Effective molecular length

Petroleum crude and its refinery products have two major component based on distillation. The portion that can be distilled under refinery conditions can be called volatiles and the nondistillables are the nonvolatiles. The volatiles can be analyzed by GC or GC-MS. The crude has both components. The distillate as the names applied, such as naphtha and kerosene contain only volatiles. When GPC is used for analyzing various distillates, the fractions separated by GPC can be characterized by GC or GC-MS. These data can be used to verify the nature of components present in various distillation cuts as a function of GPC elution volume. If the samples such as crude contains both volatiles as well as nonvolatiles, the samples should be separated into volatiles and nonvolatiles. The GPC of both components should be used to calibrate the GPC of the total crude. The parameter that can be obtained from GPC is effective molecular length. It can be used to relate other molecular parameters of interest after calibration. 

The development of rigorous theoretical treatments for the elution behavior of small molecules has been largely ignored due to the adequacy of predictive ability of log M, log effective molecular length (ref. 9) or log effective molecular volume models (ref. 10). However, the calculation of these parameters for macromolecular solutes with the same degree of confidence is not yet possible. 

Effective molecular mass between crosslinks tvtc/kg mol 1 Tensile yield strength cry/MPa Energy release rate Gic/Jm 2 Half crack opening displacement w = 6/2 = Gic/2cry w/pm Chain contour length (Eq. 7.9) lc/nm... 

Here c is the polymer concentration by weight. < the density of the polymer, a an effective bond length or measure of the coil dimensions, and to the monomeric friction factor. The subscript zero indicates the pure polymer. Since 2 (H), the mean-square end-to-end chain separation, the viscosity will be directly proportional to the polymer concentration unless the plasticizer modifies the coil swelling. At high molecular weight the monomeric friction factor is increased by the factor (MIMf)" and M, is increased relative to the undiluted polymer [equation (55)]. Thus... 

Fig. 9. The effect of interpolymer complexation on the correlation length, , and the effective molecular weight between crosslinks, Mc, in P(MAA-g-EG) graft copolymer networks with permanent, chemical crosslinks ( ).

R. E. Martin, T. Mader, F. Diederich, Monodisperse Poly(triacetylene) Rods Synthesis of a 11.9 nm Long Molecular Wire and Direct Determination of the Effective Conjugation Length by UV/Vis and Raman Spectroscopies , Angew. Chem Int. Ed. Engl. 1999,38, 817-821. 

The benzofuran-naphthyridine linked dye compound (ABAN, see Fig. 1) has been successfully converted to fluorescent organic nanoparticles [34], for which their photophysical properties such as spectral features and emission intensity are remarkably different from those at the molecular level (solution). The results are rationalized by coplanarization of the benzofuran-naphthyridine molecule in the nanoparticle to extend its effective conjugation length and hence increase the oscillator strength, as is similar to the cases described above. 

In practice, p is adjusted in the numerical calculations until the calculated Mapp agrees with the measured one. All other quantities, for instance the molecular-weight dependence of (S2)z, or the shape of the scattering curve, and the whole dynamic scattering behaviour, are now fully determined if the effective bond length is known. 

Similar to the molecular photosensitizers described above, solid semiconductor materials can absorb photons and convert light into electrical energy capable of reducing C02. In solution, a semiconductor will absorb light, and the electric field created at the solid-liquid interface effects the separation of photo-excited electron-hole pairs. The electrons can then carry out an interfacial reduction reaction at one site, while the holes can perform an interfacial oxidation at a separate site. In the following sections, details will be provided of the reduction of C02 at both bulk semiconductor electrodes that resemble their metal electrode counterparts, and semiconductor powders and colloids that approach the molecular length scale. Further information on semiconductor systems for C02 reduction is available in several excellent reviews [8, 44, 104, 105],... 

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