Amplitude Mode Model Research Articles

Electronic and vibrational spectroscopy studies of PffBT4T π-conjugated donor–acceptor copolymer

We used a variety of optical spectroscopies to investigate the charge excitations and correlated infrared (IR)-active and Raman-active vibrations in poly[(difluoro-benzothiadiazol-diyl)-alt-(di(2-octyldodecyl)-quaterthiophen-diyl)], PffBT4T, a π-conjugated donor–acceptor (DA) copolymer, which, when blended with fullerene PCBM molecules, serves as an active layer in high-performance photovoltaic solar cells. The applied optical spectroscopies in films of pristine PffBT4T and PffBT4T/PCBM blend include absorption, photoluminescence, electroabsorption, photoinduced absorption (PA), and resonant Raman scattering. We found that the PffBT4T copolymer chain contains 11 strongly coupled Raman-active vibrational modes, which are renormalized upon photogeneration of charge polarons onto the chain. As the lower energy polaron absorption band overlaps with the renormalized vibrational modes, they appear in the PA spectrum as antiresonance (AR) lines superposed onto the induced polaron absorption band. We show that the Raman scattering, doping induced, and photoinduced AR spectra in PffBT4T are well explained by the amplitude mode model (AMM), where a single vibrational propagator describes the renormalized Raman modes and their related photoinduced AR intensities in detail. Surprisingly, we found that two of the IR-active modes in the pristine copolymer must be included in the AMM propagator for explaining the complete photoinduced AR spectrum. This feature is unique to DA-copolymers and indicates that some intrachain C2v symmetry breaking occurs because of the different electron affinities of the donor and acceptor moieties.

Amplitude-Mode Spectroscopy of Charge Excitations in PTB7 π -Conjugated Donor-Acceptor Copolymer for Photovoltaic Applications

The authors show that the photogenerated polarons in the PTB7/PCBM copolymer blend, used in organic photovoltaic (OPV) solar cells, couple strongly to six vibrational modes that can be described by the amplitude-mode model. From the relative strengths of the doping-induced absorption of the polaron vibrations and electronic transitions, the polaron's effective mass is obtained, and its influence on carrier mobility unraveled. This understanding of the photophysics of such blends is the next step in engineering lightweight, low-cost, high-efficiency OPV solar panels.

Raman dispersion in polyaniline nanofibers

In this work the Raman dispersion observed for the polyaniline (PANI) nanofibers was investigated. PANI nanofibers were prepared by interfacial polymerization using HCl or HClO4 acids as dopant. The use of different acids in the aniline polymerization can produce PANI fibers with different diameters. The polymers were characterized by scanning electron microscopy (SEM), X-ray diffraction (XRD), small angle X-ray scattering (SAXS), UV–VIS-NIR and resonance Raman (RR). By using several laser lines (from 1.16 to 3.05eV) the dependency of νCN band frequencies, related to the quinoid rings, with the laser lines was investigated. The Raman dispersion of νCN frequencies was analyzed using Amplitude Mode Model (AMM). Excitation photon energy versus ∏n(ωnRωn0)2 curves were linear in region of the electronic absorption transition. The Raman dispersion of PANI nanofibers with smaller diameter (d≈30nm) shows lower dispersion D rate (slope of ∏n(ωnRωn0)2 versus laser line energies) and as consequence higher torsion of Cring-N-Cring segments. Hence, for PANI with higher morphological organization has more stacking between quinoid rings (higher torsion angles) and more electronic homogeneity (lower D rate) compared to other samples.

Raman dispersion in polyaniline base forms

Raman spectra of polyaniline in its emeraldine (EB) and pernigraniline (PB) base forms were obtained using several excitation laser lines and Raman dispersion of the bands was measured. Only the νC N band value depends on excitation wavelength for both polymeric forms. These changes of vibrational frequencies with excitation wavelength were analyzed using amplitude mode model (AMM). ∏ n ( ω n R / ω n 0 ) 2 versus excitation photon energies plot was linear in the electronic absorption transition region, for EB at ca. 640 nm and for PB at ca. 620 nm. The dispersion values, D (slope of ∏ n ( ω n R / ω n 0 ) 2 versus excitation photon energies plot) were 0.058 and 0.038 eV −1 for EB and PB, respectively, which indicate that EB has the first excited state of even parity presenting lower energy when comparing to that of PB.

