Doped Trans-polyacetylene Research Articles

Electronic states in doped trans-polyacetylene: numerical simulation of half-filled systems

Doped polyacetylene is simulated by the SSH model with a random distribution of impurities. Three types of impurities are examined. They are site- and two bond-types. One of the bond-types is named cis-type, since all the impurities are so assumed to modify the electron transfer that the dimerization is enhanced. The other is named compensated doping, since the half are for the enhancement while the other half are for reduction. Starting from a uniform dimerization, we determine the electronic states and the lattice configuration by an iteration method. Periodic boundary condition is relaxed so that the electronic wave function has a given phase difference between the left and right boundaries. The system is composed of one hundred (CH) units, electrons of the same number, and impurities of concentration up to eight percent. The sample averaging is performed over one hundred distributions of the impurities to confirm that the averaged order parameter and density of states well reproduce the results by the CPA calculations. The averaged order parameter is smaller than the impurity-free system with the site-type impurities and the compensated doping. It is larger with the cis-type impurities. With the site-type impurities, an impurity band is formed in the energy gap. With the cis-type doping, there is no impurity band. There are two in the compensated doping.

Soliton-impurity interaction in heavily doped trans-polyacetylene

The electronic structure of highly doped trans-polyacetylene is calculated for an optimized geometry of the polymer chain. The Hamilitonian applied to this system includes the Su-Schrieffer-Heeger Hamiltonian and potential terms describing intra- and inter chain electrostatic interactions. For all doping levels included in this study (up to 12%) the soliton lattice remains stable. The energy gap decreases rapidly in the doping regime 7%<y<10%, followed by a saturation above y≈10%. Including weak disorder in the positions of the dopant ions, the saturation level for the density of states at the Fermi energy is close to that obtained experimentally.

Metal-insulator transition in doped conducting polymers: Disappearance of electronic gap with persisting bond alternation

Electronic states are investigated in doped trans-polyacetylene, using the SSH model with site-type impurities randomly distributed. Each impurity accepts one electron. Lattice configuration and electronic wave functions are determined self-consistently with full lattice relaxation. The order parameter remains larger than that by Mele and Rice, as the disorder intensifies. The energy gap vanishes when the concentration is several percent and a gapless Peierls state takes place. The present results well explain the appearance of the metallic Pauli susceptibility, its magnitude, and the critical concentration, characteristic to the metal-insulator transition observed in experiments. The persistence of dimerization is also consistent with the X-ray studies. The wave function tends to extend more easily than Su's estimations.

Soliton lattice in highly doped trans-polyacetylene.

The geometrical and electronic properties of highly doped trans-polyacetylene are studied by use of a total Hamiltonian consisting of the Su-Schrieffer-Heeger Hamiltonian, describing the electron hopping along the polymer chain, an extended Hubbard term due to the intrachain electron-electron interaction, and an external Coulomb potential arising from interchain electrostatic interactions and interactions with counterions. The three-dimensional structure of the system including polymer chains and dopant ions is that obtained from x-ray crystallography studies of sodium-doped trans-polyacetylene. At all doping levels (y\ensuremath{\le}12 at. %), and for all chain lengths (100N224) included in this study, the ground-state configuration is a soliton lattice, commensurate with the periodicity of the external potential. A self-consistent treatment of the soliton charge distribution entering the external potential is essential in order to calculate the electronic properties of the system correctly. For a regular distribution of the counterions, the evolution of the single-particle gap in the electronic spectrum exhibits a sharp decrease in the gap at doping levels between y\ensuremath{\sim}8 and 10 at. %. Increasing the doping level further does not lower the gap significantly. This result indicates the possibility of having a purely electronic phase transition within the soliton-lattice configuration, in agreement with experimental data. The size of the energy gap at high doping levels is, however, in the nonmetallic regime. When disorder in the positions of the counterions is introduced, the electronic states at the soliton and conduction-band edges tail off and close the gap around the Fermi level above \ensuremath{\sim}10 at.% doping. This phenomenon occurs already at very weak (intrinsic) disorder for which the counterions are displaced by maximum one-half of a carbon-carbon bond length.

