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

Abstract

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.

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

“…Various reports clearly manifest that the D/μ relation influences the diode performance, which can be analyzed by the current density (J)−voltage (V) characteristic study with the aid of the diode ideality factor (N id ). 1,6,13,14 Here, the ideality factor has a direct correlation with the enhancement parameter, g. According to an entropy-ruled method, the governing Navamani−Shockley (NS) diode equation for molecular quantum devices is given by 8,10 Ä…”

“…Various reports clearly manifest that the D /μ relation influences the diode performance, which can be analyzed by the current density ( J )–voltage ( V ) characteristic study with the aid of the diode ideality factor ( N id ). ,,, Here, the ideality factor has a direct correlation with the enhancement parameter, g . According to an entropy-ruled method, the governing Navamani–Shockley (NS) diode equation for molecular quantum devices is given by , J = J 0 [ exp true( italicqV 3 normalΔ h normals 5 normalΔ η true) − 1 ] where J 0 is the saturation current density. Comparing eqs , , and , we can reform eq as J ∼ J 0 [ exp true( italicqV normalΔ h normals normalΔ E normalF true) − 1 ] ≡ J 0 [ exp true( italicqV normalΔ h normals k normalB normalΔ T normalF true) − 1 ] In equilibrium condition (Δ h s →1), the Navamani–Shockley diode equation becomes J = J 0 [ exp true( ...…”

“…Various reports clearly manifest that the D /μ relation influences the diode performance, which can be analyzed by the current density ( J )–voltage ( V ) characteristic study with the aid of the diode ideality factor ( N id ). ,,, Here, the ideality factor has a direct correlation with the enhancement parameter, g . According to an entropy-ruled method, the governing Navamani–Shockley (NS) diode equation for molecular quantum devices is given by , where J 0 is the saturation current density. Comparing eqs , , and , we can reform eq as In equilibrium condition (Δ h s →1), the Navamani–Shockley diode equation becomes For equilibrium nondegenerate and most of the weakly degenerate cases of a high-temperature limit ( T ≥ 150 K) (see ref ), we preserve the original Shockley diode equation from eq .…”

“…The governed mobility expression (eq ) is the quite general form for most of the quantum systems, which is originally developed from an entropy-ruled method with conjunction of the Boltzmann approach. ,, Comparing eqs and , we get D = v normalF 2 τ rel 2 = l 2 2 τ rel …”

Quantum-Classical Transition Analogy of Diffusion-Mobility Relation for Organic Semiconductors

“…14) is the quite general form for most of the quantum systems, which is originally developed from an entropy-ruled method. 8,10 Comparing Eqns. 6 and 14, we get…”