One-Dimensional Conducting System

Physical concepts useful in describing the conducting one-dimensional materials have been reviewed. The important features necessary for one-dimen-sional conducting systems are now summarized  

The basic repeat unit for either inorganic or organic systems should be planar, have a noneven number of electrons, and have an unfilled orbital with a large extension perpendicular to the plane of the molecule. This allows overlap between sites and formation of a partially filled band. 

The molecules should stack as closely as possible and have, preferably, metal-metal bonding through the orbital for inorganic materials and n orbital overlap for organic materials in order to increase the transfer matrix element, t, and hence the bandwidth. Thus, the repeat unit should be planar without bulky groups. 

The molecules should be uniformly spaced to avoid splitting the electron energy bands and the subsequent formation of a semiconductor. 

The presence of electron-withdrawing groups attached to the molecules forming the chain and/or highly polarizable molecules near the chain is useful in reducing the Coulomb repulsion between the mobile electrons. 

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Numerous macrocyclic metal complexes have been considered as building blocks of one-dimensional conducting systems. This is due to their good planarity and, in some cases, to the extended delocalised n system of their ligands. 

The highly conductive class of soHds based on TTF—TCNQ have less than complete charge transfer (- 0.6 electrons/unit for TTF—TCNQ) and display metallic behavior above a certain temperature. However, these soHds undergo a metal-to-insulator transition and behave as organic semiconductors at lower temperatures. The change from a metallic to semiconducting state in these chain-like one-dimensional (ID) systems is a result of a Peieds instabihty. Although for tme one-dimensional systems this transition should take place at 0 Kelvin, interchain interactions lead to effective non-ID behavior and inhibit the onset of the transition (6). 

Conducting Magnets Having Quasi One-Dimensional Electron System. 83... 

In this and the next sections we discuss two groups of molecule-based conducting magnets at which the %-d interaction works effectively. The first approach is the use of quasi one-dimensional electronic systems as the re-electron layers, and the other strategy is to increase the magnitude of the %-d interaction by the introduction of intermolecular halogen-halogen contacts. 

The soliton conductivity model for rrans-(CH) was put forward by Kivelson [115]. It was shown that at low temperature phonon assisted electron hopping between soliton-bound states may be the dominant conduction process in a lightly doped one - dimensional Peierls system such as polyacetylene. The presence of disorder, as represented by a spatially random distribution of charged dopant molecules causes the hopping conduction pathway to be essentially three dimensional. At the photoexitation stage, mainly neutral solitons have to be formed. These solitons maintain the soliton bands. The transport processes have to be hopping ones with a highly expressed dispersive... 

One-Dimensional Conduction In the absence of energy source terms, Q is constant with distance, as shown in Fig. 5-la. For steady conduction, the integrated form of (5-1) for a planar system with constant k and A is Eq. (5-2) or (5-3). F or the general case of variables k (k is a function of temperature) and A (cylindrical and spherical systems with radial coordinate r, as sketched in Fig. 5-2), the average heat-transfer area and thermal conductivity are defined such that... 

The flow velocities in flame systems are such that transport processes (diffusion and thermal conduction) make appreciable contributions to the overall flows, and must be considered in the analysis of the measured profiles. Indeed, these processes are responsible for the propagation of the flame into the fresh gas supporting it, and the exponential growth zone of the shock tube experiments is replaced by an initial stage of the reaction where active centres are supplied by diffusion from more reacted mixture sightly further downstream. The measured profiles are related to the kinetic reaction rates by means of the continuity equations governing the one-dimensional flowing system. Let Wi represent the concentration (g. cm" ) of any quantity i at distance y and time t, and let F,- represent the overall flux of the quantity (g. cm". sec ). Then continuity considerations require that the sum of the first distance derivative of the flux term and the first time derivative of the concentration term be equal to the mass chemical rate of formation q,- of the quantity, i.e. 

The pseudo-one dimensional conduction problem defined by the experimental system has a well-known solution [23]. While it proved difficult in practice to satisfy perfectly the boundary conditions for the ideal solution, a good enough approximation was possible such that the phase lag could be used to calculate the diffusivity directly [24]. 

Conductivity of Quasi-One-Dimensional Metal Systems with Random Impurities at TO 187 H. Fukuyama and P.A. Lee ... 

CONDUCTIVITY OF QUASI-ONE-DIMENSIONAL METAL SYSTEMS WITH RANDOM IMPURITIES AT T=0... 

Mukhopadhyay et al. first used LB films of specially substituted phthalocyanine molecules to sense toluene vapor based on the changes in the electrical conductivity [9]. Phthalocyanine and porphyrin derivatives are p-type semiconductors. The interaction with n-electron systems can lead to a cofacial orientation of the nucleus, resulting in a one-dimensional semiconducting system. The exposure to the VOCs may change the cofacial molecular orientation and, as a consequence, the conductivity. However, the interaction between the VOCs and the sensitive molecules is not very strong, as these VOCs are not strong electron donors or electron acceptors. A very low conductivity of 10 to 10 S/cm was usually measured when the sensitive layers were exposed to the VOCs, which is difficult to be detected. Therefore, in most cases, the mass transduction and UV-vis absorption method were adopted to detect the presence of organic vapors. 

The Peierls transition, characteristic of one-dimensional metallic systems, is a static, periodic lattice distortion at its transition temperature Tp, which produces a semiconducting or insulating state for T < Tp. The lattice distortion is accompanied by a spatially periodic modulation of the density of the conduction electrons, a charge-density wave. The two periods are the same and depend only on the filling of the conduction band their lattice vector is given by 2kp, that is twice the Fermi wavevector kp. 

Briithng et al. have treated the conductivity of quasi-one-dimensional CDW systems in the framework of the Boltzmann equation (see e.g. [M2] or [M3]) with scattering from longitudinal acoustic phonon [23, 24]. For the temperature dependence of the conductivity u(T), they derived an integral equation which, aside from the temperature-dependent energy gap 2A(7), contains only a single materials parameter C ... 

Part II surveys the inorganic materials which exhibit or potentially exhibit a columnar structure. Emphasis is placed on square planar third-row transition metal complexes which exhibit the properties of anisotropic electrical conductivity and the first-row transition metal complexes which exhibit anisotropic cooperative magnetic behavior. The measured chemical and physical properties of the known one-dimensional inorganic complexes are summarized and a number of potentially one-dimensional materials are surveyed. The known one-dimensional magnetic systems are then presented. An extensive reference list including citations through the beginning of 1975 is included to make it easy for the reader to go further into areas of his particular interest. 

The recent experimental confirmation of the existence of one-dimensional metallic systems has led to a rapid increase in the experimental and theoretical study of these conducting systems. The objective of this section is to acquaint the reader with the physical basis of the concepts currently being used to explain the experimental results. Emphasis is given to the development of one electron band theory because of its central importance in the description of metals and understanding the effects of lattice distortion (Peierls transition), electron correlation, disorder potentials, and interruptions in the strands. It... 

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