Anisotropy of conductivity

Instabilities caused by the anisotropy of conductivity and corresponding to a periodic deformation of the alignment of the director in a nematic monodomain under the action of a direct current or low-frequency alternating current. 

The electrical transport of KCP was reported by Zeller et The room-temperature conductivity along the molecular stacking direction is 300-400 S cm , which is 10 greater than the conductivity perpendicular to the chain direction. The temperature dependence of conductivity along the chain direction shows metallic behaviour down to around 250 K and semiconducting behaviour below that temperature. The broad maximum of conductivity around 250 K is due to the one-dimensionality of the linear-chain system. The large anisotropy of conductivity in directions parallel and perpendicular to the chains confirms the onedimensional character of KCP. 

FIGURE 2.1.22 Temperature dependence of the hole mobility in ultrapure pentacene crystals extracted from the SCLC measurements. The open symbols correspond to the valnes of p calculated under an assumption of uniform current flow across the crystal thickness solid symbols take into account the anisotropy of conductivity in pentacene. Below room temperature, the mobility increases with decreasing T as p T T where y 2.4. (From Jurchescu, O. D. et ah, Appl. Phys. Lett., 84, 3061, 2004.)... 

The anisotropy of resistance is most likely due to the different behavior of silicon on steps and terraces of vicinal surface. Si atoms on terraces under the growth conditions are donors, while on steps they are acceptors. Electrons at steps compensate the nearest holes at terraces. Thus, quasi-ID channels of p-type are formed along vicinal steps and the anisotropy of conductivity occurs. 

Due to the anisotropy of conductivity, space charges will develop as indicated in fig. 3.10.7 till the transverse electric field stops the transverse current. The local transverse field in the steady state is easily seen to be... 

Such anisotropy has macroscopic character and should be related to the morphology of the whole sample and not to the anisotropy of conductivity of CT complex crystallites themselves. The hypothesis that conductivity of the investigated materials is determined by junctions between CT complex crystallites is further confirmed by measurements of the temperature dependences of conductivity in both directions ... 

One can see from Fig, 3 that conductivity in the direction parallel to the crystal columns is nearly temperature independent being not far from the temperature dependence of conductivity found for meta-lic CT complexes. The conductivity in perpendicular direction has considerably higher activation energy because it is limited by the conductivity of the polymer matrix which separates crystal columns. These results also show that the anisotropy of conductivity of the samples obtained is temperature dependent. 

A method has been developed which makes it possible to produce conductive polymeric composites with significant anisotropy of conductivity, Due to high ratio of conductivities in two perpendicular directions the materials obtained can be treated as linear polymeric conductors. Further work along these lines is in progress. 

The conductivity of the metallic systems is typically orientation independent. In the last several decades, 2-D and 1-D metals (with anisotropy of conductivity) have been discovered. The latter are called molecular wires and may have unusual properties, but are difficult to prepare because they often undergo spontaneous dimerization of the lattice (known as the Peierls transition). 

Likewise, the perpendicular conductivity decreases with increasing substrate temperature, indicating that the conditions used for film deposition allow a further purification of the molecular material which should signiricantly improve its electrical properties. Importantly, the anisotropy of conductivity increases with substrate temperature in agreement with the proposed model of charge transport along the... 

In PPV-H2SO4 samples, the low temperature conductivity of metallic samples in both parallel and perpendicular directions to the chain axis can also be fitted to Equation 2.2 [34, 35]. However, at temperatures below 4 K, the fit is rather good even in the presence of a magnetic field, as shown in earlier works [34]. Hence, in metallic PPV samples, the localisation-interaction model is valid at low temperatures, as observed in the case of metallic (CH) samples. Moreover, the MC data in both systems are consistent with the localisation-interaction model, as explained below. Although the anisotropy of conductivity in metallic, oriented (CH) and PPV samples is nearly 100, the o(T) is rather similar in both parallel and perpendicular directions to the chain axis, indicating that an anisotropic three-dimensional model is appropriate in these systems. 

Although the anisotropy of conductivity in metallic oriented-]CH) or PPV-H2SO4 samples is nearly 100, the behaviour of the MC is identical whether the current is parallel or perpendicular to the chain axis. This suggests that high quality oriented conducting polymers behave as anisotropic three-dimensional systems in which the charge transport mechanism is nearly identical in both parallel and perpendicular directions to the chain axis. 

Like in the case of diffusion, the anisotropy of conductivity = CTy — Cxcan be positive (e.g., in conventional nematics) or negative (in smectic A, discotic... 

With the field applied, this fluctuation causes a slight periodic deflection of the electric current lines along the director proportional to the anisotropy of conductivity (ja = 0. This creates the x-component of the current that, in turn, results in the accumulation of a space charge Q(x) close to the points where angle 0 = 0. Therefore, the x-component of the field (E ) emerges. The electric current density is Jt = OtjEj where the tensor of the electric conductivity has a standard form ... 

Column structures have also been determined for carbonyl complexes of rhodium, iridium, and platinum. For platinum complexes of the formula [Pt3(CO)6] , the maximum value of n probably does not reach more than 20 (Figure 3.26) and therefore these carbonyls do not show anisotropy of conductivity. Various Ir(I) and Rh(I) complexes possessing column structures are known [IrX(CO)3] (X = C1, Br, I), [IrCl,o7(CO)2.93], [Ir(acac(CO)2], Ho.38lrCl2(CO)2(H20)2.9, Ko.58[IrCl2(CO)2], and... 

A biased photoconductor under the influence of magnetoconcentration for the case of low magnetic fields was investigated by Malyutenko and Teslenko [397, 398]. They denoted the effects of Lorentz force to carriers in such a device the transversal sweep-out ( a semiconductor with induced anisotropy of conductivity ). Their work included both theoretical and experimental investigation, and the magnetic induction they utilized did not exceed 0.2 T. 

When a low frequency ac electric field (iXIIXq) is applied to homogeneously oriented, fairly conductive nematics, a very regular vortex motion (normal rolls) is often observed, which is accompanied by a strip domain optical pattern (Kapustin-Williams domains) [238, 239] (Fig. 31b). The reason for this instability is the space charge accumulated in the bulk due to the anisotropy of conductivity. It appears in thin cells ((f = 10-100 xm) and has a well-defined voltage threshold that is independent of the thickness. The threshold can be easily calculated for the simplest steady-state, one-dimensional model shown in Fig. 32. 

With the field applied, this fluctuation results in a slight deviation of the electric current lines in the x direction proportional to the anisotropy of conductivity a =G -CTj >0, and, in turn, in an accumulation of the space charge around extremum points... 

This pair of equations has the same form as the set (Eqs (96) and (102)) for the injection instability. However, the fluid velocity is not included in the new set explicitly, and the destabilization is due to the coupling terms QEIr] and a f y/E, where Ceff is an effective constant including the anisotropy of conductivity that is responsible for the instability. The field-dependent time constant for the reaction of the director to the field was discussed earlier (Eqs (33) and (62)). Near the threshold Tj. Tq. 

Table 2.1 Conductivity and Anisotropy of Conductivity of l-(CH)r at 250 K and 1.2 K. at Ambient Pressure and 8 kbar, for Current Parallel and Perpendicular to the Chain Axis...

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