robert benda 1,3 - inria · multi-scale modelling of nano-sensors based on carbon nanotubes (cnts)...
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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