Delocalization length

Evidence has accumulated from various sources which supports the idea that polyenylic cations are implicated in other aspects of PVC degradation. Molecular orbital calculations carried out by Starnes (45) show that the charge is better stabilized at the center of the formal delocalized length of the ion than at the end and that since the process represented by equation 16 becomes more favorable with increasing sequence length, this may provide an explanation for the relatively short sequence lengths. 

Thus the ir-electron delocalization length Lj and the linear and nonlinear optical coefficients in ID conjugated systems reach their... 

Measurement of the aggregate radiative lifetime and that of its absorption spectrum half-width are the two experimental ways to estimate the value of the delocalization length. 

In addition, the excitation delocalization length of an aggregate could be estimated on the basis of the measurement of the aggregate radiative lifetime and its absorption spectrum half-width as described above [10, 11]. Such estimation, being interesting as itself, could also be regarded as the lower limit of physical dimension of the aggregate. 

Bakalis LD, Rnoester J (2000) Linear absorption as a tool to measure the exciton delocalization length in molecular assemblies. J Lumin 87-89 66-70... 

Systematic studies of well-defined materials in which specific structural variations have been made, provide the basis for structure/property relationships. These variations may include the effect of charge, hybridization, delocalization length, defect sites, quantum confinement and anharmonicity (symmetric and asymmetric). However, since NLO effects have their origins in small perturbations of ground-state electron density distributions, correlations of NLO properties with only the ground state properties leads to an incomplete understanding of the phenomena. One must also consider the various excited-state electron density distributions and transitions. 

Polaronic and bipolaronic charge states are well known in electroactive polymers, and can be observed in model oligomers with overall delocalization lengths as small as 16 atoms. It has been suggested that localized charge states may be involved in oligomers and polymers having enhanced proper-... 

However we have not yet been able to accomplish differentiation for EDG = Me2N. Thus by controlling the size of the oligomeric segment we predetermine the delocalization length of the polaronic or bipolaronic domain as well as the absorption characteristics of the polymer in either pristine or oxidized form. 

There is no doubt that polaronic and bipolaronic charge states can be supported in stable form in small oligomers in solution, or incorporated as part of a copolymer sequence. Enhanced x properties can derive from either N, P or BP states as a function of increased delocalization length, and we anticipate several families of copolymers based on the modeling studies discussed in this paper to become available in the near future to test these proposals. 

The interchain hopping transport can be described by the probability Ql(x) -where x is the effective conjugation or delocalization length-of finding a comparable mean free path on another chain weighted by the Frank-Condon factor FC. The conductivity a can then be described as a function of the concentration C of polarons, multiplied by the integral over the interchain hopping probability Pp(x) [96, 97]. 

Determined by their molecular nature, most CP nanoscale materials are either amorphous or polyerystalline. In the latter case, the size of the ordered crystalline grain/island is typically less than 10 nm [106]. This limits the electron and hole delocalization length to a similar scale. Therefore, based on this argument, unless the cross-seetion of a CP nanowire is comparable to the delocalization length, electron and hole transport in such a nanowire should follow their behavior in a 3-D bulk material. As we have discussed in the previous section, many nanowires and nanotubes prepared so far are indeed larger than the characteristic electronic localization length, and it is, in general, valid to treat these nanowires and nanotubes with the already established electronic-transport theories and models for 3-D CP materials. 

The further development of the self-consistent version of PRISM theory will be particularly important in two areas (i) liquids of flexible conjugated polymers where the electron delocalization length and interchain dispersion forces are strongly coupled to chain conformation [100], and (ii) polymer alloys where... 

The most relevant fact is that while the Gr matrix is certainly truncated at the -fl and -1 units in the Fr matrix the distance of interaction of the zero-th unit with its s-th neighbour is yet unknown since the so-called delocalization length needs to be determined [41-43], The truncation at the site s of the long ribbon of interaction submatrices is then arbitrary, Many ab initio calculations are at present dealing with this essential problem which is common to all poly-conjugated chains presently available. 

The truncation of the sum in Eq. (3-45) is then arbitrary, thus affecting the validity of the physical conclusions which may be derived. It follows that any addition or variation of terms or extension of the interactions (increase of delocalization length) will affect the numerical values of the elements of the Fr(dispersion curves [41, 42], It is apparent that the shape of the dispersion curves is a direct consequence of the electronic properties of the poly-conjugated chains [58] (Figure 3-5). 

POT Cl fibre, similar to those for POT—HCl powder. Upon stretching threefold, the (295 K) increases almost by an order of magnitude while decreases slightly to 3.2 x 10" K. On the other hand, for POT-CSA fibre, a T) at room temperature is 10 S cm and it shows much weaker temperature dependence with To 350 K, indicating that POT-CSA fibre is much closer to the localization-delocalization boundary than POT—HCl samples. A significant increase in delocalization length as 0 K for the POT-CSA fibre ( 40A as compared to that for POT—HCl powder ( 5A) also indicates the formation of the delocalized states in POT-CSA system. 

---