Diffusion of organic vapors at low concentrations in glassy PVC, polystyrene, and PMMA

Diffusion coefficients of various C₁ to C₆ organic vapors, at concentrations 0.5 wt. percent, have been determined by gravimetric sorption rate measurements on emulsion and suspension-polymerized powder samples of PVC, polystyrene, and PMMA. Fickian diffusion kinetics were observed at the lowest concentrations, with a second-stage, relaxation-controlled sorption appearing at higher concentrations. In conjunction with published data for diffusivities of fixed gases in these polymers, the results indicate that diffusivity decreases exponentially, and that diffusion activation energy (E_D) increases linearly, with increasing diameter of “spherical” penetrant molecules (e.g., the noble gases, CH₄, SF₆, CCl₄, and neopentane). Much of the observed scatter in these correlations is attributable to uncertainty in the molecular diameters. For C₄ and larger n-alkanes and other elongated or flattened molecules, diffusivities are higher, and E_D lower, than for spherical molecules of similar molar volume. This finding suggests that anisometric molecules are oriented and move along their long axes during diffusion through the glassy polymer matrix. Correlations of diffusivities with molecular dimensions suggests that transport of anisometric molecules is governed by a diameter smaller than the mean (equivalent sphere) diameter but larger than the minimum dimension of their extended-chain conformation. Among the three polymers studied, diffusivity of each penetrant, at a given temperature, decreases in the order polystyrene> PVC ≥ PMMA.     

General Discussion

Dr. Park (University of Wales, Cardiff, U. K.): I should like to take up a point about the two phase-model. It seems to me that all the varieties of this assume something rather peculiar about the initiation. I may be wrong. But is it true that the initiation is assumed to be uniform throughout the whole system?     

Über die Stetigkeit von Halbgruppen von Operatoren in intermediären Räumen

Ohne Zusammenfassung Gottfried Köthe zum 60. Geburtstag gewidmet     

A Problem in Linear Matrix Approximation

Let A be a normal operator in ??(H), H a complex Hilbert space, and let ? _A = ? {AX - XA:X ∈ ??(H)} be the commutator subspace of ??(H) associated with A. If B in ??(H) commutes with A, then B is orthogonal to ?_A with respect to the spectral norm; i.e., the null operator is an element of best approximation of B in ? _A. This was proved by J. Anderson in 1973 and extended by P. J. Maher with respect to the Schatten p-norm recently. We take a look at their result from a more approximation theoretical point of view in the finite dimensional setting; in particular, we characterize all elements of best approximation of B in R_A and prove that the metric projection of H onto ?_A is continuous.