Pyrene coefficients

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. 

The optical absorption spectra and the first reduction potentials are virtually independent of the number of pyrene units present in the molecule, as a result of the specific stereoelectronic situation. Since the orbital coefficients of the bridgehead centers are almost zero, the rings are electronically decoupled. Thus, oligopyrenes differ significantly from oligo(pflrfl-phenylene)s (OPVs). 

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)]. 

Reported vapor pressures of pyrene at various temperatures and the coefficients for the vapor pressure ... 

TABLE 4.1.1.29.3 Reported Henry s law constants and octanol-and temperature dependence equations Henry s law constant air partition coefficients of pyrene at various temperatures log Kqa ... 

Hegeman, W.J.M., van der Weijden, C.H., Loch, J.P.G. (1995) Sorption of benzo[a]pyrene and phenanthrene on suspended harbor sediment as a function of suspended sediment concentration and salinity A laboratory study using the cosolvent partition coefficient. Environ. Sci. Technol. 29, 363-371. 

Mallon, B.J., Harris, F. (1984) Octanol-water partition coefficient of benzo[a]pyrene, measurement, calculation and environmental implication. Bull. Environ. Contam. Toxicol. 32, 316-323. 

Estimates of oCbiend using a rule-of-mixtures relationship are 3.0 X 102 and 7.2 X 103 cm lor 0.2 and 5.0% polyimide, respectively. This dependence of the optimum absorption coefficient (in terms of ablation rate), OVx on fluence is consistent with the observations of Chuang et al.6% for ablation of several UV-transparent (at 308 nm) polymers sensitized with low-molecular-weight dopants, e.g., PMMA doped with pyrene. For the pyrene-PMMA system, Chuang et al.6S reported maximum etch rates for 1.2 J/cm2 at a = 7 X 102 cm 1. It should not be expected that different dopant-matrix systems would yield the same optimum absorption coefficient for a given fluence level since the thermal properties for different polymers may vary significantly. 

Figure 8.2 presents the fluorescence of pyrene on silica gel. The loading is low so that pyrene is predominantly adsorbed as nonaggregated monomers (Mi). The backward fluorescence spectrum Fb of this sample is very comparable to the spectrum in polar solvents and not distorted by reabsorption. However, the forward spectrum Ft is almost completely suppressed in the region of overlap with the o -transition and hot sidebands of the weak first absorption band Si. The absorption coefficients of the sample vary widely from k" = 0.1 cm 1 (Si-band, Aa = 350-370 nm) to k = 25 cm-1 (S2-band, 1 290-340 nm), and in a first approximation the excitation spectrum of Fh reflects this variation correctly (Figure 8.2, left). The Ff-excitation spectrum, however, has only little in common with the real absorption spectrum of the sample. 

In multicomponent systems A"0 can be written as a sum of the individual absorption coefficients A ot = 2TA , where each AT,(A ) depends in a different way on the wavelength. If one or more of the components are fluorescent, their excitation spectra are mutually attenuated by absorption filters of the other compounds. This effect is included in Eqs. (8.27) and (8.28) so that examples like that of Figure 8.4 can be quantified. The two fluorescent components are monomeric an aggregated pyrene, Mi and Mn. The fluorescence spectra of these species are clearly different from each other but the absorption spectra overlap strongly. Thus the excitation spectrum of the minority component M is totally distorted by the Mi filter (absorption maxima of Mi appear as a minima in the excitation spectrum ofM see Figure 8.4, top). In transparent samples this effect can be reduced by dilution. However, this method is not very efficient in scattering media as can be seen by solving Eqs. (8.27 and 8.28) for bSd — 0. Only the limit d 0 will produce the desired relation where fluorescence intensity and absorption coefficient of the fluorophore are linearly proportional to each other in a multicomponent system. 

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. 

Figure 1. Energy-level diagram for excimer formation. Symbols represent hv, absorbed photon k emissive rate from the monomer species k, bimolecular rate coefficient for formation of the pyrene excimer k, unimolecular rate coefficient for dissociation of the excimer and k, emissive rate from the excimer species. Note no ground-state association is indicated.

Figure 9 shows the temperature dependence of the recovered kinetic rate coefficients for the formation (k bimolecular) and dissociation (k unimolecular) of pyrene excimers in supercritical CO2 at a reduced density of 1.17. Also, shown is the bimolecular rate coefficient expected based on a simple diffusion-controlled argument (11). The value for the theoretical rate constant was obtained through use of the Smoluchowski equation (26). As previously mentioned, the viscosities utilized in the equation were calculated using the Lucas and Reichenberg formulations (16). From these experiments we obtain two key results. First, the reverse rate, k, is very temperature sensitive and increases with temperature. Second, the forward rate, kDM, 1S diffusion controlled. Further discussion will be deferred until further experiments are performed nearer the critical point where we will investigate the rate parameters as a function of density. 

Ortiz, et. al (1999) measured overall mass transfer coefficients for the aqueous dissolution of naphthalene, pyrene, and phenanthrene from oils ranging in viscosities from a light lubricating oil (86 cp) to a high viscosity oil ( 1000cp). These measurements were performed in continuous-flow systems for time periods ranging from several months up to one year. The authors hypothesize that naphthalene, pyrene, and phenanthrene dissolution from a high viscosity oil (1000 cp) results in a depleted zone within the NAPL that increases with dissolution time. 

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. 

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