Polystyrene self-diffusion

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

Callaghan and Pinder48,49 used the PGSE method in a detailed examination of the diffusion of linear polystyrene molecules dissolved in CC14. They applied standard dilute hydrodynamic theory to self-diffusion (as distinct from mutual diffusion) and identified the lowest-order concentration dependence of D with the coefficient kF, writing... 

Fig. 7. Self-diffusion of linear (open symbols) and three-armed star (filled symbols) polystyrenes (squares) and polybutadienes (circles) in CC14 extrapolated to infinite dilution, as function of polymer molecular weight (Ref. 53>, with permission).

Figure 5. Self-diffusion rates of l C-salicylic acid through polystyrene-zeolite X disks...

To commence measurements, 1 ml of labeled solution was added to one arm (donor), and at the same time an equal volume of unlabeled solution was dispensed to the remaining arm (receptor). Aliquots of 0.1 ml were withdrawn from both arms at suitable time intervals over 4r-5 days. The activity of samples from the receptor side was determined by liquid scintillation counting, and Wt/Wm vs. y/t plots were constructed. The temperature range studied was 20-50°C. (Note salicylic acid was shown not to penetrate disks composed of polystyrene alone, and self-diffusion kinetics were reproducible between different disks of the same polystyrene/zeolite composition). 

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. 

Boyd, G. Soldanho, B.A. Self diffusion of cations in and through sulfonated polystyrene cation exchange polymers. J. Am. Chem. Soc. 1953, 75, 6091. 

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.)...

IR-1 (V4). The Dp values for Dowex 50, a typical sulfonated polystyrene resin, have been shown by Boyd and Soldano (B7) to depend greatly upon the extent of cross-linking as determined by the divinylbenzene (DVB) content of the resin. For 8% DVB, the Dp values are similar to Amberlite IR-1. For 12% DVB, the usual commercial grade, self-diffusion... 

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. 

As the glass transition temperature Tg is approached, the friction coefficient C sharply increases [3] and hence becomes too small to be measured. Thus, self-diffusion measurements on undiluted polymers are usually made at temperatures far above Tg. For example, all the reported data on polystyrene melts (Tg 100°C) were taken in the range 150 - 250° C. Working at such high temperatures, however, is not simple for various technical reasons including polymer degradation. It is therefore advantageous to study polymers with Tg far below room temperature if nearly monodisperse samples are available (use of polydisperse samples should be avoided for basic research). Extimples of such polymers are poly(isoprene) and polybutadiene. 

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).]...

---