RESISTIVITY OF WIRE

Resistivity of Wire

Resistivity of Wire

1. Introduction

The optical linear properties of materials, typically the refraction index, as well as more exotic nonlinear properties in the field of photonic and optoelectronic devices, can be well understood by means of the molecular polarization properties. During the last years, we have been interested in the study of the photoinduced charge transfer polarization process, in D-bridge-A systems, in order to characterize the p-conduction channel nature of the molecular wires when the charge migration between the electron-donor group (D) and the electron-acceptor group (A), through a polyenic conductor molecular bridge, occurs in the groundand excited state.

2. The photoconduction one-dimensional model

Some time ago, based on the molecular conductance (Ga), defined as the electronic charge transferred to the acceptor group (?QA) per quantum absorption, we developed a quantum photoconduction charge transfer model in order to determine the resistance and resistivity of polyenic molecular wires in the charge transfer excited state (CTES). This last molecular parameter, resistivity, gave us a value of 1.3 Å per quantum for polyenic molecular wires when we assumed 4.5 Å2 as a mean cross-section (S) of the p-conductor channel.

However, from an experimental point of view, this model presented a particular disadvantage since the molecular resistance in the excited states is calculated in relative quantum units. By the following, the obtained resistance data cannot be compared with those of conduction measurements determined by means of classical experimental techniques. Therefore, in order to obviate this difficulty, now we have reformulated our model in a new approach by using the heuristic formulation of Landauer , based on the scattering process of electrons in one-dimensional conductor metal wires.

Two decades ago, Economou and Soukoulis [10], based on Landauer's work , derived a theoretical expression for the conductance (G) of an one-dimensional metallic conductor as:

(1)

where e is the electron charge, h is Planck's constant and F(T, R) is a function of the transmission (T) and reflection (R) probability factors of the electrons in an one-dimensional conductor, where f(T, R)=T/R and T+R=1. Then, the molecular resistance (R) of the one-dimensional conductor is:

(2)

Therefore, if the transmission probability factor (T) through the p-conduction channel of these organic molecular wires is assumed to be equivalent to the normalized charge transferred to the acceptor-electron group (Qr), where Qr is determined by means of the ?QA ratio between ?QA(n>0) and ?QA(n=0) for every n-oligomer series under study, and 0=Qr=1, we finally obtain a new equation for the molecular resistance (Rm) in excited state of the p-conduction channel involved in these n-oligomeric compounds as follows:

(3)

Rm=(h/2e2)[(1/Qr)-1] .

If we adjust our early model to this new one-dimensional conductor approach, where the molecular resistance is inversely proportional to the normalized charge transferred to the acceptor group (Qr) after photoexcitation, we found essentially the same resistance trend when (T=Qr)1.

By the following, we are able to calculate the molecular resistance (Rm) in ohmic units from Eq. 3 according to:

(4)

Rm=12.91[(1/Qr)-1] (in kO) .

3. Theoretical methods

The molecular geometry calculations of the D-bridge-CHO systems studied in this work have been obtained by means of the ...