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

Electronic Transport Properties of Molecular Clusters Sb4O6, P4Se3, and P4O6

Inorganic molecular crystal (IMC) is a trending class of materials in which structural units comprise molecular cages or clusters bonded via van der Waal forces. The structure-property relationship in IMCs is less known due to the unusual assembly of molecular clusters in these materials. In this paper, the density functional theory-calculated electronic transport properties of the molecular clusters of antimony oxide (Sb4O6), phosphorus triselenide (P4Se3), and phosphorus trioxide (P4O6) are described in detail. The calculated values of highest occupied molecular orbital-lowest unoccupied molecular orbital gaps appeared as 5.487, 2.296, and 4.425 eV for Sb4O6, P4Se3, and P4O6, respectively. The work was carried out to explore the charge transport mechanism in IMCs in order to disclose their potential in practical applications. The calculations involved charge-transfer integral based on Marcus theory to compute the electronic coupling (V), reorganization energies (λ), and hopping rate (k) in the structures. The hopping rate for Sb4O6, P4Se3, and P4O6 is found as 8.49 × 10-12, 1.28 × 10-14, and 2.51 × 10-20 s-1, respectively. The transport properties of Sb4O6 are found better, which predicts the application of the relevant IMC for device grade applications. The findings of this study are important for future application of the IMCs in electronic and optoelectronic applications.

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.

Enhanced Exciton Drift Transport through Suppressed Diffusion in One-Dimensional Guides

Drift-diffusion dynamics is investigated in a one-dimensional (1D) exciton guide at room temperature. Spatial engineering of the exciton energy in a WSe2 monolayer is achieved using local strain to confine and direct exciton transport. An unexpected and massive deviation from the Einstein relation is observed and correlated to exciton capture by defects. We find that the capture reduces exciton temperature and diffusion so much that drift transport visibility improves to 38% as excitons traverse asymmetrically over regions with occupied defect states. Based on measurements over multiple potential gradients, we estimate the exciton mobility to be 169 ± 39 cm2/(eV s) at room temperature. Experiments at elevated exciton densities reveal that the exciton drift velocity monotonically increases with exciton density, unlike exciton mobility, due to contributions from nonequilibrium many-body effects.

Quantum-Classical Transition Analogy of the Diffusion-Mobility Relation for Hopping and Band Transport Systems: Molecules to Materials

We propose a quantum-classical transition analogy for Einstein's diffusion-mobility (D/μ) relation to reveal electron-hole dynamics in both the degenerate and nondegenerate molecular and material systems. Here, one-to-one variation between differential entropy and chemical potential (Δη/Δh_s) is the proposed analogy, which unifies quantum and classical transport. The degeneracy stabilization energy on D/μ decides whether the transport is quantum or classical; accordingly, the transformation occurs in the Navamani-Shockley diode equation.