Entropy-ruled nonequilibrium charge transport in thiazolothiazole-based molecular crystals: a quantum chemical study.

The charge and energy fluctuations in molecular solids are crucial factors for a better understanding of charge transport (CT) in organic semiconductors. The energetic disorder-coupled molecular charge transport is still not well-established. Moreover, the conventional Einstein's diffusion (D)-mobility (µ) relation fails to explain the quantum features of organic semiconductors, including nonequilibrium and degenerate transport systems, where kB is the Boltzmann constant, T is the temperature and q is the electric charge. To overcome this issue, a unified version of the entropy-ruled D/µ relation was proposed by Navamani (J. Phys. Chem. Lett., 2024, 15, 2519-2528) for hopping and band transport systems as where d, η and heff are the dimension (d = 1, 2, 3), chemical potential and effective entropy, respectively. Within this context, we investigate the CT properties of 2,5-bis(4-methoxyphenyl)thiazolo[5,4-d]thiazole (MOP-TZTZ) and 2,5-bis(2,4,5 trifluorophenyl)-thiazolo[5,4-d]thiazole (TFP-TZTZ) molecular solids using electronic structure calculations and the entropy-ruled method. The CT key parameters such as charge transfer integral and site energy are computed by matrix elements of the Kohn-Sham Hamiltonian. Using Marcus theory, the charge transfer rate is numerically calculated for MOP-TZTZ and TFP-TZTZ molecular crystals under different site energy disorder (ΔEij(E⃑)) situations. Using our entropy-ruled method, the exact diffusion-mobility (D/µ) and other transport quantities such as thermodynamic density of states, conductivity, and current density are calculated for these derivatives at different applied electric field values via the site energy disorder. The theoretical results show that the molecule TFP-TZTZ has good hole mobility (∼0.012 cm2 V-1 s-1) at a site energy disorder value of 90 meV. The obtained ideality factor from the Navamani-Shockley diode current density equation categorizes the typical transport as either the Langevin-type or Shockley-Read-Hall mechanism in the studied molecular solids. Our analysis clearly shows that both the electron and hole transport in these MOP-TZTZ and TFP-TZTZ molecules follow the trap-free Langevin mechanism, which is indeed ideal for designing charge-transporting molecular devices.

Unified Entropy-Ruled Einstein's Relation for Bulk and Low-Dimensional Molecular-Material Systems: A Hopping-to-Band Shift Paradigm.

We present a unified paradigm on entropy-ruled Einstein's diffusion-mobility relation (µ/D ratio) for 1D, 2D, and 3D free-electron solid state systems. The localization transport in the extended molecules is well approximated by the continuum time-delayed hopping factor within our unified entropy-ruled transport method of noninteracting quantum systems. Moreover, we generalize an entropy-dependent diffusion relation for 1D, 2D, and 3D systems as defined by Dd,heff=Dd,heff=0⁡exp((d-1)heffd+2), where heff and d are the effective entropy and dimension (d = 1, 2, 3), respectively. This generalized relation is valid for both equilibrium and nonequilibrium transport systems since the parameter heff is closely connected with the nonequilibrium fluctuation theorem-based entropy production rule. Importantly, we herein revisit the Boltzmann approach using an entropy-ruled method for mobility calculation for the universal quantum materials that is expressed as µd=[(dd+2)qdheffdη]vF2τ2, where vF2τ2 is the diffusion constant for band transport systems and η is the chemical potential. According to our entropy-ruled µ/D relation, the Navamani-Shockley diode equation is transformed.

Effect of site energy fluctuation on charge transport in disordered organic molecules.

Effect of dynamics of site energy disorder on charge transport in organic molecular semiconductors is not yet well-established. In order to study the relationship between the dynamics of site energy disorder and charge transport, we have performed a multiscale study on dialkyl substituted thienothiophene capped benzobisthiazole (BDHTT-BBT) and methyl-substituted dicyanovinyl-capped quinquethiophene (DCV5T-Me) molecular solids. In this study, we explore the structural dynamics and correlated charge transport by electronic structure calculations, molecular dynamics, and kinetic Monte-Carlo simulations. We have also proposed the differential entropy dependent diffusion and charge density equations to study the electric field drifted diffusion property and carrier density. In this investigation, we have addressed the transformation mechanism from dynamic to static disorder in the extended stacked molecular units. Here, the decrease in the charge transfer rate due to site energy fluctuations reveals the dispersion transport along the extended π-stacked molecules. Furthermore, the calculated current density for a different set of site energy difference values shows the validity and the limitations of the Einstein relation. Based on the calculated ideality factor, we have classified the charge transport in these molecules as either the Langevin or the Shockley-Read-Hall type mechanism. Through the calculated mobility, current density, and ideality factor analysis, we categorize the applicability of molecules of interest for photovoltaic or light emitting diode applications.