A comparison of the Raman dispersion in different polyacetylenes with aromatic ring substituents

Raman dispersion data for poly-2-ethynylpyridine, poly-4-ethynylpyridine, poly-β-naphthylacetylene, poly(2-pyridinium hydrochloride-2-pyridylacetylene) and poly(2- N- t-butylpyridiniumylacetilene)iodide were obtained and analysed using the Amplitude Mode Model (AMM). The slopes of the ∏ n ( ω n R / ω n 0 ) 2 versus ω L curves ( D) ranged from 0.090 to 0.146 eV −1, substantially larger than the values reported for other photoluminescent conjugated polymers (up to 0.020 eV −1). This behaviour was interpreted as arising from the presence of a second A g (3A g) excited state close to the first one (2A g). Polymers with charged substituents presented the larger D values, as already observed for other conjugated polyacetylenes. It seems that the repulsion of the charged groups leads to flatter arrangements of the chains, increasing the conjugation length and consequently the slope of the ∏ n ( ω n R / ω n 0 ) 2 versus ω L curves.

Pressure effect on photoluminescence and Raman spectra of PPV

The pressure effect on photoluminescence (PL) and Raman spectra of the poly (para-phenylene vinylene) (PPV) has been investigated with a diamond anvil cell (DAC) under the hydrostatic pressure condition. The intensity ratios, I 1167/ I 1622 and I 1543/ I 1622, increase with pressure. This indicates that the conjugated length of PPV is enhanced at high pressures. In addition, appearance of a new Raman band corresponding to CC stretch at 1190 cm −1 shows that the chain conformation defects decreased with increasing pressure. The redshift of the PL spectra and shift to higher frequencies for Raman bands with increase in pressure are explained by combining the conjugation model with amplitude mode model.

Modelos para dispersão Raman em polímeros conjugados

Raman dispersion refers to the dependence of the position of Raman bands on the energy of the exciting radiation. In this work, the three main models currently used to explain this phenomenon (Conjugated Length Model, Amplitude Mode Model and Effective Conjugation Coordinate Model) are discussed. Raman dispersion is a consequence of p electron delocalization, but each model describes in a different way how p electron delocalization affects the position of Raman bands. Here the features, qualities and problems of the three models are highlighted.

Spectroscopic Studies of Photoexcitations in Regioregular and Regiorandom Polythiophene Films

Using a variety of optical probe techniques we studied the steady state and transient dynamics of charged and neutral photoexcitations in thin films of poly-3-alkyl thiophene with regioregular order, which forms self-assembled lamellae structures with increased interchain interaction, as well as regiorandom order that keeps a chain-like morphology. In regiorandom polythiophene films we found that intrachain excitons with correlated photoinduced absorption and stimulated emission bands are the primary photoexcitations; they give rise to a moderately strong photoluminescence band, and long-lived triplet excitons and intrachain charged polarons. In regioregular polythiophene films, on the contrary we found that the primary photoexcitations are excitons with much larger interchain component; this results in lack of stimulated emission, vanishing intersystem crossing, and a very weak photoluminescence band. The long-lived photoexcitations in regioregular polythiophene films are interchain excitons and delocalized polarons (DP) within the lamellae, with very small relaxation energy. The characteristic properties of the DP species are thoroughly investigated as a function of the alkyl side group of the polymer backbone, film deposition conditions and solvents used, as well as at high hydrostatic pressure. The quantum interference between the low energy absorption band of the DP species and a series of photoinduced infrared active vibrations, which give rise to antiresonances that are superimposed on the electronic absorption band is studied and explained by a Fano-type interference mechanism, using the amplitude mode model.

Photoinduced quantum interference antiresonances in pi-conjugated polymers.

We observed photoinduced quantum interference antiresonances between several discrete infrared-active vibrations and the lower-polaron continuous absorption band in a series of pi-conjugated polymer films having superior planar orders, where the polaron transition energy is relatively small. The photoinduced Fano-type antiresonances are well explained by extending the amplitude mode model beyond the adiabatic limit. The agreement between the data and the model confirms the presence of a continuous electronic band above the polaron state. We show that high frequency modes are strongly coupled to electrons, with implications for superconductivity.

Unified picture of three models for the resonance Raman effect in polyenes

The connections between the conjugation length model (CLM), the amplitude mode model (AMM) and the effective conjugation coordinate model (ECCM) are discussed. All three models are able to explain the main features of the unusual resonance Raman behaviour of conjugated polymers. We show that the CLM can be generalized to include the concepts of the AMM and ECCM.

Resonance Raman scattering from finite and infinite polymer chains.

