Geometric ladder

In Figure 8-1 we show the chemical structure of m-LPPP. The increase in conjugation and the reduction of geometrical defects was the main motivation to incorporate a poly(/ -phenylene)(PPP) backbone into a ladder polymer structure [21]. Due to the side groups attached to the PPP main chain excellent solubility in nonpolar solvents is achieved. This is the prerequisite for producing polymer films of high optical quality. A detailed presentation of the synthesis, sample preparation,... 

A possible explanation for the formation of this planar ladder structure can be found in the close geometrical similarity of 7 to (3-gallium. The relative positions of the Ga atoms in 7 are comparable to those found in (3-gallium (see Fig. 18), but as expected, the Ga-Ga distances in 7 are all shorter than in (3-gallium due to a more molecular kind of bonding. This means that in 7 the formation of metalloid structures is preferred over the formation of polyhedral structures, which results in the unusual arrangement of the Ga atoms. 

The photoluminescence spectrum of MeLPPP as depicted in Figure 5.8 is characterized by a steep onset at 2.69 eV and by the well-resolved vibrationally split maxima which are homologous to the excitation spectrum. The dominant photoluminescence maximum is only very slightly Stokes-shifted by -35 meV, which is due to the ladder-type structure of the polymer hindering geometrical relaxations. The steep onset of the absorption spectrum reflects the high intrachain order of MeLPPP in the film. 

It is possible to form helicates using either tetrahedral or octahedral metal ions, by applying similar geometrical arguments as for racks, ladders and grids... 

Another possibility, which mimics the geometrical situation better, is to connect the dashpots through springs in a network structure, say a fractal one, while keeping the simple forms Ek = E = const and r)k = V = const [8,9, lOOj. Again, this model gives rise to a c<> -behavior for G (ladder models are mechanical realizations for fractal elements [8,9], since they fulfill equations of the form... 

This example shows three t5rpes of circuit diagrams for two relaxation time constants with the same R and C values, resulting in a Nyquist plot that usually shows two time constants (in the case of the Ladder model only one time constant was observed due to selected values for R, R, Cj, parameters) but with various characteristic fitting parameters. CMe always has to attempt to select a circuit that represents the geometrical distribution of impedance-related processes that physically occiu- inside of the system. A criterion of simplicity also has to be applied based on selection of only feasible processes with defined and well-resolved impedance characteristics to model the system. Computer-assisted fitting is necessary to resolve the overlapping arcs in the Z and M planes, but this method typically is unable to resolve arcs with time constants that are different by less than at least a factor of 100. 

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