Polystyrene probe diffusion

Lodge and collaborators have reported an extensive series of studies of probe diffusion in polymer solutions, using QELSS to measure Dp of dilute probe polystyrenes in polyvinylmethylether orthofluorotoluene. Variables studied include the probe and matrix molecular weights, the matrix concentration, and the topology (linear and star) of... 

Figure 29. Probe diffusion of (top to bottom) 50, 100, 420, and 900 kDa polystyrenes through 110 kDa polyvinylmethyl ether in toluene, based on data in Martin [113,104], Solid lines are joint fits of all data to a stretched exponential in c and P.

Polymer diffusion through meshworks of covalently-crosslinked polymer chains has been ejcamined rarely. Antonietti and Sillescu [155] studied polystyrene chains diffusing through crosslinked polystyrene networks, while varying the crosslink density. These were solvent-free melt systems. Increasing the number of covalent crosslinks reduced the diffusion coeflScient (as measured with holographic bleaching of labelled chains) of the probe polymers. 

Martin reports Ds of hnear polystyrene probes in soluhons of a hnear poly vinyl-methylether(36,37). Equahon 8.2 accurately represents the measurements, which are limited to M/ P < 2.2. Diffusion of PMMA in polystyrene soluhons was examined by Nemoto, et a/.(47) Figure 8.29 shows that Eq. 8.2 is more accurate in the range 0.5 < M/P < 2.0. 

Extended searches of the spectrum on the time scale on which the spectrum would have decayed, if the Stokes-Einstein equation were correct in solutions of 1 MDa polyacrylic acid, found no sign of a spectral relaxation the spectrum had aheady decayed to the baseline. Lin and Phillies proposed that the discrepancy between Dp and the macroscopic q arises from shear tbinning in the probe diffusion process, namely the microviscosity found on the time and distance scales probed by the polystyrene spheres is far less than the macroscopic viscosity q. 

Phillies, et al. observed probe diffusion in aqueous dextran(12). Representative measurements of Dp and rj for two polymer molecular weights appear in Figure 9.5 together with fits to stretched exponentials. Dextran concentrations covered 0 < c < 250 g/1, using nine different dextran samples. Probes were polystyrene spheres with radius 20 or 230 nm solution viscosities were obtained... 

Ullmann, et al.O ) extended Ullmann and Philhes(31) to study probe diffusion of carboxylate-modified polystyrene spheres in aqueous polyethylene oxide Triton X-100. The Dp for most sphere matrix combinations follows a stretched exponential in c, as seen in Figure 9.18. However, Dp of the 655 nm diameter spheres shows re-entrant behavior, both in the 18.5 kDa polymer and to a lesser extent... 

Figure 9.28 Probe diffusion coefficients for (a) 350 kDa polymethylmethacrylate in good solvents tetrahydrofuran (O) and N,N-dimethylformamide (0), and the Theta solvent dioxane water ( ), after Gold, et al.(45), and (b) 67 nm polystyrene spheres in aqueous 139 kDa HPC at (O) 10 °C (good solvent conditions) and ( ) 41 (pseudo-theta point), after Phillies and Clomenil(46).

G. S. Ullmann, K. Ullmann, R. M. Lindner, and G. D. J. Phillies. Probe diffusion of polystyrene latex spheres in poly(ethylene oxide) water. J. Phys. Chem., 89 (1985), 692-700. 

K. E. Bremmell and D. E. Dunstan. Probe diffusion measurements of polystyrene latex particles in polyelectrolyte solutions of varying ionic strength. Macromolecules, 35 (2002), 1994-1999. 

G. D. J. Phillies, M. Lacroix, and J. Yambert. Probe diffusion in sodium polystyrene sulfonate-water experimental determination of sphere-chain binary hydrodynamic interactions. / Phys. Chem., 101 (1997), 5124-5130. 

Polystyrene in dimethylformamide, polymer 215 kDa and 1.1 MDa, had r/(c) determined by Onyenemezu, et al, as part of a study of probe diffusion(25). The polymers were monodisperse, My,/M < 1.07. Viscosities were obtained with an Ubbelohde dilution viscometer. Fits to stretched exponentials describe the measurements to within the scatter in the experimental results, as seen in Figure 12.5d. 

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 ... 

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. 

TABLE 2 Diffusion coefficients of probe polystyrene (PS) molecules in the PMMA gel estimated by the PFGStE H NMR method... 

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