[Paper Review] Effect of Dynamic Disorder on Charge Transport in Organic Molecules

K. Navamani, K. Senthilkumar|arXiv (Cornell University)|May 16, 2017

Molecular Junctions and Nanostructures2 references3 citations

TL;DR

This study investigates how dynamic disorder—arising from fluctuating charge transfer integrals, site energies, and stacking angles—affects charge transport in organic semiconductors like BDHTT-BBT and DCV5T-Me. Using a model based on the Troisi framework, it reveals a crossover from band-like (coherent) to incoherent hopping transport beyond a disorder drift time, with electron mobility reaching 0.36 cm²/V·s in BDHTT-BBT due to high drift force and density flux rate.

ABSTRACT

The charge transfer integral, site energy and the stacking angle fluctuations are used to study the hole and electron transport in recently synthesized dialkyl substituted thienothiophene caped benzobisthiazole (BDHTT-BBT) and methyl-substituted dicyanovinyl-capped quinquethiophene (DCV5T-Me) molecules. The charge transfer parameters, such as coherent and incoherent rate coefficients, hopping conductivity, mobility, disorder drift time, drift force, potential equilibrium rate and density flux rate are calculated and discussed. It has been observed that the charge decay up to the crossover point (or disorder drift time) is exponential, non-dispersive and charge transport follows the band-like transport. Beyond the disorder drift time, the charge decay is not fully exponential, dispersive and it follows the incoherent hopping transport. The proposed expressions for density flux and diffusion shows their dependency on dynamic disorder and is in agreement with the Troisi model on diffusion limited by thermal disorder. The density flux rate is directly related with the drift force which facilitates the charge transfer. Calculated electron hopping conductivity in the BDHTT-BBT and DCV5T-Me is 0.8 and 0.18 S/cm, respectively. Molecule BDHTT-BBT has good electron mobility of 0.36 cm^2/V s, which has larger electron density flux rate and drift force of 1.7 x10^20 C/m^3 s and 1.44x10^-12 N.

Motivation & Objective

• To understand the impact of dynamic disorder on charge transport mechanisms in organic semiconductors.
• To quantify the transition from coherent (band-like) to incoherent (hopping) transport in organic molecules under dynamic disorder.
• To evaluate charge transport parameters such as mobility, conductivity, drift force, and density flux rate in relation to dynamic fluctuations.
• To validate the proposed model against the Troisi diffusion-limited model under thermal disorder.
• To identify molecular design features that enhance electron transport efficiency in organic semiconductors.

Proposed method

• Modeling dynamic disorder via time-dependent fluctuations in charge transfer integrals, site energies, and stacking angles in BDHTT-BBT and DCV5T-Me.
• Calculating coherent and incoherent rate coefficients using time-averaged and fluctuating parameters.
• Deriving expressions for drift force, density flux rate, and potential equilibrium rate based on dynamic disorder effects.
• Computing hopping conductivity and electron mobility using the derived rate coefficients and transport parameters.
• Applying the Troisi model for diffusion-limited transport to validate the density flux and drift force dependencies on dynamic disorder.
• Performing extensive derivations (42–48 pages) to establish theoretical foundations of the transport model.

Experimental results

Research questions

• RQ1 How do dynamic fluctuations in charge transfer integrals, site energies, and stacking angles influence charge transport in organic semiconductors?
• RQ2 At what time scale does the transition from coherent to incoherent transport occur, and what determines this crossover?
• RQ3 How does the drift force relate to the density flux rate and what role does it play in enhancing charge transport?
• RQ4 To what extent do the calculated mobility and conductivity values align with experimental expectations for BDHTT-BBT and DCV5T-Me?
• RQ5 Does the proposed model reproduce the diffusion-limited behavior predicted by the Troisi model under dynamic disorder?

Key findings

• The charge decay is exponential and non-dispersive up to the disorder drift time, indicating band-like transport behavior.
• Beyond the disorder drift time, charge decay becomes dispersive and non-exponential, signaling a transition to incoherent hopping transport.
• Electron hopping conductivity is 0.8 S/cm for BDHTT-BBT and 0.18 S/cm for DCV5T-Me, with BDHTT-BBT showing superior transport properties.
• BDHTT-BBT exhibits an electron mobility of 0.36 cm²/V·s, attributed to a high drift force of 1.44×10⁻¹² N and density flux rate of 1.7×10²⁰ C/m³·s.
• The density flux rate is directly proportional to the drift force, confirming the model's consistency with the Troisi framework on thermal disorder-limited diffusion.
• The theoretical derivations confirm that dynamic disorder significantly modulates transport, with the system transitioning from coherent to incoherent transport at a well-defined time scale.