Polystyrene small-molecule diffusion

Larry Duda and Jim Vrentas were the first to systematically study the diffusion of small molecules in molten polymers, formulate a free volume-based theoretical model, and elucidate the sharp dependence of the diffusion coefficient on temperature and concentration.2 Figure 8.8 shows diffusivities of toluene in polystyrene as a function of concentration and temperature. The values were computed using the Vrentas and Duda (17) free volume model and, as shown, coincide well with available data. 

Many computational studies of the permeation of small gas molecules through polymers have appeared, which were designed to analyze, on an atomic scale, diffusion mechanisms or to calculate the diffusion coefficient and the solubility parameters. Most of these studies have dealt with flexible polymer chains of relatively simple structure such as polyethylene, polypropylene, and poly-(isobutylene) [49,50,51,52,53], There are, however, a few reports on polymers consisting of stiff chains. For example, Mooney and MacElroy [54] studied the diffusion of small molecules in semicrystalline aromatic polymers and Cuthbert et al. [55] have calculated the Henry s law constant for a number of small molecules in polystyrene and studied the effect of box size on the calculated Henry s law constants. Most of these reports are limited to the calculation of solubility coefficients at a single temperature and in the zero-pressure limit. However, there are few reports on the calculation of solubilities at higher pressures, for example the reports by de Pablo et al. [56] on the calculation of solubilities of alkanes in polyethylene, by Abu-Shargh [53] on the calculation of solubility of propene in polypropylene, and by Lim et al. [47] on the sorption of methane and carbon dioxide in amorphous polyetherimide. In the former two cases, the authors have used Gibbs ensemble Monte Carlo method [41,57] to do the calculations, and in the latter case, the authors have used an equation-of-state method to describe the gas phase. 

Molecular diffusivity of small molecules in polystyrene melts... 

Thermal degradation in multiphase polymeric systems is a chemical process that generally takes place either through polymer molecules/long-chain radical species or through reaction involving small-molecule radical species that are produced in one phase and subsequently diffuse into other phase. The thermal degradation behaviour of polystyrene (PS) [6] and polypropylene (PP) [7, 8] can be profoundly influenced by the presence of a second polymer. 

Duda for the system of polystyrene and ethylbenzene. This effect in combination with the low monomer concentrations accounts for the fact that secondary reactions of the macroradicals with small molecules capable of diffusion of inert free radicals play a dominant role in the final phase of free radical bulk polymerization. 

Most of the measurements on diffusivities of compounds in the liquid phase, in catalyst pores, have been made with small molecules. Recently Chantong and Massoth [26] measured diffusivities of non-metallic porphyrin molecules. Baltus and Anderson [27] made diffusivity measurements using narrow molecular weight fractions of a petroleum residuum. In their work tetrahydrofuran asphaltenes were separated into five fractions by gel permeation chromatography. The polystyrene equivalent average molecular weights they reported were 3000, 6000, 12000, 24000, and 48000. 

The effect of probe volume on small-molecule Ds(c) is reported by Wisnudel and Torkelson(30), who examined the diffusion of 14 probe molecules, molecular volumes 66 36 cm /mole, in 3.8 kDa polystyrene tetrahydrofuran at polymer concentrations 100 00 g/1. As seen in Figure 5.5, Ds decays exponentially with increasing probe volume, at least for probes as large as or larger than solvent... 

Gisser and Ediger(41) studied solvent and solute rotation with C and nuclear magnetic resonance. The selectivity of NMR allows separate measurement of reorientation times for multiple components of a mixture. Dilute polystyrene, polyisoprene, and polybutadiene were found to retard the rotational diffusion of the toluene solvent, polystyrene being modestly more effective as a retardant. Solvent Tr depends exponentially on polymer c, at least up to 90 g/1 of polymer. Gisser and Ediger also examined the small-molecule mixture chloronaphthalene ... 

Chapter 5 considers translation and rotation by solvent molecules in small-molecule liquids and polymer solutions. Correlations between solution properties are already more complex than might have been expected. At small rj, the diffusion coefficient and equivalent conductance of small-molecule probes in simple liquids scale as At larger rj, D and A are instead The boundary between small and large t] seen in the literature is uniformly near 5 cP. It is unclear why this particular value of r should not be system-specific. In contrast to smaU-molecule probes, mesoscopic probes such as polystyrene latex spheres in potentially highly viscous mixed solvents such as water glycerol retain D T/ri behavior over three or more orders of magnitude in rj. 

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