Electronic structure of highly conducting conjugated polymers: evolution upon doping of polyacetylene, polythiophene, and polyemeraldine

The electronic properties of three types of conducting polymers: trans-polyacetylene (proto-typical of systems with a degenerate ground state), polythiophene (as an example of compounds with a nondegenerate ground state), and polyemeraldine (which can be doped via protonation) are reviewed. The structural and electronic band structure properties of these systems are studied at various defect concentrations corresponding to undoped, lightly doped, and highly doped polymers. Geometry optimizations of oligomeric equivalents to the undoped and doped polymers are performed using the semi-empirical MNDO and AM1 methods. The electronic band structures are calculated using the VEH method. The interpretation of the optical absorption data is discussed in terms of interband transitions; for doped trans-polyacetylene including soliton defects and for doped polythiophene including bipolaron defects. For highly doped trans-polyacetylene and polythiophene as well as for protonated polyemeraldine, the electronic structure of a polaron lattice conformation is discussed and shown to be in agreement with existing optical and magnetic data on these polymers.

Metal-insulator transition in trans-polyacetylene.

We have calculated the band structure for a chain of doped trans-polyacetylene using the electronic part of the Su-Schrieffer-Heeger Hamiltonian plus the Coulomb potential arising from ions and charged solitons surrounding the chain. The lattice structure used was that determined by x rays for Na-doped polyacetylene. To agree with a number of experimental observations the donated electrons were taken to be in soliton states at all dopant concentrations. In obtaining the potential of a point charge on a chain in the metallic state, the confinement of the free electrons to a chain was taken into account. Because screening depends on the calculated energy levels, specifically on the density of states at the Fermi energy, \ensuremath{\eta}(${E}_{F}$), in the metallic state, which, in turn, depend on the potential used to obtain them, self-consistency was required in the calculations.The energy-level structure was found to depend strongly on the ion spacing, conveniently measured in terms of the average spacing a of C-H's along the chain. For ion spacing 5a, characteristic of the Na-ion-rich regions up to an average dopant concentration of \ensuremath{\sim}6%, the chain remained semiconducting. For ion spacing 4a, which appears to characterize the next phase for Na doping, metallic behavior was found for a doped chain length of \ensuremath{\sim}100 sites or more. Self-consistency was fulfilled with \ensuremath{\eta}(${E}_{F}$) equal to the value obtained from the saturation spin susceptibility in the metallic state. In addition to sufficiently long chains that the level spacing is comparable to kT, the metal-insulator transition is found to require considerable overlap of electron wave functions on adjacent solitons and a fairly deep potential well. The transition is best described as a Mott transition. Our model predicts that a sample in the metallic state at room temperature becomes semiconducting at lower temperature. Evidence for this is found in the temperature variation of the spin susceptibility and of ESR linewidth.It is argued that the energy-level distribution in the metallic state is similar for other dopants. We show also that our model is consistent with the optical absorption observed for doped polyacetylene.

Self-consistent-field calculations of the vibrational spectrum of undoped and doped transpolyacetylene

Semiempirical self-consistent-field calculations are carried out to compute the force constants for various cluster models of periodic transpolyacetylene and of neutral and charged soliton and polaron defects. The phonon spectrum of undoped polyacetylene is analyzed and compared with the vibrational spectrum of various polyene chains in which soliton or polaron defects have been introduced in a random way. The results support the interpretation that the 1100 cm−1 Raman band of undoped polyacetylene should be ascribed to a C—C single bond stretching motion weakly coupled to a C—H in-plane bending vibration. The 1292 cm−1 infrared peak of pure transpolyacetylene is ascribed to the C—H in-plane deformation, the strong adsorption at 1015 cm−1 has to be assigned to an infrared-active out-of-plane C—H deformation. The new narrow band around 1300 cm−1 seen in the infrared spectrum of doped polyacetylene is ascribed to C—C bond stretching, the additional very broad band between 800 and 900 cm−1 results from in-plane C—C—H bending and C—H out-of-plane bending motions involving relaxed bond lengths of the defect sites. The interpretation is not uniquely in favor of the soliton picture, polaron defects can serve as alternative explanation.

