Polaron and bipolaron stability on paraphenylene polymers

Abstract

Polyparaphenylene is the prototypical conjugated polymer containing phenyl rings and its properties are good references for a family of derived polymers. We investigate the structure, stability, and dynamics of polarons and bipolarons in polyparaphenylene chains under an applied electric field. To do this, we use a bidimensional SSH Hamiltonian model with the Hubbard extension, i.e., with local and nearest-neighbor Coulomb interaction, which has been designed to work with general hexagonal lattices, from which polyparaphenylene can be seen as a prominent case. Using the time-dependent Hartree-Fock approximation, we calculate the structural characteristics, the maximum field strength, supported before polarons and bipolarons gets unstable, and the maximum velocity achieved by these charge carriers. We obtained the polaron and bipolaron terminal velocity to be 0.51 Å/fs and 1.15 Å/fs, respectively. The maximum field strength determined by our calculations is 0.54 mV/Å and 0.80 mV/Å, respectively. Our results are in good agreement with other theoretical methods and experiments.

Same Charge Polaron and Bipolaron Scattering on Conducting Polymers

“…The bipolaron is just the same, but the concentration of the charge distribution sums up to the charge of two electrons. In both cases, the delocalization length is about 30 Å, in PPP, corresponding to eight phenyl rings . The lower part of Figure , on gray background, represents the chain of the PPP molecule: light blue segments are shortened bonds, dark blue ones are more shortened ones and violet, even more so; yellow to orange to red are progressively more stretched bonds.…”

“…In both cases, the delocalization length is about 30 Å, in PPP, corresponding to eight phenyl rings. 9 The lower part of Figure 1, on gray background, represents the chain of the PPP molecule: light blue segments are shortened bonds, dark blue ones are more shortened ones and violet, even more so; yellow to orange to red are progressively more stretched bonds. The upper part of Figure 1 depicts the charge distribution in two different manners: greenish points are the sums of the charges of the sites below them; black lines are the charges of each single siteslightly misaligned on purpose, to avoid superposition.…”

Polaron on harmonic lattice in electric field. Generation of coherent oscillations

“…40,41 Subsequently, the SSH model became widely used for description not only for simple conjugated polymers but more complicated systems, for example, DNA, [23][24][25][26][42][43][44] polypyrrole 45 and paraphenylene polymers (PPP). 46 The electron-phonon coupling can be taken into account in a slightly different way also, as in the case of Frohlich or Holstein polarons [52][53][54][55] or in Davydov-Scott model. 57 However, in all models the general polaron behaviour is similar.…”

Polaron in constant electric field. Generation of coherent lattice vibrations

“…В настоящее время есть все основания считать, что поляроны играют важную роль в транспорте заряда в биологических [1][2][3][4] и других неметаллических системах [5][6][7] Исторически изучение полярона на одномерных решетках началось с анализа динамики заряженного солитонав ПА [7][8][9]. Тогда же авторами (Су, Шриффер, Хигер (СШХ)) был предложен гамильтониан, получивший в дальнейшем широкое применение ввиду своей простоты и эффективности, и названный по имени авторов.…”