Diffusion-limited phosphorescence quenching interactions in polymer solutions: small molecule-small molecule interactions interpreted by free volume theory

Abstract

Diffusion-limited interactions between benzil and anthracene were studied by phosphorescence quenching in polystyrene-cyclohexane, polystyrene-toluene, poly(methyl methacrylate)-toluene, and polybutadiene-cyclohexane solutions. Values of the bimolecular diffusion-limited quenching rate constant, kq, were obtained by measuring benzil phosphorescence lifetime as a function of anthracene concentration and applying a Stern-Volmer analysis. Besides polymer species and solvent, k" was measured as a function of polymer molecular weight and concentration, up to 560 g/L. kq was found to be independent of polymer molecular weight in polystyrene-cyclohexane solutions and exhibited a slight molecular weight dependence in polystyrene-toluene solutions. The polymer concentration dependence of kq in polystyrene-cyclohexane and polystyrene-toluene solutions was found to mimic the polymer concentration dependence of the solvent self-diffusion coefficient; this result is consistent with the notion that kq/kq0 ~DJD& where Ds is the solvent self-diffusion coefficient and the subscript 0 indicates the value at zero polymer concentration. A very similar polymer concentration dependence of kq was obtained in poly(methyl methacrylate)-toluene solutions. The Vrentas-Duda free volume theory for Ds was found to predict the polymer concentration dependence of kq quantitatively for polystyrene-toluene and approximately for poly(methyl methacrylate)-toluene solutions; over the range of polymer concentrations studied in polystyrene-cyclohexane solutions, the agreement between the Vrentas-Duda theory and experimental measures of kq appears to be less satisfactory. The Fujita-Doolittle theory can also be used to fit experimental measures of kq in selected cases; however, it is possible to obtain unphysical results if the Fujita-Doolittle theory is applied over too wide a range in polymer concentration.

Bimolecular Free-Radical Termination at Low Conversion

“…Further contributions to the field of phosphorescence quenching have come from the group of Torkelson (104,117,(190)(191)(192)(193)196). Although they pointed out several weak aspects in the work of Horie and Mita regarding their polymer synthesis and data analyses (196), their findings with respect to the ratio of the rate of S-S quenching versus S-L quenching (196) and the scaling of k q with cooperative diffusion in the dilute regime (104) were similar to those of Horie and Mita.…”

“…Among other things, they focused on the inter-and intramolecular quenching of a copolymer containing a small fraction of phenyl vinyl ketone. Results of the previously mentioned phosphorescence quenching technique, for instance, have shown that this is not an unreasonable assumption as polymer only acts as an obstacle for diffusion of small molecules (189)(190)(191)(192)(193) and references therein). † This is again in agreement with Eq.…”

“…They observed that the rate of intermolecular quenching between a small species and a large copolymer (S-L interaction) was approximately a factor of 2 lower than the interaction between two small species (an S-S interaction) (187,188). Torkelson and co- † For sake of simplicity, "small" may be considered as a "polymer" of chain length 1. workers have described this behavior in terms of free volume theories (190)(191)(192)(193). 12, again assuming the independence of the individual diffusion coefficients of the two species so that small species can freely diffuse through a large polymer coil.…”

Small-Molecule Probe Diffusion in Polymer Solutions: Studies by Taylor Dispersion and Phosphorescence Quenching

“…To accomplish this study, two complementary and relatively little-employed techniques are used to obtain information on diffusion: Taylor dispersion [47][48][49][50][51][52][53][54][55] and phosphorescence quenching. 56,57 Taylor dispersion is a rapid and relatively inexpensive technique based on the dispersion of a solute in a liquid undergoing laminar tube flow. The theory was first discussed by Taylor, 47,48 and later by Aris, 49 and was applied by Ouano, 50 who demonstrated that the solute diffusion coefficient in a two-component system can be determined from the mean, t h, and variance, σ 2 , of the solute concentration profile as it exits the tube.…”

“…Phosphorescence quenching, a useful tool in obtaining information on diffusion-limited interactions in concentrated polymer solutions, is employed to determine the bimolecular quenching rate constant, k q , associated with the reduction of phosphorescence intensity with the addition of quencher, as a function of polymer concentration. Previous studies 19,56,57 have shown that for interactions involving small molecules k q can be related to the self-diffusion coefficients of the chromophore, D c , and quencher, D q , through the modified Smoluchowski equation: 58 where F is a steric factor taken to be 0.5, R T is the encounter radius between chromophore and quencher, and N A is Avogadro's number per millimole. Small molecule-polymer interactions have also been studied using phosphorescence quenching.…”