistermann, M Duval, B Tinland, Polym. Bull., 39, No.l, 101-8(1997).]...

Fig. 13. Concentration dependence of the self-diffusion coefficient and the thermodynamic factor Q for the toluene-polystyrene system at 110°C and for the o-xylene-polyethylene system at 150°C. Q = (l a>A)(d In a /d In coa- From Ref. 45.

Measurement of the Center-of-Mass Diffusion Coefficient The center-of-mass diffusion coefficient Dq we obtained here is the self-diffusion coefficient Dj. DLS cannot measure the self-diffusion coefficient. It is necessary to use more specialized techniques such as FRS, FRAP, and PFG-NMR, described in Section 3.2.11. Figures 4.39 and 4.40 show examples of FRS studies of D for dye-labeled polystyrene in benzene. ... 

Figure 4.40. Self-diffusion coefficient of dye-labeled polystyrene of different molecular weights in benzene, plotted as a function of the polymer mass fraction. The lines have a...

Figure 33.12 Self-diffusion coefficient D of seven different types of polymers (polystyrene, poly(ethyleneoxide), polyisoprene, polybutadiene, poly(dimethylsiloxane), poly(ethylene oxide), poly(methylstyrene)) versus molecular weight shows that D oc N - which differs somewhat from the N...

The mass exponent value x decreases as the temperature increases to reach a value of 3-45 at 55 C when cyclohexane can be considered as a good solvent for polystyrene. One has to note that the exponent x is larger than the predicted va e x = 3. Self-diffusion coefficient measurements lead to Dg -- Af. Assuming that is the time required for the polymer chain to diffuse on a distance of order of its radius of gyration R - (R = Tffig) we should have Present results for relaxation time therefore disagree with self-diffusion coefficient measurements. From viscosity and relaxation time measurements, we can deduce the shear elastic modulus at short times G We find that G is mass-independent and increases with concentration ... 

Dependence of Self-diffusion Coefficients in Polyethylene and Polystyrene Melts Investigated Using Modified n.m.r. Field Gradient Technique," Polymer. 24, 964-990 (1983). 

Fig. 3. Universal behaviour of the normalized self-diffusion coefficient DJDq Dq is the diffusion coefficient at infinite dilution) as a function of the reduced concentration c/c, where c is the concentration at which the labelled chains start to overlap, for polystyrene in benzene solutions. The different symbols correspond to different molecular weights in the range 78000-750000. Full symbols correspond to labelled and unlabelled chains having the same molecular weight, while open symbols correspond to a frozen matrix (P>>N) for which a pure reptational behaviour is observed (from Ref. (19)).

Figure 8.4 Self-diffusion coefficient of ( ) 130 and (0) 180 g/1 polystyrene dibutylphthalate. Ds (M) follows a stretched exponential at smaller M and a power law at larger M. Original measurements by Nemoto, et al. ).

N. Nemoto, T. Kojima, T. Inoue, and M. Kurata. Self-diffusion of polymers in the concentrated regime I. Temperature dependence of the self-diffusion coefficient and the steady viscosity of polystyrene in dibutyl phthalate. Polym. /., 20 (1988), 875-881. 

Figure 9.17 Solutions of bovine serum albumin, showing their viscosity ( ) and self-diffusion coefficient (0) (from Refs. (29,30)), and Dp of 322 ( ) and 655 (O) nm polystyrene spheres, with corresponding stretched exponentials in protein c, from data of Ullmann, et al.(28).

Z. Sun and C. H. Wang. Light scattering from mixtures of two polystyrenes in toluene and self-diffusion coefficients. Macromolecules, 30 (1997), 4939 944. 

Norio Nemoto, Michael R. Landry, Icksam Noh, Toshiaki Kitano, Jeffrey A. Wesson, and Hyuk Yu, Concentration Dependence of Self-Diffusion Coefficient by Forced Rayleigh Scattering Polystyrene in Tetrahydrofuran , Macromolecules, 18,1985, pp 308-310. 

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