Solitons In Polyacetylene Research Articles

Dynamics of an Acoustic Polaron in One-Dimensional Electron-Lattice System

The dynamical behavior of an acoustic polaron in typical non-degenerate conjugated polymer, polydiacetylene, is numerically studied by using Su-Schrieffer-Heeger's model for the one dimensional electron-lattice system. It is confirmed that the velocity of a polaron accelerated by a constant electric field shows a saturation to a velocity close to the sound velocity of the system, and that the width of a moving polaron decreases as a monotonic function of the velocity tending to zero at the saturation velocity. The effective mass of a polaron is estimated to be about one hundred times as heavy as the bare electron mass. Furthermore the linear mode analysis in the presence of a polaron is carried out, leading to the conclusion that there is only one localized mode, i.e. the translational mode. This is confirmed also from the phase shift of extended modes. There is no localized mode corresponding to the amplitude mode in the case of the soliton in polyacetylene. Nevertheless the width of a moving polaron shows small oscillations in time. This is found to be related to the lowest odd symmetry extended mode and to be due to the finite size effect.

Macro-Experimental Observation of the Staggered Mode in Lattice System

The staggered mode of solitons in polyacetylene which is first discovered by Sun et al. is one of the typical gap soliton studied in lattice system. Using a one dimensional damped and parametrically driven pendulum lattice, we have observed a stable staggered mode which can be explained successfully by a nonlinear Schrödinger equation under the multiple scale approximation.

ELECTRON NUCLEAR DOUBLE RESONANCE SPECTROSCOPY OF SOLITONS AND POLARONS IN CONJUGATED POLYMERS

Novel elementary excitations such as solitons and polarons in conjugated polymers carry unpaired electrons. In this case electron nuclear double resonance (ENDOR) of protons on the conjugated chain provides a unique method to observe their wavefunctions. This information has two significant meanings. Firstly, it gives the spatial extension of solitons and polarons, the quantity that is essential in examining the reality of these self-localized excitations. Secondly, it directly probes the degree of electron correlation. In the case of finite electron correlation, negative spin sites appear in the spin-density distribution. The unique and detailed determination of the wavefunctions containing such information can be made only after the careful studies of oriented polymers because of the non-single-crystalline nature of these materials. In this article I review our ENDOR studies on solitons in polyacetylene and polarons in poly(paraphenylene vinylene), performed using stretch-oriented samples. All the analyses are based on the properties of π-electrons which show characteristic anisotropy in oriented samples. The observed spin distributions are compared with theoretical results as well as shown as the basis for further analyses of conjugated polymers.

Electric Conduction Due to Charged Solitons in Polyacetylene*

In order to estimate the mobility of a charged soliton in polyacetylene, the dynamics of a soliton in an electric field is numerically investigated in the presence of a phenomenological damping of the lattice motion. Except for the damping term in the equation of motion for the lattice displacements, the dynamics is assumed to be determined by Su, Schrieffer and Heeger's model. It is shown that a Drude-type treatment of the soliton motion is applicable. The mobility is found to be µ=88.9 cm 2 /Volt·sec, and the conductivity is estimated to be σ=7.54×10 3 Ω -1 cm -1 on the assumption that the concentration of the solitons is one per 100 carbon atoms. The present result is compatible with experimental data in the non-magnetic regime.

Dynamics of solitons in polyacetylene in the step-potential model

In treating the motion of solitonic exitations in polyacetylene Newton's equation is used to approximate the lattice dynamics. The force field is obtained from the deviation of the π-electron densities in the bonds from their equilibrium densities. The π-electron density distributions are evaluated with the step-potential model. This model of a nearly free π-electron coupled to the elastic lattice of σ-bonded hydrocarbon ions is the conceptually simplest approach and has no free parameters. The electron-phonon coupling constant is scaled to butadiene and benzene. It is shown that a neutral kink moves frictionless for velocities up to three times the velocity of sound and shakes off phonons at higher velocities. This is in contrast to the results of the SSH-model, where the maximum velocity of the neutral kink is expected to be in a considerable range (0.6−4.0 times velocity of sound) depending on adjustable parameters.

Effects of the second and third neighbor hopping interactions on the electronic states of soliton in polyacetylene

We have studied the energy spectra and the electronic states of a soliton in the weakly coupled electron-phonon systems using an extension of SSH model that includes non-nearest neighbor hopping interactions. The results show that: (1) the electron-hole symmetry of the energy band structure implied by SSH model is broken, and the energy gap 2Δ increases. (2) for a negative charged soliton, only two bound states have been found, one of them is the midgap state, another is a new shallow state near the bottom of the conduction band; for a neutral soliton, all three bound states exist as in the SSH model, but their localizations are strengthened; for a positive charged soliton, four bound states have been found, one of which is an additional state near the top of the conduction band.

