The distribution function of relaxation times underlying the nonexponential relaxation function of Williams and Watts is derived and compared with the analogous Cole–Davidson distribution function. In order to make the comparison between the two distribution functions, a simple empirical relationship between the Cole–Davidson and Williams–Watts parameters was determined which may be used to compare data analyzed using the two fitting functions. Although the relaxation functions are similar to each other, the distribution functions are quite dissimilar. The Cole–Davidson distribution shows a sharp long time cutoff, while the Williams–Watts distribution decays approximately exponentially at long times. Finally, several useful relations between relaxation and distribution functions are summarized or derived, and the limitations of deriving distribution functions from relaxation functions are discussed.

The synthesis of hybrid nanoparticles was conducted by the atom transfer radical polymerization (ATRP) of styrene and (meth)acrylates from colloidal surfaces. Colloidal initiators were prepared by the functionalization of silica colloids with 2-bromoisobutyrate groups. ATRP from colloidal surfaces was then performed to attach well-defined homopolymers and block copolymers to an inorganic core. Kinetics of the ATRP of styrene (Sty), n-butyl acrylate (BA), and methyl methacrylate (MMA) under identical reaction conditions were investigated. Hybrid nanoparticles containing block copolymers of pSty-b-pBA (M n = 22 300; M w/M n = 1.20), pMMA-b-pBA (M n = 29 400; M w/M n = 1.28), and pBA-b-pMMA (M n = 17 300; M w/M n = 1.28) were prepared, and hydrolysis of silica cores by hydrofluoric acid treatment enabled characterization of cleaved copolymers using size exclusion chromatography and 1H NMR. Ultrathin films of hybrid nanoparticles were examined using transmission electron microscopy and atomic force microscopy.

ABSTRACT:The effect of the chain constraint on the glass-transition temperature of polystyrene (pS) was studied in the context of polymer tethering to curved surfaces. The synthesis and characterization of silica-graft-polystyrene (SiO 2 -g-pS) hybrid nanoparticles is reported. Silica nanoparticles possessing covalently bound pS chains were prepared by the atom transfer radical polymerization of styrene from functionalized colloidal surfaces. These hybrid nanoparticles serve as interesting examples of spherical polymer brushes, as a high density of grafted pS was achieved on the inorganic colloid. The confirmation of a brushlike extension of immobilized chains in a good solvent was obtained with dynamic light scattering in toluene of SiO 2 -g-pS colloids possessing various molar masses of tethered pS. The solid-state morphology of SiO 2 -g-pS ultrathin films was assessed with transmission electron microscopy, and this confirmed that the silica colloids were well-dispersed in a matrix of the tethered polymer. Differential scanning calorimetry was used to study the effects of tethering and chain immobilization on the glass-transition temperature of pS. The measured glass-transition temperature of annealed bulk films of the hybrid nanoparticles was elevated with respect to the value for pure bulk pS. The enhancements ranged from 13 to 2 K for SiO 2 -g-pS brushes possessing tethered pS with number-average molecular weights of 5230 and 32,670 g/mol, respectively.

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The effective diffusivity of a solute within a pore of comparable size is frequently found to be less than its value in bulk solution. This phenomenon is known as "hindered" or "restricted" diffusion and it arises fundamentally from the fact that the characteristic dimension of the solute molecule is no longer small compared to that of the pore through which it passes. Hindered diffusion is observed in a number of important fields such as gel permeation chromatography, heterogeneous catalysis, and membrane separations. Hindered diffusion of narrow molecular weight fractions of two polysaccharides was measured in microporous membranes with well-defined pore geometry. The two polysaccharides examined were dextran, a flexible coiled polymer of 1,6-glucopyranose units, and ficoll, a highly branched copolymer of sucrose and epichlorohydrin. The ratio of the membrane diffusion coefficient (D) to the bulk solution diffusion coefficient (D"), determined by light scattering, was examined as a function of the relative solute size to membrane pore size (r8/rp). Values of D/D" were found to be significantly greater for dextran than ficoll over most of the range of rs/rp examined.The ficoll data agree very well with a hydrodynamic model of diffusion based on a hard sphere in a tube.