Pyrene diffusion coefficients

Transport Properties Although the densities of SCFs can approach those of conventional liquids, transport properties are more favorable because viscosities remain lower and diffusion coefficients remain higher. Furthermore, CO2 diffuses through condensed-liquid phases (e.g., adsorbents and polymers) faster than do typical solvents which have larger molecular sizes. For example, at 35°C the estimated pyrene diffusion coefficient in polymethylmethacrylate increases by 4 orders of magnitude when the CO2 content is increased from 8 to 17 wt % with pressure [Cao, Johnston, and Webber, Macromolecules, 38(4), 1335-1340 (2005)]. 

Equations (4-5) and (4-7) are alternative expressions for the estimation of the diffusion-limited rate constant, but these equations are not equivalent, because Eq. (4-7) includes the assumption that the Stokes-Einstein equation is applicable. Olea and Thomas" measured the kinetics of quenching of pyrene fluorescence in several solvents and also measured diffusion coefficients. The diffusion coefficients did not vary as t) [as predicted by Eq. (4-6)], but roughly as Tf. Thus Eq. (4-7) is not valid, in this system, whereas Eq. (4-5), used with the experimentally measured diffusion coefficients, gave reasonable agreement with measured rate constants. 

Note, however that the concepts about the lipid membrane as the isotropic, structureless medium are oversimplified. It is well known [19, 190] that the rates and character of the molecular motion in the lateral direction and across the membrane are quite different. This is true for both the molecules inserted in the lipid bilayer and the lipid molecules themselves. Thus, for example, while it still seems possible to characterize the lateral movement of the egg lecithin molecule by the diffusion coefficient D its movement across the membrane seems to be better described by the so-called flip-flop mechanism when two lipid molecules from the inner and outer membrane monolayers of the vesicle synchronously change locations with each other [19]. The value of D, = 1.8 x 10 8 cm2 s 1 [191] corresponds to the time of the lateral diffusion jump of lecithin molecule, Le. about 10 7s. The characteristic time of flip-flop under the same conditions is much longer (about 6.5 hours) [19]. The molecules without long hydrocarbon chains migrate much more rapidly. For example for pyrene D, = 1.4x 10 7 cm2 s1 [192]. 

Johnson and Willson interpreted the main feature of the observations on solid polyethylene doped with aromatic solutes in terms of an ionic mechanism it was analogous to that proposed for irradiated frozen glassy-alkane-systems in which ionization occurred with G = 3 — 4 [96], The produced charged species, electron and positive hole, were both mobile as indicated by the radiation-induced conductivity. The production of excited states of aromatic solutes was caused mainly by ion-electron neutralization. The ion-ion recombination was relatively slow but it might contribute to the delayed fluorescence observed. On the basis of Debye-Simoluchovski equation, they evaluated the diffusion coefficients of the radical anion of naphthalene and pyrene as approximately 4 x 10 12 and 1 x 10 12 m2 s 1 respectively the values were about three orders of magnitude less than those found in typical liquid systems. 

By use of the Taylor dispersion method, diffusion coefficients for pyrene solubilized in micelles of octadecyltrimethylammonium chloride (CigTAC) and tetradecyltrimethyl-ammonium bromide (C14TAB) have been measur in aqueous NaCl and NaBr solutions, respectively, at 35 °C. These values can be regarded as tracer diffusion coefficients for the micelles b use essentially all pyrene molecules are solubilized in the micelles. In the range... 

Figures 1 and 2 show diffusion coefficients of pyrene solubilized in C igTAC and C14TAB micelles, respectively, at 35 °C. Because essentially all pyrene molecules are solubilized in the micelles, the diffusion coefficients can be interpreted as tracer diffusion coefficients of the micelles. Diffusion coefficients decrease with increasing concentration of the micelles, and increase with increasing concentration of the salts added. Diffusion coefficients at erne s, Dcmc> obtained by extrapolation, and are listed in Table 1...

Thus, the kinetics of diffusion-controlled bimolecular electron-transfer reactions in the micellar interiors differ from that in the homogeneous solution. Numerous data have shown that Eq. 9 reproduces the dynamics of electron-transfer reactions within micelle interiors [80]. Diffusion coefficients (D) estimated from Eqs. 8 and 9 are very similar to those obtained by independent measurements. For example, Eq. 8 gave ku = 7.5 X 10 s for electron transfer from excited pyrene to CH2I2 in SDS micelles [79b]. One estimates from Eq. 8, with = 20 A and ai = 1.5 (calculated assuming d = 7 A), a value of Z) = 1.3 x 10 cm s, nearly identical with the experimentally determined value of Z) = lO " cm s [45]. 