Dynamics of solitons in polyacetylene with interchain coupling.

The interchain charge transfer and interactions of two chains are studied numerically through the dynamics of charged and neutral solitons in the presence of an electric field by using the Su-Schrieffer-Heeger model. The electric field is introduced in terms of a time-dependent vector potential which is included in the Hamiltonian through a Peierls substitution of the phase factor to the transfer integral. The effects of confinement on the soliton motion are determined. In particular, the viability of a single moving soliton to cross an interacting region between two parallel chains is analyzed, and its relationship to soliton velocity and interaction region extent is determined. The interchain charge-transfer probability is considered. The charge-transfer probability in a collision between a charged and a neutral soliton belonging to neighboring chains is determined. It is shown that a pair of solitons, one on each chain, can move freely together in an oscillatory way, without any confinement. The oscillation frequency is estimated and its relationship to experimental data is clarified.

Velocity damping of moving soliton in polyacetylene

We present studies of velocity relaxation of moving soliton in polyacetylene by using numerical simulations within Su-Schrieffer-Heeger's (SSH) model. The system is assumed to include the phenomenological damping in the lattice dynamics. The soliton is accelerated by an external electric field to get an initial velocity. After the field was cut off, the soliton velocity declines exponentially. It is shown that the soliton can be viewed as a particle obeying the Drude theory.

Dynamics of solitons in polyacetylene in the step-potential model

In treating the motion of solitonic exitations in polyacetylene Newton's equation is used to approximate the lattice dynamics. The force field is obtained from the deviation of the π-electron densities in the bonds from their equilibrium densities. The π-electron density distributions are evaluated with the step-potential model of a nearly free π-electron coupled to the lattice distortion. Kinks move frictionless for velocities up to three times the velocity of sound and shake off phonons at higher velocities. Excitation leads to a localized defect, which is breathing and later evolving into a kink and an anti-kink moving apart. Scattered neutral kinks are either trapped or repel each other depending on the occupation of their states.

Amplitude Mode around a Moving Soliton in Polyacetylene*

Amplitude mode around a moving soliton in polyacetylene is studied by the numerical simulations of the motion of the charged soliton in an external electric field within Su, Schrieffer and Heeger's model. Its shape is visualized by numerically subtracting the Goldstone mode from the time derivatives of the lattice displacements, which are thought to be decomposed into linear normal modes around the (moving) soliton. The frequency of the amplitude mode as a function of the soliton velocity is estimated from the oscillations of the soliton width and the lattice potential energy, the latter oscillation being considered to be induced mainly by the amplitude oscillation. The frequency is found to increase as the velocity deviates from zero.

Ultrafast spectroscopy of conducting polymers

We have used various experimental techniques in the femtosecond and picosecond time domains to study the ultrafast time response, the optical nonlinearities and the character of the fundamental photoexcitations in conducting polymers with (polyacetylene) and without (polythiophene, polydiacetylene) degenerate ground states. Using the technique of photoinduced absorption (PA) we found that photoexcitations in conducting polymers become self trapped in about 300 fs. They form charged and neutral solitons in polyacetylene and polarons and singlet or triplet excitons in other polymers. Due to the existence of disorder and inhomogeneity in conducting polymers thin films, the dynamics of the PA signal, which is due to recombination, is in the form of a power law t −α (α < 1) or stretched exponential exp [−( t/τ) β] (β < 1). The decays are sensitive to high pressure showing that the recombination is dominated by 3D defects in the chains, which act as recombination centers. We have also measured the magnitude and dynamical response of the third order nonlinear optical coefficient χ( 3) in conducting polymers thin films,using the femtosecond degenerate four wave mixing (DFWM) technique. χ( 3) was in the range of 10 −11 to 10 −8 esu depending on the resonance excitation conditions. Also the dynamical response of χ( 3) for resonant and non-resonant conditions is categorically different. We found, however, that the dephasing time of the photoexcitations (< 50 fs) does not depend on resonance excitation conditions.

Motion of Charged Soliton in Polyacetylene Due to Electric Field. IV. Damping of Soliton Velocity

We study velocity damping of a moving soliton in polyacetylene by using numerical simulations within Su, Schrieffer and Heeger's model. The system is assumed to be at absolute zero of temperature and involves no impurity. In order to get an initial velocity the soliton is accelerated by applying an external electric field. The relaxation time of the soliton velocity has a minimum value when the initial velocity is around the sound velocity of this system. This is a result of the interaction between the moving soliton and the acoustic phonons emitted by the soliton itself. We find that the damping of the soliton velocity is caused by the energy transfer from the moving soliton to the acoustic phonons. The transfer is enhanced when the soliton is surrounded by the acoustic phonons.

