Multi-scale modelling of nano-sensors based on carbon nanotubes (CNTs) and conjugated polymers for water quality monitoring

Robert BENDA1,3

Supervisors: Bérengère LEBENTAL1,2, Éric CANCES 3, Gaël Zucchi 1

1Laboratoire de Physique des Interfaces et des Couches Minces (LPICM), UMR 7647, IPP, Ecole Polytechnique-CNRS, Route de Saclay, 91128 Palaiseau, France

2Université Paris-Est, IFSTTAR, 14-20 bld Newton, 77447 Marne la Vallée, France

3CERMICS, Ecole des Ponts , 6 & 8 avenue Blaise Pascal, 77455 Marne-la-Vallée Cedex 2, France and INRIA (MATHERIALS).

20 nm

30 nm

Abstract We study resistive chemical sensors based on percolating networks of CNTs functionalized non-covalently by conjugated polymers. A change of resistance is expected in water upon

complexation of a target ion by a specifically designed polymer probe. Multi-scale modelling aims at understanding and predicting the response of the sensor.

Macroscopic system : Functionalized CNTs ink printed in-between two metallic electrodes :

• in water • under increasing concentration of a target ion

• under applied voltage (I-V characteristic)

Objectives : • Find all possible sources of variation of the total

sensor resistance. • Predict the sensibility of the whole system

towards all possible ions in water.

Bibliography

[1] Benda R., Cancès E. & Lebental B. (2019), Effective resistance of random percolating networks of stick nanowires: Functional dependence on elementary physical parameters. Journal of Applied Physics, 126(4), 044306. [2] Benda R., Zucchi G., Cancès E. & Lebental B., Insights into the π-π interaction driven non-covalent functionalization of carbon nanotubes of various diameters by conjugated fluorene and carbazole copolymers, submitted.

[3] K. Malde and al., Automated force field topology builder (ATB) and repository: Version 1.0, Journal of Chemical Theory and Computation , 7(12), 4026, 2011. [4] A. C. T. van Duin and al., ReaxFF : a Reactive Force Field for Hydrocarbons, J. Phys. Chem. A, 105 (41), pp 9396-9409, 2001.

[5]. A. K. Rappe and al., Charge equilibration for Molecular Dynamics simulations, The Journal of Physical Chemistry, 95 (8), 3358-3363, 1991.

Example : 20 μm x 20 μm

channel

N random conducting wires of size l*

Upper electrode

• Expected working principle of the sensor at the nanotube segment scale.

• Similar resistance changes (due to ion/polymer probe interaction) possible at the CNT/CNT

junctions and electrode/CNT contacts .

In water

Conjugated polymer

Sensing probe

Lower electrode

Examples of some scales already studied :

CNTs random percolating network

(resistance or I-V characteristic at room T)

Statistical generalization

Conclusion and perspectives • The methodology developed across the different scales enables the assisted design of polymer chain structures and sensing probes, thanks to simulations results.

• Links between the different scales are still to be done (parameters of models at larger scales fed by the outputs of the models at lower scales). • How to scale up from (possible) equilibrium geometries of the system derived at classical FF (or QM level), to electronic transport modulation in CNTs ?

Monomer probe / target ion interaction (geometry, energy,

electronic distribution)

Effective resistance of random percolating networks of nanowires [1]

• Model : graph and adjacency matrix representing the network (nodes duplicated at each CNT/CNT junction) . • Equivalent resistance computed numerically : separation of the dependence on geometrical and physical parameters.

• Relative sensitivity of the sensors to variations of ρ and Rc (for instance) depends only on the ratio 𝐴(𝑁,

𝐿

𝑙∗)

𝐵(𝑁,𝐿

𝑙∗) .

• Example : N=100 (above percolation), L=l=20 μm, l*=5 μm, ρ=6 kΩ/μm, 𝑅𝑐=100 kΩ, 𝑅𝑚, 𝑤=10 kΩ : 𝑅𝑒𝑞

= 68 kΩ + 352 kΩ +13 kΩ=433 kΩ.

Non-covalent functionalization of CNTs by conjugated polymers [2] • Goal : polymer assisted design (sensing purposes). Better understanding of π-π stacking interactions.

• Systems studied : CNTs (diameters from 1.7 to 9 nm) and polyfluorene polymers or fluorene:carbazole copolymers (varying probes, alkyl chain length and initial geometry). • Model : classical force field (ReaxFF) [4], atomic (geometry dependent) partial charges [5]. • Method : molecular dynamics simulations (NVT ensemble, T=300 K). Possible adsorbed geometries extracted after adsorption and further minimized (at 0 K). • Geometrical and energetical features of polymer adsorption on (DW)CNTs surface analysed. Result : 40 kcal/mol average interaction energy / monomer if no loop, 32 kcal/mol in case of loops / coiled adsorption.

Examples of possible adsorption geometries for

two 30 monomers long fluorene:carbazole

copolymers with different sensing probes on a 9 nm

diameter outer shell (right : DWNT)

Monomer probe – target ion interaction • Goal : understand the selectivity of probes to target ions. Probe assisted design. • Systems studied : probe + ions, varying ion initial position. • Models compared : GROMOS FF, AMOEBA polarizable FF, QM.

• Validation of the force field parametrization [3]: Comparison of binding sites and binding energies (in vacuo) for different levels of theory.

• Perspective : Once parametrization validated : simulations in solvent (free energies, residence times of ions in the binding sites).

Cu2+ -- probe complex minimized at the QM level (DFT, PBE functional, DZVP basis) LUMO orbital HOMO orbital (d character)

CU 1.95 Å

22.3°

DFT and force fields

Polymer / CNT interaction, π-π stacking (geometry, energy)

ReaxFF force field

Polymer + target ions (interaction

probabilities, conformational changes)

Monomer / CNT interaction (charge transfer)

DFT or wave- function theory

CNT or graphene slice + monomer + target ion (geometry, electronic

distribution)

DFT

CNT (pristine or functionalized) : electrical properties (resistance)

Semi-classical transport theory (Boltzmann equation ?)

Input geometry

Input geometry Junction between two CNTs

(pristine or functionalized) : electrical properties (resistance

or I-V characteristic)

Statistical averaging yielding input parameters / resistance probability distributions

With / without water

With / without water

Without water

Without water

With / without water Without water

Without water

Monte-Carlo methods. Separate geometrical / (individual

component) physical parameters

CU

linear junctions contacts

CU