It is important to emphasize that a fluorescent solute molecule samples a large number of microheterogeneities. Indeed, because the excited-state fluorescence lifetime x is relatively long (for pyrene [25] it has a value of the order of 1 x 10 x 10 s) and the diffusion coefficient D [26] is on the order of 10 cm /s, the solute samples a region charac-... 

The term exdmer is used when the excited dye forms a transient fluorescent dimeric complex with another fluorophore of the same kind. The exdmer fluorescence is usually red shifted with respect to that of the monomer (see Fig. 6.28) The most widely used types of eocdmer-forming probes are pyrene (see Fig. 6.28) and perylene and their derivatives. The ratio of the maxima of the excimer to the monomer spectra can be used to judge the efficiency of exdmer formation. This (Ex/Mo)-ratio depends on the concentration of the dye and is controlled by the diffusion properties. It allows, when using pyrene or perylene labeled fatty acids or phospholipids (see Fig. 6.28), the estimation of the probe s lateral diffusion coefficients in lipid bilayer membranes. Thus, membrane fluidity can be measured by monitoring the fluorescence spectra of such an exdmer probe. 

One of the few systematic investigations of this matter is a study of the electron-transfer reactions between various acceptors and excited pyrene molecules [13,d], in a series of straight-chain hydrocarbons from n-heptane (C7H10) to squalane (C30H62) the diffusion coefficients of the reactants were measured as well as the rate constants in each solvent. The rate constants deviated markedly from Equation (2.3), based on viscosity, by a factor of up to 10, but much less from Equation (2.1) based on diffusion coefficients. With nitrobenzene as acceptor the ratio of the observed values of k to the Smoluchowski value 4 r was constant within a few per cent. 

The increase of fluorescence intensity with time associated to the capture of pyrene by poly(styrene)-poly(meth-acrylic acid) micelles or the capture of perylene by poly(2-cinnamoylethyl methacrylate)-poly(acrylic acid) micelles revealed a two-step process. For the first system, the analysis of the slow process (probe penetration in the micelle core) using the same diffusion equation as for the release process yielded a value of the diffusion coefficient close to that inferred from the release of pyrene by the same micelles. ... 

From the difficulties encountered with interpretation of CVs which the discussions above amply show, it would appear that other voltammetric methods, especially differential methods, would have found wider application to CPs. This has unfortunately not been the case. The results in Figs. 4-17-a.b.c and 4-18 represent some of the few studies of this nature. In Fig. 4-17. the results of CV and of Differential Pulse Voltammetry (DPV) are compared. The latter is a technique in which a small potential pulse is superimposed on a staircase potential function with the difference between the post-pulse and pre-pulse current measured (inset in Fig. 4-171. The differential method yields peak-shaped curves unencumbered by residual current tails, as in CVs, and thus a clearer identification of peaks and their widths. Fig. 4-19 then shows DPV of Poly(phenylene vinylene) used to compute the bandgap, as described earlier. Normal Pulse Voltammetry (NPV), in which a sort of digital pulse-ramp is applied in place of the analog ramp of CV and the current sampled at the end of the pulse [50], has been applied to poly(l-amino pyrene) [48], yielding redox potentials as well as diffusion coefficients (Fig. 4-181. Other differential methods such as Square Wave Voltammetry have been applied to poly(aromatic amines) in the author s laboratories. There is however little other extant work with pulse voltammetry of CPs, although the very brief results above clearly provide a strong indication for it. 

NPV results may also be used to calculate apparent diffusion coefficients also employing Cottrell relationships. Oyama et al. [48] have used the NPV voltam-mograms of Fig. 4-19 (III.24.flO) to calculate apparent diffusion coefficients (with t now being replaced by r, the NPV sampling time) for C104 in poly(1-amino-pyrene), of 1.3 X 10- ° cmVs. 

In this paper, we present a preliminary analysis of the steady-state and time-resolved fluorescence of pyrene in supercritical C02. In addition, we employ steady-state absorbance spectroscopy to determine pyrene solubility and determine the ground-state interactions. Similarly, the steady-state excitation and emission spectra gives us qualitative insights into the excimer formation process. Finally, time-resolved fluorescence experiments yield the entire ensemble of rate coefficients associated with the observed pyrene emission (Figure 1). From these rates we can then determine if the excimer formation process is diffusion controlled in supercritical C02. 

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