A quantum chemical study of interchain hopping model of negatively charged solitons in polyacetylene

Phonon-assisted interchain hopping of negatively charged solitons in polyacetylene has been studied using a local chemical reaction model CH + CH4 CH4 + CH. Quantum chemical characteristics of the electron transfer process have been analyzed in terms of the dynamic electron density and the mutual polarization moment. The CH stretching vibrational motion of CH4, which is a local model of the sp3 defect, has been found to play a significant role for the electron transfer. The excitation of the corresponding vibrational mode of the sp3 defect would promote the interchain hopping of the charged soliton. The electron transfer process has also been studied in terms of the “regional” density functional theory. It has been shown that the driving force of the electron transfer is represented by the regional chemical potentials.

Motion of Charged Soliton in PolyacetyleneDue to Electric Field.III. Energetics

In numerical simulations on a moving charged soliton in polyacetylene, the behavior of the total, electric, lattice potential and lattice Kinetic energies are analyzed. In order to induce physically natural motion, the soliton is accelerated by a uniform electronic field as in the previous papers of this series. During the acceleration the electronic energy shows an almost monotone decrease while the lattice potential energy increases in an almost monotone way. These two energies have also an oscillating component which is related to the previously reported oscillation of the soliton width. On the contrary the total and the lattice kinetic energies show no oscillation. The relation between the total energy e tot and the soliton velocity υ is well fitted to a functional form e tot (υ)=e tot (0)-( M s υ m 2 /2) ln (1-υ 2 /υ m 2 ) where υ m is the saturation velocity of about three times the sound velocity and M s the soliton effective mass of four to five times the bare electron mass.

Motion of charged soliton in polyacetylene due to electric field

The behaviour of a moving soliton in polyacetylene is numerically studied from the first principle by using Su-Schrieffer-Heeger's (SSH) model. The motion is introduced by applying an electric field to a system with a static charged soliton. The time dependences of the electronic wave functions and the lattice displacements are determined selfconsistently. The electric field is given in terms of a time dependent vector potential, and therefore the periodic boundary condition can be maintained.

A chemical approach to the orbitals of organic polymers

The electronic structure of the prototypical unsaturated and saturated organic polymers poly- acetylene and polyethylene is elucidated by a building-up process starting from a linear carbon chain, which is then kinked and finally has one or two hydrogen atoms attached to it. In this process the common features as well as the differences between polyacetylene and polyethylene (semiconductor vs large band gap insulator, unsaturation vs saturation) emerge in a natural way. The emphasis is on bringing together the essential concepts of solid-state physics and simple ideas of chemical bonding. Some topics of special interest, such as bond alternation and solitons in polyacetylene, are also discussed, in as simple and chemical manner as poasible.

Motion of Charged Soliton in Polyacetylene Due to Electric Field. II. Behavior of Width

By numerical simulations treating the motion of a charged soliton in polyacetylene, we analyze the width of a moving soliton. The motion of the soliton is induced by applying an electric field as in the previous work. The soliton width is estimated by two methods; one is from the excess charge density profile and the other from the distortion in the lattice displacement. Both results indicate that the width decreases as the soliton velocity increases. Quantitatively, however, the amount of decrease is different in the two cases; the maximum change of the width is about 10% in the former case whereas it is 20% in the latter. Furthermore, the width obtained from the lattice distortion is found to oscillate as a function of time, consistently with the excitation of the amplitude mode around a soliton.

ELECTRON CORRELATION AND SOLITON

The electron correlation and soliton in polyacetylene have been studied with the CBF method. By considering the complete electron-electron interaction, we concluded that the stable static configuration of a PA chain with odd atoms and a single electric charge is a soliton. With the increase of e-e interaction strength U and interaction range α/β the localization of soliton is enhanced, and the soliton creation energy is reduced, so although the e-e interaction is considered, the conclusion that soliton is main charged carrier in high conducting polymers is still tenable.

Functional treatment of solitons in polyacetylene

The authors apply functional methods to the study of polyacetylene. They represent the polyacetylene free energy as a functional determinant ratio, obtain the uniform dimerization equation and calculate the soliton creation energy in some limiting cases.

Motion of Charged Soliton in Polyacetylene Due to Electric Field

Real time dynamics of a moving charged soliton in polyacetylene is studied numerically by using Su-Schrieffer-Heeger's model. An electric field is introduced to the system through a time dependent vector potential which can be included into the Hamiltonian through the Peierls substitution of the phase factor to the transfer integral. Several interesting properties of the moving soliton are obtained, e.g. , the Brownian-like motion of the soliton due to the soliton-phonon interaction, the saturation of the soliton velocity, the saturation velocity being independent of the applied electric field strength, while the time needed to attain the saturation velocity is, roughly speaking, linearly dependent on the logarithm of the applied field.