Prediction band

APPROXIMATE VALUES OF CHARACTERISTIC PARAMETERS IMPORTANT IN PREDICTING BAND BROADENING... 

Fig. 6.7. Calibration straight line with relevant upper and lower confidence and prediction bands...

H. Liang and Y. Liu, Recursion equations in predicting band with under gradient elution. J. ChromatogrA 1040 (2004) 19-31. 

In principle, it should be possible to design and synthesise a polymer with a sufficiently small band gap that it would be conducting without doping. Bredas 4I1) has discussed theoretical calculations of the band-gap of polymers based on polyisothianaphthene. A number of polymers have band-gaps predicted to be less than 1 eV, with polyisonaphthothiophene having a predicted band-gap of almost zero. Jenekhe412 has made polymers with a band-gap of 0.73 eV, based on polythiophene with alternating aromatic and quinonoid units (Fig. 12). 

The predicted band structure, merging considerations of band width and orbital topology, is that of 16. To make a real estimate, one would need an actual calculation of the various overlaps, and these in turn would depend on the Pf Pt separation. 

Notice that the gap vanishes for a homopolar semiconductor, which is true also for the exact bands, and if V were equal to V , it would simply be equal to times the predicted band width, p4K,. Thus, qualitatively, the gap is in very simple correspondence with the polarity of the system. The observed splittings are from 30 percent to 45 percent lower than those predicted in the K,-only theory by Eq. (6-12). The value is not modified as we add additional matrix elements within the Bond Orbital Approximation (Pantelides and Harrison, 1975). P rom Eqs. (6-3) and (6-4) we see that the situation is greatly complicated if the Bond Orbital Approximation is not u.scd (that is, bonding antibonding matrix elements are added), though of course the predicted gaps do go to zero as the polarity goes to zero in any case. 

It should be noted here that the overall shape of the K-phase FS can also be obtained by a simple free-electron treatment. With the usual parabolic bands and the known electron density one obtains a circular FS which cuts the Brillouin zone at approximately the point where the calculated gaps in Fig, 2.19 occur. Folding back these FS parts into the first Brillouin zone results in an only slightly modified topology compared to the calculated tight-binding FS of K-(ET)2l3. The effective masses estimated from the predicted band-structures are close to the free-electron mass, rrie. These values, however, are in contradiction to the experimentally extracted masses from optical [165, 166] and also dHvA or SdH measurements (see Sect. 4.2). 

In summary, the experimentally obtained FS topology of the k phase is principally in good agreement with the predicted band structure. Some of the salts exhibit an extreme 2D electronic structure, even by standards of ET compounds. Especially for /t-(ET)2l3 strong deviations from the 3D Lifshitz-Kosevich theory are observed. On the other hand, the dHvA signal of At-(ET)2Cu(NCS)2 is fully compatible with the 3D theory and even the extraction of the electron-phonon coupling constant was possible. The effective cyclotron masses for the MB orbit are 3.9 me for the first and 7me for the latter salt. How far this reflects the different TcS of these two compounds needs further investigation. 

Figure 4.38 shows the measured magnetization at T = 0.5 K for a field applied perpendicular to the conducting planes [372]. Clearly two different dHvA frequencies are visible in the signal. A slow oscillation of 730 T is superimposed on a dominant high frequency of 4170T. These frequencies correspond to FS areas which are more consistent with the band-structure calculation for the orthorhombic unit cell (Fig. 4.37a) but are in disagreement with the predicted band structure for the monoclinic cell (Fig. 4.37b). 

As a final point, in 6>-(ET)2l3 at fields below 2T additional very slow SdH oscillations were observed [373]. The reported frequencies were somewhere between 2 and 12 T and were more 3D in character. Very small effective cyclotron masses of 0.05 me and 0.014 me were obtained. From the predicted band structures these extremely small 3D FS pockets cannot be understood. Further work is necessary to verify these observations. 

Whenever numerical calculations are carried out to predict band profiles from equilibrium isotherms and kinetic data (see Chapter 10) or to derive the equilibrium isotherms from acquired band profiles (see Chapters 3 and 4), it is imperative accurately to model the actual boundary condition, i.e., to perform the calculations using the concentration profile of the feed as it enters into the column. The importance of the selection of the boimdary condition, of its modeling in certain cases, has been demonstrated many times [42—45]. Figure 2.4 illustrates the importance of following this recommendation when comparing experimental and calculated band profiles. 

A similarly high Voc for ITO/PPV/Al photovoltaic devices also was observed by other groups. Jenekhe et al. [63, 64] report the observation of a quantum efficiency IPCE of 5% in ITO/PPV/Al photodiodes and of a power conversion efficiency of approximately 0.1% under low light intensities of 1 mW/cm. The typical film thickness of their devices was varied between 100 to 600 nm. The open circuit voltage of these devices, as defined with respect to the ITO electrode, was measured as 1.2 V. The high open circuit voltage was explained by the formation of a Schottky barrier at the Al/PPV interface. The predicted band bending due the PPV/Al interface formation was verified by XPS measurements [65, 66]. 

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