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 D d , h e f f = D d , h e f f = 0 ⁡ exp ( ( d - 1 ) h e f f d + 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 μ d = [ ( d d + 2 ) q d h e f f d η ] v F 2 τ 2 , where v F 2 τ 2 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.

Generalization on Entropy-Ruled Charge and Energy Transport for Organic Solids and Biomolecular Aggregates

Herein, a generalized version of the entropy-ruled charge and energy transport mechanism for organic solids and biomolecular aggregates is presented. The effects of thermal disorder and electric field on electronic transport in molecular solids have been quantified by entropy, which eventually varies with respect to the typical disorder (static or dynamic). Based on our previous differential entropy (h _s )-driven charge transport method, we explore the nonsteady carrier energy flux principle for soft matter systems from small organic solids to macrobiomolecular aggregates. Through this principle, the synergic nature of charge and energy transport in different organic systems is addressed. In this work, entropy is the key parameter to classify whether the carrier dynamics is in a nonsteady or steady state. Besides that, we also propose the formulation for unifying the hopping and band transport, which provides the relaxation time-hopping rate relation and the relaxation time-effective mass ratio. The calculated disorder drift time (or entropy-weighted carrier drift time) for hole transport in an alkyl-substituted triphenylamine (TPA) molecular device is 9.3 × 10^-7 s, which illustrates nuclear dynamics-coupled charge transfer kinetics. The existence of nonequilibrium transport is anticipated while the carrier dynamics is in the nonsteady state, which is further examined from the rate of traversing potential in octupolar molecules. Our entropy-ruled Einstein model connects the adiabatic band and nonadiabatic hopping transport mechanisms. The logarithmic current density at different electric field-assisted site energy differences provides information about the typical transport (whether trap-free diffusion or trap-assisted recombination) in molecular devices, which reflects in the Navamani-Shockley diode equation.

Charge Transport and Optical Absorption Properties of Dibenzocoronene Tetracarboxdiimide Based Liquid Crystalline Molecules: A Theoretical Study

Structure, optical absorption, and charge transport properties of dibenzocoronene tetracarboxdiimide (DCDI) based molecules were studied using electronic structure calculations. Based on the optimized neutral, cationic, and anionic geometries the ionized state properties, such as ionization potential, electron affinity, hole extraction potential, electron extraction potentials, and reorganization energy, were calculated. On the basis of the ground state geometry of the studied molecules, the absorption spectra were calculated using the time-dependent density functional theory (TDDFT) method at the PBE0/def-TZVP level of theory. It has been observed that the substitution of different functional groups significantly alters the absorption spectra of DCDI. The methoxy- (OCH₃-) substituted DCDI molecule has a maximum absorption wavelength of 529 nm. The charge transport parameters, such as the charge transfer integral, spatial overlap integral, and the site energy, are calculated directly from the Kohn-Sham matrix elements. The reorganization energy for the presence of excess positive and negative charges and the charge transfer rate calculated from Marcus' theory were used to find the mobility of charge carriers. The computed results show that the mobility of charge carriers is strongly influenced by the functional groups present on the DCDI molecule. The effect of intermolecular structural fluctuations on charge transport properties was studied through molecular dynamics and Monte Carlo simulations based on the polaron hopping mechanism. The calculated charge carrier mobility shows that the cyano- (CN-) substituted DCDI molecules are having n-type semiconducting property while, methoxy- (OCH₃-) and thiol- (SH-) substituted DCDI molecules exhibit ambipolar semiconducting properties.

Impact of N-substitution on structural, electronic, optical, and vibrational properties of a thiophene–phenylene co-oligomer

Properties of the organic semiconductors can be finely tuned via changes in their molecular structure.

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.

Impact of tunable 2-(1H-indol-3-yl)acetonitrile based fluorophores towards optical, thermal and electroluminescence properties

Herein, we have synthesized 4,5-diphenyl-1H-imidazole and 2-(1H-indol-3-yl)acetonitrile based donor–π–acceptor fluorophores and studied their optical, thermal, electroluminescence properties. Both the fluorophores exhibit high fluorescence quantum yield (Φ_f = <0.6) and good thermal stability (T_d10 = <300 °C), and could be excellent candidates for OLED applications. Moreover, the ground and excited state properties of the compounds were analysed in various solvents with different polarities. The geometric and electronic structures of the fluorophores in the ground and excited states have been studied using density functional theory (DFT) and time-dependent density functional theory (TDDFT) methods. The absorption of BIPIAN and BITIAN in various solvents corresponds to S₀ → S₁ transitions and the most intense bands with respect to the higher oscillator strengths are mainly contributed by HOMO → LUMO transition. Significantly, the vacuum deposited non-doped OLED device was fabricated using BITIAN as an emitter, and the device shows electroluminescence (EL) at 564 nm, maximum current efficiency (CE) 0.687 cd A⁻¹ and a maximum external quantum efficiency (EQE) of 0.24%.

Herein, we have synthesized 4,5-diphenyl-1H-imidazole and 2-(1H-indol-3-yl)acetonitrile based donor–π–acceptor fluorophores and studied their optical, thermal, electroluminescence properties.

Optoelectronic performance comparison of new thiophene linked benzimidazole conjugates with diverse substitution patterns

In an approach to develop efficient organic optoelectronic devices to be used in light-driven systems, a series of three thiophene linked benzimidazole conjugates were synthesized and characterized. The combination of two thiophene rings to a benzimidazole core decorated with different functional groups (such as OCH₃, N(CH₃)₂, CF₃) resulted in donor-acceptor type molecular scaffold. The effect of the electronic behavior of the substituents on the optical, electrochemical, morphological and electron/hole transporting properties of the dyes were systematically investigated. DTBI2 dye exhibited distinct absorption properties among the other studied dyes because N,N-dimethylamino group initiated intramolecular charge transfer (ICT) process in the studied solvents. In solid state, the dyes exhibit peaks extending up to 600nm. Depending on the solvent polarities, dyes show significant wavelength changes on their fluorescence emission spectra in the excited states. Morphological parameters of the thin films spin-coated from CHCl₃ solution were investigated by using AFM instrument; furthermore photovoltaic responses are reported, even though photovoltaic performances of the fabricated solar cells with different configurations are quite low.

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.

Dynamic disorder and electric field affect the charge (hole and electron) transport in host-materials for OLEDs.

Rational design of cyclopenta[b]naphthalenes for better optoelectronic applications and their photophysical properties using DFT/TD-DFT methods

The optical properties of cyclopenta[b]naphthalenes (CPNs) can be fine-tuned by suitable substitutions and DFT calculations show that they can make efficient OLEDs.

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 dynamic disorder on charge carrier dynamics in Ph4DP and Ph4DTP molecules

Electronic structure calculations were used to study the charge transport and optical properties of 2,2′,6,6′-tetraphenyldipyranylidene (Ph4DP) and its sulfur analogue 2,2′,6,6′-tetraphenyldithiopyranylidene (Ph4DTP) based molecules.