Length and Time-Dependent Rates in Diffusion-Controlled Reactions with Conjugated Polymers

Abstract

Rate constants for diffusion-controlled reactions of solvated electrons with conjugated fluorene oligomers (oF) and polymers (pF) were measured in liquid tetrahydrofuran (THF). Preparative gel permeation chromatography (GPC) was used to separate the polyfluorenes into fractions having narrowed distributions of lengths. Both oF and pF’s were used in determinations of the attachment rate constants k_inf as a function of length, where k_inf refers to the rate coefficients at long times where they are indeed constant. The results find that in going from oF₁ to pF₁₃₃, k_inf increases by a factor of 16, which is much smaller than that of the 133-fold increase in length. The extent of this increase and its change with length are in excellent agreement with published theoretical models that describe diffusion to long thin objects as either prolate spheroids or one-dimensional arrays of spheres. As the concentration of polymer was increased, the effects of large transient terms in the rate constant were observed. As predicted by the Smoluchowski diffusion equation, with modifications by more contemporary theorists, these transient effects are larger and persist to longer times for the larger molecules. For the longest molecule, pF₁₃₃, k(t) increases by more than a decade at short times. In that case, the “transient term” becomes dominant and the rate coefficient is approximately proportional to the square of the effective reaction radius in contrast to the linear dependence usual for diffusional reactions. The size of these transient effects and their quantitative confirmation are unprecedented.