The infrared and Raman spectrum of trans-polyacetylene: A self-consistent-field study

Using force constants which have been obtained for the first time from semi-empirical self-consistent-field calculations on various cluster models of periodic trans-polyacetylene and of neutral and charged soliton and polaron defects the infrared and Raman spectrum of undoped and doped trans-polyacetylene is analyzed and interpreted.

The Evolution of Structure During The Alkali Metal Doping of Polyacetylene and Poly(p-Phenylene)

Abstract The progression of phases which evolve during the alkali metal doping of polyacetylene and poly(p-phenylene) is examined using newly developed structure concepts, crystal packing analysis, and diffraction and electrochemical data. At least for alkali metals larger than Li+, at dopant concentrations above a few percent the alkali metal ions aggregate in columns within the host polymer lattice. Structural variations result for polyacetylene both from the degree these columns are filled and the chain-to-column ratio. More limited phase variation results for poly(p-phenylene), where 2,3, and 4 chain/column structures are observed, but the metal-metal spacing within the columns is fixed. Structural models are presented for the 2 chain/column complex of poly(p-phenylene) and the 3 chain/column complexes of K and Rb doped trans polyacetylene.

Effects of Doping Induced Disorder in Polyacetylene

Abstract In this paper, the effects of disorder on the electronic structure of doped trans-polyacetylene are evaluated. In effect, at the high doping levels currently obtained on (CH)x, it is not realistic to consider the dopant molecules as isolated impurities. Therefore we have examinated in this work how a random distribution of dopant molecules broadens the impurity levels lying within the band gap. We consider a model where the molecules form covalent bonds with the neighbouring n orbitals. Making use of the SSH model for (CH)X chain, the electronic density of states is obtained by averaging the Green's function over the random distribution of dopants along the lines of a cluster CPA. From our results, we discuss the formation of impurity bands in the gap and their dependence on both the doping concentration and the chemical nature of the doping molecules.

Frequency response of hopping systems: Application to polyacetylene

Hopping mechanisms for conductivity are characterized by a broad distribution of hopping rates. We have calculated the ratio of the conductivity in the high-frequency regime (frequency greater than the maximum hopping frequency) and its dc value. The results for isoenergetic hopping and variable-range hopping are shown to differ, although both are found to be independent of the details of the hopping attempt frequency. These results are applied to the experimental data for doped trans-polyacetylene. Charge conduction in undoped and lightly doped trans-polyacetylene is in agreement with isoenergetic hopping consistent with intersoliton electron hopping. In contrast, the data for trans-polyacetylene doped to 0.01-0.05 ${\mathrm{I}}_{3}$ per carbon are in better agreement with variable-range hopping, consistent with the proposal of variable-range hopping among pinned solitons. These results support a change in the charge transport mechanism as polyacetylene is doped.

13C high-resolution NMR study of doped polyacetylene

13C high resolution NMR spectra of doped trans polyacetylene, (CH) x , have been measured. A spectrum of (CH) x doped with AsF 5 shows a downfield shift, while that with potassium an upfield shift. The charge distribution and the existence of sp 3 hybridized carbon on halogen-doped (CH) x chains are discussed.

Peierls distortion and vibrational spectra in undoped and doped trans-polyacetylene

We analyze the conditions under which the vibrational spectrum can provide information on the existence of the Peierls distortion in undoped trans-polyacetylene. If in the doped material sections of undimerized chains are generated, calculations predict a Raman active A g band approximately between 1300-1250 cm −1.