Theoretical modeling of charge transport in triphenylamine-benzimidazole based organic solids for their application as host-materials in phosphorescent OLEDs.

The dynamic disorder and electric field effects on charge transport in triphenylamine-benzimidazole based molecular solids have been investigated using electronic structure calculations, molecular dynamics and Monte-Carlo simulations. During the charge propagation, the energy loss of the carrier in each hopping step is monitored by Monte-Carlo simulation. We derive a survival probability correlated momentum-energy distribution for drift-diffusion analysis and we demonstrate the dispersion initiated charge trapping mechanism which is indeed ideal for light emission efficiency via recombination. In the present model, the proposed carrier drift energy-current density expression and Shockley diode current density equation are used to study the current density-voltage characteristics; accordingly the ideality factor (∼1.8-2.0) dictates the deviation of Einstein's classical diffusion-mobility relation (where the ideality factor is unity). The dual mechanism of electric field assisted site energy gap on coherent-like transport and the electric field stretched dispersion on recombination are observed in tris(3'-(1-phenyl-1H-benzimidazole-2-yl)biphenyl-4-yl)amine (TBBI) and tris(4'-(1-phenyl-1H-benzimidazole-2-yl)biphenyl-4-yl)amine (TIBN) molecular systems, which can be used as host materials in organic light emitting diodes (OLEDs). We find the transport going from coherent to incoherent, due to the conversion mechanism of dynamic to static disorder. This can also be a controlled by applied electric field. By adjusting the applied electric field, film thickness and changing the π-stacked molecular aggregation via substitutions, one can fix the dispersive parameter and accordingly calculate the charge transport properties to design efficient host-materials for photovoltaic and light emitting diode devices.

Forth-back oscillated charge carrier motion in dynamically disordered hexathienocoronene molecules: a theoretical study.

Electronic structure calculations were performed to investigate the charge transport properties of hexathienocoronene (HTC) based molecules. The effective displacement of the charge carrier along the π-orbital of nearby molecules is calculated by monitoring the forth and back oscillations of the charge carrier through kinetic Monte Carlo simulation. The charge transport parameters such as charge transfer rate, mobility, hopping conductivity, localized charge density, time average effective mass and degeneracy pressure are calculated and used to study the charge transport mechanism in the studied molecules. The existence of degeneracy levels facilitates the charge transfer and is analyzed through degeneracy pressure. Theoretical results show that the site energy difference in the dynamically disordered system controls the forth-back oscillation of charge carrier and facilitates the unidirectional charge transport mechanism along the sequential localized sites. The ethyl substituted HTC has good hole and electron hopping conductivity of 415 and 894 S cm(-1), respectively, whereas unsubstituted HTC has the small hole mobility of 0.06 cm(2) V(-1) s(-1) which is due to large average effective mass of 1.42 × 10(-28) kg.

Effect of structural fluctuations on charge carrier mobility in thiophene, thiazole and thiazolothiazole based oligomers.

Charge transport properties of thiophene, thiazole and thiazolothiazole based oligomers have been studied using electronic structure calculations. The charge transport parameters such as charge transfer integral and site energy are calculated through matrix elements of Kohn-Sham Hamiltonian. The reorganization energy for the presence of excess positive and negative charges and rate of charge transfer calculated from Marcus theory are used to find the mobility of charge carriers. The effect of structural fluctuations on charge transport was studied through the polaron hopping model. Theoretical results show that for the studied oligomers, the charge transfer kinetics follows the static non-Condon effect and the charge transfer decay at particular site is exponential, non-dispersive and the rate coefficient is time independent. It has been observed that the thiazole derivatives have good hole and electron mobility.