Three models for interpreting resonance Raman (RR) spectra of conjugated polymers are compared for the example of a strictly one-dimensional infinite or finite bond-alternating chain: the amplitude-mode model (AMM), the effective-conjugation-coordinate model (ECCM), and the conjugation-length model (CLM). The most characteristic behavior for the RR spectra of conjugated polymers is the change of line shape and line position of Raman modes with laser excitation energy, which is called a dispersion effect. This effect is considered to originate from inhomogeneities in the effective electron-phonon coupling constant \ensuremath{\lambda}\ifmmode \tilde{}\else \~{}\fi{} (AMM), in the effective force constant ${\mathit{f}}_{\mathit{J}\mathit{a}}$ (ECCM), or in the effective conjugation length N (CLM). Generalizing the CLM, we give a unifying picture for the three models mentioned above. The \ensuremath{\pi}-electron system is described by the Longuet-Higgins--Salem Hamiltonian, which includes the \ensuremath{\sigma} compressibility; and the RR cross section is evaluated with Albrecht's theory. By calculating \ensuremath{\lambda}\ifmmode \tilde{}\else \~{}\fi{}(N) and ${\mathit{f}}_{\mathit{J}\mathit{a}}$(N), it is shown that all inhomogeneities originate from a distribution in N. For correct calculations, no cyclic boundary conditions should be used. Extending Albrecht's theory to an infinite linear chain, we show the connection between the molecular-physics approximation (CLM) and the solid-state-physics approximation (AMM) for the RR intensity. There are two peaks in the excitation profile: one for the incoming and another for the outgoing resonance. Finally, we show that the usual Franck-Condon analysis is not appropriate for medium-long linear chains because of the dramatic difference in the shape of the total-energy hypersurface for ground and excited states.

A comparative study of the resonance Raman effect in linear polyenes: Conjugation length model, GF-formalism and amplitude mode model

The conjugation length model, the amplitude mode model and the effective conjugation coordinate model for resonance Raman spectra are compared using a very simple system of a linear Peierls chain. The Hamiltonian used was Hückel-type with σ-compressibility. Vibrational frequencies, vibrational coupling constants, electronic transition energies and transition matrix elements can be evaluated explicitly for finite and infinite chains in each of the three models. In this way we can quantitatively evaluate for which specific problems the individual methods apply and for which they fail.

Conjugation length dependence of Raman scattering in a series of linear polyenes: Implications for polyacetylene

We have measured the solid state Raman scattering spectra of a homologous series of linear polyenes, with the number of alternated double bonds varying from 3 to 12. While we find a linear dependence of the Raman shifts of resonantly coupled modes with inverse conjugation length, we have also followed the suggestion of previous work in examining the inverse square product of the several Raman frequencies as a function of the logarithm of the measured energy gap of the molecule. This provides a linear relationship, as found for trans-polyacetylene, a result which is qualitatively consistent with the amplitude mode model of Horovitz and co-workers. We also find, consistent with previous work on polyacetylene, a monotonic decrease in the ratios of oscillator strengths of the two strongest bands with conjugation length, as recently predicted by a series of molecular dynamics calculations. Suggested interpretations of a number of qualitative observations, including splitting of modes for shorter conjugation length, are offered, and the implications for the structure of trans-polyacetylene are discussed. The present work confirms that the previously measured dispersion in the Raman spectra of trans-polyacetylene is due to a distribution of conjugation lengths and brings into question some of the quantitative aspects of the amplitude mode model.

Resonant Raman scattering and photoinduced infrared active vibration spectroscopy of poly(isothianaphthene)

Resonant Raman scattering and photoinduced absorption of infrared active vibrations in poly(isothianaphthene) are reported. The data are analysed by the amplitude mode model taking into account the reduction of the thiophene backbone bond length alteration due to the benzene rings. We have found for poly(isothianaphthene) a renormalized vibrational force constant similar to that of polythiophene. We show that this result is compatible with both the small band gap and the reduced effective π-bandwidth.

Photoinduced absorption and resonant Raman scattering of polythiophene

Resonant Raman scattering (RRS) and photoinduced absorption (PA) measurement in polythiophene are reported. The RRS is analyzed by the amplitude mode model modified to include an additive extrinsic component Δ e. For polythiophene we obtain a ld gap 2 Δ = 2.2 eV and 2 Δ e = 0.22 eV. The dominant photo-carriers generated with an above the gap excitation are charged bipolarons with two correlated electronic PA bands at 0.45 eV and 1.25 eV and several IR active vibrations. The PA spectrum yields for the bipolaron mass M ≅ m e in good agreement with theoretical predictions.

Charge density waves and the complete Raman and photoinduced absorption spectra in polyacetylene copolymers t-[(C 2H 2) y(C 2D 2) 1−y] x

The complicated spectra of resonance Raman scattering and photoinduced IR absorption of [(C 2H 2) y(C 2D 2) 1−y] x are presented and analyzed in the framework of the amplitude mode model. All the features of the spectra are explained with the assumption of interaction between the amplitude modes and low intensity modes of the same symmetry which are found in the pure crystals as well.

Amplitude modes and absorption in T-polyacetylene-like systems: Polaroid K and polyvinylene

Polaroid K and polyvinylene contain trans -polyacetylene chains embedded in polyvinyl alcohol. We show that while the resonance Raman scattering of polaroid K consists of non shifting primary lines and “dispersive” satellites as in polyacetylene, no primary lines are observed in the spectra of polyvinylene and they consist of dispersive lines only. Analysis is made using the amplitude mode model yielding a gap successively increasing from (CH) x to polaroid K and polyvinylene. This is also verified by the absorption spectra.