Polyacetylene doped with iron trichloride : Improved conductivity and stability

Trans polyacetylene (CH) x has been doped with FeCl 3 solutions in Nitromethane. In the “in-situ” EPR experiment we have observed the evolution of the EPR spectra with time during the doping process. That enabled us to gain information about the rate of dopant diffusion in solid material. Both EPR and conductivity measurements show that the doped material is reasonably stable even in the presence of air. Raman spectroscopic studies show the usual features observed in doped trans polyacetylene.

The importance of impurity states in doped transpolyacetylene

The authors assess the importance of the impurity states of a doped trans-polyacetylene chain. The impurity potential is modelled by a point charge that is located off the chain and screened phenomenologically with the bulk dielectric constant. The common assumption that the impurity levels of a dimerised chain closely approximate the hydrogenic levels of a point charge impurity in invalid when the impurity is not on the chain. Additional nonhydrogenic states occur. One of the new states is much deeper in the gap. The formation energies for charged soliton and charged polaron lattice distortions are found by solving the Su-Schrieffer-Haeger model for polyacetylene with an impurity added. The impurity states severely modify the structure of the soliton distortion. The charged polaron distortion, not the charged soliton distortion, is the most stable distortion that can be formed during doping with gap states consistent with the observed mid-gap absorption.

Vibrational dynamics and structure of doped polyacetylene as a one-dimensional disordered crystal

Vibrational infrared and Raman spectra of doped trans polyacetylene are interpreted on the basis of dynamical calculations which consider the system as a one-dimensional crystal containing structural disorder on the molecular level. Several types of structural defects have been studied. The spectroscopic evidence of topological solitons is not unique and an alternative model can be proposed.

Far infrared optical properties of pure and SbF5 doped trans polyacetylene

Far infrared transmission and reflection measurements are reported. Optical constants are studied and compared with previous results obtained with iodine and AsF5 doping. It is shown that optical properties of SbF5 doped films vary from one side to the other suggesting that the repartition of the dopant inside the material is not homogeneous. Transmissions- and Reflexionsmessungen im fernen IR werden durchgeführt. Die optischen Konstanten werden untersucht und mit früheren Ergebnissen an Jod- und AsF5-dotierten Proben verglichen. Es wird gezeigt, daß die optischen Eigenschaften von SbF5-dotierten Schichten sich von einer Seite zur anderen ändern, was zeigt, daß die Umverteilung des Dopanten im Material nicht homogen verläuft.

Spectroscopic studies on doped polyacetylene and β-carotene

In order to elucidate the structural details of doped polyacetylene (a highly conducting organic polymer), the optical absorption, Raman, and infrared spectra of not only trans-(CH)x doped with iodine, AsF5, and SO3 but also β-carotene doped with iodine and SO3 were studied. The infrared spectra of two kinds of isotopically substituted polyacetylenes (CD)x and (13CH)x doped with iodine were also observed. Analysis of the experimental results shows that upon doping each of the four vibrational branches (ν1–ν4) in the 1600–900 cm−1 region of a polyene chain splits into two groups, namely, the higher frequency group and the lower frequency one. The former group consists of the ’’gerade’’ vibrations of polyene parts which are not directly attacked by dopants but are perturbed along the chain, whereas the latter is made up of the ’’ungerade’’ vibrations of the positively charged polyene part with the doped site at its center. The Raman bands in the higher-frequency group of ν1 (mainly the C=C stretching mode) observed with various laser lines give definite information on the segments of conjugated trans double bonds existing in doped polyacetylene. The Raman spectra are also useful for clarifying the structures of dopants. In the infrared spectra of doped trans-(CD)x and (13CH)x the bands appearing on doping all showed respective isotope shifts which confirmed the view that these bands are of vibrational origin. In many respects doped β-carotene proved to be a useful model of doped trans-polyacetylene.